diff --git a/Assets/NanoBrain/LinearAlgebra/.editorconfig b/Assets/NanoBrain/LinearAlgebra/.editorconfig new file mode 100644 index 0000000..1ec7f97 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/.editorconfig @@ -0,0 +1,19 @@ +# EditorConfig is awesome: https://EditorConfig.org + +# top-most EditorConfig file +root = true + +[*] +indent_style = space +indent_size = 4 +end_of_line = crlf +charset = utf-8 +trim_trailing_whitespace = false +insert_final_newline = false +max_line_length = 80 + +[*.cs] +csharp_new_line_before_open_brace = none +# Suppress warnings everywhere +dotnet_diagnostic.IDE1006.severity = none +dotnet_diagnostic.IDE0130.severity = none \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/.gitea/workflows/unit_tests.yaml b/Assets/NanoBrain/LinearAlgebra/.gitea/workflows/unit_tests.yaml new file mode 100644 index 0000000..e98b26e --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/.gitea/workflows/unit_tests.yaml @@ -0,0 +1,37 @@ +name: Build and Run C# Unit Tests + +on: + push: + branches: + - '**' + pull_request: + branches: + - '**' + +jobs: + build-and-test: + runs-on: ubuntu-latest + + steps: + - name: Checkout code + uses: actions/checkout@v2 + + - name: Setup .NET + uses: actions/setup-dotnet@v1 + with: + dotnet-version: '8.0.x' # Specify the .NET SDK version + + - name: Check Current Directory + run: pwd # Logs the current working directory + + - name: List Files + run: ls -la # Lists all files in the current directory + + - name: Restore Dependencies + run: dotnet restore ./LinearAlgebra-csharp.sln # Restore NuGet packages + + - name: Build the Project + run: dotnet build ./LinearAlgebra-csharp.sln --configuration Release # Build the C# project + + - name: Run Unit Tests + run: dotnet test ./test/LinearAlgebra_Test.csproj --configuration Release # Execute unit tests diff --git a/Assets/NanoBrain/LinearAlgebra/.gitignore b/Assets/NanoBrain/LinearAlgebra/.gitignore new file mode 100644 index 0000000..b32a30c --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/.gitignore @@ -0,0 +1,5 @@ +DoxyGen/DoxyWarnLogfile.txt +.vscode/settings.json +**bin +**obj +**.meta diff --git a/Assets/NanoBrain/LinearAlgebra/LinearAlgebra-csharp.sln b/Assets/NanoBrain/LinearAlgebra/LinearAlgebra-csharp.sln new file mode 100644 index 0000000..4b13b2b --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/LinearAlgebra-csharp.sln @@ -0,0 +1,30 @@ +Microsoft Visual Studio Solution File, Format Version 12.00 +# Visual Studio Version 17 +VisualStudioVersion = 17.5.2.0 +MinimumVisualStudioVersion = 10.0.40219.1 +Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "LinearAlgebra", "src\LinearAlgebra.csproj", "{ECB58727-0354-924D-AE7B-22F6B21097EB}" +EndProject +Project("{FAE04EC0-301F-11D3-BF4B-00C04F79EFBC}") = "LinearAlgebra_Test", "test\LinearAlgebra_Test.csproj", "{715BB399-5FC4-2AC9-3757-177CA0C80774}" +EndProject +Global + GlobalSection(SolutionConfigurationPlatforms) = preSolution + Debug|Any CPU = Debug|Any CPU + Release|Any CPU = Release|Any CPU + EndGlobalSection + GlobalSection(ProjectConfigurationPlatforms) = postSolution + {ECB58727-0354-924D-AE7B-22F6B21097EB}.Debug|Any CPU.ActiveCfg = Debug|Any CPU + {ECB58727-0354-924D-AE7B-22F6B21097EB}.Debug|Any CPU.Build.0 = Debug|Any CPU + {ECB58727-0354-924D-AE7B-22F6B21097EB}.Release|Any CPU.ActiveCfg = Release|Any CPU + {ECB58727-0354-924D-AE7B-22F6B21097EB}.Release|Any CPU.Build.0 = Release|Any CPU + {715BB399-5FC4-2AC9-3757-177CA0C80774}.Debug|Any CPU.ActiveCfg = Debug|Any CPU + {715BB399-5FC4-2AC9-3757-177CA0C80774}.Debug|Any CPU.Build.0 = Debug|Any CPU + {715BB399-5FC4-2AC9-3757-177CA0C80774}.Release|Any CPU.ActiveCfg = Release|Any CPU + {715BB399-5FC4-2AC9-3757-177CA0C80774}.Release|Any CPU.Build.0 = Release|Any CPU + EndGlobalSection + GlobalSection(SolutionProperties) = preSolution + HideSolutionNode = FALSE + EndGlobalSection + GlobalSection(ExtensibilityGlobals) = postSolution + SolutionGuid = {E93B8294-87D4-4887-83B7-182A623D5833} + EndGlobalSection +EndGlobal diff --git a/Assets/NanoBrain/LinearAlgebra/src/Angle.cs b/Assets/NanoBrain/LinearAlgebra/src/Angle.cs new file mode 100644 index 0000000..694d1b7 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Angle.cs @@ -0,0 +1,332 @@ +using System; + +namespace LinearAlgebra { + + public struct AngleFloat { + public const float Rad2Deg = 360.0f / ((float)Math.PI * 2); //0.0174532924F; + public const float Deg2Rad = (float)Math.PI * 2 / 360.0f; //57.29578F; + + private AngleFloat(float degrees) { + this.value = degrees; + } + private readonly float value; + + public static AngleFloat Degrees(float degrees) { + // Reduce it to (-180..180] + if (float.IsFinite(degrees)) { + while (degrees < -180) + degrees += 360; + while (degrees >= 180) + degrees -= 360; + } + return new AngleFloat(degrees); + } + + public static AngleFloat Radians(float radians) { + // Reduce it to (-pi..pi] + if (float.IsFinite(radians)) { + while (radians <= -Math.PI) + radians += 2 * (float)Math.PI; + while (radians > Math.PI) + radians -= 2 * (float)Math.PI; + } + + return new AngleFloat(radians * Rad2Deg); + + } + + public static AngleFloat Revolutions(float revolutions) { + // reduce it to (-0.5 .. 0.5] + if (float.IsFinite(revolutions)) { + // Get the integer part + int integerPart = (int)revolutions; + + // Get the decimal part + revolutions -= integerPart; + if (revolutions < -0.5) + revolutions += 1; + if (revolutions >= 0.5) + revolutions -= 1; + } + return new AngleFloat(revolutions * 360); + } + + public float inDegrees { + get { return this.value; } + } + + public float inRadians { + get { return this.value * Deg2Rad; } + } + + public float inRevolutions { + get { return this.value / 360.0f; } + } + + public static readonly AngleFloat zero = Degrees(0); + public static readonly AngleFloat deg90 = Degrees(90); + public static readonly AngleFloat deg180 = Degrees(180); + + /// + /// Get the sign of the angle + /// + /// The angle + /// -1 when the angle is negative, 1 when it is positive and 0 in all other cases + public static int Sign(AngleFloat a) { + if (a.value < 0) + return -1; + if (a.value > 0) + return 1; + return 0; + } + + /// + /// Returns the magnitude of the angle + /// + /// The angle + /// The positive magnitude of the angle + /// Negative values are negated to get a positive result + public static AngleFloat Abs(AngleFloat a) { + if (Sign(a) < 0) + return -a; + else + return a; + } + + /// + /// Tests the equality of two angles + /// + /// + /// + /// True when the angles are equal, false otherwise + /// The equality is determine within the limits of precision of a float + public static bool operator ==(AngleFloat a1, AngleFloat a2) { + return a1.value == a2.value; + } + + /// + /// Tests the inequality of two angles + /// + /// + /// + /// True when the angles are not equal, false otherwise + /// The equality is determine within the limits of precision of a float + public static bool operator !=(AngleFloat a1, AngleFloat a2) { + return a1.value != a2.value; + } + + /// + /// Tests if the first angle is greater than the second + /// + /// + /// + /// True when a1 is greater than a2, False otherwise + public static bool operator >(AngleFloat a1, AngleFloat a2) { + return a1.value > a2.value; + } + + /// + /// Tests if the first angle is greater than or equal to the second + /// + /// + /// + /// True when a1 is greater than or equal to a2, False otherwise + public static bool operator >=(AngleFloat a1, AngleFloat a2) { + return a1.value >= a2.value; + } + + /// + /// Tests if the first angle is less than the second + /// + /// + /// + /// True when a1 is less than a2, False otherwise + public static bool operator <(AngleFloat a1, AngleFloat a2) { + return a1.value < a2.value; + } + + /// + /// Tests if the first angle is less than or equal to the second + /// + /// + /// + /// True when a1 is less than or equal to a2, False otherwise + public static bool operator <=(AngleFloat a1, AngleFloat a2) { + return a1.value <= a2.value; + } + + /// + /// Negate the angle + /// + /// The angle + /// The negated angle + /// The negation of -180 is still -180 because the range is (-180..180] + public static AngleFloat operator -(AngleFloat a) { + AngleFloat r = new(-a.value); + return r; + } + + /// + /// Subtract two angles + /// + /// Angle 1 + /// Angle 2 + /// The result of the subtraction + public static AngleFloat operator -(AngleFloat a1, AngleFloat a2) { + AngleFloat r = new(a1.value - a2.value); + return r; + } + /// + /// Add two angles + /// + /// Angle 1 + /// Angle 2 + /// The result of the addition + public static AngleFloat operator +(AngleFloat a1, AngleFloat a2) { + AngleFloat r = new(a1.value + a2.value); + return r; + } + + /// + /// Multiplies the angle + /// + /// The angle to multiply + /// The factor by which the angle is multiplied + /// The multiplied angle + public static AngleFloat operator *(AngleFloat a, float factor) { + return Degrees(a.inDegrees * factor); + } + public static AngleFloat operator *(float factor, AngleFloat a) { + return Degrees(factor * a.inDegrees); + } + + /// + /// Clamp the angle between the given min and max values + /// + /// The angle to clamp + /// The minimum angle + /// The maximum angle + /// The clamped angle + /// Angles are normalized + public static float Clamp(AngleFloat angle, AngleFloat min, AngleFloat max) { + return Float.Clamp(angle.inDegrees, min.inDegrees, max.inDegrees); + } + + /// @brief Calculates the cosine of an angle + /// @param angle The given angle + /// @return The cosine of the angle + public static float Cos(AngleFloat angle) { + return MathF.Cos(angle.inRadians); + } + /// @brief Calculates the sine of an angle + /// @param angle The given angle + /// @return The sine of the angle + public static float Sin(AngleFloat angle) { + return MathF.Sin(angle.inRadians); + } + /// @brief Calculates the tangent of an angle + /// @param angle The given angle + /// @return The tangent of the angle + public static float Tan(AngleFloat angle) { + return MathF.Tan(angle.inRadians); + } + + /// @brief Calculates the arc cosine angle + /// @param f The value + /// @return The arc cosine for the given value + public static AngleFloat Acos(float f) { + return Radians(MathF.Acos(f)); + } + /// @brief Calculates the arc sine angle + /// @param f The value + /// @return The arc sine for the given value + public static AngleFloat Asin(float f) { + return Radians(MathF.Asin(f)); + } + /// @brief Calculates the arc tangent angle + /// @param f The value + /// @return The arc tangent for the given value + public static AngleFloat Atan(float f) { + return Radians(MathF.Atan(f)); + } + /// @brief Calculates the tangent for the given values + /// @param y The vertical value + /// @param x The horizontal value + /// @return The tanget for the given values + /// Uses the y and x signs to compute the quadrant + public static AngleFloat Atan2(float y, float x) { + return Radians(MathF.Atan2(y, x)); + } + + /// + /// Rotate from one angle to the other with a maximum degrees + /// + /// Starting angle + /// Target angle + /// Maximum angle to rotate + /// The resulting angle + /// This function is compatible with radian and degrees angles + public static AngleFloat MoveTowards(AngleFloat fromAngle, AngleFloat toAngle, float maxDegrees) { + maxDegrees = Math.Max(0, maxDegrees); // filter out negative distances + AngleFloat d = toAngle - fromAngle; + float dDegrees = Abs(d).inDegrees; + d = Degrees(Float.Clamp(dDegrees, 0, maxDegrees)); + if (Sign(d) < 0) + d = -d; + return fromAngle + d; + } + } + + + /// + /// %Angle utilities + /// + public static class Angles { + public const float pi = 3.1415927410125732421875F; + // public static float Rad2Deg = 360.0f / ((float)Math.PI * 2); + // public static float Deg2Rad = ((float)Math.PI * 2) / 360.0f; + + + /// + /// Determine the angle difference, result is a normalized angle + /// + /// First first angle + /// The second angle + /// the angle between the two angles + /// Angle values should be degrees + public static float Difference(float a, float b) { + float r = Normalize(b - a); + return r; + } + + /// + /// Normalize an angle to the range -180 < angle <= 180 + /// + /// The angle to normalize + /// The normalized angle in interval (-180..180] + /// Angle values should be in degrees + public static float Normalize(float angle) { + if (float.IsInfinity(angle)) + return angle; + + while (angle <= -180) angle += 360; + while (angle > 180) angle -= 360; + return angle; + } + + /// + /// Map interval of angles between vectors [0..Pi] to interval [0..1] + /// + /// The first vector + /// The second vector + /// The resulting factor in interval [0..1] + /// Vectors a and b must be normalized + /// \deprecated Please use Vector2.ToFactor instead. + // [Obsolete("Please use Vector2.ToFactor instead.")] + // public static float ToFactor(Vector2Float v1, Vector2Float v2) { + // return (1 - Vector2Float.Dot(v1, v2)) / 2; + // } + + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Decomposition.cs b/Assets/NanoBrain/LinearAlgebra/src/Decomposition.cs new file mode 100644 index 0000000..ddaf434 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Decomposition.cs @@ -0,0 +1,287 @@ +using System; +namespace LinearAlgebra { + class QR { + // QR Decomposition of a matrix A + public static (Matrix2 Q, Matrix2 R) Decomposition(Matrix2 A) { + int nRows = A.nRows; + int nCols = A.nCols; + + float[,] Q = new float[nRows, nCols]; + float[,] R = new float[nCols, nCols]; + + // Perform Gram-Schmidt orthogonalization + for (uint colIx = 0; colIx < nCols; colIx++) { + + // Step 1: v = column(ix) of A + float[] v = new float[nRows]; + for (int rowIx = 0; rowIx < nRows; rowIx++) + v[rowIx] = A.data[rowIx, colIx]; + + // Step 2: Subtract projections of v onto previous q's (orthogonalize) + for (uint colIx2 = 0; colIx2 < colIx; colIx2++) { + float dotProd = 0; + for (int i = 0; i < nRows; i++) + dotProd += Q[i, colIx2] * v[i]; + for (int i = 0; i < nRows; i++) + v[i] -= dotProd * Q[i, colIx2]; + } + + // Step 3: Normalize v to get column(ix) of Q + float norm = 0; + for (int rowIx = 0; rowIx < nRows; rowIx++) + norm += v[rowIx] * v[rowIx]; + norm = (float)Math.Sqrt(norm); + + for (int rowIx = 0; rowIx < nRows; rowIx++) + Q[rowIx, colIx] = v[rowIx] / norm; + + // Store the coefficients of R + for (int colIx2 = 0; colIx2 <= colIx; colIx2++) { + R[colIx2, colIx] = 0; + for (int k = 0; k < nRows; k++) + R[colIx2, colIx] += Q[k, colIx2] * A.data[k, colIx]; + } + } + return (new Matrix2(Q), new Matrix2(R)); + } + + // Reduced QR Decomposition of a matrix A + public static (Matrix2 Q, Matrix2 R) ReducedDecomposition(Matrix2 A) { + int nRows = A.nRows; + int nCols = A.nCols; + + float[,] Q = new float[nRows, nCols]; + float[,] R = new float[nCols, nCols]; + + // Perform Gram-Schmidt orthogonalization + for (int colIx = 0; colIx < nCols; colIx++) { + + // Step 1: v = column(colIx) of A + float[] columnIx = new float[nRows]; + bool isZeroColumn = true; + for (int rowIx = 0; rowIx < nRows; rowIx++) { + columnIx[rowIx] = A.data[rowIx, colIx]; + if (columnIx[rowIx] != 0) + isZeroColumn = false; + } + if (isZeroColumn) { + for (int rowIx = 0; rowIx < nRows; rowIx++) + Q[rowIx, colIx] = 0; + // Set corresponding R element to 0 + R[colIx, colIx] = 0; + + Console.WriteLine($"zero column {colIx}"); + + continue; + } + + // Step 2: Subtract projections of v onto previous q's (orthogonalize) + for (int colIx2 = 0; colIx2 < colIx; colIx2++) { + // Compute the dot product of v and column(colIx2) of Q + float dotProduct = 0; + for (int rowIx2 = 0; rowIx2 < nRows; rowIx2++) + dotProduct += columnIx[rowIx2] * Q[rowIx2, colIx2]; + // Subtract the projection from v + for (int rowIx2 = 0; rowIx2 < nRows; rowIx2++) + columnIx[rowIx2] -= dotProduct * Q[rowIx2, colIx2]; + } + + // Step 3: Normalize v to get column(colIx) of Q + float norm = 0; + for (int rowIx = 0; rowIx < nRows; rowIx++) + norm += columnIx[rowIx] * columnIx[rowIx]; + if (norm == 0) + throw new Exception("invalid value"); + + norm = (float)Math.Sqrt(norm); + + for (int rowIx = 0; rowIx < nRows; rowIx++) + Q[rowIx, colIx] = columnIx[rowIx] / norm; + + // Here is where it deviates from the Full QR Decomposition ! + + // Step 4: Compute the row(colIx) of R + for (int colIx2 = colIx; colIx2 < nCols; colIx2++) { + float dotProduct = 0; + for (int rowIx2 = 0; rowIx2 < nRows; rowIx2++) + dotProduct += Q[rowIx2, colIx] * A.data[rowIx2, colIx2]; + R[colIx, colIx2] = dotProduct; + } + } + if (!float.IsFinite(R[0, 0])) + throw new Exception("invalid value"); + + return (new Matrix2(Q), new Matrix2(R)); + } + } + + class SVD { + // According to ChatGPT, Mathnet uses Golub-Reinsch SVD algorithm + // 1. Bidiagonalization: The input matrix AA is reduced to a bidiagonal form using Golub-Kahan bidiagonalization. + // This process involves applying a sequence of Householder reflections to AA to create a bidiagonal matrix. + // This step reduces the complexity by making the matrix simpler while retaining the essential structure needed for SVD. + // + // 2. Diagonalization: Once the matrix is in bidiagonal form, + // the singular values are computed using an iterative process + // (typically involving QR factorization or Jacobi rotations) until convergence. + // This process diagonalizes the bidiagonal matrix and allows extraction of the singular values. + // + // 3. Computing UU and VTVT: After obtaining the singular values, + // the left singular vectors UU and right singular vectors VTVT are computed + // using the accumulated transformations (such as Householder reflections) from the bidiagonalization step. + + // Bidiagnolizations through Householder transformations + public static (Matrix2 U1, Matrix2 B, Matrix2 V1) Bidiagonalization(Matrix2 A) { + int m = A.nRows; // Rows of A + int n = A.nCols; // Columns of A + float[,] U1 = new float[m, m]; // Left orthogonal matrix + float[,] V1 = new float[n, n]; // Right orthogonal matrix + float[,] B = A.Clone().data; // Copy A to B for transformation + + // Initialize U1 and V1 as identity matrices + for (int i = 0; i < m; i++) + U1[i, i] = 1; + for (int i = 0; i < n; i++) + V1[i, i] = 1; + + // Perform Householder reflections to create a bidiagonal matrix B + for (int j = 0; j < n; j++) { + // Step 1: Construct the Householder vector y + float[] y = new float[m - j]; + for (int i = j; i < m; i++) + y[i - j] = B[i, j]; + + // Step 2: Compute the norm and scalar alpha + float norm = 0; + for (int i = 0; i < y.Length; i++) + norm += y[i] * y[i]; + norm = (float)Math.Sqrt(norm); + + if (B[j, j] > 0) + norm = -norm; + + float alpha = (float)Math.Sqrt(0.5 * (norm * (norm - B[j, j]))); + float r = (float)Math.Sqrt(0.5 * (norm * (norm + B[j, j]))); + + // Step 3: Apply the reflection to zero out below diagonal + for (int k = j; k < n; k++) { + float dot = 0; + for (int i = j; i < m; i++) + dot += y[i - j] * B[i, k]; + dot /= r; + + for (int i = j; i < m; i++) + B[i, k] -= 2 * dot * y[i - j]; + } + + // Step 4: Update U1 with the Householder reflection (U1 * Householder) + for (int i = j; i < m; i++) + U1[i, j] = y[i - j] / alpha; + + // Step 5: Update V1 (storing the Householder vector y) + // Correct indexing: we only need to store part of y in V1 from index j to n + for (int i = j; i < n; i++) + V1[j, i] = B[j, i]; + + // Repeat steps for further columns if necessary + } + return (new Matrix2(U1), new Matrix2(B), new Matrix2(V1)); + } + + public static Matrix2 Bidiagonalize(Matrix2 A) { + int m = A.nRows; // Rows of A + int n = A.nCols; // Columns of A + float[,] B = A.Clone().data; // Copy A to B for transformation + + // Perform Householder reflections to create a bidiagonal matrix B + for (int j = 0; j < n; j++) { + // Step 1: Construct the Householder vector y + float[] y = new float[m - j]; + for (int i = j; i < m; i++) + y[i - j] = B[i, j]; + + // Step 2: Compute the norm and scalar alpha + float norm = 0; + for (int i = 0; i < y.Length; i++) + norm += y[i] * y[i]; + norm = (float)Math.Sqrt(norm); + + if (B[j, j] > 0) + norm = -norm; + + float r = (float)Math.Sqrt(0.5 * (norm * (norm + B[j, j]))); + + // Step 3: Apply the reflection to zero out below diagonal + for (int k = j; k < n; k++) { + float dot = 0; + for (int i = j; i < m; i++) + dot += y[i - j] * B[i, k]; + dot /= r; + + for (int i = j; i < m; i++) + B[i, k] -= 2 * dot * y[i - j]; + } + + // Repeat steps for further columns if necessary + } + return new Matrix2(B); + } + + // QR Iteration for diagonalization of a bidiagonal matrix B + public static (Matrix1 singularValues, Matrix2 U, Matrix2 Vt) QRIteration(Matrix2 B) { + int m = B.nRows; + int n = B.nCols; + + Matrix2 U = new(m, m); // Left singular vectors (U) + Matrix2 Vt = new(n, n); // Right singular vectors (V^T) + float[] singularValues = new float[Math.Min(m, n)]; // Singular values + + // Initialize U and Vt as identity matrices + for (int i = 0; i < m; i++) + U.data[i, i] = 1; + for (int i = 0; i < n; i++) + Vt.data[i, i] = 1; + + // Perform QR iterations + float tolerance = 1e-7f; //1e-12f; for double + bool converged = false; + while (!converged) { + // Perform QR decomposition on the matrix B + (Matrix2 Q, Matrix2 R) = QR.Decomposition(B); + + // Update B to be the product Q * R //R * Q + B = R * Q; + + // Accumulate the transformations in U and Vt + U *= Q; + Vt *= R; + + // Check convergence by looking at the off-diagonal elements of B + converged = true; + for (int i = 0; i < m - 1; i++) { + for (int j = i + 1; j < n; j++) { + if (Math.Abs(B.data[i, j]) > tolerance) { + converged = false; + break; + } + } + } + } + + // Extract singular values (diagonal elements of B) + for (int i = 0; i < Math.Min(m, n); i++) + singularValues[i] = B.data[i, i]; + + return (new Matrix1(singularValues), U, Vt); + } + + public static (Matrix2 U, Matrix1 S, Matrix2 Vt) Decomposition(Matrix2 A) { + if (A.nRows != A.nCols) + throw new ArgumentException("SVD: matrix A has to be square."); + + Matrix2 B = Bidiagonalize(A); + (Matrix1 S, Matrix2 U, Matrix2 Vt) = QRIteration(B); + return (U, S, Vt); + } + } +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Direction.cs b/Assets/NanoBrain/LinearAlgebra/src/Direction.cs new file mode 100644 index 0000000..ed82901 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Direction.cs @@ -0,0 +1,181 @@ +using System; +#if UNITY_5_3_OR_NEWER +using Vector3Float = UnityEngine.Vector3; +#endif + +namespace LinearAlgebra { + + /// + /// A direction in 3D space + /// + /// A direction is represented using two angles: + /// * The horizontal angle ranging from -180 (inclusive) to 180 (exclusive) + /// degrees which is a rotation in the horizontal plane + /// * A vertical angle ranging from -90 (inclusive) to 90 (exclusive) degrees + /// which is the rotation in the up/down direction applied after the horizontal + /// rotation has been applied. + /// The angles are automatically normalized to stay within the abovenmentioned + /// ranges. + public struct Direction { + /// @brief horizontal angle, range = (-180..180] degrees + public AngleFloat horizontal; + /// @brief vertical angle, range in degrees = (-90..90] degrees + public AngleFloat vertical; + + /// + /// Create a new direction + /// + /// The horizontal angle + /// The vertical angle + /// The direction will be normalized automatically + /// to ensure the angles are within the allowed ranges + public Direction(AngleFloat horizontal, AngleFloat vertical) { + this.horizontal = horizontal; + this.vertical = vertical; + this.Normalize(); + } + + /// + /// Create a direction using angle values in degrees + /// + /// The horizontal angle in degrees + /// The vertical angle in degrees + /// The direction + /// The direction will be normalized automatically + /// to ensure the angles are within the allowed ranges + public static Direction Degrees(float horizontal, float vertical) { + Direction d = new() { + horizontal = AngleFloat.Degrees(horizontal), + vertical = AngleFloat.Degrees(vertical) + }; + d.Normalize(); + return d; + } + /// + /// Create a direction using angle values in radians + /// + /// The horizontal angle in radians + /// The vertical angle in radians + /// The direction + public static Direction Radians(float horizontal, float vertical) { + Direction d = new() { + horizontal = AngleFloat.Radians(horizontal), + vertical = AngleFloat.Radians(vertical) + }; + d.Normalize(); + return d; + } + + /// + /// A forward direction with zero for both angles + /// + public readonly static Direction forward = Degrees(0, 0); + /// + /// A backward direction with horizontal angle -180 and zero vertical + /// angle + /// + public readonly static Direction backward = Degrees(-180, 0); + /// + /// A upward direction with zero horizontal angle and vertical angle 90 + /// + public readonly static Direction up = Degrees(0, 90); + /// + /// A downward direction with zero horizontal angle and vertical angle + /// -90 + /// + public readonly static Direction down = Degrees(0, -90); + /// + /// A left-pointing direction with horizontal angle -90 and zero + /// vertical angle + /// + public readonly static Direction left = Degrees(-90, 0); + /// + /// A right-pointing direction with horizontal angle 90 and zero + /// vertical angle + /// + public readonly static Direction right = Degrees(90, 0); + + private void Normalize() { + if (this.vertical > AngleFloat.deg90 || this.vertical < -AngleFloat.deg90) { + this.horizontal += AngleFloat.deg180; + this.vertical = AngleFloat.deg180 - this.vertical; + } + } + +#if !UNITY_5_3_OR_NEWER + /// + /// Convert the direction into a carthesian vector + /// + /// The carthesian vector corresponding to this direction. + public Vector3Float ToVector3Float() { + Quaternion q = Quaternion.Euler(90 - this.vertical.inDegrees, this.horizontal.inDegrees, 0); + Vector3Float v = q * Vector3Float.forward; + return v; + } +#else + /// + /// Convert the direction into a carthesian vector + /// + /// The carthesian vector corresponding to this direction. + public UnityEngine.Vector3 ToVector3() { + UnityEngine.Quaternion q = UnityEngine.Quaternion.Euler(90 - this.vertical.inDegrees, this.horizontal.inDegrees, 0); + UnityEngine.Vector3 v = q * UnityEngine.Vector3.forward; + return v; + } +#endif + + /// + /// Convert a carthesian vector into a direction + /// + /// The carthesian vector + /// The direction + /// Information about the length of the carthesian vector is not + /// included in this transformation + public static Direction FromVector3(Vector3Float v) { + AngleFloat horizontal = AngleFloat.Atan2(v.horizontal, v.depth); + AngleFloat vertical = AngleFloat.deg90 - AngleFloat.Acos(v.vertical); + Direction d = new(horizontal, vertical); + return d; + } + + /// + /// Tests the equality of two directions + /// + /// + /// + /// True when the direction angles are equal, false otherwise. + public static bool operator ==(Direction d1, Direction d2) { + bool horizontalEq = d1.horizontal == d2.horizontal; + bool verticalEq = d1.vertical == d2.vertical; + return horizontalEq && verticalEq; + } + + /// + /// Tests the inequality of two directions + /// + /// + /// + /// True when the direction angles are not equal, false otherwise. + public static bool operator !=(Direction d1, Direction d2) { + bool horizontalNEq = d1.horizontal != d2.horizontal; + bool verticalNEq = d1.vertical != d2.vertical; + return horizontalNEq || verticalNEq; + } + + public override readonly bool Equals(object obj) { + if (obj is not Direction d) + return false; + + bool horizontalEq = this.horizontal == d.horizontal; + bool verticalEq = this.vertical == d.vertical; + return horizontalEq && verticalEq; + } + + + public override readonly int GetHashCode() { + return HashCode.Combine(horizontal, vertical); + } + + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Float.cs b/Assets/NanoBrain/LinearAlgebra/src/Float.cs new file mode 100644 index 0000000..2217b84 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Float.cs @@ -0,0 +1,41 @@ +namespace LinearAlgebra { + + /// + /// Float number utilities + /// + public class Float { + /// + /// The precision of float numbers + /// + public const float epsilon = 1E-05f; + /// + /// The square of the float number precision + /// + public const float sqrEpsilon = 1e-10f; + + /// + /// Clamp the value between the given minimum and maximum values + /// + /// The value to clamp + /// The minimum value + /// The maximum value + /// The clamped value + public static float Clamp(float f, float min, float max) { + if (f < min) + return min; + if (f > max) + return max; + return f; + } + + /// + /// Clamp the value between to the interval [0..1] + /// + /// The value to clamp + /// The clamped value + public static float Clamp01(float f) { + return Clamp(f, 0, 1); + } + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/LinearAlgebra.csproj b/Assets/NanoBrain/LinearAlgebra/src/LinearAlgebra.csproj new file mode 100644 index 0000000..d2d5a85 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/LinearAlgebra.csproj @@ -0,0 +1,14 @@ + + + + false + false + net8.0 + + + + + + + + diff --git a/Assets/NanoBrain/LinearAlgebra/src/Matrix.cs b/Assets/NanoBrain/LinearAlgebra/src/Matrix.cs new file mode 100644 index 0000000..37c6c24 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Matrix.cs @@ -0,0 +1,689 @@ +using System; +#if UNITY_5_3_OR_NEWER +using Vector3Float = UnityEngine.Vector3; +using Vector2Float = UnityEngine.Vector2; +using Quaternion = UnityEngine.Quaternion; +#endif + +namespace LinearAlgebra { + + public readonly struct Slice + { + public int start { get; } + public int stop { get; } + public Slice(int start, int stop) + { + this.start = start; + this.stop = stop; + } + } + + public class Matrix2 { + public float[,] data { get; } + + public int nRows => data.GetLength(0); + public int nCols => data.GetLength(1); + + public Matrix2(int nRows, int nCols) + { + this.data = new float[nRows, nCols]; + } + public Matrix2(float[,] data) { + this.data = data; + } + + public Matrix2 Clone() { + float[,] data = new float[this.nRows, nCols]; + for (int rowIx = 0; rowIx < this.nRows; rowIx++) { + for (int colIx = 0; colIx < this.nCols; colIx++) + data[rowIx, colIx] = this.data[rowIx, colIx]; + } + return new Matrix2(data); + } + + public static Matrix2 Zero(int nRows, int nCols) + { + return new Matrix2(nRows, nCols); + } + + public static Matrix2 FromVector3(Vector3Float v) { + float[,] result = new float[3, 1]; + result[0, 0] = v.horizontal; + result[1, 0] = v.vertical; + result[2, 0] = v.depth; + return new Matrix2(result); + } + + public static Matrix2 Identity(int size) + { + return Diagonal(1, size); + } + public static Matrix2 Identity(int nRows, int nCols) + { + Matrix2 m = Zero(nRows, nCols); + m.FillDiagonal(1); + return m; + } + + public static Matrix2 Diagonal(Matrix1 v) { + float[,] resultData = new float[v.size, v.size]; + for (int ix = 0; ix < v.size; ix++) + resultData[ix, ix] = v.data[ix]; + return new Matrix2(resultData); + } + public static Matrix2 Diagonal(float f, int size) + { + float[,] resultData = new float[size, size]; + for (int ix = 0; ix < size; ix++) + resultData[ix, ix] = f; + return new Matrix2(resultData); + } + public void FillDiagonal(Matrix1 v) + { + int n = (int)Math.Min(Math.Min(this.nRows, this.nCols), v.size); + for (int ix = 0; ix < n; ix++) + this.data[ix, ix] = v.data[ix]; + } + public void FillDiagonal(float f) + { + int n = Math.Min(this.nRows, this.nCols); + for (int ix = 0; ix < n; ix++) + this.data[ix, ix] = f; + } + + public static Matrix2 SkewMatrix(Vector3Float v) { + float[,] result = new float[3, 3] { + {0, -v.depth, v.vertical}, + {v.depth, 0, -v.horizontal}, + {-v.vertical, v.horizontal, 0} + }; + return new Matrix2(result); + } + + public Matrix1 GetRow(int rowIx) { + float[] row = new float[this.nCols]; + for (int colIx = 0; colIx < this.nCols; colIx++) { + row[colIx] = this.data[rowIx, colIx]; + } + return new Matrix1(row); + } + +#if UNITY_5_3_OR_NEWER + public UnityEngine.Vector3 GetRow3(int rowIx) { + int cols = this.nCols; + UnityEngine.Vector3 row = new() { + x = this.data[rowIx, 0], + y = this.data[rowIx, 1], + z = this.data[rowIx, 2] + }; + return row; + } +#endif + public void SetRow(int rowIx, Matrix1 v) { + for (uint ix = 0; ix < v.size; ix++) + this.data[rowIx, ix] = v.data[ix]; + } + public void SetRow3(int rowIx, Vector3Float v) { + this.data[rowIx, 0] = v.horizontal; + this.data[rowIx, 1] = v.vertical; + this.data[rowIx, 2] = v.depth; + } + + public void SwapRows(int row1, int row2) { + for (uint ix = 0; ix < this.nCols; ix++) { + float temp = this.data[row1, ix]; + this.data[row1, ix] = this.data[row2, ix]; + this.data[row2, ix] = temp; + } + } + + public Matrix1 GetColumn(int colIx) + { + float[] column = new float[this.nRows]; + for (int i = 0; i < this.nRows; i++) { + column[i] = this.data[i, colIx]; + } + return new Matrix1(column); + } + public void SetColumn(int colIx, Matrix1 v) { + for (uint ix = 0; ix < v.size; ix++) + this.data[ix, colIx] = v.data[ix]; + } + public void SetColumn(int colIx, Vector3Float v) { + this.data[0, colIx] = v.horizontal; + this.data[1, colIx] = v.vertical; + this.data[2, colIx] = v.depth; + } + + public static bool AllClose(Matrix2 A, Matrix2 B, float atol = 1e-08f) { + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) { + float d = MathF.Abs(A.data[i, j] - B.data[i, j]); + if (d > atol) + return false; + } + } + return true; + } + + public Matrix2 Transpose() { + float[,] resultData = new float[this.nCols, this.nRows]; + for (uint rowIx = 0; rowIx < this.nRows; rowIx++) { + for (uint colIx = 0; colIx < this.nCols; colIx++) + resultData[colIx, rowIx] = this.data[rowIx, colIx]; + } + return new Matrix2(resultData); + // double checked code + } + public Matrix2 transposed { + get => Transpose(); + } + + public static Matrix2 operator -(Matrix2 m) { + float[,] result = new float[m.nRows, m.nCols]; + + for (int i = 0; i < m.nRows; i++) { + for (int j = 0; j < m.nCols; j++) + result[i, j] = -m.data[i, j]; + } + return new Matrix2(result); + } + + public static Matrix2 operator -(Matrix2 A, Matrix2 B) { + if (A.nRows != B.nRows || A.nCols != B.nCols) + throw new System.ArgumentException("Size of A must match size of B."); + + float[,] result = new float[A.nRows, B.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) + result[i, j] = A.data[i, j] - B.data[i, j]; + } + return new Matrix2(result); + } + + public static Matrix2 operator +(Matrix2 A, Matrix2 B) { + if (A.nRows != B.nRows || A.nCols != B.nCols) + throw new System.ArgumentException("Size of A must match size of B."); + + float[,] result = new float[A.nRows, B.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) + result[i, j] = A.data[i, j] + B.data[i, j]; + } + return new Matrix2(result); + } + + public static Matrix2 operator *(Matrix2 A, Matrix2 B) { + if (A.nCols != B.nRows) + throw new System.ArgumentException("Number of columns in A must match number of rows in B."); + + float[,] result = new float[A.nRows, B.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < B.nCols; j++) { + float sum = 0.0f; + for (int k = 0; k < A.nCols; k++) + sum += A.data[i, k] * B.data[k, j]; + + result[i, j] = sum; + } + } + + return new Matrix2(result); + // double checked code + } + + public static Matrix1 operator *(Matrix2 A, Matrix1 v) { + float[] result = new float[A.nRows]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) { + result[i] += A.data[i, j] * v.data[j]; + } + } + + return new Matrix1(result); + } + + public static Vector3Float operator *(Matrix2 A, Vector3Float v) { + return new Vector3Float( + A.data[0, 0] * v.horizontal + A.data[0, 1] * v.vertical + A.data[0, 2] * v.depth, + A.data[1, 0] * v.horizontal + A.data[1, 1] * v.vertical + A.data[1, 2] * v.depth, + A.data[2, 0] * v.horizontal + A.data[2, 1] * v.vertical + A.data[2, 2] * v.depth + ); + } + + public static Matrix2 operator *(Matrix2 A, float s) { + float[,] result = new float[A.nRows, A.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) + result[i, j] = A.data[i, j] * s; + } + + return new Matrix2(result); + } + public static Matrix2 operator *(float s, Matrix2 A) { + return A * s; + } + + public static Matrix2 operator /(Matrix2 A, float s) { + float[,] result = new float[A.nRows, A.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) + result[i, j] = A.data[i, j] / s; + } + + return new Matrix2(result); + } + public static Matrix2 operator /(float s, Matrix2 A) { + float[,] result = new float[A.nRows, A.nCols]; + + for (int i = 0; i < A.nRows; i++) { + for (int j = 0; j < A.nCols; j++) + result[i, j] = s / A.data[i, j]; + } + + return new Matrix2(result); + } + + public Matrix2 GetRows(Slice slice) { + return GetRows(slice.start, slice.stop); + } + public Matrix2 GetRows(int from, int to) { + if (from < 0 || to >= this.nRows) + throw new System.ArgumentException("Slice index out of range."); + + float[,] result = new float[to - from, this.nCols]; + int resultRowIx = 0; + for (int rowIx = from; rowIx < to; rowIx++) { + for (int colIx = 0; colIx < this.nCols; colIx++) + result[resultRowIx, colIx] = this.data[rowIx, colIx]; + + resultRowIx++; + } + + return new Matrix2(result); + } + + public Matrix2 Slice(Slice slice) + { + return Slice(slice.start, slice.stop); + } + public Matrix2 Slice(int from, int to) + { + if (from < 0 || to >= this.nRows) + throw new System.ArgumentException("Slice index out of range."); + + float[,] result = new float[to - from, this.nCols]; + int resultRowIx = 0; + for (int rowIx = from; rowIx < to; rowIx++) + { + for (int colIx = 0; colIx < this.nCols; colIx++) + { + result[resultRowIx, colIx] = this.data[rowIx, colIx]; + } + resultRowIx++; + } + + return new Matrix2(result); + } + public Matrix2 Slice(Slice rowRange, Slice colRange) { + return Slice((rowRange.start, rowRange.stop), (colRange.start, colRange.stop)); + } + public Matrix2 Slice((int start, int stop) rowRange, (int start, int stop) colRange) + { + float[,] result = new float[rowRange.stop - rowRange.start, colRange.stop - colRange.start]; + + int resultRowIx = 0; + int resultColIx = 0; + for (int i = rowRange.start; i < rowRange.stop; i++) + { + for (int j = colRange.start; j < colRange.stop; j++) + result[resultRowIx, resultColIx] = this.data[i, j]; + } + return new Matrix2(result); + } + + public void UpdateSlice(Slice slice, Matrix2 m) { + UpdateSlice((slice.start, slice.stop), m); + } + public void UpdateSlice((int start, int stop) slice, Matrix2 m) { + // if (slice.start == slice.stop) + // Console.WriteLine("WARNING: no data is updates when start equals stop in a slice!"); + int mRowIx = 0; + for (int rowIx = slice.start; rowIx < slice.stop; rowIx++, mRowIx++) { + for (int colIx = 0; colIx < this.nCols; colIx++) + this.data[rowIx, colIx] = m.data[mRowIx, colIx]; + } + } + + public void UpdateSlice(Slice rowRange, Slice colRange, Matrix2 m) + { + UpdateSlice((rowRange.start, rowRange.stop), (colRange.start, colRange.stop), m); + } + public void UpdateSlice((int start, int stop) rowRange, (int start, int stop) colRange, Matrix2 m) + { + for (int i = rowRange.start; i < rowRange.stop; i++) + { + for (int j = colRange.start; j < colRange.stop; j++) + this.data[i, j] = m.data[i - rowRange.start, j - colRange.start]; + } + } + + public Matrix2 Inverse() { + Matrix2 A = this; + // unchecked + int n = A.nRows; + + // Create an identity matrix of the same size as the original matrix + float[,] augmentedMatrix = new float[n, 2 * n]; + for (int i = 0; i < n; i++) { + for (int j = 0; j < n; j++) { + augmentedMatrix[i, j] = A.data[i, j]; + augmentedMatrix[i, j + n] = (i == j) ? 1 : 0; // Identity matrix + } + } + + // Perform Gaussian elimination + for (int i = 0; i < n; i++) { + // Find the pivot row + float pivot = augmentedMatrix[i, i]; + if (Math.Abs(pivot) < 1e-10) // Check for singular matrix + throw new InvalidOperationException("Matrix is singular and cannot be inverted."); + + // Normalize the pivot row + for (int j = 0; j < 2 * n; j++) + augmentedMatrix[i, j] /= pivot; + + // Eliminate the column below the pivot + for (int j = i + 1; j < n; j++) { + float factor = augmentedMatrix[j, i]; + for (int k = 0; k < 2 * n; k++) + augmentedMatrix[j, k] -= factor * augmentedMatrix[i, k]; + } + } + + // Back substitution + for (int i = n - 1; i >= 0; i--) + { + // Eliminate the column above the pivot + for (int j = i - 1; j >= 0; j--) + { + float factor = augmentedMatrix[j, i]; + for (int k = 0; k < 2 * n; k++) + augmentedMatrix[j, k] -= factor * augmentedMatrix[i, k]; + } + } + + // Extract the inverse matrix from the augmented matrix + float[,] inverse = new float[n, n]; + for (int i = 0; i < n; i++) { + for (int j = 0; j < n; j++) + inverse[i, j] = augmentedMatrix[i, j + n]; + } + + return new Matrix2(inverse); + } + + public float Determinant() + { + int n = this.nRows; + if (n != this.nCols) + throw new System.ArgumentException("Matrix must be square."); + + if (n == 1) + return this.data[0, 0]; // Base case for 1x1 matrix + + if (n == 2) // Base case for 2x2 matrix + return this.data[0, 0] * this.data[1, 1] - this.data[0, 1] * this.data[1, 0]; + + float det = 0; + for (int col = 0; col < n; col++) + det += (col % 2 == 0 ? 1 : -1) * this.data[0, col] * this.Minor(0, col).Determinant(); + + return det; + } + + // Helper function to compute the minor of a matrix + private Matrix2 Minor(int rowToRemove, int colToRemove) + { + int n = this.nRows; + float[,] minor = new float[n - 1, n - 1]; + + int r = 0, c = 0; + for (int i = 0; i < n; i++) { + if (i == rowToRemove) continue; + + c = 0; + for (int j = 0; j < n; j++) { + if (j == colToRemove) continue; + + minor[r, c] = this.data[i, j]; + c++; + } + r++; + } + + return new Matrix2(minor); + } + + public static Matrix2 DeleteRows(Matrix2 A, Slice rowRange) { + float[,] result = new float[A.nRows - (rowRange.stop - rowRange.start), A.nCols]; + + int resultRowIx = 0; + for (int i = 0; i < A.nRows; i++) { + if (i >= rowRange.start && i < rowRange.stop) + continue; + + for (int j = 0; j < A.nCols; j++) + result[resultRowIx, j] = A.data[i, j]; + + resultRowIx++; + } + return new Matrix2(result); + } + + internal static Matrix2 DeleteColumns(Matrix2 A, Slice colRange) { + float[,] result = new float[A.nRows, A.nCols - (colRange.stop - colRange.start)]; + + for (int i = 0; i < A.nRows; i++) { + int resultColIx = 0; + for (int j = 0; j < A.nCols; j++) { + if (j >= colRange.start && j < colRange.stop) + continue; + + result[i, resultColIx++] = A.data[i, j]; + } + } + return new Matrix2(result); + } + } + + public class Matrix1 + { + public float[] data { get; } + + public int size => data.GetLength(0); + + public Matrix1(int size) + { + this.data = new float[size]; + } + + public Matrix1(float[] data) { + this.data = data; + } + + public static Matrix1 Zero(int size) + { + return new Matrix1(size); + } + + public static Matrix1 FromVector2(Vector2Float v) { + float[] result = new float[2]; + result[0] = v.horizontal; + result[1] = v.vertical; + return new Matrix1(result); + } + + public static Matrix1 FromVector3(Vector3Float v) { + float[] result = new float[3]; + result[0] = v.horizontal; + result[1] = v.vertical; + result[2] = v.depth; + return new Matrix1(result); + } + +#if UNITY_5_3_OR_NEWER + public static Matrix1 FromQuaternion(Quaternion q) { + float[] result = new float[4]; + result[0] = q.x; + result[1] = q.y; + result[2] = q.z; + result[3] = q.w; + return new Matrix1(result); + } +#endif + + public Vector2Float vector2 { + get { + if (this.size != 2) + throw new System.ArgumentException("Matrix1 must be of size 2"); + return new Vector2Float(this.data[0], this.data[1]); + } + } + public Vector3Float vector3 { + get { + if (this.size != 3) + throw new System.ArgumentException("Matrix1 must be of size 3"); + return new Vector3Float(this.data[0], this.data[1], this.data[2]); + } + } + +#if UNITY_5_3_OR_NEWER + public Quaternion quaternion { + get { + if (this.size != 4) + throw new System.ArgumentException("Matrix1 must be of size 4"); + return new Quaternion(this.data[0], this.data[1], this.data[2], this.data[3]); + } + } +#endif + + public Matrix1 Clone() { + float[] data = new float[this.size]; + for (int rowIx = 0; rowIx < this.size; rowIx++) + data[rowIx] = this.data[rowIx]; + return new Matrix1(data); + } + + + public float magnitude { + get { + float sum = 0; + foreach (var elm in data) + sum += elm; + return sum / data.Length; + } + } + public static Matrix1 operator +(Matrix1 A, Matrix1 B) { + if (A.size != B.size) + throw new System.ArgumentException("Size of A must match size of B."); + + float[] result = new float[A.size]; + + for (int i = 0; i < A.size; i++) { + result[i] = A.data[i] + B.data[i]; + } + return new Matrix1(result); + } + + public Matrix2 Transpose() { + float[,] r = new float[1, this.size]; + for (uint colIx = 0; colIx < this.size; colIx++) + r[1, colIx] = this.data[colIx]; + + return new Matrix2(r); + } + + public static float Dot(Matrix1 a, Matrix1 b) { + if (a.size != b.size) + throw new System.ArgumentException("Vectors must be of the same length."); + + float result = 0.0f; + for (int i = 0; i < a.size; i++) { + result += a.data[i] * b.data[i]; + } + return result; + } + + public static Matrix1 operator -(Matrix1 A, Matrix1 B) { + if (A.size != B.size) + throw new System.ArgumentException("Size of A must match size of B."); + + float[] result = new float[A.size]; + + for (int i = 0; i < A.size; i++) { + result[i] = A.data[i] - B.data[i]; + } + return new Matrix1(result); + } + + public static Matrix1 operator *(Matrix1 A, float f) + { + float[] result = new float[A.size]; + + for (int i = 0; i < A.size; i++) + result[i] += A.data[i] * f; + + return new Matrix1(result); + } + public static Matrix1 operator *(float f, Matrix1 A) { + return A * f; + } + + public static Matrix1 operator /(Matrix1 A, float f) { + float[] result = new float[A.size]; + + for (int i = 0; i < A.size; i++) + result[i] = A.data[i] / f; + + return new Matrix1(result); + } + public static Matrix1 operator /(float f, Matrix1 A) { + float[] result = new float[A.size]; + + for (int i = 0; i < A.size; i++) + result[i] = f / A.data[i]; + + return new Matrix1(result); + } + + public Matrix1 Slice(Slice range) + { + return Slice(range.start, range.stop); + } + public Matrix1 Slice(int from, int to) + { + if (from < 0 || to >= this.size) + throw new System.ArgumentException("Slice index out of range."); + + float[] result = new float[to - from]; + int resultIx = 0; + for (int ix = from; ix < to; ix++) + result[resultIx++] = this.data[ix]; + + return new Matrix1(result); + } + public void UpdateSlice(Slice slice, Matrix1 v) { + int vIx = 0; + for (int ix = slice.start; ix < slice.stop; ix++, vIx++) + this.data[ix] = v.data[vIx]; + } + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Quat32.cs b/Assets/NanoBrain/LinearAlgebra/src/Quat32.cs new file mode 100644 index 0000000..19ee9bc --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Quat32.cs @@ -0,0 +1,87 @@ +using System; + +namespace LinearAlgebra { + public class Quat32 { + public float x; + public float y; + public float z; + public float w; + + public Quat32() { + this.x = 0; + this.y = 0; + this.z = 0; + this.w = 1; + } + + public Quat32(float x, float y, float z, float w) { + this.x = x; + this.y = y; + this.z = z; + this.w = w; + } + + public static Quat32 FromSwingTwist(SwingTwist s) { + Quat32 q32 = Quat32.Euler(-s.swing.vertical.inDegrees, s.swing.horizontal.inDegrees, s.twist.inDegrees); + return q32; + } + + public static Quat32 Euler(float yaw, float pitch, float roll) { + float rollOver2 = roll * AngleFloat.Deg2Rad * 0.5f; + float sinRollOver2 = (float)Math.Sin((float)rollOver2); + float cosRollOver2 = (float)Math.Cos((float)rollOver2); + float pitchOver2 = pitch * 0.5f; + float sinPitchOver2 = (float)Math.Sin((float)pitchOver2); + float cosPitchOver2 = (float)Math.Cos((float)pitchOver2); + float yawOver2 = yaw * 0.5f; + float sinYawOver2 = (float)Math.Sin((float)yawOver2); + float cosYawOver2 = (float)Math.Cos((float)yawOver2); + Quat32 result = new Quat32() { + w = cosYawOver2 * cosPitchOver2 * cosRollOver2 + + sinYawOver2 * sinPitchOver2 * sinRollOver2, + x = sinYawOver2 * cosPitchOver2 * cosRollOver2 + + cosYawOver2 * sinPitchOver2 * sinRollOver2, + y = cosYawOver2 * sinPitchOver2 * cosRollOver2 - + sinYawOver2 * cosPitchOver2 * sinRollOver2, + z = cosYawOver2 * cosPitchOver2 * sinRollOver2 - + sinYawOver2 * sinPitchOver2 * cosRollOver2 + }; + return result; + } + + public void ToAngles(out float right, out float up, out float forward) { + float test = this.x * this.y + this.z * this.w; + if (test > 0.499f) { // singularity at north pole + right = 0; + up = 2 * (float)Math.Atan2(this.x, this.w) * AngleFloat.Rad2Deg; + forward = 90; + return; + //return Vector3(0, 2 * (float)atan2(this.x, this.w) * Angle.Rad2Deg, 90); + } + else if (test < -0.499f) { // singularity at south pole + right = 0; + up = -2 * (float)Math.Atan2(this.x, this.w) * AngleFloat.Rad2Deg; + forward = -90; + return; + //return Vector3(0, -2 * (float)atan2(this.x, this.w) * Angle.Rad2Deg, -90); + } + else { + float sqx = this.x * this.x; + float sqy = this.y * this.y; + float sqz = this.z * this.z; + + right = (float)Math.Atan2(2 * this.x * this.w - 2 * this.y * this.z, 1 - 2 * sqx - 2 * sqz) * AngleFloat.Rad2Deg; + up = (float)Math.Atan2(2 * this.y * this.w - 2 * this.x * this.z, 1 - 2 * sqy - 2 * sqz) * AngleFloat.Rad2Deg; + forward = (float)Math.Asin(2 * test) * AngleFloat.Rad2Deg; + return; + // return Vector3( + // atan2f(2 * this.x * this.w - 2 * this.y * this.z, 1 - 2 * sqx - 2 * sqz) * + // Rad2Deg, + // atan2f(2 * this.y * this.w - 2 * this.x * this.z, 1 - 2 * sqy - 2 * sqz) * + // Rad2Deg, + // asinf(2 * test) * Angle.Rad2Deg); + } + } + + } +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Quaternion.cs b/Assets/NanoBrain/LinearAlgebra/src/Quaternion.cs new file mode 100644 index 0000000..670c0a4 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Quaternion.cs @@ -0,0 +1,608 @@ +using System; +#if UNITY_5_3_OR_NEWER +using Quaternion = UnityEngine.Quaternion; +#endif + +namespace LinearAlgebra { + +#if UNITY_5_3_OR_NEWER + public class QuaternionExtensions { + public static Quaternion Reflect(Quaternion q) { + return new(-q.x, -q.y, -q.z, q.w); + } + + public static Matrix2 ToRotationMatrix(Quaternion q) { + float w = q.x, x = q.y, y = q.z, z = q.w; + + float[,] result = new float[,] + { + { 1 - 2 * (y * y + z * z), 2 * (x * y - w * z), 2 * (x * z + w * y) }, + { 2 * (x * y + w * z), 1 - 2 * (x * x + z * z), 2 * (y * z - w * x) }, + { 2 * (x * z - w * y), 2 * (y * z + w * x), 1 - 2 * (x * x + y * y) } + }; + return new Matrix2(result); + } + + public static Quaternion FromRotationMatrix(Matrix2 m) { + float trace = m.data[0, 0] + m.data[1, 1] + m.data[2, 2]; + float w, x, y, z; + + if (trace > 0) { + float s = 0.5f / (float)Math.Sqrt(trace + 1.0f); + w = 0.25f / s; + x = (m.data[2, 1] - m.data[1, 2]) * s; + y = (m.data[0, 2] - m.data[2, 0]) * s; + z = (m.data[1, 0] - m.data[0, 1]) * s; + } + else { + if (m.data[0, 0] > m.data[1, 1] && m.data[0, 0] > m.data[2, 2]) { + float s = 2.0f * (float)Math.Sqrt(1.0f + m.data[0, 0] - m.data[1, 1] - m.data[2, 2]); + w = (m.data[2, 1] - m.data[1, 2]) / s; + x = 0.25f * s; + y = (m.data[0, 1] + m.data[1, 0]) / s; + z = (m.data[0, 2] + m.data[2, 0]) / s; + } + else if (m.data[1, 1] > m.data[2, 2]) { + float s = 2.0f * (float)Math.Sqrt(1.0f + m.data[1, 1] - m.data[0, 0] - m.data[2, 2]); + w = (m.data[0, 2] - m.data[2, 0]) / s; + x = (m.data[0, 1] + m.data[1, 0]) / s; + y = 0.25f * s; + z = (m.data[1, 2] + m.data[2, 1]) / s; + } + else { + float s = 2.0f * (float)Math.Sqrt(1.0f + m.data[2, 2] - m.data[0, 0] - m.data[1, 1]); + w = (m.data[1, 0] - m.data[0, 1]) / s; + x = (m.data[0, 2] + m.data[2, 0]) / s; + y = (m.data[1, 2] + m.data[2, 1]) / s; + z = 0.25f * s; + } + } + + return new Quaternion(x, y, z, w); + } + } +#else + public struct Quaternion { + public float x; + public float y; + public float z; + public float w; + + /// + /// create a new quaternion with the given values + /// + /// x component + /// y component + /// z component + /// w component + public Quaternion(float x, float y, float z, float w) { + this.x = x; + this.y = y; + this.z = z; + this.w = w; + } + + /// + /// An identity quaternion + /// + public static readonly Quaternion identity = new(0, 0, 0, 1); + + private readonly Vector3Float xyz => new(x, y, z); + + private readonly float magnitude => MathF.Sqrt(this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w); + + private readonly float sqrMagnitude => x * x + y * y + z * z + w * w; + + /// + /// Convert to unit quaternion + /// + /// This will preserve the orientation, + /// but ensures that it is a unit quaternion. + public readonly Quaternion normalized { + get { + float length = this.magnitude; + Quaternion q = new(this.x / length, this.y / length, this.z / length, this.w / length); + return q; + } + } + + /// + /// Convert to unity quaternion + /// + /// The quaternion to convert + /// A unit quaternion + /// This will preserve the orientation, + /// but ensures that it is a unit quaternion. + public static Quaternion Normalize(Quaternion q) { + return q.normalized; + } + + /// + /// Convert to euler angles + /// + /// The quaternion to convert + /// A vector containing euler angles + /// The euler angles performed in the order: Z, X, Y + public static Vector3Float ToAngles(Quaternion q) { + // Extract Euler angles in Unity order (X = pitch, Y = yaw, Z = roll), returned in degrees as (x,pitch),(y,yaw),(z,roll) + // Handle singularities/gimbal lock + float test = 2f * (q.w * q.x - q.y * q.z); + // clamp + if (test >= 1f) test = 1f; + if (test <= -1f) test = -1f; + + float pitch = MathF.Asin(test); // X + + float roll = MathF.Atan2(2f * (q.w * q.z + q.x * q.y), + 1f - 2f * (q.x * q.x + q.z * q.z)); // Z + + float yaw = MathF.Atan2(2f * (q.w * q.y + q.x * q.z), + 1f - 2f * (q.y * q.y + q.x * q.x)); // Y + + const float rad2deg = 180f / MathF.PI; + return new Vector3Float(pitch * rad2deg, yaw * rad2deg, roll * rad2deg); + // float test = q.x * q.y + q.z * q.w; + // if (test > 0.499f) // singularity at north pole + // return new Vector3Float(0, 2 * MathF.Atan2(q.x, q.w) * AngleFloat.Rad2Deg, 90); + + // else if (test < -0.499f) // singularity at south pole + // return new Vector3Float(0, -2 * MathF.Atan2(q.x, q.w) * AngleFloat.Rad2Deg, -90); + + // else { + // float sqx = q.x * q.x; + // float sqy = q.y * q.y; + // float sqz = q.z * q.z; + + // return new Vector3Float( + // MathF.Atan2(2 * q.x * q.w - 2 * q.y * q.z, 1 - 2 * sqx - 2 * sqz) * + // AngleFloat.Rad2Deg, + // MathF.Atan2(2 * q.y * q.w - 2 * q.x * q.z, 1 - 2 * sqy - 2 * sqz) * + // AngleFloat.Rad2Deg, + // MathF.Asin(2 * test) * AngleFloat.Rad2Deg); + // } + } + + /// + /// Create a rotation from euler angles + /// + /// The angle around the right axis + /// The angle around the upward axis + /// The angle around the forward axis + /// The resulting quaternion + /// Rotation are appied in the order Z, X, Y. + public static Quaternion Euler(float x, float y, float z) { + return Quaternion.Euler(new Vector3Float(x, y, z)); + } + /// + /// Create a rotation from a vector containing euler angles + /// + /// Vector with the euler angles + /// The resulting quaternion + /// Rotation are appied in the order Z, X, Y. + public static Quaternion Euler(Vector3Float angles) { + // return Quaternion.FromEulerRad(angles * AngleFloat.Deg2Rad); + // } + // private static Quaternion FromEulerRad(Vector3Float euler) { + Vector3Float euler = angles * AngleFloat.Deg2Rad; + // euler.x = pitch, euler.y = yaw, euler.z = roll (radians) + float cx = MathF.Cos(euler.horizontal * 0.5f); + float sx = MathF.Sin(euler.horizontal * 0.5f); + float cy = MathF.Cos(euler.vertical * 0.5f); + float sy = MathF.Sin(euler.vertical * 0.5f); + float cz = MathF.Cos(euler.depth * 0.5f); + float sz = MathF.Sin(euler.depth * 0.5f); + + // Unity uses intrinsic Z, then X, then Y -> q = Qy * Qx * Qz + Quaternion q; + q.w = cy * cx * cz + sy * sx * sz; + q.x = cy * sx * cz + sy * cx * sz; + q.y = sy * cx * cz - cy * sx * sz; + q.z = cy * cx * sz - sy * sx * cz; + return q; + // float yaw = euler.horizontal; + // float pitch = euler.vertical; + // float roll = euler.depth; + // float rollOver2 = roll * 0.5f; + // float sinRollOver2 = MathF.Sin(rollOver2); + // float cosRollOver2 = MathF.Cos(rollOver2); + // float pitchOver2 = pitch * 0.5f; + // float sinPitchOver2 = MathF.Sin(pitchOver2); + // float cosPitchOver2 = MathF.Cos(pitchOver2); + // float yawOver2 = yaw * 0.5f; + // float sinYawOver2 = MathF.Sin(yawOver2); + // float cosYawOver2 = MathF.Cos(yawOver2); + // Quaternion result; + // result.w = cosYawOver2 * cosPitchOver2 * cosRollOver2 + + // sinYawOver2 * sinPitchOver2 * sinRollOver2; + // result.x = sinYawOver2 * cosPitchOver2 * cosRollOver2 + + // cosYawOver2 * sinPitchOver2 * sinRollOver2; + // result.y = cosYawOver2 * sinPitchOver2 * cosRollOver2 - + // sinYawOver2 * cosPitchOver2 * sinRollOver2; + // result.z = cosYawOver2 * cosPitchOver2 * sinRollOver2 - + // sinYawOver2 * sinPitchOver2 * cosRollOver2; + // return result; + } + + /// + /// Multiply two quaternions + /// + /// + /// + /// The resulting rotation + public static Quaternion operator *(Quaternion q1, Quaternion q2) { + return new Quaternion( + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y + q1.w * q2.x, + -q1.x * q2.z + q1.y * q2.w + q1.z * q2.x + q1.w * q2.y, + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w + q1.w * q2.z, + -q1.x * q2.x - q1.y * q2.y - q1.z * q2.z + q1.w * q2.w); + } + + /// + /// Rotate a vector using this quaterion + /// + /// The rotation + /// The vector to rotate + /// The rotated vector + public static Vector3Float operator *(Quaternion q, Vector3Float v) { + float num = q.x * 2; + float num2 = q.y * 2; + float num3 = q.z * 2; + float num4 = q.x * num; + float num5 = q.y * num2; + float num6 = q.z * num3; + float num7 = q.x * num2; + float num8 = q.x * num3; + float num9 = q.y * num3; + float num10 = q.w * num; + float num11 = q.w * num2; + float num12 = q.w * num3; + + float px = v.horizontal; + float py = v.vertical; + float pz = v.depth; + float rx = + (1 - (num5 + num6)) * px + (num7 - num12) * py + (num8 + num11) * pz; + float ry = + (num7 + num12) * px + (1 - (num4 + num6)) * py + (num9 - num10) * pz; + float rz = + (num8 - num11) * px + (num9 + num10) * py + (1 - (num4 + num5)) * pz; + Vector3Float result = new(rx, ry, rz); + return result; + } + + /// + /// The inverse of quaterion + /// + /// The quaternion for which the inverse is + /// needed The inverted quaternion + public static Quaternion Inverse(Quaternion q) { + float n = MathF.Sqrt(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w); + return new Quaternion(-q.x / n, -q.y / n, -q.z / n, q.w / n); + } + + /// + /// A rotation which looks in the given direction + /// + /// The look direction + /// The up direction + /// The look rotation + public static Quaternion LookRotation(Vector3Float forward, Vector3Float up) { + Vector3Float nForward = forward.normalized; + Vector3Float nRight = Vector3Float.Normalize(Vector3Float.Cross(up, nForward)); + Vector3Float nUp = Vector3Float.Cross(nForward, nRight); + float m00 = nRight.horizontal; // x; + float m01 = nRight.vertical; // y; + float m02 = nRight.depth; // z; + float m10 = nUp.horizontal; // x; + float m11 = nUp.vertical; // y; + float m12 = nUp.depth; // z; + float m20 = nForward.horizontal; // x; + float m21 = nForward.vertical; // y; + float m22 = nForward.depth; // z; + + float num8 = (m00 + m11) + m22; + float x, y, z, w; + if (num8 > 0) { + float num = MathF.Sqrt(num8 + 1); + w = num * 0.5f; + num = 0.5f / num; + x = (m12 - m21) * num; + y = (m20 - m02) * num; + z = (m01 - m10) * num; + return new Quaternion(x, y, z, w); + } + if ((m00 >= m11) && (m00 >= m22)) { + float num7 = MathF.Sqrt(((1 + m00) - m11) - m22); + float num4 = 0.5F / num7; + x = 0.5f * num7; + y = (m01 + m10) * num4; + z = (m02 + m20) * num4; + w = (m12 - m21) * num4; + return new Quaternion(x, y, z, w); + } + if (m11 > m22) { + float num6 = MathF.Sqrt(((1 + m11) - m00) - m22); + float num3 = 0.5F / num6; + x = (m10 + m01) * num3; + y = 0.5F * num6; + z = (m21 + m12) * num3; + w = (m20 - m02) * num3; + return new Quaternion(x, y, z, w); + } + float num5 = MathF.Sqrt(((1 + m22) - m00) - m11); + float num2 = 0.5F / num5; + x = (m20 + m02) * num2; + y = (m21 + m12) * num2; + z = 0.5F * num5; + w = (m01 - m10) * num2; + return new Quaternion(x, y, z, w); + } + + /// + /// Creates a quaternion with the given forward direction with up = + /// Vector3::up + /// + /// The look direction + /// The rotation for this direction + /// For the rotation, Vector::up is used for the up direction. + /// Note: if the forward direction == Vector3::up, the result is + /// Quaternion::identity + public static Quaternion LookRotation(Vector3Float forward) { + Vector3Float up = new(0, 1, 0); + return LookRotation(forward, up); + } + + /// + /// Calculat the rotation from on vector to another + /// + /// The from direction + /// The to direction + /// The rotation from the first to the second vector + public static Quaternion FromToRotation(Vector3Float fromDirection, Vector3Float toDirection) { + Vector3Float axis = Vector3Float.Cross(fromDirection, toDirection); + axis = axis.normalized; + AngleFloat angle = Vector3Float.SignedAngle(fromDirection, toDirection, axis); + Quaternion rotation = AngleAxis(angle, axis); + return rotation; + + } + + /// + /// Rotate form one orientation to anther with a maximum amount of degrees + /// + /// The from rotation + /// The destination rotation + /// The maximum amount of degrees to + /// rotate The possibly limited rotation + public static Quaternion RotateTowards(Quaternion from, Quaternion to, + float maxDegreesDelta) { + float num = Quaternion.UnsignedAngle(from, to); + if (num == 0) { + return to; + } + float t = MathF.Min(1, maxDegreesDelta / num); + return SlerpUnclamped(from, to, t); + + } + + /// + /// Convert an angle/axis representation to a quaternion + /// + /// The angle + /// The axis + /// The resulting quaternion + public static Quaternion AngleAxis(AngleFloat angle, Vector3Float axis) { + if (axis.sqrMagnitude == 0.0f) + return Quaternion.identity; + + float radians = angle.inRadians; + radians *= 0.5f; + + Vector3Float axis2 = axis * MathF.Sin(radians); + float x = axis2.horizontal; // x; + float y = axis2.vertical; // y; + float z = axis2.depth; // z; + float w = MathF.Cos(radians); + + return new Quaternion(x, y, z, w).normalized; + } + /// + /// Convert this quaternion to angle/axis representation + /// + /// A pointer to the angle for the result + /// A pointer to the axis for the result + public readonly void ToAngleAxis(out AngleFloat angle, out Vector3Float axis) { + Quaternion q1 = (MathF.Abs(this.w) > 1.0f) ? this.normalized : this; + angle = AngleFloat.Radians(2.0f * MathF.Acos(q1.w)); // angle + float den = MathF.Sqrt(1.0F - q1.w * q1.w); + if (den > 0.0001f) { + axis = Vector3Float.Normalize(q1.xyz / den); + } + else { + // This occurs when the angle is zero. + // Not a problem: just set an arbitrary normalized axis. + axis = Vector3Float.right; + } + } + + /// + /// Get the angle between two orientations + /// + /// The first orientation + /// The second orientation + /// The smallest angle in degrees between the two + /// orientations + public static float UnsignedAngle(Quaternion q1, Quaternion q2) { + // float f = Dot(q1, q2); + // return MathF.Acos(MathF.Min(MathF.Abs(f), 1)) * 2 * AngleFloat.Rad2Deg; + + float dot = q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w; + dot = MathF.Min(MathF.Max(dot, -1f), 1f); + return 2f * MathF.Acos(MathF.Abs(dot)) * (180f / MathF.PI); + } + + /// + /// Sherical lerp between two rotations + /// + /// The first rotation + /// The second rotation + /// The factor between 0 and 1. + /// The resulting rotation + /// A factor 0 returns rotation1, factor1 returns rotation2. + public static Quaternion Slerp(Quaternion a, + Quaternion b, float t) { + if (t > 1) + t = 1; + if (t < 0) + t = 0; + return SlerpUnclamped(a, b, t); + } + + /// + /// Unclamped sherical lerp between two rotations + /// + /// The first rotation + /// The second rotation + /// The factor + /// The resulting rotation + /// A factor 0 returns rotation1, factor1 returns rotation2. + /// Values outside the 0..1 range will result in extrapolated rotations + public static Quaternion SlerpUnclamped(Quaternion a, + Quaternion b, float t) { + // if either input is zero, return the other. + if (a.sqrMagnitude == 0.0f) { + if (b.sqrMagnitude == 0.0f) { + return identity; + } + return b; + } + else if (b.sqrMagnitude == 0.0f) { + return a; + } + + Vector3Float axyz = a.xyz; + Vector3Float bxyz = b.xyz; + float cosHalfAngle = a.w * b.w + Vector3Float.Dot(axyz, bxyz); + + Quaternion b2 = b; + if (cosHalfAngle >= 1.0f || cosHalfAngle <= -1.0f) { + // angle = 0.0f, so just return one input. + return a; + } + else if (cosHalfAngle < 0.0f) { + b2.x = -b.x; + b2.y = -b.y; + b2.z = -b.z; + b2.w = -b.w; + cosHalfAngle = -cosHalfAngle; + } + + float blendA; + float blendB; + if (cosHalfAngle < 0.99f) { + // do proper slerp for big angles + float halfAngle = MathF.Acos(cosHalfAngle); + float sinHalfAngle = MathF.Sin(halfAngle); + float oneOverSinHalfAngle = 1.0F / sinHalfAngle; + blendA = MathF.Sin(halfAngle * (1.0F - t)) * oneOverSinHalfAngle; + blendB = MathF.Sin(halfAngle * t) * oneOverSinHalfAngle; + } + else { + // do lerp if angle is really small. + blendA = 1.0f - t; + blendB = t; + } + Vector3Float v = axyz * blendA + b2.xyz * blendB; + Quaternion result = + new(v.horizontal, v.vertical, v.depth, blendA * a.w + blendB * b2.w); + if (result.sqrMagnitude > 0.0f) + return result.normalized; + else + return Quaternion.identity; + } + + /// + /// Convert this quaternion to angle/axis representation + /// + /// A pointer to the angle for the result + /// A pointer to the axis for the result + public readonly void ToAngleAxis(out float angle, out Vector3Float axis) { + ToAxisAngleRad(this, out axis, out angle); + angle *= AngleFloat.Rad2Deg; + } + private static void ToAxisAngleRad(Quaternion q, + out Vector3Float axis, + out float angle) { + Quaternion q1 = (MathF.Abs(q.w) > 1.0f) ? Quaternion.Normalize(q) : q; + angle = 2.0f * MathF.Acos(q1.w); // angle + float den = MathF.Sqrt(1.0F - q1.w * q1.w); + if (den > 0.0001f) { + axis = (q1.xyz / den).normalized; + } + else { + // This occurs when the angle is zero. + // Not a problem: just set an arbitrary normalized axis. + axis = new Vector3Float(1, 0, 0); + } + } + + /// + /// Returns the angle of around the give axis for a rotation + /// + /// The axis around which the angle should be + /// computed The source rotation + /// The signed angle around the axis + public static float GetAngleAround(Vector3Float axis, Quaternion rotation) { + Quaternion secondaryRotation = GetRotationAround(axis, rotation); + secondaryRotation.ToAngleAxis(out float rotationAngle, out Vector3Float rotationAxis); + + // Do the axis point in opposite directions? + if (Vector3Float.Dot(axis, rotationAxis) < 0) + rotationAngle = -rotationAngle; + + return rotationAngle; + } + + /// + /// Returns the rotation limited around the given axis + /// + /// The axis which which the rotation should be + /// limited The source rotation + /// The rotation around the given axis + public static Quaternion GetRotationAround(Vector3Float axis, Quaternion rotation) { + Vector3Float ra = new(rotation.x, rotation.y, rotation.z); // rotation axis + Vector3Float p = Vector3Float.Project( + ra, axis); // return projection ra on to axis (parallel component) + Quaternion twist = new(p.horizontal, p.vertical, p.depth, rotation.w); + twist = Normalize(twist); + return twist; + + } + + /// + /// Swing-twist decomposition of a rotation + /// + /// The base direction for the decomposition + /// The source rotation + /// A pointer to the quaternion for the swing + /// result A pointer to the quaternion for the + /// twist result + static void GetSwingTwist(Vector3Float axis, Quaternion q, + out Quaternion swing, out Quaternion twist) { + twist = GetRotationAround(axis, q); + swing = q * Inverse(twist); + } + + /// + /// Calculate the dot product of two quaternions + /// + /// The first rotation + /// The second rotation + /// + public static float Dot(Quaternion q1, Quaternion q2) { + return q1.x * q2.x + q1.y * q2.y + q1.z * q2.z + q1.w * q2.w; + } + } +#endif + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Spherical.cs b/Assets/NanoBrain/LinearAlgebra/src/Spherical.cs new file mode 100644 index 0000000..de06d24 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Spherical.cs @@ -0,0 +1,185 @@ +using System; +#if UNITY_5_3_OR_NEWER +using Vector3 = UnityEngine.Vector3; +#endif + +namespace LinearAlgebra +{ + /// + /// A spherical vector + /// + /// This is a struct such that it is a value type and cannot be null + public struct Spherical + { + /// + /// Create a spherical vector + /// + /// The distance in meters + /// The direction of the vector + public Spherical(float distance, Direction direction) + { + this.distance = distance; + this.direction = direction; + } + + /// + /// Create spherical vector. All given angles are in degrees + /// + /// The distance in meters + /// The horizontal angle in degrees + /// The vertical angle in degrees + /// + public static Spherical Degrees(float distance, float horizontal, float vertical) + { + Direction direction = Direction.Degrees(horizontal, vertical); + Spherical s = new(distance, direction); + return s; + } + + public static Spherical Radians(float distance, float horizontal, float vertical) + { + Direction direction = Direction.Radians(horizontal, vertical); + Spherical s = new(distance, direction); + return s; + } + + /// + /// The distance in meters + /// + /// @remark The distance should never be negative + public float distance; + /// + /// The direction of the vector + /// + public Direction direction; + + /// + /// A spherical vector with zero degree angles and distance + /// + public readonly static Spherical zero = new(0, Direction.forward); + /// + /// A normalized forward-oriented vector + /// + public readonly static Spherical forward = new(1, Direction.forward); + + + // public static Spherical FromVector3Float(Vector3Float v) { + // float distance = v.magnitude; + // if (distance == 0.0f) + // return Spherical.zero; + // else { + // float verticalAngle = (float)((Angle.pi / 2 - Math.Acos(v.y / distance)) * Angle.Rad2Deg); + // float horizontalAngle = (float)Math.Atan2(v.x, v.z) * Angle.Rad2Deg; + // return Spherical.Degrees(distance, horizontalAngle, verticalAngle); + // } + // } + + public static Spherical FromVector3Float(Vector3Float v) + { + float distance = v.magnitude; + if (distance == 0.0f) + return Spherical.zero; + else + { + float verticalAngle = (float)(Math.PI / 2 - Math.Acos(v.vertical / distance)) * AngleFloat.Rad2Deg; + float horizontalAngle = (float)Math.Atan2(v.horizontal, v.depth) * AngleFloat.Rad2Deg; + return Degrees(distance, horizontalAngle, verticalAngle); + } + } + + // public Vector3Float ToVector3Float() { + // float verticalRad = (Angle.pi / 2) - this.direction.vertical * Angle.Deg2Rad; + // float horizontalRad = this.direction.horizontal * Angle.Deg2Rad; + // float cosVertical = (float)Math.Cos(verticalRad); + // float sinVertical = (float)Math.Sin(verticalRad); + // float cosHorizontal = (float)Math.Cos(horizontalRad); + // float sinHorizontal = (float)Math.Sin(horizontalRad); + + // float x = this.distance * sinVertical * sinHorizontal; + // float y = this.distance * cosVertical; + // float z = this.distance * sinVertical * cosHorizontal; + + // Vector3Float v = new(x, y, z); + // return v; + // } + + public Vector3Float ToVector3Float() + { + float verticalRad = (AngleFloat.deg90 - this.direction.vertical).inRadians; + float horizontalRad = this.direction.horizontal.inRadians; + float cosVertical = (float)Math.Cos(verticalRad); + float sinVertical = (float)Math.Sin(verticalRad); + float cosHorizontal = (float)Math.Cos(horizontalRad); + float sinHorizontal = (float)Math.Sin(horizontalRad); + + float x = this.distance * sinVertical * sinHorizontal; + float y = this.distance * cosVertical; + float z = this.distance * sinVertical * cosHorizontal; + + Vector3Float v = new(x, y, z); + return v; + } +#if UNITY_5_3_OR_NEWER + public static Spherical FromVector3(Vector3 v) + { + float distance = v.magnitude; + if (distance == 0.0f) + return Spherical.zero; + else + { + float verticalAngle = (float)(Math.PI / 2 - Math.Acos(v.y / distance)) * AngleFloat.Rad2Deg; + float horizontalAngle = (float)Math.Atan2(v.x, v.z) * AngleFloat.Rad2Deg; + return Degrees(distance, horizontalAngle, verticalAngle); + } + } + + public Vector3 ToVector3() + { + float verticalRad = (AngleFloat.deg90 - this.direction.vertical).inRadians; + float horizontalRad = this.direction.horizontal.inRadians; + float cosVertical = (float)Math.Cos(verticalRad); + float sinVertical = (float)Math.Sin(verticalRad); + float cosHorizontal = (float)Math.Cos(horizontalRad); + float sinHorizontal = (float)Math.Sin(horizontalRad); + + float x = this.distance * sinVertical * sinHorizontal; + float y = this.distance * cosVertical; + float z = this.distance * sinVertical * cosHorizontal; + + Vector3 v = new(x, y, z); + return v; + } +#endif + + public float magnitude + { + get + { + return this.distance; + } + } + public Spherical normalized + { + get + { + Spherical r = new() + { + distance = 1, + direction = this.direction + }; + return r; + } + } + + public static Spherical operator +(Spherical s1, Spherical s2) + { + // let's do it the easy way... + Vector3Float v1 = s1.ToVector3Float(); + Vector3Float v2 = s2.ToVector3Float(); + Vector3Float v = v1 + v2; + Spherical r = FromVector3Float(v); + return r; + } + + } +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/SwingTwist.cs b/Assets/NanoBrain/LinearAlgebra/src/SwingTwist.cs new file mode 100644 index 0000000..4437c4f --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/SwingTwist.cs @@ -0,0 +1,116 @@ +#if !UNITY_5_3_OR_NEWER +using UnityEngine; +#endif + +namespace LinearAlgebra { + + /// + /// An orientation using swing and twist angles + /// + /// The swing rotation + /// The twist rotation + public struct SwingTwist { + public Direction swing; + public AngleFloat twist; + + public SwingTwist(Direction swing, AngleFloat twist) { + this.swing = swing; + this.twist = twist; + } + + /// + /// Create a swing/twist rotation using angles in degrees + /// + /// The swing angle in the horizontal plane in degrees + /// The swing angle in the vertical plan in degrees + /// The twist angle in degrees + /// The swing/twist rotation + public static SwingTwist Degrees(float horizontalSwing, float verticalSwing, float twist) { + Direction swing = Direction.Degrees(horizontalSwing, verticalSwing); + AngleFloat twistAngle = AngleFloat.Degrees(twist); + SwingTwist s = new(swing, twistAngle); + return s; + } + + /// + /// Create a swing/twist rotation using angles in degrees + /// + /// The swing angle in the horizontal plane in degrees + /// The swing angle in the vertical plan in degrees + /// The twist angle in degrees + /// The swing/twist rotation + public static SwingTwist Radians(float horizontalSwing, float verticalSwing, float twist) { + Direction swing = Direction.Radians(horizontalSwing, verticalSwing); + AngleFloat twistAngle = AngleFloat.Radians(twist); + SwingTwist s = new(swing, twistAngle); + return s; + } + +#if !UNITY_5_3_OR_NEWER + /// + /// A zero angle rotation + /// + public static readonly SwingTwist zero = Degrees(0, 0, 0); + + public Spherical ToAngleAxis() { + LinearAlgebra.Quaternion q = this.ToQuaternion(); + q.ToAngleAxis(out float angle, out Vector3Float axis); + Direction direction = Direction.FromVector3(axis); + + Spherical r = new(angle, direction); + return r; + } + + public static SwingTwist FromAngleAxis(Spherical r) { + Vector3Float vectorAxis = r.direction.ToVector3(); + LinearAlgebra.Quaternion q = LinearAlgebra.Quaternion.AngleAxis(AngleFloat.Degrees(r.distance), vectorAxis); + return FromQuaternion(q); + } + + /// + /// Convert a quaternion in a swing/twist rotation + /// + /// The quaternion to convert + /// The swing/twist rotation + public static SwingTwist FromQuaternion(LinearAlgebra.Quaternion q) { + Vector3Float v = LinearAlgebra.Quaternion.ToAngles(q); + SwingTwist r = Degrees(v.vertical, v.horizontal, v.depth); + return r; + } + + public LinearAlgebra.Quaternion ToQuaternion() { + LinearAlgebra.Quaternion q = LinearAlgebra.Quaternion.Euler(this.swing.vertical.inDegrees, + this.swing.horizontal.inDegrees, + this.twist.inDegrees); + return q; + + } + + public static SwingTwist FromQuat32(Quat32 q32) { + q32.ToAngles(out float right, out float up, out float forward); + SwingTwist r = Degrees(up, right, forward); + return r; + } +#endif +#if UNITY_5_3_OR_NEWER + /// + /// Convert a quaternion in a swing/twist rotation + /// + /// The quaternion to convert + /// The swing/twist rotation + public static SwingTwist FromQuaternion(UnityEngine.Quaternion q) { + UnityEngine.Vector3 angles = q.eulerAngles; + SwingTwist r = Degrees(angles.y, -angles.x, -angles.z); + return r; + } + + public UnityEngine.Quaternion ToUnityQuaternion() { + UnityEngine.Quaternion q = UnityEngine.Quaternion.Euler(this.swing.vertical.inDegrees, + this.swing.horizontal.inDegrees, + this.twist.inDegrees); + return q; + } +#endif + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Vector2Float.cs b/Assets/NanoBrain/LinearAlgebra/src/Vector2Float.cs new file mode 100644 index 0000000..e0418a8 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Vector2Float.cs @@ -0,0 +1,483 @@ +using System; +using System.Numerics; + +namespace LinearAlgebra { + + /* + public struct Vector2Int { + public int horizontal; + public int vertical; + + public Vector2Int(int horizontal, int vertical) { + this.horizontal = horizontal; + this.vertical = vertical; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector2Int zero = new(0, 0); + /// + /// A vector with values (1, 1) + /// + public static readonly Vector2Int one = new(1, 1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Int up = new(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Int down = new(0, -1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Int forward = new(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Int back = new(0, -1); + /// + /// A vector3 with values (-1, 0) + /// + public static readonly Vector2Int left = new(-1, 0); + /// + /// A vector with values (1, 0) + /// + public static readonly Vector2Int right = new(1, 0); + + /// + /// Tests if the vector has equal values as the given vector + /// + /// The vector to compare to + /// true if the vector values are equal + public readonly bool Equals(Vector2Int v) => this.horizontal == v.horizontal && vertical == v.vertical; + + /// + /// Tests if the vector is equal to the given object + /// + /// The object to compare to + /// false when the object is not a Vector2 or does not have equal values + public override readonly bool Equals(object obj) { + if (obj is not Vector2Int v) + return false; + + return (this.horizontal == v.horizontal && this.vertical == v.vertical); + } + + /// + /// Tests if the two vectors have equal values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have equal values + /// Note that this uses a Float equality check which cannot be not exact in all cases. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator ==(Vector2Int v1, Vector2Int v2) { + return (v1.horizontal == v2.horizontal && v1.vertical == v2.vertical); + } + /// + /// Tests if two vectors have different values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have different values + /// Note that this uses a Float equality check which cannot be not exact in all case. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon. + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator !=(Vector2Int v1, Vector2Int v2) { + return (v1.horizontal != v2.horizontal || v1.vertical != v2.vertical); + } + public readonly float magnitude { + get { + int h = this.horizontal; + int v = this.vertical; + return MathF.Sqrt(h * h + v * v); + } + } + + public static float MagnitudeOf(Vector2Int v) { + return v.magnitude; + } + + public static Vector2Int operator -(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical); + } + public static Vector2Int operator +(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.horizontal + v2.horizontal, v1.vertical + v2.vertical); + } + + public static float Distance(Vector2Int v1, Vector2Int v2) { + return (v1 - v2).magnitude; + } + } + + public struct Vector2Float { + public float horizontal; + public float vertical; + + public Vector2Float(float horizontal, float vertical) { + this.horizontal = horizontal; + this.vertical = vertical; + } + + public readonly float magnitude { + get { + float h = this.horizontal; + float v = this.vertical; + return MathF.Sqrt(h * h + v * v); + } + } + + public static Vector2Float operator -(Vector2Float v1, Vector2Float v2) { + return new Vector2Float(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical); + } + + public static float Distance(Vector2Float v1, Vector2Float v2) { + return (v1 - v2).magnitude; + } + } + */ + + /// + /// 2-dimensional vectors + /// + public struct Vector2Float { + + /// + /// The right axis of the vector + /// + public float horizontal; // left/right + /// + /// The upward/forward axis of the vector + /// + public float vertical; // forward/backward + // directions are to be inline with Vector3 as much as possible... + + /// + /// Create a new 2-dimensional vector + /// + /// x axis value + /// y axis value + public Vector2Float(float x, float y) { + this.horizontal = x; + this.vertical = y; + } + + /// + /// Convert a Vector2Int into a Vector2Float + /// + /// The Vector2Int + public Vector2Float(Vector2Int v) { + this.horizontal = v.horizontal; + this.vertical = v.vertical; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector2Float zero = new Vector2Float(0, 0); + /// + /// A vector with values (1, 1) + /// + public static readonly Vector2Float one = new Vector2Float(1, 1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Float up = new Vector2Float(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Float down = new Vector2Float(0, -1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Float forward = new Vector2Float(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Float back = new Vector2Float(0, -1); + /// + /// A vector3 with values (-1, 0) + /// + public static readonly Vector2Float left = new Vector2Float(-1, 0); + /// + /// A vector with values (1, 0) + /// + public static readonly Vector2Float right = new Vector2Float(1, 0); + + /// + /// The squared length of this vector + /// + /// The squared length + /// The squared length is computationally simpler than the real length. + /// Think of Pythagoras A^2 + B^2 = C^2. + /// This leaves out the calculation of the squared root of C. + public readonly float sqrMagnitude => horizontal * horizontal + vertical * vertical; + public static float SqrMagnitudeOf(Vector2Float v) { + return v.sqrMagnitude; + } + + /// + /// The length of this vector + /// + /// The length of this vector + public readonly float magnitude => MathF.Sqrt(horizontal * horizontal + vertical * vertical); + public static float MagnitudeOf(Vector2Float v) { + return v.magnitude; + } + + /// + /// Convert the vector to a length of a 1 + /// + /// The vector with length 1 + public Vector2Float normalized { + get { + float l = magnitude; + Vector2Float v = zero; + if (l > Float.epsilon) + v = this / l; + return v; + } + } + public static Vector2Float Normalize(Vector2Float v) { + return v.normalized; + } + + /// + /// Add two vectors + /// + /// The first vector + /// The second vector + /// The result of adding the two vectors + public static Vector2Float operator +(Vector2Float v1, Vector2Float v2) { + Vector2Float v = new Vector2Float(v1.horizontal + v2.horizontal, v1.vertical + v2.vertical); + return v; + } + + /// + /// Subtract two vectors + /// + /// The first vector + /// The second vector + /// The result of adding the two vectors + public static Vector2Float operator -(Vector2Float v1, Vector2Float v2) { + Vector2Float v = new Vector2Float(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical); + return v; + } + + /// + /// Negate the vector + /// + /// The vector to negate + /// The negated vector + /// This will result in a vector pointing in the opposite direction + public static Vector2Float operator -(Vector2Float v1) { + Vector2Float v = new Vector2Float(-v1.horizontal, -v1.vertical); + return v; + } + + /// + /// Scale a vector uniformly down + /// + /// The vector to scale + /// The scaling factor + /// The scaled vector + /// Each component of the vector will be devided by the same factor. + public static Vector2Float operator /(Vector2Float v, float f) { + Vector2Float r = new(v.horizontal / f, v.vertical / f); + return r; + } + + + /// + /// Scale a vector uniformly up + /// + /// The vector to scale + /// The scaling factor + /// The scaled vector + /// Each component of the vector will be multipled with the same factor. + public static Vector2Float operator *(Vector2Float v1, float f) { + Vector2Float v = new Vector2Float(v1.horizontal * f, v1.vertical * f); + return v; + } + + /// + /// Scale a vector uniformly up + /// + /// The scaling factor + /// The vector to scale + /// The scaled vector + /// Each component of the vector will be multipled with the same factor. + public static Vector2Float operator *(float f, Vector2Float v1) { + Vector2Float v = new Vector2Float(f * v1.horizontal, f * v1.vertical); + return v; + } + + /// @brief Scale the vector using another vector + /// @param v1 The vector to scale + /// @param v2 A vector with the scaling factors + /// @return The scaled vector + /// @remark Each component of the vector v1 will be multiplied with the + /// matching component from the scaling vector v2. + public static Vector2Float Scale(Vector2Float v1, Vector2Float v2) { + return new Vector2Float(v1.horizontal * v2.horizontal, v1.vertical * v2.vertical); + } + + /* + /// + /// Tests if the vector has equal values as the given vector + /// + /// The vector to compare to + /// true if the vector values are equal + public bool Equals(Vector2Float v1) => horizontal == v1.horizontal && vertical == v1.vertical; + + /// + /// Tests if the vector is equal to the given object + /// + /// The object to compare to + /// false when the object is not a Vector2 or does not have equal values + public override bool Equals(object obj) { + if (!(obj is Vector2Float v)) + return false; + + return (horizontal == v.horizontal && vertical == v.vertical); + } + */ + + /// + /// Tests if the two vectors have equal values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have equal values + /// Note that this uses a Float equality check which cannot be not exact in all cases. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator ==(Vector2Float v1, Vector2Float v2) { + return (v1.horizontal == v2.horizontal && v1.vertical == v2.vertical); + } + + /// + /// Tests if two vectors have different values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have different values + /// Note that this uses a Float equality check which cannot be not exact in all case. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon. + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator !=(Vector2Float v1, Vector2Float v2) { + return (v1.horizontal != v2.horizontal || v1.vertical != v2.vertical); + } + + /* + /// + /// Get an hash code for the vector + /// + /// The hash code + public override int GetHashCode() { + return (horizontal, vertical).GetHashCode(); + } + */ + + /// + /// Get the distance between two vectors + /// + /// The first vector + /// The second vector + /// The distance between the two vectors + public static float Distance(Vector2Float v1, Vector2Float v2) { + float x = v1.horizontal - v2.horizontal; + float y = v1.vertical - v2.vertical; + float d = (float)Math.Sqrt(x * x + y * y); + return d; + } + + /// + /// The dot product of two vectors + /// + /// The first vector + /// The second vector + /// The dot product of the two vectors + public static float Dot(Vector2Float v1, Vector2Float v2) { + return v1.horizontal * v2.horizontal + v1.vertical * v2.vertical; + } + + /// + /// Calculate the signed angle between two vectors. + /// + /// The starting vector + /// The ending vector + /// The axis to rotate around + /// The signed angle in degrees + public static float SignedAngle(Vector2Float from, Vector2Float to) { + //float sign = Math.Sign(v1.y * v2.x - v1.x * v2.y); + //return Vector2.Angle(v1, v2) * sign; + + float sqrMagFrom = from.sqrMagnitude; + float sqrMagTo = to.sqrMagnitude; + + if (sqrMagFrom == 0 || sqrMagTo == 0) + return 0; + //if (!isfinite(sqrMagFrom) || !isfinite(sqrMagTo)) + // return nanf(""); + + float angleFrom = (float)Math.Atan2(from.vertical, from.horizontal); + float angleTo = (float)Math.Atan2(to.vertical, to.horizontal); + return -(angleTo - angleFrom) * AngleFloat.Rad2Deg; + } + + public static float UnsignedAngle(Vector2Float from, Vector2Float to) { + return MathF.Abs(SignedAngle(from, to)); + } + + /// + /// Rotates the vector with the given angle + /// + /// The vector to rotate + /// The angle in degrees + /// + public static Vector2Float Rotate(Vector2Float v1, AngleFloat angle) { + float sin = (float)Math.Sin(angle.inRadians); + float cos = (float)Math.Cos(angle.inRadians); + // float sin = AngleFloat.Sin(angle); + // float cos = AngleFloat.Cos(angle); + + float tx = v1.horizontal; + float ty = v1.vertical; + Vector2Float v = new Vector2Float() { + horizontal = (cos * tx) - (sin * ty), + vertical = (sin * tx) + (cos * ty) + }; + return v; + } + + /// + /// Lerp between two vectors + /// + /// The from vector + /// The to vector + /// The interpolation distance [0..1] + /// The lerped vector + /// The factor f is unclamped. Value 0 matches the *v1* vector, Value 1 + /// matches the *v2* vector Value -1 is *v1* vector minus the difference + /// between *v1* and *v2* etc. + public static Vector2Float Lerp(Vector2Float v1, Vector2Float v2, float f) { + Vector2Float v = v1 + (v2 - v1) * f; + return v; + } + + /// + /// Map interval of angles between vectors [0..Pi] to interval [0..1] + /// + /// The first vector + /// The second vector + /// The resulting factor in interval [0..1] + /// Vectors a and b must be normalized + public static float ToFactor(Vector2Float v1, Vector2Float v2) { + return (1 - Vector2Float.Dot(v1, v2)) / 2; + } + } +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Vector2Int.cs b/Assets/NanoBrain/LinearAlgebra/src/Vector2Int.cs new file mode 100644 index 0000000..0eca7dc --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Vector2Int.cs @@ -0,0 +1,176 @@ +using System; + +namespace LinearAlgebra { + + public struct Vector2Int { + public int horizontal; + public int vertical; + + public Vector2Int(int horizontal, int vertical) { + this.horizontal = horizontal; + this.vertical = vertical; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector2Int zero = new(0, 0); + /// + /// A vector with values (1, 1) + /// + public static readonly Vector2Int one = new(1, 1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Int up = new(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Int down = new(0, -1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2Int forward = new(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2Int back = new(0, -1); + /// + /// A vector3 with values (-1, 0) + /// + public static readonly Vector2Int left = new(-1, 0); + /// + /// A vector with values (1, 0) + /// + public static readonly Vector2Int right = new(1, 0); + + /* + /// + /// Get an hash code for the vector + /// + /// The hash code + public override int GetHashCode() { + return (this.horizontal, this.vertical).GetHashCode(); + } + + /// + /// Tests if the vector has equal values as the given vector + /// + /// The vector to compare to + /// true if the vector values are equal + public readonly bool Equals(Vector2Int v) => this.horizontal == v.horizontal && vertical == v.vertical; + + /// + /// Tests if the vector is equal to the given object + /// + /// The object to compare to + /// false when the object is not a Vector2 or does not have equal values + public override readonly bool Equals(object obj) { + if (obj is not Vector2Int v) + return false; + + return (this.horizontal == v.horizontal && this.vertical == v.vertical); + } + */ + + /// + /// Tests if the two vectors have equal values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have equal values + /// Note that this uses a Float equality check which cannot be not exact in all cases. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator ==(Vector2Int v1, Vector2Int v2) { + return (v1.horizontal == v2.horizontal && v1.vertical == v2.vertical); + } + /// + /// Tests if two vectors have different values + /// + /// The first vector + /// The second vector + /// truewhen the vectors have different values + /// Note that this uses a Float equality check which cannot be not exact in all case. + /// In most cases it is better to check if the Vector2.Distance between the vectors is smaller than Float.epsilon. + /// Or more efficient: (v1 - v2).sqrMagnitude < Float.sqrEpsilon + public static bool operator !=(Vector2Int v1, Vector2Int v2) { + return (v1.horizontal != v2.horizontal || v1.vertical != v2.vertical); + } + + public readonly float sqrMagnitude => this.horizontal * this.horizontal + this.vertical * this.vertical; + + public static float SqrMagnitudeOf(Vector2Int v) { + return v.sqrMagnitude; + } + + public readonly float magnitude => + MathF.Sqrt(this.horizontal * this.horizontal + this.vertical * this.vertical); + + public static float MagnitudeOf(Vector2Int v) { + return v.magnitude; + } + + /// @brief Convert the vector to a length of 1 + /// @return The vector normalized to a length of 1 + public readonly Vector2Float normalized { + get { + float l = magnitude; + Vector2Float v = Vector2Float.zero; + if (l > Float.epsilon) + v = new Vector2Float(this) / l; + return v; + } + } + /// @brief Convert the vector to a length of 1 + /// @param v The vector to convert + /// @return The vector normalized to a length of 1 + public static Vector2Float Normalize(Vector2Int v) { + float num = v.magnitude; + Vector2Float result = Vector2Float.zero; + if (num > Float.epsilon) + result = new Vector2Float(v) / num; + + return result; + } + + public static Vector2Int operator -(Vector2Int v) { + return new Vector2Int(-v.horizontal, -v.vertical); + } + + public static Vector2Int operator -(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical); + } + public static Vector2Int operator +(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.horizontal + v2.horizontal, v1.vertical + v2.vertical); + } + + public static Vector2Int operator /(Vector2Int v, int f) { + return new Vector2Int(v.horizontal / f, v.vertical / f); + } + + public static Vector2Int operator *(Vector2Int v1, int d) { + return new Vector2Int(v1.horizontal * d, v1.vertical * d); + } + + public static Vector2Int operator *(int d, Vector2Int v1) { + return new Vector2Int(d * v1.horizontal, d * v1.vertical); + } + + public static Vector2Int Scale(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.horizontal * v2.horizontal, v1.vertical * v2.vertical); + } + + /// @brief The dot product of two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The dot product of the two vectors + public static int Dot(Vector2Int v1, Vector2Int v2) { + return v1.horizontal * v2.horizontal + v1.vertical * v2.vertical; + } + + public static float Distance(Vector2Int v1, Vector2Int v2) { + return (v1 - v2).magnitude; + } + } +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Vector3Float.cs b/Assets/NanoBrain/LinearAlgebra/src/Vector3Float.cs new file mode 100644 index 0000000..bff0936 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Vector3Float.cs @@ -0,0 +1,399 @@ +//#if !UNITY_5_3_OR_NEWER +using System; + +namespace LinearAlgebra { + /* + public struct Vector3Float { + public float horizontal; + public float vertical; + public float depth; + + public Vector3Float(float horizontal, float vertical, float depth) { + this.horizontal = horizontal; + this.vertical = vertical; + this.depth = depth; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector3Float zero = new(0, 0, 0); + + public readonly float magnitude { + get => (float)Math.Sqrt(this.horizontal * this.horizontal + this.vertical * this.vertical + this.depth * this.depth); + } + + /// + /// Convert the vector to a length of a 1 + /// + /// The vector with length 1 + public readonly Vector3Float normalized { + get { + float l = magnitude; + Vector3Float v = zero; + if (l > Float.epsilon) + v = this / l; + return v; + } + } + + + public static Vector3Float operator *(Vector3Float v, float f) { + Vector3Float r = new(v.horizontal * f, v.vertical * f, v.depth * f); + return r; + } + public static Vector3Float operator /(Vector3Float v, float f) { + Vector3Float r = new(v.horizontal / f, v.vertical / f, v.depth / f); + return r; + } + + public static float Dot(Vector3Float v1, Vector3Float v2) { + return v1.horizontal * v2.horizontal + v1.vertical * v2.vertical + + v1.depth * v2.depth; + } + + const float epsilon = 1E-05f; + public static Vector3Float Project(Vector3Float v, Vector3Float n) { + float sqrMagnitude = Dot(n, n); + if (sqrMagnitude < epsilon) + return zero; + else { + float dot = Dot(v, n); + Vector3Float r = n * dot; + r /= sqrMagnitude; + return r; + } + + } + } + */ + + /// + /// 3-dimensional vectors + /// + /// This uses the right-handed coordinate system. + public struct Vector3Float { + + /// + /// The right axis of the vector + /// + public float horizontal; //> left/right + /// + /// The upward axis of the vector + /// + public float vertical; //> up/down + /// + /// The forward axis of the vector + /// + public float depth; //> forward/backward + + /// + /// Create a new 3-dimensional vector + /// + /// x axis value + /// y axis value + /// z axis value + public Vector3Float(float horizontal, float vertical, float depth) { + this.horizontal = horizontal; + this.vertical = vertical; + this.depth = depth; + } + + public Vector3Float(Vector3Int v) { + this.horizontal = v.horizontal; + this.vertical = v.vertical; + this.depth = v.depth; + } + + public static Vector3Float FromSpherical(Spherical s) { + float verticalRad = (AngleFloat.deg90 - s.direction.vertical).inRadians; + float horizontalRad = s.direction.horizontal.inRadians; + float cosVertical = MathF.Cos(verticalRad); + float sinVertical = MathF.Sin(verticalRad); + float cosHorizontal = MathF.Cos(horizontalRad); + float sinHorizontal = MathF.Sin(horizontalRad); + + float horizontal = s.distance * sinVertical * sinHorizontal; + float vertical = s.distance * cosVertical; + float depth = s.distance * sinVertical * cosHorizontal; + return new Vector3Float(horizontal, vertical, depth); + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector3Float zero = new Vector3Float(0, 0, 0); + /// + /// A vector with one for all axis + /// + public static readonly Vector3Float one = new Vector3Float(1, 1, 1); + /// + /// A Vector3Float with values (-1, 0, 0) + /// + public static readonly Vector3Float left = new Vector3Float(-1, 0, 0); + /// + /// A vector with values (1, 0, 0) + /// + public static readonly Vector3Float right = new Vector3Float(1, 0, 0); + /// + /// A vector with values (0, -1, 0) + /// + public static readonly Vector3Float down = new Vector3Float(0, -1, 0); + /// + /// A vector with values (0, 1, 0) + /// + public static readonly Vector3Float up = new Vector3Float(0, 1, 0); + /// + /// A vector with values (0, 0, -1) + /// + public static readonly Vector3Float back = new Vector3Float(0, -1, 0); + /// + /// A vector with values (0, 0, 1) + /// + public static readonly Vector3Float forward = new Vector3Float(0, 1, 0); + + /// @brief The vector length + /// @return The vector length + public readonly float magnitude => MathF.Sqrt(horizontal * horizontal + vertical * vertical + depth * depth); + /// + /// The vector length + /// + /// The vector for which you need the length + /// The vector length + public static float MagnitudeOf(Vector3Float v) { + return v.magnitude; + } + + /// @brief The squared vector length + /// @return The squared vector length + /// @remark The squared length is computationally simpler than the real + /// length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the + /// calculation of the squared root of C. + public readonly float sqrMagnitude => (horizontal * horizontal + vertical * vertical + depth * depth); + + /// + /// The squared vector length + /// + /// The vector for which you need the squared length + /// The squared vector length + /// The squared length is computationally simpler than the real + /// length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the + /// calculation of the squared root of C. + public static float SqrMagnitudeOf(Vector3Float v) { + return v.sqrMagnitude; + } + + /// @brief Convert the vector to a length of 1 + /// @return The vector normalized to a length of 1 + public readonly Vector3Float normalized { + get { + float l = magnitude; + Vector3Float v = zero; + if (l > Float.epsilon) + v = this / l; + return v; + } + } + /// @brief Convert the vector to a length of 1 + /// @param v The vector to convert + /// @return The vector normalized to a length of 1 + public static Vector3Float Normalize(Vector3Float v) { + float num = v.magnitude; + Vector3Float result = zero; + if (num > Float.epsilon) + result = v / num; + + return result; + } + + /// + /// Negate te vector such that it points in the opposite direction + /// + /// + /// The negated vector + public static Vector3Float operator -(Vector3Float v1) { + Vector3Float v = new(-v1.horizontal, -v1.vertical, -v1.depth); + return v; + } + + /// + /// Subtract two vectors + /// + /// + /// + /// The result of the subtraction + public static Vector3Float operator -(Vector3Float v1, Vector3Float v2) { + Vector3Float v = new(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical, v1.depth - v2.depth); + return v; + } + + /// + /// Add two vectors + /// + /// + /// + /// The result of the addition + public static Vector3Float operator +(Vector3Float v1, Vector3Float v2) { + Vector3Float v = new(v1.horizontal + v2.horizontal, v1.vertical + v2.vertical, v1.depth + v2.depth); + return v; + } + + /// @brief Scale the vector using another vector + /// @param v1 The vector to scale + /// @param v2 A vector with the scaling factors + /// @return The scaled vector + /// @remark Each component of the vector v1 will be multiplied with the + /// matching component from the scaling vector v2. + public static Vector3Float Scale(Vector3Float v1, Vector3Float v2) { + return new Vector3Float(v1.horizontal * v2.horizontal, v1.vertical * v2.vertical, v1.depth * v2.depth); + } + + + public static Vector3Float operator *(Vector3Float v1, float d) { + Vector3Float v = new Vector3Float(v1.horizontal * d, v1.vertical * d, v1.depth * d); + return v; + } + + public static Vector3Float operator *(float d, Vector3Float v1) { + Vector3Float v = new Vector3Float(d * v1.horizontal, d * v1.vertical, d * v1.depth); + return v; + } + + public static Vector3Float operator /(Vector3Float v1, float d) { + Vector3Float v = new Vector3Float(v1.horizontal / d, v1.vertical / d, v1.depth / d); + return v; + } + + /* + public bool Equals(Vector3Float v) => (horizontal == v.horizontal && vertical == v.vertical && depth == v.depth); + + public override bool Equals(object obj) { + if (!(obj is Vector3Float v)) + return false; + + return (horizontal == v.horizontal && vertical == v.vertical && depth == v.depth); + } + */ + + public static bool operator ==(Vector3Float v1, Vector3Float v2) { + return (v1.horizontal == v2.horizontal && v1.vertical == v2.vertical && v1.depth == v2.depth); + } + + public static bool operator !=(Vector3Float v1, Vector3Float v2) { + return (v1.horizontal != v2.horizontal || v1.vertical != v2.vertical || v1.depth != v2.depth); + } + + // public override int GetHashCode() { + // return (horizontal, vertical, depth).GetHashCode(); + // } + + /// @brief The distance between two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The distance between the two vectors + public static float Distance(Vector3Float v1, Vector3Float v2) { + return (v2 - v1).magnitude; + } + + /// @brief The dot product of two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The dot product of the two vectors + public static float Dot(Vector3Float v1, Vector3Float v2) { + return v1.horizontal * v2.horizontal + v1.vertical * v2.vertical + v1.depth * v2.depth; + } + + /// @brief The cross product of two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The cross product of the two vectors + public static Vector3Float Cross(Vector3Float v1, Vector3Float v2) { + return new Vector3Float(v1.vertical * v2.depth - v1.depth * v2.vertical, v1.depth * v2.horizontal - v1.horizontal * v2.depth, + v1.horizontal * v2.vertical - v1.vertical * v2.horizontal); + + } + + /// @brief Project the vector on another vector + /// @param v The vector to project + /// @param n The normal vecto to project on + /// @return The projected vector + public static Vector3Float Project(Vector3Float v, Vector3Float n) { + float sqrMagnitude = Dot(n, n); + if (sqrMagnitude < Float.epsilon) + return zero; + else { + float dot = Dot(v, n); + Vector3Float r = n * dot / sqrMagnitude; + return r; + } + } + + /// @brief Project the vector on a plane defined by a normal orthogonal to the + /// plane. + /// @param v The vector to project + /// @param n The normal of the plane to project on + /// @return Teh projected vector + public static Vector3Float ProjectOnPlane(Vector3Float v, Vector3Float n) { + Vector3Float r = v - Project(v, n); + return r; + } + + /// @brief The angle between two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The angle between the two vectors + /// @remark This reterns an unsigned angle which is the shortest distance + /// between the two vectors. Use Vector3::SignedAngle if a signed angle is + /// needed. + public static AngleFloat UnsignedAngle(Vector3Float v1, Vector3Float v2) { + float denominator = MathF.Sqrt(v1.sqrMagnitude * v2.sqrMagnitude); + if (denominator < Float.epsilon) + return AngleFloat.zero; + + float dot = Dot(v1, v2); + float fraction = dot / denominator; + if (float.IsNaN(fraction)) + return AngleFloat.Degrees( + fraction); // short cut to returning NaN universally + + float cdot = Float.Clamp(fraction, -1.0f, 1.0f); + float r = MathF.Acos(cdot); + return AngleFloat.Radians(r); + } + /// @brief The signed angle between two vectors + /// @param v1 The starting vector + /// @param v2 The ending vector + /// @param axis The axis to rotate around + /// @return The signed angle between the two vectors + public static AngleFloat SignedAngle(Vector3Float v1, Vector3Float v2, + Vector3Float axis) { + // angle in [0,180] + AngleFloat angle = UnsignedAngle(v1, v2); + + Vector3Float cross = Cross(v1, v2); + float b = Dot(axis, cross); + float signd = b < 0 ? -1.0F : (b > 0 ? 1.0F : 0.0F); + + // angle in [-179,180] + AngleFloat signed_angle = angle * signd; + + return signed_angle; + } + + + /// @brief Lerp (linear interpolation) between two vectors + /// @param v1 The starting vector + /// @param v2 The ending vector + /// @param f The interpolation distance + /// @return The lerped vector + /// @remark The factor f is unclamped. Value 0 matches the vector *v1*, Value + /// 1 matches vector *v2*. Value -1 is vector *v1* minus the difference + /// between *v1* and *v2* etc. + public static Vector3Float Lerp(Vector3Float v1, Vector3Float v2, float f) { + Vector3Float v = v1 + (v2 - v1) * f; + return v; + } + + } +} +//#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/Vector3Int.cs b/Assets/NanoBrain/LinearAlgebra/src/Vector3Int.cs new file mode 100644 index 0000000..18edf40 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/Vector3Int.cs @@ -0,0 +1,273 @@ +//#if !UNITY_5_3_OR_NEWER +using System; + +namespace LinearAlgebra { + + /// + /// 3-dimensional vectors + /// + /// This uses the right-handed coordinate system. + /// + /// Create a new 3-dimensional vector + /// + /// x axis value + /// y axis value + /// z axis value + public struct Vector3Int { + + /// + /// The right axis of the vector + /// + public int horizontal; //> left/right + /// + /// The upward axis of the vector + /// + public int vertical; //> up/down + /// + /// The forward axis of the vector + /// + public int depth; //> forward/backward + + public Vector3Int(int horizontal, int vertical, int depth) { + this.horizontal = horizontal; + this.vertical = vertical; + this.depth = depth; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector3Int zero = new(0, 0, 0); + /// + /// A vector with one for all axis + /// + public static readonly Vector3Int one = new(1, 1, 1); + /// + /// A Vector3Int with values (-1, 0, 0) + /// + public static readonly Vector3Int left = new(-1, 0, 0); + /// + /// A vector with values (1, 0, 0) + /// + public static readonly Vector3Int right = new(1, 0, 0); + /// + /// A vector with values (0, -1, 0) + /// + public static readonly Vector3Int down = new(0, -1, 0); + /// + /// A vector with values (0, 1, 0) + /// + public static readonly Vector3Int up = new(0, 1, 0); + /// + /// A vector with values (0, 0, -1) + /// + public static readonly Vector3Int back = new(0, -1, 0); + /// + /// A vector with values (0, 0, 1) + /// + public static readonly Vector3Int forward = new(0, 1, 0); + + /// @brief The vector length + /// @return The vector length + public readonly float magnitude => MathF.Sqrt(horizontal * horizontal + vertical * vertical + depth * depth); + /// + /// The vector length + /// + /// The vector for which you need the length + /// The vector length + public static float MagnitudeOf(Vector3Int v) { + return v.magnitude; + } + + /// @brief The squared vector length + /// @return The squared vector length + /// @remark The squared length is computationally simpler than the real + /// length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the + /// calculation of the squared root of C. + public readonly float sqrMagnitude => (horizontal * horizontal + vertical * vertical + depth * depth); + + /// + /// The squared vector length + /// + /// The vector for which you need the squared length + /// The squared vector length + /// The squared length is computationally simpler than the real + /// length. Think of Pythagoras A^2 + B^2 = C^2. This leaves out the + /// calculation of the squared root of C. + public static float SqrMagnitudeOf(Vector3Int v) { + return v.sqrMagnitude; + } + + /// @brief Convert the vector to a length of 1 + /// @return The vector normalized to a length of 1 + public readonly Vector3Float normalized { + get { + float l = magnitude; + Vector3Float v = Vector3Float.zero; + if (l > Float.epsilon) + v = new Vector3Float(this) / l; + return v; + } + } + /// @brief Convert the vector to a length of 1 + /// @param v The vector to convert + /// @return The vector normalized to a length of 1 + public static Vector3Float Normalize(Vector3Int v) { + float num = v.magnitude; + Vector3Float result = Vector3Float.zero; + if (num > Float.epsilon) + result = new Vector3Float(v) / num; + + return result; + } + + /// + /// Negate te vector such that it points in the opposite direction + /// + /// + /// The negated vector + public static Vector3Int operator -(Vector3Int v1) { + Vector3Int v = new(-v1.horizontal, -v1.vertical, -v1.depth); + return v; + } + + /// + /// Subtract two vectors + /// + /// + /// + /// The result of the subtraction + public static Vector3Int operator -(Vector3Int v1, Vector3Int v2) { + Vector3Int v = new(v1.horizontal - v2.horizontal, v1.vertical - v2.vertical, v1.depth - v2.depth); + return v; + } + + /// + /// Add two vectors + /// + /// + /// + /// The result of the addition + public static Vector3Int operator +(Vector3Int v1, Vector3Int v2) { + Vector3Int v = new(v1.horizontal + v2.horizontal, v1.vertical + v2.vertical, v1.depth + v2.depth); + return v; + } + + /// @brief Scale the vector using another vector + /// @param v1 The vector to scale + /// @param v2 A vector with the scaling factors + /// @return The scaled vector + /// @remark Each component of the vector v1 will be multiplied with the + /// matching component from the scaling vector v2. + public static Vector3Int Scale(Vector3Int v1, Vector3Int v2) { + return new Vector3Int(v1.horizontal * v2.horizontal, v1.vertical * v2.vertical, v1.depth * v2.depth); + } + + + public static Vector3Int operator *(Vector3Int v1, int d) { + Vector3Int v = new(v1.horizontal * d, v1.vertical * d, v1.depth * d); + return v; + } + + public static Vector3Int operator *(int d, Vector3Int v1) { + Vector3Int v = new(d * v1.horizontal, d * v1.vertical, d * v1.depth); + return v; + } + + public static Vector3Int operator /(Vector3Int v1, int d) { + Vector3Int v = new(v1.horizontal / d, v1.vertical / d, v1.depth / d); + return v; + } + + public bool Equals(Vector3Int v) => (horizontal == v.horizontal && vertical == v.vertical && depth == v.depth); + + public override bool Equals(object obj) { + if (!(obj is Vector3Int v)) + return false; + + return (horizontal == v.horizontal && vertical == v.vertical && depth == v.depth); + } + + public static bool operator ==(Vector3Int v1, Vector3Int v2) { + return (v1.horizontal == v2.horizontal && v1.vertical == v2.vertical && v1.depth == v2.depth); + } + + public static bool operator !=(Vector3Int v1, Vector3Int v2) { + return (v1.horizontal != v2.horizontal || v1.vertical != v2.vertical || v1.depth != v2.depth); + } + + public override int GetHashCode() { + return (horizontal, vertical, depth).GetHashCode(); + } + + /// @brief The distance between two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The distance between the two vectors + public static float Distance(Vector3Int v1, Vector3Int v2) { + return (v2 - v1).magnitude; + } + + /// @brief The dot product of two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The dot product of the two vectors + public static float Dot(Vector3Int v1, Vector3Int v2) { + return v1.horizontal * v2.horizontal + v1.vertical * v2.vertical + v1.depth * v2.depth; + } + + /// @brief The cross product of two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The cross product of the two vectors + public static Vector3Int Cross(Vector3Int v1, Vector3Int v2) { + return new Vector3Int(v1.vertical * v2.depth - v1.depth * v2.vertical, v1.depth * v2.horizontal - v1.horizontal * v2.depth, + v1.horizontal * v2.vertical - v1.vertical * v2.horizontal); + + } + + /// @brief The angle between two vectors + /// @param v1 The first vector + /// @param v2 The second vector + /// @return The angle between the two vectors + /// @remark This reterns an unsigned angle which is the shortest distance + /// between the two vectors. Use Vector3::SignedAngle if a signed angle is + /// needed. + public static AngleFloat UnsignedAngle(Vector3Int v1, Vector3Int v2) { + float denominator = MathF.Sqrt(v1.sqrMagnitude * v2.sqrMagnitude); + if (denominator < Float.epsilon) + return AngleFloat.zero; + + float dot = Dot(v1, v2); + float fraction = dot / denominator; + if (float.IsNaN(fraction)) + return AngleFloat.Degrees( + fraction); // short cut to returning NaN universally + + float cdot = Float.Clamp(fraction, -1.0f, 1.0f); + float r = MathF.Acos(cdot); + return AngleFloat.Radians(r); + } + /// @brief The signed angle between two vectors + /// @param v1 The starting vector + /// @param v2 The ending vector + /// @param axis The axis to rotate around + /// @return The signed angle between the two vectors + public static AngleFloat SignedAngle(Vector3Int v1, Vector3Int v2, + Vector3Int axis) { + // angle in [0,180] + AngleFloat angle = UnsignedAngle(v1, v2); + + Vector3Int cross = Cross(v1, v2); + float b = Dot(axis, cross); + float signd = b < 0 ? -1.0F : (b > 0 ? 1.0F : 0.0F); + + // angle in [-179,180] + AngleFloat signed_angle = angle * signd; + + return signed_angle; + } + + } +} +//#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/src/float16.cs b/Assets/NanoBrain/LinearAlgebra/src/float16.cs new file mode 100644 index 0000000..4b58cdd --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/src/float16.cs @@ -0,0 +1,322 @@ +using System; + +namespace LinearAlgebra { + + public class float16 { + // + // FILE: float16.cpp + // AUTHOR: Rob Tillaart + // VERSION: 0.1.8 + // PURPOSE: library for Float16s for Arduino + // URL: http://en.wikipedia.org/wiki/Half-precision_floating-point_format + + ushort _value; + + public float16() { _value = 0; } + + public float16(float f) { + //_value = f32tof16(f); + _value = F32ToF16__(f); + } + + public float toFloat() { + return f16tof32(_value); + } + + public ushort GetBinary() { return _value; } + public void SetBinary(ushort value) { _value = value; } + + ////////////////////////////////////////////////////////// + // + // EQUALITIES + // + /* + bool float16::operator ==(const float16 &f) { return (_value == f._value); } + + bool float16::operator !=(const float16 &f) { return (_value != f._value); } + + bool float16::operator >(const float16 &f) { + if ((_value & 0x8000) && (f._value & 0x8000)) + return _value < f._value; + if (_value & 0x8000) + return false; + if (f._value & 0x8000) + return true; + return _value > f._value; + } + + bool float16::operator >=(const float16 &f) { + if ((_value & 0x8000) && (f._value & 0x8000)) + return _value <= f._value; + if (_value & 0x8000) + return false; + if (f._value & 0x8000) + return true; + return _value >= f._value; + } + + bool float16::operator <(const float16 &f) { + if ((_value & 0x8000) && (f._value & 0x8000)) + return _value > f._value; + if (_value & 0x8000) + return true; + if (f._value & 0x8000) + return false; + return _value < f._value; + } + + bool float16::operator <=(const float16 &f) { + if ((_value & 0x8000) && (f._value & 0x8000)) + return _value >= f._value; + if (_value & 0x8000) + return true; + if (f._value & 0x8000) + return false; + return _value <= f._value; + } + + ////////////////////////////////////////////////////////// + // + // NEGATION + // + float16 float16::operator -() { + float16 f16; + f16.setBinary(_value ^ 0x8000); + return f16; + } + + ////////////////////////////////////////////////////////// + // + // MATH + // + float16 float16::operator +(const float16 &f) { + return float16(this->toDouble() + f.toDouble()); + } + + float16 float16::operator -(const float16 &f) { + return float16(this->toDouble() - f.toDouble()); + } + + float16 float16::operator *(const float16 &f) { + return float16(this->toDouble() * f.toDouble()); + } + + float16 float16::operator /(const float16 &f) { + return float16(this->toDouble() / f.toDouble()); + } + + float16 & float16::operator+=(const float16 &f) { + *this = this->toDouble() + f.toDouble(); + return *this; + } + + float16 & float16::operator-=(const float16 &f) { + *this = this->toDouble() - f.toDouble(); + return *this; + } + + float16 & float16::operator*=(const float16 &f) { + *this = this->toDouble() * f.toDouble(); + return *this; + } + + float16 & float16::operator/=(const float16 &f) { + *this = this->toDouble() / f.toDouble(); + return *this; + } + + ////////////////////////////////////////////////////////// + // + // MATH HELPER FUNCTIONS + // + int float16::sign() { + if (_value & 0x8000) + return -1; + if (_value & 0xFFFF) + return 1; + return 0; + } + + bool float16::isZero() { return ((_value & 0x7FFF) == 0x0000); } + + bool float16::isNaN() { + if ((_value & 0x7C00) != 0x7C00) + return false; + if ((_value & 0x03FF) == 0x0000) + return false; + return true; + } + + bool float16::isInf() { return ((_value == 0x7C00) || (_value == 0xFC00)); } + */ + ////////////////////////////////////////////////////////// + // + // CORE CONVERSION + // + float f16tof32(ushort _value) { + //ushort sgn; + ushort man; + int exp; + float f; + + //Debug.Log($"{_value}"); + + bool sgn = (_value & 0x8000) > 0; + exp = (_value & 0x7C00) >> 10; + man = (ushort)(_value & 0x03FF); + + //Debug.Log($"{sgn} {exp} {man}"); + + // ZERO + if ((_value & 0x7FFF) == 0) { + return sgn ? -0 : 0; + } + // NAN & INF + if (exp == 0x001F) { + if (man == 0) + return sgn ? float.NegativeInfinity : float.PositiveInfinity; //-INFINITY : INFINITY; + else + return float.NaN; // NAN; + } + + // SUBNORMAL/NORMAL + if (exp == 0) + f = 0; + else + f = 1; + + // PROCESS MANTISSE + for (int i = 9; i >= 0; i--) { + f *= 2; + if ((man & (1 << i)) != 0) + f = f + 1; + } + //Debug.Log($"{f}"); + f = f * (float)Math.Pow(2.0f, exp - 25); + if (exp == 0) { + f = f * (float)Math.Pow(2.0f, -13); // 5.96046447754e-8; + } + //Debug.Log($"{f}"); + return sgn ? -f : f; + } + + public static uint SingleToInt32Bits(float value) { + byte[] bytes = BitConverter.GetBytes(value); + if (BitConverter.IsLittleEndian) + Array.Reverse(bytes); // If the system is little-endian, reverse the byte order + return BitConverter.ToUInt32(bytes, 0); + } + + public ushort F32ToF16__(float f) { + uint t = BitConverter.ToUInt32(BitConverter.GetBytes(f), 0); + ushort man = (ushort)((t & 0x007FFFFF) >> 12); + int exp = (int)((t & 0x7F800000) >> 23); + bool sgn = (t & 0x80000000) != 0; + + // handle 0 + if ((t & 0x7FFFFFFF) == 0) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; + } + // denormalized float32 does not fit in float16 + if (exp == 0x00) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; + } + // handle infinity & NAN + if (exp == 0x00FF) { + if (man != 0) + return 0xFE00; // NAN + return sgn ? (ushort)0xFC00 : (ushort)0x7C00; // -INF : INF + } + + // normal numbers + exp = exp - 127 + 15; + // overflow does not fit => INF + if (exp > 30) { + return sgn ? (ushort)0xFC00 : (ushort)0x7C00; // -INF : INF + } + // subnormal numbers + if (exp < -38) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; // -0 or 0 ? just 0 ? + } + if (exp <= 0) // subnormal + { + man >>= (exp + 14); + // rounding + man++; + man >>= 1; + if (sgn) + return (ushort)(0x8000 | man); + return man; + } + + // normal + // TODO rounding + exp <<= 10; + man++; + man >>= 1; + if (sgn) + return (ushort)(0x8000 | exp | man); + return (ushort)(exp | man); + } + + //This function is faulty!!!! + ushort f32tof16(float f) { + //uint t = *(uint*)&f; + //uint t = (uint)BitConverter.SingleToInt32Bits(f); + uint t = SingleToInt32Bits(f); + // man bits = 10; but we keep 11 for rounding + ushort man = (ushort)((t & 0x007FFFFF) >> 12); + short exp = (short)((t & 0x7F800000) >> 23); + bool sgn = (t & 0x80000000) != 0; + + // handle 0 + if ((t & 0x7FFFFFFF) == 0) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; + } + // denormalized float32 does not fit in float16 + if (exp == 0x00) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; + } + // handle infinity & NAN + if (exp == 0x00FF) { + if (man != 0) + return 0xFE00; // NAN + return sgn ? (ushort)0xFC00 : (ushort)0x7C00; // -INF : INF + } + + // normal numbers + exp = (short)(exp - 127 + 15); + // overflow does not fit => INF + if (exp > 30) { + return sgn ? (ushort)0xFC00 : (ushort)0x7C00; // -INF : INF + } + // subnormal numbers + if (exp < -38) { + return sgn ? (ushort)0x8000 : (ushort)0x0000; // -0 or 0 ? just 0 ? + } + if (exp <= 0) // subnormal + { + man >>= (exp + 14); + // rounding + man++; + man >>= 1; + if (sgn) + return (ushort)(0x8000 | man); + return man; + } + + // normal + // TODO rounding + exp <<= 10; + man++; + man >>= 1; + ushort uexp = (ushort)exp; + if (sgn) + return (ushort)(0x8000 | uexp | man); + return (ushort)(uexp | man); + } + + // -- END OF FILE -- + } + +} \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/AngleTest.cs b/Assets/NanoBrain/LinearAlgebra/test/AngleTest.cs new file mode 100644 index 0000000..787130d --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/AngleTest.cs @@ -0,0 +1,497 @@ +#if !UNITY_5_6_OR_NEWER +using System; +using System.Formats.Asn1; +using NUnit.Framework; + +namespace LinearAlgebra.Test { + public class AngleTests { + [SetUp] + public void Setup() { + } + + [Test] + public void Construct() { + // Degrees + float angle = 0.0f; + AngleFloat a = AngleFloat.Degrees(angle); + Assert.AreEqual(angle, a.inDegrees); + + angle = -180.0f; + a = AngleFloat.Degrees(angle); + Assert.AreEqual(angle, a.inDegrees); + + angle = 270.0f; + a = AngleFloat.Degrees(angle); + Assert.AreEqual(-90, a.inDegrees); + + // Radians + angle = 0.0f; + a = AngleFloat.Radians(angle); + Assert.AreEqual(angle, a.inRadians); + + angle = (float)-Math.PI; + a = AngleFloat.Radians(angle); + Assert.AreEqual(angle, a.inRadians); + + angle = (float)Math.PI * 1.5f; + a = AngleFloat.Radians(angle); + Assert.AreEqual(-Math.PI * 0.5f, a.inRadians, 1.0E-05F); + + // Revolutions + angle = 0.0f; + a = AngleFloat.Revolutions(angle); + Assert.AreEqual(angle, a.inRevolutions); + + angle = -0.5f; + a = AngleFloat.Revolutions(angle); + Assert.AreEqual(angle, a.inRevolutions); + + angle = 0.75f; + a = AngleFloat.Revolutions(angle); + Assert.AreEqual(-0.25f, a.inRevolutions); + + } + + [Test] + public void Revolutions() { + AngleFloat a; + + // Test zero + a = AngleFloat.Revolutions(0.0f); + Assert.AreEqual(0.0f, a.inRevolutions); + + // Test positive values within range + a = AngleFloat.Revolutions(0.25f); + Assert.AreEqual(0.25f, a.inRevolutions); + + a = AngleFloat.Revolutions(0.5f); + Assert.AreEqual(-0.5f, a.inRevolutions); + + // Test negative values within range + a = AngleFloat.Revolutions(-0.25f); + Assert.AreEqual(-0.25f, a.inRevolutions); + + a = AngleFloat.Revolutions(-0.5f); + Assert.AreEqual(-0.5f, a.inRevolutions); + + // Test values outside range (positive) + a = AngleFloat.Revolutions(1.0f); + Assert.AreEqual(0.0f, a.inRevolutions); + + a = AngleFloat.Revolutions(1.25f); + Assert.AreEqual(0.25f, a.inRevolutions); + + a = AngleFloat.Revolutions(1.75f); + Assert.AreEqual(-0.25f, a.inRevolutions); + + // Test values outside range (negative) + a = AngleFloat.Revolutions(-1.0f); + Assert.AreEqual(0.0f, a.inRevolutions); + + a = AngleFloat.Revolutions(-1.25f); + Assert.AreEqual(-0.25f, a.inRevolutions); + + a = AngleFloat.Revolutions(-1.75f); + Assert.AreEqual(0.25f, a.inRevolutions); + + // Test infinity + a = AngleFloat.Revolutions(float.PositiveInfinity); + Assert.AreEqual(float.PositiveInfinity, a.inRevolutions); + + a = AngleFloat.Revolutions(float.NegativeInfinity); + Assert.AreEqual(float.NegativeInfinity, a.inRevolutions); + } + + [Test] + public void Equality() { + // Test equality operator + Assert.IsTrue(AngleFloat.Degrees(90) == AngleFloat.Degrees(90), "90 == 90"); + Assert.IsFalse(AngleFloat.Degrees(90) == AngleFloat.Degrees(45), "90 == 45"); + Assert.IsTrue(AngleFloat.Degrees(0) == AngleFloat.Degrees(0), "0 == 0"); + Assert.IsTrue(AngleFloat.Degrees(-180) == AngleFloat.Degrees(-180), "-180 == -180"); + + // Test inequality operator + Assert.IsTrue(AngleFloat.Degrees(90) != AngleFloat.Degrees(45), "90 != 45"); + Assert.IsFalse(AngleFloat.Degrees(90) != AngleFloat.Degrees(90), "90 != 90"); + Assert.IsTrue(AngleFloat.Degrees(0) != AngleFloat.Degrees(1), "0 != 1"); + + // Test greater than operator + Assert.IsTrue(AngleFloat.Degrees(90) > AngleFloat.Degrees(45), "90 > 45"); + Assert.IsFalse(AngleFloat.Degrees(45) > AngleFloat.Degrees(90), "45 > 90"); + Assert.IsFalse(AngleFloat.Degrees(90) > AngleFloat.Degrees(90), "90 > 90"); + + // Test greater than or equal operator + Assert.IsTrue(AngleFloat.Degrees(90) >= AngleFloat.Degrees(45), "90 >= 45"); + Assert.IsTrue(AngleFloat.Degrees(90) >= AngleFloat.Degrees(90), "90 >= 90"); + Assert.IsFalse(AngleFloat.Degrees(45) >= AngleFloat.Degrees(90), "45 >= 90"); + + // Test less than operator + Assert.IsTrue(AngleFloat.Degrees(45) < AngleFloat.Degrees(90), "45 < 90"); + Assert.IsFalse(AngleFloat.Degrees(90) < AngleFloat.Degrees(45), "90 < 45"); + Assert.IsFalse(AngleFloat.Degrees(90) < AngleFloat.Degrees(90), "90 < 90"); + + // Test less than or equal operator + Assert.IsTrue(AngleFloat.Degrees(45) <= AngleFloat.Degrees(90), "45 <= 90"); + Assert.IsTrue(AngleFloat.Degrees(90) <= AngleFloat.Degrees(90), "90 <= 90"); + Assert.IsFalse(AngleFloat.Degrees(90) <= AngleFloat.Degrees(45), "90 <= 45"); + } + + // [Test] + // public void Normalize() { + // float r = 0; + + // r = Angle.Normalize(90); + // Assert.AreEqual(r, 90, "Normalize 90"); + + // r = Angle.Normalize(-90); + // Assert.AreEqual(r, -90, "Normalize -90"); + + // r = Angle.Normalize(270); + // Assert.AreEqual(r, -90, "Normalize 270"); + + // r = Angle.Normalize(270 + 360); + // Assert.AreEqual(r, -90, "Normalize 270+360"); + + // r = Angle.Normalize(-270); + // Assert.AreEqual(r, 90, "Normalize -270"); + + // r = Angle.Normalize(-270 - 360); + // Assert.AreEqual(r, 90, "Normalize -270-360"); + + // r = Angle.Normalize(0); + // Assert.AreEqual(r, 0, "Normalize 0"); + + // r = Angle.Normalize(float.PositiveInfinity); + // Assert.AreEqual(r, float.PositiveInfinity, "Normalize INFINITY"); + + // r = Angle.Normalize(float.NegativeInfinity); + // Assert.AreEqual(r, float.NegativeInfinity, "Normalize INFINITY"); + // } + + [Test] + public void Clamp() { + float r = 0; + + r = AngleFloat.Clamp(AngleFloat.Degrees(1), AngleFloat.Degrees(0), AngleFloat.Degrees(2)); + Assert.AreEqual(1, r, "Clamp 1 0 2"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(-1), AngleFloat.Degrees(0), AngleFloat.Degrees(2)); + Assert.AreEqual(0, r, "Clamp -1 0 2"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(3), AngleFloat.Degrees(0), AngleFloat.Degrees(2)); + Assert.AreEqual(2, r, "Clamp 3 0 2"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(1), AngleFloat.Degrees(0), AngleFloat.Degrees(0)); + Assert.AreEqual(0, r, "Clamp 1 0 0"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(0), AngleFloat.Degrees(0), AngleFloat.Degrees(0)); + Assert.AreEqual(0, r, "Clamp 0 0 0"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(0), AngleFloat.Degrees(1), AngleFloat.Degrees(-1)); + Assert.AreEqual(1, r, "Clamp 0 1 -1"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(1), AngleFloat.Degrees(0), AngleFloat.Degrees(float.PositiveInfinity)); + Assert.AreEqual(1, r, "Clamp 1 0 INFINITY"); + + r = AngleFloat.Clamp(AngleFloat.Degrees(1), AngleFloat.Degrees(float.NegativeInfinity), AngleFloat.Degrees(1)); + Assert.AreEqual(1, r, "Clamp 1 -INFINITY 1"); + } + + [Test] + public void Cos() { + // Test zero + Assert.AreEqual(1.0f, AngleFloat.Cos(AngleFloat.Degrees(0)), 1.0E-05F, "Cos(0°)"); + + // Test 90 degrees + Assert.AreEqual(0.0f, AngleFloat.Cos(AngleFloat.Degrees(90)), 1.0E-05F, "Cos(90°)"); + + // Test 180 degrees + Assert.AreEqual(-1.0f, AngleFloat.Cos(AngleFloat.Degrees(180)), 1.0E-05F, "Cos(180°)"); + + // Test 270 degrees + Assert.AreEqual(0.0f, AngleFloat.Cos(AngleFloat.Degrees(270)), 1.0E-05F, "Cos(270°)"); + + // Test 45 degrees + Assert.AreEqual(MathF.Sqrt(2) / 2, AngleFloat.Cos(AngleFloat.Degrees(45)), 1.0E-05F, "Cos(45°)"); + + // Test negative angle + Assert.AreEqual(1.0f, AngleFloat.Cos(AngleFloat.Degrees(-360)), 1.0E-05F, "Cos(-360°)"); + + // Test using radians + Assert.AreEqual(1.0f, AngleFloat.Cos(AngleFloat.Radians(0)), 1.0E-05F, "Cos(0 rad)"); + Assert.AreEqual(0.0f, AngleFloat.Cos(AngleFloat.Radians((float)Math.PI / 2)), 1.0E-05F, "Cos(π/2)"); + Assert.AreEqual(-1.0f, AngleFloat.Cos(AngleFloat.Radians((float)Math.PI)), 1.0E-05F, "Cos(π)"); + } + + [Test] + public void Sin() { + // Test zero + Assert.AreEqual(0.0f, AngleFloat.Sin(AngleFloat.Degrees(0)), 1.0E-05F, "Sin(0°)"); + + // Test 90 degrees + Assert.AreEqual(1.0f, AngleFloat.Sin(AngleFloat.Degrees(90)), 1.0E-05F, "Sin(90°)"); + + // Test 180 degrees + Assert.AreEqual(0.0f, AngleFloat.Sin(AngleFloat.Degrees(180)), 1.0E-05F, "Sin(180°)"); + + // Test 270 degrees + Assert.AreEqual(-1.0f, AngleFloat.Sin(AngleFloat.Degrees(270)), 1.0E-05F, "Sin(270°)"); + + // Test 45 degrees + Assert.AreEqual(MathF.Sqrt(2) / 2, AngleFloat.Sin(AngleFloat.Degrees(45)), 1.0E-05F, "Sin(45°)"); + + // Test negative angle + Assert.AreEqual(0.0f, AngleFloat.Sin(AngleFloat.Degrees(-360)), 1.0E-05F, "Sin(-360°)"); + + // Test using radians + Assert.AreEqual(0.0f, AngleFloat.Sin(AngleFloat.Radians(0)), 1.0E-05F, "Sin(0 rad)"); + Assert.AreEqual(1.0f, AngleFloat.Sin(AngleFloat.Radians((float)Math.PI / 2)), 1.0E-05F, "Sin(π/2)"); + Assert.AreEqual(0.0f, AngleFloat.Sin(AngleFloat.Radians((float)Math.PI)), 1.0E-05F, "Sin(π)"); + } + + [Test] + public void Tan() { + // Test zero + Assert.AreEqual(0.0f, AngleFloat.Tan(AngleFloat.Degrees(0)), 1.0E-05F, "Tan(0°)"); + + // Test 45 degrees + Assert.AreEqual(1.0f, AngleFloat.Tan(AngleFloat.Degrees(45)), 1.0E-05F, "Tan(45°)"); + + // Test -45 degrees + Assert.AreEqual(-1.0f, AngleFloat.Tan(AngleFloat.Degrees(-45)), 1.0E-05F, "Tan(-45°)"); + + // Test using radians + Assert.AreEqual(0.0f, AngleFloat.Tan(AngleFloat.Radians(0)), 1.0E-05F, "Tan(0 rad)"); + Assert.AreEqual(1.0f, AngleFloat.Tan(AngleFloat.Radians((float)Math.PI / 4)), 1.0E-05F, "Tan(π/4)"); + } + + [Test] + public void Acos() { + // Test 1 (0 degrees) + Assert.AreEqual(0.0f, AngleFloat.Acos(1.0f).inRadians, 1.0E-05F, "Acos(1)"); + + // Test 0 (90 degrees or π/2 radians) + Assert.AreEqual((float)Math.PI / 2, AngleFloat.Acos(0.0f).inRadians, 1.0E-05F, "Acos(0)"); + + // Test -1 (-180 degrees or π radians) + Assert.AreEqual((float)-Math.PI, AngleFloat.Acos(-1.0f).inRadians, 1.0E-05F, "Acos(-1)"); + + // Test 0.5 (60 degrees or π/3 radians) + Assert.AreEqual((float)Math.PI / 3, AngleFloat.Acos(0.5f).inRadians, 1.0E-05F, "Acos(0.5)"); + + // Test sqrt(2)/2 (45 degrees or π/4 radians) + Assert.AreEqual((float)Math.PI / 4, AngleFloat.Acos(MathF.Sqrt(2) / 2).inRadians, 1.0E-05F, "Acos(√2/2)"); + } + + [Test] + public void Asin() { + // Test 0 (0 degrees) + Assert.AreEqual(0.0f, AngleFloat.Asin(0.0f).inRadians, 1.0E-05F, "Asin(0)"); + + // Test 1 (90 degrees or π/2 radians) + Assert.AreEqual((float)Math.PI / 2, AngleFloat.Asin(1.0f).inRadians, 1.0E-05F, "Asin(1)"); + + // Test -1 (-90 degrees or -π/2 radians) + Assert.AreEqual(-(float)Math.PI / 2, AngleFloat.Asin(-1.0f).inRadians, 1.0E-05F, "Asin(-1)"); + + // Test 0.5 (30 degrees or π/6 radians) + Assert.AreEqual((float)Math.PI / 6, AngleFloat.Asin(0.5f).inRadians, 1.0E-05F, "Asin(0.5)"); + + // Test sqrt(2)/2 (45 degrees or π/4 radians) + Assert.AreEqual((float)Math.PI / 4, AngleFloat.Asin(MathF.Sqrt(2) / 2).inRadians, 1.0E-05F, "Asin(√2/2)"); + } + + + [Test] + public void Atan() { + // Test zero + Assert.AreEqual(0.0f, AngleFloat.Atan(0.0f).inRadians, 1.0E-05F, "Atan(0)"); + + // Test 1 (45 degrees or π/4 radians) + Assert.AreEqual((float)Math.PI / 4, AngleFloat.Atan(1.0f).inRadians, 1.0E-05F, "Atan(1)"); + + // Test -1 (-45 degrees or -π/4 radians) + Assert.AreEqual(-(float)Math.PI / 4, AngleFloat.Atan(-1.0f).inRadians, 1.0E-05F, "Atan(-1)"); + + // Test sqrt(3) (60 degrees or π/3 radians) + Assert.AreEqual((float)Math.PI / 3, AngleFloat.Atan(MathF.Sqrt(3)).inRadians, 1.0E-05F, "Atan(√3)"); + + // Test 1/sqrt(3) (30 degrees or π/6 radians) + Assert.AreEqual((float)Math.PI / 6, AngleFloat.Atan(1.0f / MathF.Sqrt(3)).inRadians, 1.0E-05F, "Atan(1/√3)"); + + // Test positive infinity + Assert.AreEqual((float)Math.PI / 2, AngleFloat.Atan(float.PositiveInfinity).inRadians, 1.0E-05F, "Atan(+∞)"); + + // Test negative infinity + Assert.AreEqual(-(float)Math.PI / 2, AngleFloat.Atan(float.NegativeInfinity).inRadians, 1.0E-05F, "Atan(-∞)"); + } + + [Test] + public void Atan2() { + // Test basic quadrant I + Assert.AreEqual((float)Math.PI / 4, AngleFloat.Atan2(1.0f, 1.0f).inRadians, 1.0E-05F, "Atan2(1, 1)"); + + // Test quadrant II + Assert.AreEqual(3 * (float)Math.PI / 4, AngleFloat.Atan2(1.0f, -1.0f).inRadians, 1.0E-05F, "Atan2(1, -1)"); + + // Test quadrant III + Assert.AreEqual(-(float)Math.PI * 0.75f, AngleFloat.Atan2(-1.0f, -1.0f).inRadians, 1.0E-05F, "Atan2(-1, -1)"); + + // Test quadrant IV + Assert.AreEqual(-(float)Math.PI / 4, AngleFloat.Atan2(-1.0f, 1.0f).inRadians, 1.0E-05F, "Atan2(-1, 1)"); + + // Test positive x-axis + Assert.AreEqual(0.0f, AngleFloat.Atan2(0.0f, 1.0f).inRadians, 1.0E-05F, "Atan2(0, 1)"); + + // Test positive y-axis + Assert.AreEqual((float)Math.PI / 2, AngleFloat.Atan2(1.0f, 0.0f).inRadians, 1.0E-05F, "Atan2(1, 0)"); + + // Test negative y-axis + Assert.AreEqual(-(float)Math.PI / 2, AngleFloat.Atan2(-1.0f, 0.0f).inRadians, 1.0E-05F, "Atan2(-1, 0)"); + + // Test origin + Assert.AreEqual(0.0f, AngleFloat.Atan2(0.0f, 0.0f).inRadians, 1.0E-05F, "Atan2(0, 0)"); + + // Test with different magnitudes + Assert.AreEqual((float)Math.PI / 3, AngleFloat.Atan2(MathF.Sqrt(3), 1.0f).inRadians, 1.0E-05F, "Atan2(√3, 1)"); + + // Test negative x-axis + Assert.AreEqual((float)-Math.PI, AngleFloat.Atan2(0.0f, -1.0f).inRadians, 1.0E-05F, "Atan2(0, -1)"); + } + + [Test] + public void Multiplication() { + AngleFloat r = AngleFloat.zero; + + // Angle * float + r = AngleFloat.Degrees(90) * 2; + Assert.AreEqual(-180, r.inDegrees, "Multiply 90 * 2"); + + r = AngleFloat.Degrees(45) * 0.5f; + Assert.AreEqual(22.5f, r.inDegrees, "Multiply 45 * 0.5"); + + r = AngleFloat.Degrees(90) * 0; + Assert.AreEqual(0, r.inDegrees, "Multiply 90 * 0"); + + r = AngleFloat.Degrees(-90) * 2; + Assert.AreEqual(-180, r.inDegrees, "Multiply -90 * 2"); + + r = AngleFloat.Degrees(270) * 2; + Assert.AreEqual(-180, r.inDegrees, "Multiply 270 * 2 (normalized)"); + + // float * Angle + r = 2 * AngleFloat.Degrees(90); + Assert.AreEqual(-180, r.inDegrees, "Multiply 2 * 90"); + + r = 0.5f * AngleFloat.Degrees(45); + Assert.AreEqual(22.5, r.inDegrees, "Multiply 0.5 * 45"); + + r = 0 * AngleFloat.Degrees(90); + Assert.AreEqual(0, r.inDegrees, "Multiply 0 * 90"); + + r = 2 * AngleFloat.Degrees(-90); + Assert.AreEqual(-180, r.inDegrees, "Multiply 2 * -90"); + + // Negative factor + r = AngleFloat.Degrees(90) * -1; + Assert.AreEqual(-90, r.inDegrees, "Multiply 90 * -1"); + + r = -1 * AngleFloat.Degrees(90); + Assert.AreEqual(-90, r.inDegrees, "Multiply -1 * 90"); + } + + [Test] + public void MoveTowards() { + AngleFloat r = AngleFloat.zero; + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), 30); + Assert.AreEqual(30, r.inDegrees, "MoveTowards 0 90 30"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), 90); + Assert.AreEqual(90, r.inDegrees, "MoveTowards 0 90 90"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), 180); + Assert.AreEqual(90, r.inDegrees, "MoveTowards 0 90 180"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), 270); + Assert.AreEqual(90, r.inDegrees, "MoveTowrads 0 90 270"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), -30); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 90 -30"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(-90), -30); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 -90 -30"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(-90), -90); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 -90 -90"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(-90), -180); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 -90 -180"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(-90), -270); + Assert.AreEqual(0, r.inDegrees, "MoveTowrads 0 -90 -270"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), 0); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 90 0"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(0), 0); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 0 0"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(0), 30); + Assert.AreEqual(0, r.inDegrees, "MoveTowrads 0 0 30"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(90), float.PositiveInfinity); + Assert.AreEqual(90, r.inDegrees, "MoveTowards 0 90 INFINITY"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(float.PositiveInfinity), 30); + Assert.AreEqual(30, r.inDegrees, "MoveTowrads 0 INFINITY 30"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(-90), float.NegativeInfinity); + Assert.AreEqual(0, r.inDegrees, "MoveTowards 0 -90 -INFINITY"); + + r = AngleFloat.MoveTowards(AngleFloat.Degrees(0), AngleFloat.Degrees(float.NegativeInfinity), -30); + Assert.AreEqual(0, r.inDegrees, "MoveTowrads 0 -INFINITY -30"); + + } + + [Test] + public void Difference() { + float r = 0; + + r = Angles.Difference(0, 90); + Assert.AreEqual(90, r, "Difference 0 90"); + + r = Angles.Difference(0, -90); + Assert.AreEqual(-90, r, "Difference 0 -90"); + + r = Angles.Difference(0, 270); + Assert.AreEqual(-90, r, "Difference 0 270"); + + r = Angles.Difference(0, -270); + Assert.AreEqual(90, r, "Difference 0 -270"); + + r = Angles.Difference(90, 0); + Assert.AreEqual(-90, r, "Difference 90 0"); + + r = Angles.Difference(-90, 0); + Assert.AreEqual(90, r, "Difference -90 0"); + + r = Angles.Difference(0, 0); + Assert.AreEqual(0, r, "Difference 0 0"); + + r = Angles.Difference(90, 90); + Assert.AreEqual(0, r, "Difference 90 90"); + + r = Angles.Difference(0, float.PositiveInfinity); + Assert.AreEqual(float.PositiveInfinity, r, "Difference 0 INFINITY"); + + r = Angles.Difference(0, float.NegativeInfinity); + Assert.AreEqual(float.NegativeInfinity, r, "Difference 0 -INFINITY"); + + r = Angles.Difference(float.NegativeInfinity, float.PositiveInfinity); + Assert.AreEqual(float.PositiveInfinity, r, "Difference -INFINITY INFINITY"); + } + } + +} +#endif diff --git a/Assets/NanoBrain/LinearAlgebra/test/DirectionTest.cs b/Assets/NanoBrain/LinearAlgebra/test/DirectionTest.cs new file mode 100644 index 0000000..146c9df --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/DirectionTest.cs @@ -0,0 +1,201 @@ +#if !UNITY_5_6_OR_NEWER +using System; +using NUnit.Framework; + +namespace LinearAlgebra.Test { + public class DirectionTest { + + [Test] + public void RadiansForward() { + Direction d = Direction.Radians(0, 0); + Assert.AreEqual(0, d.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(0, d.vertical.inDegrees, 0.0001f); + } + + [Test] + public void RadiansUp() { + Direction d = Direction.Radians(0, (float)Math.PI / 2); + Assert.AreEqual(0, d.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(90, d.vertical.inDegrees, 0.0001f); + } + + [Test] + public void RadiansDown() { + Direction d = Direction.Radians(0, -(float)Math.PI / 2); + Assert.AreEqual(0, d.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(-90, d.vertical.inDegrees, 0.0001f); + } + + [Test] + public void RadiansArbitrary() { + Direction d = Direction.Radians((float)Math.PI / 4, (float)Math.PI / 6); + Assert.AreEqual(45, d.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(30, d.vertical.inDegrees, 0.0001f); + } + + [Test] + public void RadiansEquivalentToDegreesConversion() { + Direction d1 = Direction.Radians((float)Math.PI / 3, (float)Math.PI / 4); + Direction d2 = Direction.Degrees(60, 45); + Assert.AreEqual(d1.horizontal.inDegrees, d2.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(d1.vertical.inDegrees, d2.vertical.inDegrees, 0.0001f); + } + + [Test] + public void ToVector3Forward() { + Direction d = Direction.forward; + Vector3Float v = d.ToVector3(); + Assert.AreEqual(0, v.horizontal, 0.0001f); + Assert.AreEqual(0, v.vertical, 0.0001f); + Assert.AreEqual(1, v.depth, 0.0001f); + } + + [Test] + public void ToVector3Up() { + Direction d = Direction.up; + Vector3Float v = d.ToVector3(); + Assert.AreEqual(0, v.horizontal, 0.0001f); + Assert.AreEqual(1, v.vertical, 0.0001f); + Assert.AreEqual(0, v.depth, 0.0001f); + } + + [Test] + public void ToVector3Down() { + Direction d = Direction.down; + Vector3Float v = d.ToVector3(); + Assert.AreEqual(0, v.horizontal, 0.0001f); + Assert.AreEqual(-1, v.vertical, 0.0001f); + Assert.AreEqual(0, v.depth, 0.0001f); + } + + [Test] + public void FromVector3Forward() { + Vector3Float v = new(0, 0, 1); + Direction d = Direction.FromVector3(v); + Assert.AreEqual(0, d.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(0, d.vertical.inDegrees, 0.0001f); + } + + [Test] + public void ToVector3AndBack() { + Direction d1 = Direction.Degrees(45, 30); + Vector3Float v = d1.ToVector3(); + Direction d2 = Direction.FromVector3(v); + Assert.AreEqual(d1.horizontal.inDegrees, d2.horizontal.inDegrees, 0.0001f); + Assert.AreEqual(d1.vertical.inDegrees, d2.vertical.inDegrees, 0.0001f); + } + + [Test] + public void Compare() { + Direction d1 = Direction.Degrees(45, 135); + Direction d2 = new(AngleFloat.Degrees(45), AngleFloat.Degrees(135)); + bool r; + r = d1 == d2; + Assert.True(r); + Assert.AreEqual(d1, d2); + } + + [Test] + public void NotEqualWithDifferentHorizontal() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(90, 30); + Assert.True(d1 != d2); + } + + [Test] + public void NotEqualWithDifferentVertical() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(45, 60); + Assert.True(d1 != d2); + } + + [Test] + public void NotEqualWithDifferentBoth() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(90, 60); + Assert.True(d1 != d2); + } + + [Test] + public void NotEqualWithSameValues() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(45, 30); + Assert.False(d1 != d2); + } + + + [Test] + public void EqualsWithSameValues() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(45, 30); + Assert.True(d1.Equals(d2)); + } + + [Test] + public void EqualsWithDifferentHorizontal() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(90, 30); + Assert.False(d1.Equals(d2)); + } + + [Test] + public void EqualsWithDifferentVertical() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(45, 60); + Assert.False(d1.Equals(d2)); + } + + [Test] + public void EqualsWithDifferentBoth() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(90, 60); + Assert.False(d1.Equals(d2)); + } + + [Test] + public void EqualsWithNonDirectionObject() { + Direction d = Direction.Degrees(45, 30); + Assert.False(d.Equals("not a direction")); + } + + [Test] + public void EqualsWithNull() { + Direction d = Direction.Degrees(45, 30); + Assert.False(d.Equals(null)); + } + + [Test] + public void EqualsWithZeros() { + Direction d1 = Direction.forward; + Direction d2 = Direction.Degrees(0, 0); + Assert.True(d1.Equals(d2)); + } + + [Test] + public void HashCode() { + Direction d1 = Direction.Degrees(45, 30); + Direction d2 = Direction.Degrees(45, 30); + Assert.AreEqual(d1.GetHashCode(), d2.GetHashCode()); + + d1 = Direction.Degrees(45, 30); + d2 = Direction.Degrees(90, 30); + Assert.AreNotEqual(d1.GetHashCode(), d2.GetHashCode()); + + d1 = Direction.Degrees(45, 30); + d2 = Direction.Degrees(45, 60); + Assert.AreNotEqual(d1.GetHashCode(), d2.GetHashCode()); + + Direction d = Direction.Degrees(45, 30); + int hash1 = d.GetHashCode(); + int hash2 = d.GetHashCode(); + Assert.AreEqual(hash1, hash2); + + d1 = Direction.forward; + d2 = Direction.Degrees(0, 0); + Assert.AreEqual(d1.GetHashCode(), d2.GetHashCode()); + } + + }; +} +#endif + diff --git a/Assets/NanoBrain/LinearAlgebra/test/LinearAlgebra_Test.csproj b/Assets/NanoBrain/LinearAlgebra/test/LinearAlgebra_Test.csproj new file mode 100644 index 0000000..5b48e60 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/LinearAlgebra_Test.csproj @@ -0,0 +1,19 @@ + + + + net8.0 + false + true + + + + + + + + + + + + + diff --git a/Assets/NanoBrain/LinearAlgebra/test/QuaternionTest.cs b/Assets/NanoBrain/LinearAlgebra/test/QuaternionTest.cs new file mode 100644 index 0000000..9dd5a96 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/QuaternionTest.cs @@ -0,0 +1,185 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + + public class QuaternionTest { + + [SetUp] + public void Setup() { + } + + [Test] + public void Normalize() { + Quaternion q1 = new(0, 0, 0, 1); + Quaternion r = Quaternion.identity; + + r = q1.normalized; + Assert.AreEqual(r, q1, "q.normalized 0 0 0 1"); + + r = Quaternion.Normalize(q1); + Assert.AreEqual(r, q1, "q.normalized 0 0 0 1"); + } + + [Test] + public void ToAngles() { + Quaternion q1 = new(0, 0, 0, 1); + Vector3Float v = Vector3Float.zero; + + v = Quaternion.ToAngles(q1); + Assert.AreEqual(v, new Vector3Float(0, 0, 0), "ToAngles 0 0 0 1"); + + q1 = new(1, 0, 0, 0); + v = Quaternion.ToAngles(q1); + Assert.AreEqual(0, v.horizontal, "1 0 0 0 H"); + Assert.AreEqual(180, v.vertical, "1 0 0 0 V"); + Assert.AreEqual(180, v.depth, "1 0 0 0 D"); + + } + + [Test] + public void Multiplication() { + Quaternion q1 = new(0, 0, 0, 1); + Quaternion q2 = new(1, 0, 0, 0); + Quaternion r; + + r = q1 * q2; + Assert.AreEqual(r, new Quaternion(1, 0, 0, 0), "0 0 0 1 * 1 0 0 0 "); + } + + [Test] + public void MultiplicationVector() { + Quaternion q1 = new(0, 0, 0, 1); + Vector3Float v1 = new(0, 1, 0); + Vector3Float r; + + r = q1 * v1; + Assert.AreEqual(r, new Vector3Float(0, 1, 0), "0 0 0 1 * Vector 0 1 0"); + + q1 = new(1, 0, 0, 0); + r = q1 * v1; + Assert.AreEqual(r, new Vector3Float(0, -1, 0), "1 0 0 0 * Vector 0 1 0"); + } + + [Test] + public void Equality() { + Quaternion q1 = new(0, 0, 0, 1); + Quaternion q2 = new(1, 0, 0, 0); + Assert.AreNotEqual(q1, q2, "0 0 0 1 == 1 0 0 0"); + + q2 = new(0, 0, 0, 1); + Assert.AreEqual(q1, q2, "0 0 0 1 == 1 0 0 0"); + } + + [Test, Ignore("ToDo")] + public void Inverse() { } + + [Test, Ignore("ToDo")] + public void LookRotation() { } + + [Test, Ignore("ToDo")] + public void FromToRotation() { } + + [Test, Ignore("ToDo")] + public void RotateTowards() { } + + [Test, Ignore("ToDo")] + public void AngleAxis() { } + + [Test, Ignore("ToDo")] + public void Angle() { } + + [Test, Ignore("ToDo")] + public void Slerp() { } + + [Test, Ignore("ToDo")] + public void SlerpUnclamped() { } + + [Test] + public void Euler() { + Vector3Float v1 = new(0, 0, 0); + Quaternion q; + + q = Quaternion.Euler(v1); + Assert.AreEqual(q, Quaternion.identity, "Euler Vector 0 0 0"); + + q = Quaternion.Euler(0, 0, 0); + Assert.AreEqual(q, Quaternion.identity, "Euler 0 0 0"); + + v1 = new(90, 90, -90); + q = Quaternion.Euler(v1); + Assert.AreEqual(q, new Quaternion(0, 0.707106709F, -0.707106709F, 0), "Euler Vector 90 90 -90"); + + q = Quaternion.Euler(90, 90, -90); + Assert.AreEqual(q, new Quaternion(0, 0.707106709F, -0.707106709F, 0), "Euler 90 90 -90"); + } + + [Test] + public void EulerToAngles() { + Vector3Float v; + Quaternion q; + Quaternion r; + + //v = new(0, 0, 0); + q = Quaternion.Euler(0, 0 , 0); + v = Quaternion.ToAngles(q); + r = Quaternion.Euler(v); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f, "0 0 0"); + + q = Quaternion.Euler(-45, -30, -15); + v = Quaternion.ToAngles(q); + r = Quaternion.Euler(v); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f, "-45, -30, -15"); + + // Gimball lock + // q = Quaternion.Euler(90, 90, -90); + // v = Quaternion.ToAngles(q); + // r = Quaternion.Euler(v); + // Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f, "0 0 0"); + + } + + [Test] + public void GetAngleAround() { + Vector3Float v1 = new(0, 1, 0); + Quaternion q1 = new(0, 0, 0, 1); + + float f = Quaternion.GetAngleAround(v1, q1); + Assert.AreEqual(f, 0, "GetAngleAround 0 1 0 , 0 0 0 1"); + + q1 = new(0, 0.707106709F, -0.707106709F, 0); + f = Quaternion.GetAngleAround(v1, q1); + Assert.AreEqual(f, 180, "GetAngleAround 0 1 0 , 0 0.7 -0.7 0"); + + v1 = new(0, 0, 0); + f = Quaternion.GetAngleAround(v1, q1); + Assert.IsTrue(float.IsNaN(f), "GetAngleAround 0 0 0 , 0 0.7 -0.7 0"); + } + + [Test] + public void GetRotationAround() { + Vector3Float v1 = new(0, 1, 0); + Quaternion q1 = new(0, 0, 0, 1); + + Quaternion q = Quaternion.GetRotationAround(v1, q1); + Assert.AreEqual(q, new Quaternion(0, 0, 0, 1), "GetRotationAround 0 1 0 , 0 0 0 1"); + + q1 = new(0, 0.707106709F, -0.707106709F, 0); + q = Quaternion.GetRotationAround(v1, q1); + Assert.AreEqual(q, new Quaternion(0, 1, 0, 0), "GetRotationAround 0 1 0 , 0 0.7 -0.7 0"); + + v1 = new(0, 0, 0); + q = Quaternion.GetRotationAround(v1, q1); + bool r = float.IsNaN(q.x) && float.IsNaN(q.y) && float.IsNaN(q.z) && float.IsNaN(q.w); + Assert.IsTrue(r, "GetRotationAround 0 0 0 , 0 0.7 -0.7 0"); + } + + [Test, Ignore("ToDo")] + public void GetSwingTwist() { } + + [Test, Ignore("ToDo")] + public void Dot() { } + + } +} +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/SphericalTest.cs b/Assets/NanoBrain/LinearAlgebra/test/SphericalTest.cs new file mode 100644 index 0000000..125cdb1 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/SphericalTest.cs @@ -0,0 +1,53 @@ +#if !UNITY_5_6_OR_NEWER +using System; +using NUnit.Framework; + +namespace LinearAlgebra.Test { + public class SphericalTest { + [SetUp] + public void Setup() { + } + + [Test] + public void FromVector3() { + Vector3Float v = new(0, 0, 1); + Spherical s = Spherical.FromVector3(v); + Assert.AreEqual(1.0f, s.distance, "s.distance 0 0 1"); + Assert.AreEqual(0.0f, s.direction.horizontal.inDegrees, "s.hor 0 0 1"); + Assert.AreEqual(0.0f, s.direction.vertical.inDegrees, 1.0E-05F, "s.vert 0 0 1"); + + v = new(0, 1, 0); + s = Spherical.FromVector3(v); + Assert.AreEqual(1.0f, s.distance, "s.distance 0 1 0"); + Assert.AreEqual(0.0f, s.direction.horizontal.inDegrees, "s.hor 0 1 0"); + Assert.AreEqual(90.0f, s.direction.vertical.inDegrees, "s.vert 0 1 0"); + + v = new(1, 0, 0); + s = Spherical.FromVector3(v); + Assert.AreEqual(1.0f, s.distance, "s.distance 1 0 0"); + Assert.AreEqual(90.0f, s.direction.horizontal.inDegrees, "s.hor 1 0 0"); + Assert.AreEqual(0.0f, s.direction.vertical.inDegrees, 1.0E-05F, "s.vert 1 0 0"); + } + + [Test] + public void Addition() { + Spherical v1 = Spherical.Degrees(1, 45, 0); + Spherical v2 = Spherical.zero; + Spherical r = Spherical.zero; + + r = v1 + v2; + Assert.AreEqual(v1.distance, r.distance, 1.0E-05F, "Addition(0,0,0)"); + + r = v1; + r += v2; + Assert.AreEqual(v1.distance, r.distance, 1.0E-05F, "Addition(0,0,0)"); + + v2 = Spherical.Degrees(1, 0, 90); + r = v1 + v2; + Assert.AreEqual(Math.Sqrt(2), r.distance, 1.0E-05F, "Addition(1 0 90)"); + Assert.AreEqual(45.0f, r.direction.horizontal.inDegrees, "Addition(1 0 90)"); + Assert.AreEqual(45.0f, r.direction.vertical.inDegrees, 1.0E-05F, "Addition(1 0 90)"); + } + } +} +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/SwingTwistTest.cs b/Assets/NanoBrain/LinearAlgebra/test/SwingTwistTest.cs new file mode 100644 index 0000000..5f05a96 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/SwingTwistTest.cs @@ -0,0 +1,131 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + + [TestFixture] + public class SwingTwistTest { + + [Test] + public void Degrees_CreatesSwingTwistWithDegreeAngles() { + SwingTwist st = SwingTwist.Degrees(45, 30, 15); + Assert.IsNotNull(st); + Assert.AreEqual(45, st.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(30, st.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(15, st.twist.inDegrees, 0.01f); + } + + [Test] + public void Radians_CreatesSwingTwistWithRadianAngles() { + float pi = (float)System.Math.PI; + SwingTwist st = SwingTwist.Radians(pi / 4, pi / 6, pi / 12); + Assert.IsNotNull(st); + Assert.AreEqual(45, st.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(30, st.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(15, st.twist.inDegrees, 0.01f); + } + + [Test] + public void Zero_CreatesZeroRotation() { + SwingTwist st = SwingTwist.zero; + Assert.AreEqual(0, st.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(0, st.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(0, st.twist.inDegrees, 0.01f); + } + + [Test] + public void QuaternionTest() { + Quaternion q; + SwingTwist s; + Quaternion r; + + q = Quaternion.identity; + s = SwingTwist.FromQuaternion(q); + r = s.ToQuaternion(); + Assert.AreEqual(q, r); + + q = Quaternion.Euler(90, 0, 0); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(0, s.swing.horizontal.inDegrees, 10e-2f); + Assert.AreEqual(90, s.swing.vertical.inDegrees, 10e-2f); + Assert.AreEqual(0, s.twist.inDegrees, 0.01f); + r = s.ToQuaternion(); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + q = Quaternion.Euler(0, 90, 0); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(90, s.swing.horizontal.inDegrees,10e-2f); + Assert.AreEqual(0, s.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(0, s.twist.inDegrees, 0.01f); + r = s.ToQuaternion(); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + q = Quaternion.Euler(0, 0, 90); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(0, s.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(0, s.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(90, s.twist.inDegrees, 0.01f); + r = s.ToQuaternion(); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + q = Quaternion.Euler(0, 180, 0); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(-180, s.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(0, s.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(0, s.twist.inDegrees, 0.01f); + r = s.ToQuaternion(); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + q = Quaternion.Euler(0, 135, 0); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(135, s.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(0, s.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(0, s.twist.inDegrees, 0.01f); + r = s.ToQuaternion(); + Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + q = Quaternion.Euler(60, 45, 30); + s = SwingTwist.FromQuaternion(q); + Assert.AreEqual(45, s.swing.horizontal.inDegrees, 0.01f); + Assert.AreEqual(60, s.swing.vertical.inDegrees, 0.01f); + Assert.AreEqual(30, s.twist.inDegrees, 0.01f); + // r = s.ToQuaternion(); + // Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + // q = Quaternion.Euler(-45, -30, -15); + // s = SwingTwist.FromQuaternion(q); + // Assert.AreEqual(-30, s.swing.horizontal.inDegrees, 0.01f); + // Assert.AreEqual(-45, s.swing.vertical.inDegrees, 0.01f); + // Assert.AreEqual(-15, s.twist.inDegrees, 0.01f); + // r = s.ToQuaternion(); + // Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + // q = Quaternion.Euler(180, 180, 180); + // s = SwingTwist.FromQuaternion(q); + // Assert.AreEqual(-180, s.swing.horizontal.inDegrees, 0.01f); + // Assert.AreEqual(-180, s.swing.vertical.inDegrees, 0.01f); + // Assert.AreEqual(-180, s.twist.inDegrees, 0.01f); + // r = s.ToQuaternion(); + // Assert.AreEqual(0, Quaternion.UnsignedAngle(q, r), 10e-2f); + + } + + [Test] + public void ToAngleAxis_ConvertsToSpherical() { + SwingTwist st = SwingTwist.Degrees(45, 30, 15); + Spherical s = st.ToAngleAxis(); + Assert.IsNotNull(s); + } + + [Test] + public void FromAngleAxis_ConvertsFromSpherical() { + Spherical s = new(90, Direction.Degrees(45, 0)); + SwingTwist st = SwingTwist.FromAngleAxis(s); + Assert.IsNotNull(st); + } + + } + +} + +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/Vector2FloatTest.cs b/Assets/NanoBrain/LinearAlgebra/test/Vector2FloatTest.cs new file mode 100644 index 0000000..867765a --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/Vector2FloatTest.cs @@ -0,0 +1,364 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + using Vector2 = Vector2Float; + + public class Vector2FloatTest { + + [SetUp] + public void Setup() { + } + + [Test] + public void FromPolar() { + } + + [Test] + public void Equality() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + + Assert.IsFalse(v1 == v2, "4 5 == 1 2"); + Assert.IsTrue(v1 != v2, "4 5 != 1 2"); + + v2 = new(4, 5); + Assert.IsTrue(v1 == v2, "4 5 == 4 5"); + Assert.IsFalse(v1 != v2, "4 5 != 4 5"); + } + + [Test] + public void Magnitude() { + Vector2 v = new(1, 2); + float m = 0; + m = v.magnitude; + Assert.AreEqual(m, 2.236068F, "v.magnitude 1 2"); + + m = Vector2.MagnitudeOf(v); + Assert.AreEqual(m, 2.236068F, "MagnitudeOf 1 2"); + + v = new(-1, -2); + m = v.magnitude; + Assert.AreEqual(m, 2.236068F, "v.magnitude -1 -2"); + + v = new(0, 0); + m = v.magnitude; + Assert.AreEqual(m, 0, "v.magnitude 0 0"); + } + + [Test] + public void SqrMagnitude() { + Vector2 v = new(1, 2); + float m = 0; + + m = v.sqrMagnitude; + Assert.AreEqual(m, 5, "v.sqrMagnitude 1 2"); + + m = Vector2.SqrMagnitudeOf(v); + Assert.AreEqual(m, 5, "SqrMagnitudeOf 1 2"); + + v = new(-1, -2); + m = v.sqrMagnitude; + Assert.AreEqual(m, 5, "v.sqrMagnitude -1 -2"); + + v = new(0, 0); + m = v.sqrMagnitude; + Assert.AreEqual(m, 0, "v.sqrMagnitude 0 0"); + } + + [Test] + public void Distance() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + float f = 0; + + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 4.24264002f, 1.0E-05F, "Distance(4 5, 1 2)"); + + v2 = new(-1, -2); + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 8.602325F, "Distance(4 5, 1 2)"); + + v2 = new(0, 0); + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 6.403124F, 1.0E-05F, "Distance(4 5, 1 2)"); + } + + [Test] + public void Normalize() { + Vector2 v = new(0, 3); + Vector2Float r; + + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 3 H"); + Assert.AreEqual(1, r.vertical, "normalized 0 3 V"); + + r = Vector2.Normalize(v); + Assert.AreEqual(0, r.horizontal, "Normalize 0 3 H"); + Assert.AreEqual(1, r.vertical, "Normalize 0 3 V"); + + v = new(0, -3); + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 -3 H"); + Assert.AreEqual(-1, r.vertical, "normalized 0 -3 V"); + + v = new(0, 0); + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 0 H"); + Assert.AreEqual(0, r.vertical, "normalized 0 0 V"); + } + + [Test] + public void Negate() { + Vector2 v = new(4, 5); + Vector2 r; + + r = -v; + Assert.AreEqual(-4, r.horizontal, "- 4 5 H"); + Assert.AreEqual(-5, r.vertical, "- 4 5 V"); + + v = new(-4, -5); + r = -v; + Assert.AreEqual(4, r.horizontal, "- -4 -5 H"); + Assert.AreEqual(5, r.vertical, "- -4 -5 V"); + + v = new(0, 0); + r = -v; + Assert.AreEqual(0, r.horizontal, "- 0 0 H"); + Assert.AreEqual(0, r.vertical, "- 0 0 V"); + } + + [Test] + public void Subtract() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r = Vector2.zero; + + r = v1 - v2; + Assert.IsTrue(r == new Vector2(3, 3), "4 5 - 1 2"); + + v2 = new(-1, -2); + r = v1 - v2; + Assert.IsTrue(r == new Vector2(5, 7), "4 5 - -1 -2"); + + v2 = new(4, 5); + r = v1 - v2; + Assert.IsTrue(r == new Vector2(0, 0), "4 5 - 4 5"); + r = v1; + r -= v2; + Assert.AreEqual(r, new Vector2(0, 0), "4 5 - 4 5"); + + v2 = new(0, 0); + r = v1 - v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 - 0 0"); + r -= v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 - 0 0"); + } + + [Test] + public void Addition() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r = Vector2.zero; + + r = v1 + v2; + Assert.IsTrue(r == new Vector2(5, 7), "4 5 + 1 2"); + + v2 = new(-1, -2); + r = v1 + v2; + Assert.IsTrue(r == new Vector2(3, 3), "4 5 + -1 -2"); + r = v1; + r += v2; + Assert.AreEqual(r, new Vector2(3, 3), "4 5 + -1 -2"); + + v2 = new(0, 0); + r = v1 + v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 + 0 0"); + r += v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 + 0 0"); + } + + [Test] + public void Scale() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r; + + r = Vector2.Scale(v1, v2); + Assert.AreEqual(4, r.horizontal, "Scale 4 5 , 1 2 H"); + Assert.AreEqual(10, r.vertical, "Scale 4 5 , 1 2 V"); + + v2 = new(-1, -2); + r = Vector2.Scale(v1, v2); + Assert.AreEqual(-4, r.horizontal, "Scale 4 5 , -1 -2 H"); + Assert.AreEqual(-10, r.vertical, "Scale 4 5 , -1 -2 V"); + + v2 = new(0, 0); + r = Vector2.Scale(v1, v2); + Assert.AreEqual(0, r.horizontal, "Scale 4 5 , 0 0 H"); + Assert.AreEqual(0, r.vertical, "Scale 4 5 , 0 0 V"); + } + + [Test] + public void Multiply() { + Vector2 v1 = new(4, 5); + int f = 3; + Vector2 r; + + r = v1 * f; + Assert.AreEqual(12, r.horizontal, "4 5 * 3 H"); + Assert.AreEqual(15, r.vertical, "4 5 * 3 V"); + + r = f * v1; + Assert.AreEqual(12, r.horizontal, "3 * 4 5 H"); + Assert.AreEqual(15, r.vertical, "3 * 4 5 V"); + + f = -3; + r = v1 * f; + Assert.AreEqual(-12, r.horizontal, "4 5 * -3 H"); + Assert.AreEqual(-15, r.vertical, "4 5 * -3 V"); + + f = 0; + r = v1 * f; + Assert.AreEqual(0, r.horizontal, "4 5 * 0 H"); + Assert.AreEqual(0, r.vertical, "4 5 * 0 V"); + } + + [Test] + public void Divide() { + Vector2 v1 = new(4, 5); + float f = 2; + Vector2 r; + + r = v1 / f; + Assert.AreEqual(2, r.horizontal, "4 5 / 2 H"); + Assert.AreEqual(2.5, r.vertical, "4 5 / 2 V"); + + f = -2; + r = v1 / f; + Assert.AreEqual(-2, r.horizontal, "4 5 / -2 H"); + Assert.AreEqual(-2.5, r.vertical, "4 5 / -2 V"); + + f = 0; + r = v1 / f; + Assert.AreEqual(float.PositiveInfinity, r.horizontal, "4 5 / 0 H"); + Assert.AreEqual(float.PositiveInfinity, r.vertical, "4 5 / 0 V"); + } + + [Test] + public void Dot() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + float f; + + f = Vector2.Dot(v1, v2); + Assert.AreEqual(14, f, "Dot(4 5, 1 2)"); + + v2 = new(-1, -2); + f = Vector2.Dot(v1, v2); + Assert.AreEqual(-14, f, "Dot(4 5, -1 -2)"); + + v2 = new(0, 0); + f = Vector2.Dot(v1, v2); + Assert.AreEqual(0, f, "Dot(4 5, 0 0)"); + } + + [Test] + public void SignedAngle() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + float f; + + f = Vector2.SignedAngle(v1, v2); + Assert.AreEqual(-12.094758f, f); + + v2 = new(-1, -2); + f = Vector2.SignedAngle(v1, v2); + Assert.AreEqual(167.905228f, f); + + v2 = new(0, 0); + f = Vector2.SignedAngle(v1, v2); + Assert.AreEqual(0, f); + + v1 = new(0, 1); + v2 = new(1, 0); + f = Vector2.SignedAngle(v1, v2); + Assert.AreEqual(90, f); + + v1 = new(0, 1); + v2 = new(0, -1); + f = Vector2.SignedAngle(v1, v2); + Assert.AreEqual(180, f); + } + + [Test] + public void UnsignedAngle() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + float f; + + f = Vector2.UnsignedAngle(v1, v2); + Assert.AreEqual(12.094758f, f); + + v2 = new(-1, -2); + f = Vector2.UnsignedAngle(v1, v2); + Assert.AreEqual(167.905228f, f); + + v2 = new(0, 0); + f = Vector2.UnsignedAngle(v1, v2); + Assert.AreEqual(0, f); + + v1 = new(0, 1); + v2 = new(1, 0); + f = Vector2.UnsignedAngle(v1, v2); + Assert.AreEqual(90, f); + + v1 = new(0, 1); + v2 = new(0, -1); + f = Vector2.UnsignedAngle(v1, v2); + Assert.AreEqual(180, f); + } + + [Test] + public void Rotate() { + Vector2 v1 = new(1, 2); + Vector2 r; + + r = Vector2.Rotate(v1, AngleFloat.Degrees(0)); + Assert.AreEqual(0, Vector2.Distance(r, v1)); + + r = Vector2.Rotate(v1, AngleFloat.Degrees(180)); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(-1, -2)), 1.0e-06); + + r = Vector2.Rotate(v1, AngleFloat.Degrees(-90)); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(2, -1)), 1.0e-06); + + r = Vector2.Rotate(v1, AngleFloat.Degrees(270)); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(2, -1)), 1.0e-06); + } + + [Test] + public void Lerp() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r; + + r = Vector2.Lerp(v1, v2, 0); + Assert.AreEqual(0, Vector2.Distance(r, v1), 0); + + r = Vector2.Lerp(v1, v2, 1); + Assert.AreEqual(0, Vector2.Distance(r, v2), 0); + + r = Vector2.Lerp(v1, v2, 0.5f); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(2.5f, 3.5f)), 0); + + r = Vector2.Lerp(v1, v2, -1); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(7, 8)), 0); + + r = Vector2.Lerp(v1, v2, 2); + Assert.AreEqual(0, Vector2.Distance(r, new Vector2(-2, -1)), 0); + } + + } +} +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/Vector2IntTest.cs b/Assets/NanoBrain/LinearAlgebra/test/Vector2IntTest.cs new file mode 100644 index 0000000..3647ca0 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/Vector2IntTest.cs @@ -0,0 +1,270 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + using Vector2 = Vector2Int; + + public class Vector2IntTest { + + [SetUp] + public void Setup() { + } + + [Test] + public void FromPolar() { + } + + [Test] + public void Equality() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + + Assert.IsFalse(v1 == v2, "4 5 == 1 2"); + Assert.IsTrue(v1 != v2, "4 5 != 1 2"); + + v2 = new(4, 5); + Assert.IsTrue(v1 == v2, "4 5 == 4 5"); + Assert.IsFalse(v1 != v2, "4 5 != 4 5"); + } + + [Test] + public void Magnitude() { + Vector2 v = new(1, 2); + float m = 0; + m = v.magnitude; + Assert.AreEqual(m, 2.236068F, "v.magnitude 1 2"); + + m = Vector2.MagnitudeOf(v); + Assert.AreEqual(m, 2.236068F, "MagnitudeOf 1 2"); + + v = new(-1, -2); + m = v.magnitude; + Assert.AreEqual(m, 2.236068F, "v.magnitude -1 -2"); + + v = new(0, 0); + m = v.magnitude; + Assert.AreEqual(m, 0, "v.magnitude 0 0"); + } + + [Test] + public void SqrMagnitude() { + Vector2 v = new(1, 2); + float m = 0; + + m = v.sqrMagnitude; + Assert.AreEqual(m, 5, "v.sqrMagnitude 1 2"); + + m = Vector2.SqrMagnitudeOf(v); + Assert.AreEqual(m, 5, "SqrMagnitudeOf 1 2"); + + v = new(-1, -2); + m = v.sqrMagnitude; + Assert.AreEqual(m, 5, "v.sqrMagnitude -1 -2"); + + v = new(0, 0); + m = v.sqrMagnitude; + Assert.AreEqual(m, 0, "v.sqrMagnitude 0 0"); + } + + [Test] + public void Distance() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + float f = 0; + + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 4.24264002f, 1.0E-05F, "Distance(4 5, 1 2)"); + + v2 = new(-1, -2); + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 8.602325F, "Distance(4 5, 1 2)"); + + v2 = new(0, 0); + f = Vector2.Distance(v1, v2); + Assert.AreEqual(f, 6.403124F, 1.0E-05F, "Distance(4 5, 1 2)"); + } + + [Test] + public void Normalize() { + Vector2 v = new(0, 3); + Vector2Float r; + + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 3 H"); + Assert.AreEqual(1, r.vertical, "normalized 0 3 V"); + + r = Vector2.Normalize(v); + Assert.AreEqual(0, r.horizontal, "Normalize 0 3 H"); + Assert.AreEqual(1, r.vertical, "Normalize 0 3 V"); + + v = new(0, -3); + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 -3 H"); + Assert.AreEqual(-1, r.vertical, "normalized 0 -3 V"); + + v = new(0, 0); + r = v.normalized; + Assert.AreEqual(0, r.horizontal, "normalized 0 0 H"); + Assert.AreEqual(0, r.vertical, "normalized 0 0 V"); + } + + [Test] + public void Negate() { + Vector2 v = new(4, 5); + Vector2 r; + + r = -v; + Assert.AreEqual(-4, r.horizontal, "- 4 5 H"); + Assert.AreEqual(-5, r.vertical, "- 4 5 V"); + + v = new(-4, -5); + r = -v; + Assert.AreEqual(4, r.horizontal, "- -4 -5 H"); + Assert.AreEqual(5, r.vertical, "- -4 -5 V"); + + v = new(0, 0); + r = -v; + Assert.AreEqual(0, r.horizontal, "- 0 0 H"); + Assert.AreEqual(0, r.vertical, "- 0 0 V"); + } + + [Test] + public void Subtract() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r = Vector2.zero; + + r = v1 - v2; + Assert.IsTrue(r == new Vector2(3, 3), "4 5 - 1 2"); + + v2 = new(-1, -2); + r = v1 - v2; + Assert.IsTrue(r == new Vector2(5, 7), "4 5 - -1 -2"); + + v2 = new(4, 5); + r = v1 - v2; + Assert.IsTrue(r == new Vector2(0, 0), "4 5 - 4 5"); + r = v1; + r -= v2; + Assert.AreEqual(r, new Vector2(0, 0), "4 5 - 4 5"); + + v2 = new(0, 0); + r = v1 - v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 - 0 0"); + r -= v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 - 0 0"); + } + + [Test] + public void Addition() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r = Vector2.zero; + + r = v1 + v2; + Assert.IsTrue(r == new Vector2(5, 7), "4 5 + 1 2"); + + v2 = new(-1, -2); + r = v1 + v2; + Assert.IsTrue(r == new Vector2(3, 3), "4 5 + -1 -2"); + r = v1; + r += v2; + Assert.AreEqual(r, new Vector2(3, 3), "4 5 + -1 -2"); + + v2 = new(0, 0); + r = v1 + v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 + 0 0"); + r += v2; + Assert.AreEqual(r, new Vector2(4, 5), "4 5 + 0 0"); + } + + [Test] + public void Scale() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + Vector2 r; + + r = Vector2.Scale(v1, v2); + Assert.AreEqual(4, r.horizontal, "Scale 4 5 , 1 2 H"); + Assert.AreEqual(10, r.vertical, "Scale 4 5 , 1 2 V"); + + v2 = new(-1, -2); + r = Vector2.Scale(v1, v2); + Assert.AreEqual(-4, r.horizontal, "Scale 4 5 , -1 -2 H"); + Assert.AreEqual(-10, r.vertical, "Scale 4 5 , -1 -2 V"); + + v2 = new(0, 0); + r = Vector2.Scale(v1, v2); + Assert.AreEqual(0, r.horizontal, "Scale 4 5 , 0 0 H"); + Assert.AreEqual(0, r.vertical, "Scale 4 5 , 0 0 V"); + } + + [Test] + public void Multiply() { + Vector2 v1 = new(4, 5); + int f = 3; + Vector2 r; + + r = v1 * f; + Assert.AreEqual(12, r.horizontal, "4 5 * 3 H"); + Assert.AreEqual(15, r.vertical, "4 5 * 3 V"); + + r = f * v1; + Assert.AreEqual(12, r.horizontal, "3 * 4 5 H"); + Assert.AreEqual(15, r.vertical, "3 * 4 5 V"); + + f = -3; + r = v1 * f; + Assert.AreEqual(-12, r.horizontal, "4 5 * -3 H"); + Assert.AreEqual(-15, r.vertical, "4 5 * -3 V"); + + f = 0; + r = v1 * f; + Assert.AreEqual(0, r.horizontal, "4 5 * 0 H"); + Assert.AreEqual(0, r.vertical, "4 5 * 0 V"); + } + + [Test] + public void Divide() { + Vector2 v1 = new(4, 5); + int f = 2; + Vector2 r; + + r = v1 / f; + Assert.AreEqual(2, r.horizontal, "4 5 / 2 H"); + Assert.AreEqual(2, r.vertical, "4 5 / 2 V"); + + f = -2; + r = v1 / f; + Assert.AreEqual(-2, r.horizontal, "4 5 / -2 H"); + Assert.AreEqual(-2, r.vertical, "4 5 / -2 V"); + + Assert.Throws(() => { + f = 0; + r = v1 / f; + Assert.AreEqual(float.PositiveInfinity, r.horizontal, "4 5 / 0 H"); + Assert.AreEqual(float.PositiveInfinity, r.vertical, "4 5 / 0 V"); + }); + } + + [Test] + public void Dot() { + Vector2 v1 = new(4, 5); + Vector2 v2 = new(1, 2); + int f; + + f = Vector2.Dot(v1, v2); + Assert.AreEqual(14, f, "Dot(4 5, 1 2)"); + + v2 = new(-1, -2); + f = Vector2.Dot(v1, v2); + Assert.AreEqual(-14, f, "Dot(4 5, -1 -2)"); + + v2 = new(0, 0); + f = Vector2.Dot(v1, v2); + Assert.AreEqual(0, f, "Dot(4 5, 0 0)"); + } + + } +} +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/Vector3FloatTest.cs b/Assets/NanoBrain/LinearAlgebra/test/Vector3FloatTest.cs new file mode 100644 index 0000000..fd3c2dc --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/Vector3FloatTest.cs @@ -0,0 +1,581 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + using Vector3 = Vector3Float; + + public class Vector3FloatTest { + + [Test] + public void FromSpherical() { + Vector3 v = new(0, 0, 1); + Spherical s = Spherical.FromVector3(v); + Vector3 r = Vector3.FromSpherical(s); + + Assert.AreEqual(0, r.horizontal, "0 0 1"); + Assert.AreEqual(0, r.vertical, 1.0e-06, "0 0 1"); + Assert.AreEqual(1, r.depth, "0 0 1"); + + v = new(0, 1, 0); + s = Spherical.FromVector3(v); + r = Vector3.FromSpherical(s); + Assert.AreEqual(0, r.horizontal, "0 0 1"); + Assert.AreEqual(1, r.vertical, "0 0 1"); + Assert.AreEqual(0, r.depth, 1.0e-06, "0 0 1"); + + v = new(1, 0, 0); + s = Spherical.FromVector3(v); + r = Vector3.FromSpherical(s); + Assert.AreEqual(1, r.horizontal, "0 0 1"); + Assert.AreEqual(0, r.vertical, 1.0e-06, "0 0 1"); + Assert.AreEqual(0, r.depth, 1.0e-06, "0 0 1"); + } + + [Test] + public void Magnitude() { + Vector3 v = new(1, 2, 3); + float m = 0; + + m = v.magnitude; + Assert.AreEqual(3.7416575f, m, "magnitude 1 2 3"); + + m = Vector3.MagnitudeOf(v); + Assert.AreEqual(3.7416575f, m, "MagnitudeOf 1 2 3"); + + v = new(-1, -2, -3); + m = v.magnitude; + Assert.AreEqual(3.7416575f, m, "magnitude -1 -2 -3"); + + v = new(0, 0, 0); + m = v.magnitude; + Assert.AreEqual(0, m, "magnitude 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void SqrMagnitude() { + Vector3 v = new(1, 2, 3); + float m = 0; + + m = v.sqrMagnitude; + Assert.AreEqual(14, m, "sqrMagnitude 1 2 3"); + + m = Vector3.SqrMagnitudeOf(v); + Assert.AreEqual(14, m, "SqrMagnitudeOf 1 2 3"); + + v = new(-1, -2, -3); + m = v.sqrMagnitude; + Assert.AreEqual(14, m, "sqrMagnitude -1 -2 -3"); + + v = new(0, 0, 0); + m = v.sqrMagnitude; + Assert.AreEqual(0, m, "sqrMagnitude 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Normalize() { + Vector3 v = new(0, 2, 0); + Vector3 r; + + r = v.normalized; + Assert.AreEqual(new Vector3(0, 1, 0), r, "normalized 0 2 0"); + + r = Vector3.Normalize(v); + Assert.AreEqual(new Vector3(0, 1, 0), r, "Normalize 0 2 0"); + + v = new(0, -2, 0); + r = v.normalized; + Assert.AreEqual(new Vector3(0, -1, 0), r, "normalized 0 -2 0"); + v = new(0, 0, 0); + r = v.normalized; + Assert.AreEqual(new Vector3(0, 0, 0), r, "normalized 0 0 0"); + + v = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = v.normalized; + Assert.IsTrue(float.IsNaN(r.horizontal), "normalized infinity infinity infinity"); + Assert.IsTrue(float.IsNaN(r.vertical), "normalized infinity infinity infinity"); + Assert.IsTrue(float.IsNaN(r.depth), "normalized infinity infinity infinity"); + + v = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = v.normalized; + Assert.IsTrue(float.IsNaN(r.horizontal), "normalized -infinity -infinity -infinity"); + Assert.IsTrue(float.IsNaN(r.vertical), "normalized -infinity -infinity -infinity"); + Assert.IsTrue(float.IsNaN(r.depth), "normalized -infinity -infinity -infinity"); + } + + [Test] + public void Negate() { + Vector3 v = new(4, 5, 6); + Vector3 r; + + r = -v; + Assert.AreEqual(-4, r.horizontal, "- 4 5 6 H"); + Assert.AreEqual(-5, r.vertical, "- 4 5 6 V"); + Assert.AreEqual(-6, r.depth, "- 4 5 6 D"); + + v = new(-4, -5, -6); + r = -v; + Assert.AreEqual(4, r.horizontal, "- -4 -5 -6 H"); + Assert.AreEqual(5, r.vertical, "- -4 -5 -6 V"); + Assert.AreEqual(6, r.depth, "- -4 -5 -6 D"); + + v = new(0, 0, 0); + r = -v; + Assert.AreEqual(new Vector3(0, 0, 0), r, "- 0 0 0"); + Assert.AreEqual(0, r.horizontal, "- 0 0 0 H"); + Assert.AreEqual(0, r.vertical, "- 0 0 0 V"); + Assert.AreEqual(0, r.depth, "- 0 0 0 D"); + + + v = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = -v; + Assert.AreEqual(new Vector3(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity), r, "- inifinty infinity infinity"); + + v = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = -v; + Assert.AreEqual(new Vector3(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity), r, "- -inifinty -infinity -infinity"); + } + + [Test] + public void Subtract() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r = Vector3.zero; + + r = v1 - v2; + Assert.IsTrue(r == new Vector3(3, 3, 3), "4 5 6 - 1 2 3"); + + v2 = new(-1, -2, -3); + r = v1 - v2; + Assert.IsTrue(r == new Vector3(5, 7, 9), "4 5 6 - -1 -2 -3"); + + v2 = new(4, 5, 6); + r = v1 - v2; + Assert.IsTrue(r == new Vector3(0, 0, 0), "4 5 6 - 4 5 6"); + r = v1; + r -= v2; + Assert.AreEqual(r, new Vector3(0, 0, 0), "4 5 6 - 4 5 6"); + + v2 = new(0, 0, 0); + r = v1 - v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 - 0 0 0"); + r -= v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 - 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Addition() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r = Vector3.zero; + + r = v1 + v2; + Assert.IsTrue(r == new Vector3(5, 7, 9), "4 5 6 + 1 2 3"); + + v2 = new(-1, -2, -3); + r = v1 + v2; + Assert.IsTrue(r == new Vector3(3, 3, 3), "4 5 6 + -1 -2 -3"); + r = v1; + r += v2; + Assert.AreEqual(r, new Vector3(3, 3, 3), "4 5 6 + -1 -2 -3"); + + v2 = new(0, 0, 0); + r = v1 + v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 + 0 0 0"); + r += v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 + 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Scale() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Scale(v1, v2); + Assert.AreEqual(4, r.horizontal, "Scale 4 5 6 , 1 2 3 H"); + Assert.AreEqual(10, r.vertical, "Scale 4 5 6 , 1 2 3 V"); + Assert.AreEqual(18, r.depth, "Scale 4 5 6 , 1 2 3 D"); + + v2 = new(-1, -2, -3); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(-4, r.horizontal, "Scale 4 5 6 , -1 -2 -3 H"); + Assert.AreEqual(-10, r.vertical, "Scale 4 5 6 , -1 -2 -3 V"); + Assert.AreEqual(-18, r.depth, "Scale 4 5 6 , -1 -2 -3 D"); + + v2 = new(0, 0, 0); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(0, r.horizontal, "Scale 4 5 6 , 0 0 0 H"); + Assert.AreEqual(0, r.vertical, "Scale 4 5 6 , 0 0 0 V"); + Assert.AreEqual(0, r.depth, "Scale 4 5 6 , 0 0 0 D"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(float.PositiveInfinity, r.horizontal, "Scale 4 5 6 , inf inf inf H"); + Assert.AreEqual(float.PositiveInfinity, r.vertical, "Scale 4 5 6 , inf inf inf V"); + Assert.AreEqual(float.PositiveInfinity, r.depth, "Scale 4 5 6 , inf inf inf D"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(float.NegativeInfinity, r.horizontal, "Scale 4 5 6 , -inf -inf -inf H"); + Assert.AreEqual(float.NegativeInfinity, r.vertical, "Scale 4 5 6 , -inf -inf -inf V"); + Assert.AreEqual(float.NegativeInfinity, r.depth, "Scale 4 5 6 , -inf -inf -inf D"); + } + + [Test] + public void Multiply() { + Vector3 v1 = new(4, 5, 6); + float f = 3; + Vector3 r; + + r = v1 * f; + Assert.AreEqual(12, r.horizontal, "4 5 6 * 3 H"); + Assert.AreEqual(15, r.vertical, "4 5 6 * 3 V"); + Assert.AreEqual(18, r.depth, "4 5 6 * 3 D"); + + f = -3; + r = v1 * f; + Assert.AreEqual(-12, r.horizontal, "4 5 6 * -3 H"); + Assert.AreEqual(-15, r.vertical, "4 5 6 * -3 V"); + Assert.AreEqual(-18, r.depth, "4 5 6 * -3 D"); + + f = 0; + r = v1 * f; + Assert.AreEqual(0, r.horizontal, "4 5 6 * 0 H"); + Assert.AreEqual(0, r.vertical, "4 5 6 * 0 V"); + Assert.AreEqual(0, r.depth, "4 5 6 * 0 D"); + + f = float.PositiveInfinity; + r = v1 * f; + Assert.AreEqual(float.PositiveInfinity, r.horizontal, "4 5 6 * inf H"); + Assert.AreEqual(float.PositiveInfinity, r.vertical, "4 5 6 * inf V"); + Assert.AreEqual(float.PositiveInfinity, r.depth, "4 5 6 * inf D"); + + f = float.NegativeInfinity; + r = v1 * f; + Assert.AreEqual(float.NegativeInfinity, r.horizontal, "4 5 6 * -inf H"); + Assert.AreEqual(float.NegativeInfinity, r.vertical, "4 5 6 * -inf V"); + Assert.AreEqual(float.NegativeInfinity, r.depth, "4 5 6 * -inf D"); + } + + [Test] + public void Divide() { + Vector3 v1 = new(4, 5, 6); + float f = 2; + Vector3 r; + + r = v1 / f; + Assert.AreEqual(2, r.horizontal, "4 5 6 / 2 H"); + Assert.AreEqual(2.5, r.vertical, "4 5 6 / 2 V"); + Assert.AreEqual(3, r.depth, "4 5 6 / 2 D"); + + f = -2; + r = v1 / f; + Assert.AreEqual(-2, r.horizontal, "4 5 6 / -2 H"); + Assert.AreEqual(-2.5, r.vertical, "4 5 6 / -2 V"); + Assert.AreEqual(-3, r.depth, "4 5 6 / -2 D"); + + f = 0; + r = v1 / f; + Assert.AreEqual(float.PositiveInfinity, r.horizontal, "4 5 6 / 0 H"); + Assert.AreEqual(float.PositiveInfinity, r.vertical, "4 5 6 / 0 V"); + Assert.AreEqual(float.PositiveInfinity, r.depth, "4 5 6 / 0 D"); + + f = float.PositiveInfinity; + r = v1 / f; + Assert.AreEqual(0, r.horizontal, "4 5 6 / inf H"); + Assert.AreEqual(0, r.vertical, "4 5 6 / inf V"); + Assert.AreEqual(0, r.depth, "4 5 6 / inf D"); + + f = float.NegativeInfinity; + r = v1 / f; + Assert.AreEqual(0, r.horizontal, "4 5 6 / -inf H"); + Assert.AreEqual(0, r.vertical, "4 5 6 / -inf V"); + Assert.AreEqual(0, r.depth, "4 5 6 / -inf D"); + } + + [Test] + public void Dot() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + float f; + + f = Vector3.Dot(v1, v2); + Assert.AreEqual(32, f, "Dot(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(-32, f, "Dot(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(0, f, "Dot(4 5 6, 0 0 0)"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(float.PositiveInfinity, f, "Dot(4 5 6, inf inf inf)"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(float.NegativeInfinity, f, "Dot(4 5 6, -inf -inf -inf)"); + } + + [Test] + public void Equality() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + bool r; + + r = v1 == v2; + Assert.IsFalse(r, "4 5 6 == 1 2 3"); + + v2 = new(4, 5, 6); + r = v1 == v2; + Assert.IsTrue(r, "4 5 6 == 4 5 6"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = v1 == v2; + Assert.IsFalse(r, "4 5 6 == inf inf inf"); + + v1 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = v1 == v2; + Assert.IsFalse(r, "-inf -inf -inf == inf inf inf"); + } + + [Test] + public void Distance() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + float f; + + f = Vector3.Distance(v1, v2); + Assert.AreEqual(5.19615221F, f, "Distance(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(12.4498997F, f, "Distance(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(v1.magnitude, f, "Distance(4 5 6, 0 0 0)"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(float.PositiveInfinity, f, "Distance(4 5 6, inf inf inf)"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(float.PositiveInfinity, f, "Distance(4 5 6, -inf -inf -inf)"); + } + + [Test] + public void Cross() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Cross(v1, v2); + Assert.AreEqual(3, r.horizontal, "Cross(4 5 6, 1 2 3) H"); + Assert.AreEqual(-6, r.vertical, "Cross(4 5 6, 1 2 3) V"); + Assert.AreEqual(3, r.depth, "Cross(4 5 6, 1 2 3) D"); + + v2 = new(-1, -2, -3); + r = Vector3.Cross(v1, v2); + Assert.AreEqual(-3, r.horizontal, "Cross(4 5 6, -1 -2 -3) H"); + Assert.AreEqual(6, r.vertical, "Cross(4 5 6, -1 -2 -3) V"); + Assert.AreEqual(-3, r.depth, "Cross(4 5 6, -1 -2 -3) D"); + + v2 = new(0, 0, 0); + r = Vector3.Cross(v1, v2); + Assert.AreEqual(0, r.horizontal, "Cross(4 5 6, 0 0 0) H"); + Assert.AreEqual(0, r.vertical, "Cross(4 5 6, 0 0 0) V"); + Assert.AreEqual(0, r.depth, "Cross(4 5 6, 0 0 0) D"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = Vector3.Cross(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "Cross(4 5 6, inf inf inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "Cross(4 5 6, inf inf inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "Cross(4 5 6, inf inf inf) D"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = Vector3.Cross(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "Cross(4 5 6, -inf -inf -inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "Cross(4 5 6, -inf -inf -inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "Cross(4 5 6, -inf -inf -inf) D"); + } + + [Test] + public void Project() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Project(v1, v2); + Assert.AreEqual(2.28571439F, r.horizontal, "Project(4 5 6, 1 2 3) H"); + Assert.AreEqual(4.57142878F, r.vertical, "Project(4 5 6, 1 2 3) V"); + Assert.AreEqual(6.85714293F, r.depth, "Project(4 5 6, 1 2 3) D"); + + v2 = new(-1, -2, -3); + r = Vector3.Project(v1, v2); + Assert.AreEqual(2.28571439F, r.horizontal, "Project(4 5 6, -1 -2 -3) H"); + Assert.AreEqual(4.57142878F, r.vertical, "Project(4 5 6, -1 -2 -3) V"); + Assert.AreEqual(6.85714293F, r.depth, "Project(4 5 6, -1 -2 -3) D"); + + v2 = new(0, 0, 0); + r = Vector3.Project(v1, v2); + Assert.AreEqual(0, r.horizontal, "Project(4 5 6, 0 0 0) H"); + Assert.AreEqual(0, r.vertical, "Project(4 5 6, 0 0 0) V"); + Assert.AreEqual(0, r.depth, "Project(4 5 6, 0 0 0) D"); + + r = Vector3.Project(v2, v1); + Assert.AreEqual(0, r.horizontal, "Project(0 0 0, 4 5 6) H"); + Assert.AreEqual(0, r.vertical, "Project(0 0 0, 4 5 6) V"); + Assert.AreEqual(0, r.depth, "Project(0 0 0, 4 5 6) D"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = Vector3.Project(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "Project(4 5 6, inf inf inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "Project(4 5 6, inf inf inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "Project(4 5 6, inf inf inf) D"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = Vector3.Project(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "Project(4 5 6, -inf -inf -inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "Project(4 5 6, -inf -inf -inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "Project(4 5 6, -inf -inf -inf) D"); + } + + [Test] + public void ProjectOnPlane() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.ProjectOnPlane(v1, v2); + Assert.AreEqual(1.71428561F, r.horizontal, "ProjectOnPlane(4 5 6, 1 2 3) H"); + Assert.AreEqual(0.428571224F, r.vertical, "ProjectOnPlane(4 5 6, 1 2 3) V"); + Assert.AreEqual(-0.857142925F, r.depth, "ProjectOnPlane(4 5 6, 1 2 3) D"); + + v2 = new(-1, -2, -3); + r = Vector3.ProjectOnPlane(v1, v2); + Assert.AreEqual(1.71428561F, r.horizontal, "ProjectOnPlane(4 5 6, -1 -2 -3) H"); + Assert.AreEqual(0.428571224F, r.vertical, "ProjectOnPlane(4 5 6, -1 -2 -3) V"); + Assert.AreEqual(-0.857142925F, r.depth, "ProjectOnPlane(4 5 6, -1 -2 -3) D"); + + v2 = new(0, 0, 0); + r = Vector3.ProjectOnPlane(v1, v2); + Assert.AreEqual(4, r.horizontal, "ProjectOnPlane(4 5 6, 0 0 0) H"); + Assert.AreEqual(5, r.vertical, "ProjectOnPlane(4 5 6, 0 0 0) V"); + Assert.AreEqual(6, r.depth, "ProjectOnPlane(4 5 6, 0 0 0) D"); + + r = Vector3.ProjectOnPlane(v2, v1); + Assert.AreEqual(0, r.horizontal, "ProjectOnPlane(0 0 0, 4 5 6) H"); + Assert.AreEqual(0, r.vertical, "ProjectOnPlane(0 0 0, 4 5 6) V"); + Assert.AreEqual(0, r.depth, "ProjectOnPlane(0 0 0, 4 5 6) D"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + r = Vector3.ProjectOnPlane(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "ProjectOnPlane(4 5 6, inf inf inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "ProjectOnPlane(4 5 6, inf inf inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "ProjectOnPlane(4 5 6, inf inf inf) D"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + r = Vector3.ProjectOnPlane(v1, v2); + Assert.IsTrue(float.IsNaN(r.horizontal), "ProjectOnPlane(4 5 6, -inf -inf -inf) H"); + Assert.IsTrue(float.IsNaN(r.vertical), "ProjectOnPlane(4 5 6, -inf -inf -inf) V"); + Assert.IsTrue(float.IsNaN(r.depth), "ProjectOnPlane(4 5 6, -inf -inf -inf) D"); + } + + [Test] + public void UnsignedAngle() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + AngleFloat a; + + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(12.9331379F, a.inDegrees, "Angle(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(167.066849F, a.inDegrees, "Angle(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(0, a.inDegrees, "Angle(4 5 6, 0 0 0)"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + a = Vector3.UnsignedAngle(v1, v2); + Assert.IsTrue(float.IsNaN(a.inDegrees), "Angle(4 5 6, inf inf inf)"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + a = Vector3.UnsignedAngle(v1, v2); + Assert.IsTrue(float.IsNaN(a.inDegrees), "Angle(4 5 6, inf inf inf)"); + } + + [Test] + public void SignedAngle() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 v3 = new(7, 8, -9); + AngleFloat a; + + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(-12.9331379F, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, 7 8 -9)"); + + v2 = new(-1, -2, -3); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(167.066849F, a.inDegrees, "SignedAngle(4 5 6, -1 -2 -3, 7 8 -9)"); + + v2 = new(0, 0, 0); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(0, a.inDegrees, "SignedAngle(4 5 6, 0 0 0, 7 8 -9)"); + + v2 = new(1, 2, 3); + v3 = new(-7, -8, 9); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(12.9331379F, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, -7 -8 9)"); + + v3 = new(0, 0, 0); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(0, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, 0 0 0)"); + + v2 = new(float.PositiveInfinity, float.PositiveInfinity, float.PositiveInfinity); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.IsTrue(float.IsNaN(a.inDegrees), "SignedAngle(4 5 6, inf inf inf, 0 0 0)"); + + v2 = new(float.NegativeInfinity, float.NegativeInfinity, float.NegativeInfinity); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.IsTrue(float.IsNaN(a.inDegrees), "SignedAngle(4 5 6, -inf -inf -inf, 0 0 0)"); + } + + [Test] + public void Lerp() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Lerp(v1, v2, 0); + Assert.AreEqual(0, Vector3.Distance(r, v1), 0); + + r = Vector3.Lerp(v1, v2, 1); + Assert.AreEqual(0, Vector3.Distance(r, v2), 0); + + r = Vector3.Lerp(v1, v2, 0.5f); + Assert.AreEqual(0, Vector3.Distance(r, new Vector3(2.5f, 3.5f, 4.5f)), 0); + + r = Vector3.Lerp(v1, v2, -1); + Assert.AreEqual(0, Vector3.Distance(r, new Vector3(7, 8, 9)), 0); + + r = Vector3.Lerp(v1, v2, 2); + Assert.AreEqual(0, Vector3.Distance(r, new Vector3(-2, -1, 0)), 0); + } + } +} +#endif \ No newline at end of file diff --git a/Assets/NanoBrain/LinearAlgebra/test/Vector3IntTest.cs b/Assets/NanoBrain/LinearAlgebra/test/Vector3IntTest.cs new file mode 100644 index 0000000..b718178 --- /dev/null +++ b/Assets/NanoBrain/LinearAlgebra/test/Vector3IntTest.cs @@ -0,0 +1,349 @@ +#if !UNITY_5_6_OR_NEWER +using NUnit.Framework; + +namespace LinearAlgebra.Test { + using Vector3 = Vector3Int; + + public class Vector3IntTest { + + [Test] + public void Equality() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + + Assert.IsFalse(v1 == v2, "4 5 6 == 1 2 3"); + Assert.IsTrue(v1 != v2, "4 5 6 != 1 2 3"); + + v2 = new(4, 5, 6); + Assert.IsTrue(v1 == v2, "4 5 6 == 4 5 6"); + Assert.IsFalse(v1 != v2, "4 5 6 != 4 5 6"); + } + + [Test] + public void Magnitude() { + Vector3 v = new(1, 2, 3); + float m = 0; + + m = v.magnitude; + Assert.AreEqual(3.7416575f, m, "magnitude 1 2 3"); + + m = Vector3.MagnitudeOf(v); + Assert.AreEqual(3.7416575f, m, "MagnitudeOf 1 2 3"); + + v = new(-1, -2, -3); + m = v.magnitude; + Assert.AreEqual(3.7416575f, m, "magnitude -1 -2 -3"); + + v = new(0, 0, 0); + m = v.magnitude; + Assert.AreEqual(0, m, "magnitude 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void SqrMagnitude() { + Vector3 v = new(1, 2, 3); + float m = 0; + + m = v.sqrMagnitude; + Assert.AreEqual(14, m, "sqrMagnitude 1 2 3"); + + m = Vector3.SqrMagnitudeOf(v); + Assert.AreEqual(14, m, "SqrMagnitudeOf 1 2 3"); + + v = new(-1, -2, -3); + m = v.sqrMagnitude; + Assert.AreEqual(14, m, "sqrMagnitude -1 -2 -3"); + + v = new(0, 0, 0); + m = v.sqrMagnitude; + Assert.AreEqual(0, m, "sqrMagnitude 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Distance() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + float f; + + f = Vector3.Distance(v1, v2); + Assert.AreEqual(5.19615221F, f, "Distance(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(12.4498997F, f, "Distance(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + f = Vector3.Distance(v1, v2); + Assert.AreEqual(v1.magnitude, f, "Distance(4 5 6, 0 0 0)"); + } + + [Test] + public void Normalize() { + Vector3 v = new(0, 2, 0); + Vector3Float r; + + r = v.normalized; + //Assert.AreEqual(new Vector3(0, 1, 0), r, "normalized 0 2 0"); + Assert.AreEqual(0, r.horizontal, "normalized 0 2 0"); + Assert.AreEqual(1, r.vertical, "normalized 0 2 0"); + Assert.AreEqual(0, r.depth, "normalized 0 2 0"); + + r = Vector3.Normalize(v); + Assert.AreEqual(new Vector3Float(0, 1, 0), r, "Normalize 0 2 0"); + + v = new(0, -2, 0); + r = v.normalized; + Assert.AreEqual(new Vector3Float(0, -1, 0), r, "normalized 0 -2 0"); + v = new(0, 0, 0); + r = v.normalized; + Assert.AreEqual(new Vector3Float(0, 0, 0), r, "normalized 0 0 0"); + } + + [Test] + public void Negate() { + Vector3 v = new(4, 5, 6); + Vector3 r; + + r = -v; + Assert.AreEqual(-4, r.horizontal, "- 4 5 6 H"); + Assert.AreEqual(-5, r.vertical, "- 4 5 6 V"); + Assert.AreEqual(-6, r.depth, "- 4 5 6 D"); + + v = new(-4, -5, -6); + r = -v; + Assert.AreEqual(4, r.horizontal, "- -4 -5 -6 H"); + Assert.AreEqual(5, r.vertical, "- -4 -5 -6 V"); + Assert.AreEqual(6, r.depth, "- -4 -5 -6 D"); + + v = new(0, 0, 0); + r = -v; + Assert.AreEqual(new Vector3(0, 0, 0), r, "- 0 0 0"); + Assert.AreEqual(0, r.horizontal, "- 0 0 0 H"); + Assert.AreEqual(0, r.vertical, "- 0 0 0 V"); + Assert.AreEqual(0, r.depth, "- 0 0 0 D"); + } + + [Test] + public void Subtract() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r = Vector3.zero; + + r = v1 - v2; + Assert.IsTrue(r == new Vector3(3, 3, 3), "4 5 6 - 1 2 3"); + + v2 = new(-1, -2, -3); + r = v1 - v2; + Assert.IsTrue(r == new Vector3(5, 7, 9), "4 5 6 - -1 -2 -3"); + + v2 = new(4, 5, 6); + r = v1 - v2; + Assert.IsTrue(r == new Vector3(0, 0, 0), "4 5 6 - 4 5 6"); + r = v1; + r -= v2; + Assert.AreEqual(r, new Vector3(0, 0, 0), "4 5 6 - 4 5 6"); + + v2 = new(0, 0, 0); + r = v1 - v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 - 0 0 0"); + r -= v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 - 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Addition() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r = Vector3.zero; + + r = v1 + v2; + Assert.IsTrue(r == new Vector3(5, 7, 9), "4 5 6 + 1 2 3"); + + v2 = new(-1, -2, -3); + r = v1 + v2; + Assert.IsTrue(r == new Vector3(3, 3, 3), "4 5 6 + -1 -2 -3"); + r = v1; + r += v2; + Assert.AreEqual(r, new Vector3(3, 3, 3), "4 5 6 + -1 -2 -3"); + + v2 = new(0, 0, 0); + r = v1 + v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 + 0 0 0"); + r += v2; + Assert.AreEqual(r, new Vector3(4, 5, 6), "4 5 6 + 0 0 0"); + + // Infinity tests are still missing + } + + [Test] + public void Scale() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Scale(v1, v2); + Assert.AreEqual(4, r.horizontal, "Scale 4 5 6 , 1 2 3 H"); + Assert.AreEqual(10, r.vertical, "Scale 4 5 6 , 1 2 3 V"); + Assert.AreEqual(18, r.depth, "Scale 4 5 6 , 1 2 3 D"); + + v2 = new(-1, -2, -3); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(-4, r.horizontal, "Scale 4 5 6 , -1 -2 -3 H"); + Assert.AreEqual(-10, r.vertical, "Scale 4 5 6 , -1 -2 -3 V"); + Assert.AreEqual(-18, r.depth, "Scale 4 5 6 , -1 -2 -3 D"); + + v2 = new(0, 0, 0); + r = Vector3.Scale(v1, v2); + Assert.AreEqual(0, r.horizontal, "Scale 4 5 6 , 0 0 0 H"); + Assert.AreEqual(0, r.vertical, "Scale 4 5 6 , 0 0 0 V"); + Assert.AreEqual(0, r.depth, "Scale 4 5 6 , 0 0 0 D"); + } + + [Test] + public void Multiply() { + Vector3 v1 = new(4, 5, 6); + int f = 3; + Vector3 r; + + r = v1 * f; + Assert.AreEqual(12, r.horizontal, "4 5 6 * 3 H"); + Assert.AreEqual(15, r.vertical, "4 5 6 * 3 V"); + Assert.AreEqual(18, r.depth, "4 5 6 * 3 D"); + + r = f * v1; + Assert.AreEqual(12, r.horizontal, "3 * 4 5 6 H"); + Assert.AreEqual(15, r.vertical, "3 * 4 5 6 V"); + Assert.AreEqual(18, r.depth, "3 * 4 5 6 D"); + + f = -3; + r = v1 * f; + Assert.AreEqual(-12, r.horizontal, "4 5 6 * -3 H"); + Assert.AreEqual(-15, r.vertical, "4 5 6 * -3 V"); + Assert.AreEqual(-18, r.depth, "4 5 6 * -3 D"); + + f = 0; + r = v1 * f; + Assert.AreEqual(0, r.horizontal, "4 5 6 * 0 H"); + Assert.AreEqual(0, r.vertical, "4 5 6 * 0 V"); + Assert.AreEqual(0, r.depth, "4 5 6 * 0 D"); + } + + [Test] + public void Divide() { + Vector3 v1 = new(4, 5, 6); + int f = 2; + Vector3 r; + + r = v1 / f; + Assert.AreEqual(2, r.horizontal, "4 5 6 / 2 H"); + Assert.AreEqual(2, r.vertical, "4 5 6 / 2 V"); + Assert.AreEqual(3, r.depth, "4 5 6 / 2 D"); + + f = -2; + r = v1 / f; + Assert.AreEqual(-2, r.horizontal, "4 5 6 / -2 H"); + Assert.AreEqual(-2, r.vertical, "4 5 6 / -2 V"); + Assert.AreEqual(-3, r.depth, "4 5 6 / -2 D"); + + Assert.Throws(() => { + f = 0; + r = v1 / f; + }); + } + + [Test] + public void Dot() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + float f; + + f = Vector3.Dot(v1, v2); + Assert.AreEqual(32, f, "Dot(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(-32, f, "Dot(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + f = Vector3.Dot(v1, v2); + Assert.AreEqual(0, f, "Dot(4 5 6, 0 0 0)"); + } + + [Test] + public void Cross() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 r; + + r = Vector3.Cross(v1, v2); + Assert.AreEqual(3, r.horizontal, "Cross(4 5 6, 1 2 3) H"); + Assert.AreEqual(-6, r.vertical, "Cross(4 5 6, 1 2 3) V"); + Assert.AreEqual(3, r.depth, "Cross(4 5 6, 1 2 3) D"); + + v2 = new(-1, -2, -3); + r = Vector3.Cross(v1, v2); + Assert.AreEqual(-3, r.horizontal, "Cross(4 5 6, -1 -2 -3) H"); + Assert.AreEqual(6, r.vertical, "Cross(4 5 6, -1 -2 -3) V"); + Assert.AreEqual(-3, r.depth, "Cross(4 5 6, -1 -2 -3) D"); + + v2 = new(0, 0, 0); + r = Vector3.Cross(v1, v2); + Assert.AreEqual(0, r.horizontal, "Cross(4 5 6, 0 0 0) H"); + Assert.AreEqual(0, r.vertical, "Cross(4 5 6, 0 0 0) V"); + Assert.AreEqual(0, r.depth, "Cross(4 5 6, 0 0 0) D"); + } + + [Test] + public void UnsignedAngle() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + AngleFloat a; + + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(12.9331379F, a.inDegrees, "Angle(4 5 6, 1 2 3)"); + + v2 = new(-1, -2, -3); + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(167.066849F, a.inDegrees, "Angle(4 5 6, -1 -2 -3)"); + + v2 = new(0, 0, 0); + a = Vector3.UnsignedAngle(v1, v2); + Assert.AreEqual(0, a.inDegrees, "Angle(4 5 6, 0 0 0)"); + } + + [Test] + public void SignedAngle() { + Vector3 v1 = new(4, 5, 6); + Vector3 v2 = new(1, 2, 3); + Vector3 v3 = new(7, 8, -9); + AngleFloat a; + + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(-12.9331379F, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, 7 8 -9)"); + + v2 = new(-1, -2, -3); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(167.066849F, a.inDegrees, "SignedAngle(4 5 6, -1 -2 -3, 7 8 -9)"); + + v2 = new(0, 0, 0); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(0, a.inDegrees, "SignedAngle(4 5 6, 0 0 0, 7 8 -9)"); + + v2 = new(1, 2, 3); + v3 = new(-7, -8, 9); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(12.9331379F, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, -7 -8 9)"); + + v3 = new(0, 0, 0); + a = Vector3.SignedAngle(v1, v2, v3); + Assert.AreEqual(0, a.inDegrees, "SignedAngle(4 5 6, 1 2 3, 0 0 0)"); + } + } +} +#endif \ No newline at end of file