diff --git a/LinearAlgebra/.editorconfig b/LinearAlgebra/.editorconfig new file mode 100644 index 0000000..1ec7f97 --- /dev/null +++ b/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/LinearAlgebra/.gitignore b/LinearAlgebra/.gitignore new file mode 100644 index 0000000..f0b2f47 --- /dev/null +++ b/LinearAlgebra/.gitignore @@ -0,0 +1,6 @@ +DoxyGen/DoxyWarnLogfile.txt +.vscode/settings.json +**bin +**obj +**.meta +*.sln diff --git a/LinearAlgebra/src/Angle.cs b/LinearAlgebra/src/Angle.cs new file mode 100644 index 0000000..1490983 --- /dev/null +++ b/LinearAlgebra/src/Angle.cs @@ -0,0 +1,233 @@ +using System; +using System.Reflection.Emit; + +namespace LinearAlgebra { + + public class Angle { + 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 Angle(float degrees) { + this.value = degrees; + } + private readonly float value = 0; + + public static readonly Angle zero = new(0); + + public static Angle Degrees(float degrees) { + // Reduce it to (-180..180] + if (float.IsFinite(degrees)) { + while (degrees < -180) + degrees += 360; + while (degrees >= 180) + degrees -= 360; + } + return new Angle(degrees); + } + + public static Angle 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 Angle(radians * Rad2Deg); + + } + + public static Angle 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 Angle(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; } + } + + /// + /// 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(Angle 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 Angle Abs(Angle a) { + if (Sign(a) < 0) + return -a; + else + return a; + } + + /// + /// Negate the angle + /// + /// The angle + /// The negated angle + /// The negation of -180 is still -180 because the range is (-180..180] + public static Angle operator -(Angle a) { + Angle r = new(-a.value); + return r; + } + + /// + /// Subtract two angles + /// + /// Angle 1 + /// Angle 2 + /// The result of the subtraction + public static Angle operator -(Angle a1, Angle a2) { + Angle r = new(a1.value - a2.value); + return r; + } + /// + /// Add two angles + /// + /// Angle 1 + /// Angle 2 + /// The result of the addition + public static Angle operator +(Angle a1, Angle a2) { + Angle r = new(a1.value + a2.value); + return r; + } + + /// + /// 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(Angle angle, Angle min, Angle max) { + return Float.Clamp(angle.inDegrees, min.inDegrees, max.inDegrees); + } + + /// + /// 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 Angle MoveTowards(Angle fromAngle, Angle toAngle, float maxDegrees) { + maxDegrees = Math.Max(0, maxDegrees); // filter out negative distances + Angle 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(Vector2 v1, Vector2 v2) { + return (1 - Vector2.Dot(v1, v2)) / 2; + } + + // Normalize all vector angles to the range -180 < angle < 180 + //public static Vector3 Normalize(Vector3 angles) { + // float x = Normalize(angles.x); + // float y = Normalize(angles.y); + // float z = Normalize(angles.z); + // return new Vector3(x, y, z); + //} + + // Returns the signed angle in degrees between from and to. + //public static float SignedAngle(Vector3 from, Vector3 to) { + // float angle = Vector3.Angle(from, to); + // Vector3 cross = Vector3.Cross(from, to); + // if (cross.y < 0) angle = -angle; + // return angle; + //} + + // Returns the signed angle in degrees between from and to. + //public static float SignedAngle(Vector2 from, Vector2 to) { + // float sign = Math.Sign(from.y * to.x - from.x * to.y); + // return Vector2.Angle(from, to) * sign; + //} + + //public static Quaternion ToQuaternion(Rotation orientation) { + // return new Quaternion(orientation.x, orientation.y, orientation.z, orientation.w); + //} + } +} \ No newline at end of file diff --git a/LinearAlgebra/src/Decomposition.cs b/LinearAlgebra/src/Decomposition.cs new file mode 100644 index 0000000..ddaf434 --- /dev/null +++ b/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/LinearAlgebra/src/Direction.cs b/LinearAlgebra/src/Direction.cs new file mode 100644 index 0000000..297eff9 --- /dev/null +++ b/LinearAlgebra/src/Direction.cs @@ -0,0 +1,87 @@ +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 class Direction { + public float horizontal; + public float vertical; + + public Direction() { + horizontal = 0; + vertical = 0; + } + public Direction(Angle horizontal, Angle vertical) { + this.horizontal = horizontal.inDegrees; + + } + // public Direction(float horizontal, float vertical) { + // this.horizontal = horizontal; + // this.vertical = vertical; + // //Normalize(); + // } + + public static Direction Degrees(float horizontal, float vertical) { + Direction d = new() { + horizontal = horizontal, + vertical = vertical + }; + //Normalize(); + return d; + } + public static Direction Radians(float horizontal, float vertical) { + Direction d = new() { + horizontal = horizontal * Angle.Rad2Deg, + vertical = vertical * Angle.Rad2Deg + }; + //Normalize(); + return d; + } + + public readonly static Direction forward = Degrees(0, 0); + public readonly static Direction backward = Degrees(-180, 0); + public readonly static Direction up = Degrees(0, 90); + public readonly static Direction down = Degrees(0, -90); + public readonly static Direction left = Degrees(-90, 0); + public readonly static Direction right = Degrees(90, 0); + + public void Normalize() { + if (this.vertical > 90 || this.vertical < -90) { + this.horizontal += 180; + this.vertical = 180 - this.vertical; + } + } + + public Vector3Float ToVector3() + { + float verticalRad = ((float)Math.PI / 2) - this.vertical * Angle.Deg2Rad; + float horizontalRad = this.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 = sinVertical * sinHorizontal; + float y = cosVertical; + float z = sinVertical * cosHorizontal; + + Vector3Float v = new(x, y, z); + return v; + } + } + +} \ No newline at end of file diff --git a/LinearAlgebra/src/Float.cs b/LinearAlgebra/src/Float.cs new file mode 100644 index 0000000..2217b84 --- /dev/null +++ b/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/LinearAlgebra/src/LinearAlgebra.csproj b/LinearAlgebra/src/LinearAlgebra.csproj new file mode 100644 index 0000000..14d3947 --- /dev/null +++ b/LinearAlgebra/src/LinearAlgebra.csproj @@ -0,0 +1,14 @@ + + + + false + false + net5.0 + + + + + + + + diff --git a/LinearAlgebra/src/Matrix.cs b/LinearAlgebra/src/Matrix.cs new file mode 100644 index 0000000..5196d48 --- /dev/null +++ b/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.x; + result[1, 0] = v.y; + result[2, 0] = v.z; + 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.z, v.y}, + {v.z, 0, -v.x}, + {-v.y, v.x, 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 Vector3Float GetRow3(int rowIx) { + int cols = this.nCols; + Vector3Float 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.x; + this.data[rowIx, 1] = v.y; + this.data[rowIx, 2] = v.z; + } + + 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.x; + this.data[1, colIx] = v.y; + this.data[2, colIx] = v.z; + } + + 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.x + A.data[0, 1] * v.y + A.data[0, 2] * v.z, + A.data[1, 0] * v.x + A.data[1, 1] * v.y + A.data[1, 2] * v.z, + A.data[2, 0] * v.x + A.data[2, 1] * v.y + A.data[2, 2] * v.z + ); + } + + 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.x; + result[1] = v.y; + return new Matrix1(result); + } + + public static Matrix1 FromVector3(Vector3Float v) { + float[] result = new float[3]; + result[0] = v.x; + result[1] = v.y; + result[2] = v.z; + 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/LinearAlgebra/src/Quat32.cs b/LinearAlgebra/src/Quat32.cs new file mode 100644 index 0000000..f13266d --- /dev/null +++ b/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, s.swing.horizontal, s.twist); + return q32; + } + + public static Quat32 Euler(float yaw, float pitch, float roll) { + float rollOver2 = roll * Angle.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) * Angle.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) * Angle.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) * Angle.Rad2Deg; + up = (float)Math.Atan2(2 * this.y * this.w - 2 * this.x * this.z, 1 - 2 * sqy - 2 * sqz) * Angle.Rad2Deg; + forward = (float)Math.Asin(2 * test) * Angle.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/LinearAlgebra/src/Quaternion.cs b/LinearAlgebra/src/Quaternion.cs new file mode 100644 index 0000000..52dd26b --- /dev/null +++ b/LinearAlgebra/src/Quaternion.cs @@ -0,0 +1,81 @@ +using System; +#if UNITY_5_3_OR_NEWER +using Quaternion = UnityEngine.Quaternion; +#endif + +namespace LinearAlgebra { + + public class QuaternionOf { + public T x; + public T y; + public T z; + public T w; + + public QuaternionOf(T x, T y, T z, T w) { + this.x = x; + this.y = y; + this.z = z; + this.w = w; + } + +#if UNITY_5_3_OR_NEWER + 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); + } +#endif + } + + // public class Quaternion : QuaternionOf { + // public Quaternion(float x, float y, float z, float w) : base(x, y, z, w) { } + // } +} \ No newline at end of file diff --git a/LinearAlgebra/src/Spherical.cs b/LinearAlgebra/src/Spherical.cs new file mode 100644 index 0000000..183aa01 --- /dev/null +++ b/LinearAlgebra/src/Spherical.cs @@ -0,0 +1,134 @@ +using System; +#if UNITY_5_3_OR_NEWER +//using Vector3Float = UnityEngine.Vector3; +using Vector3 = UnityEngine.Vector3; +#endif + +namespace LinearAlgebra { + /// + /// A spherical vector + /// + public class Spherical { + + /// + /// Create a default vector with zero distance + /// + public Spherical() { + this.distance = 0; + this.direction = new Direction(); + } + + /// + /// 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 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)) * Angle.Rad2Deg; + float horizontalAngle = (float)Math.Atan2(v.x, v.z) * Angle.Rad2Deg; + return Spherical.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 Vector3 ToVector3() { + float verticalRad = (float)(Math.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; + + Vector3 v = new(x, y, z); + return v; + } + + public static Spherical operator +(Spherical s1, Spherical s2) { + // let's do it the easy way... + Vector3 v1 = s1.ToVector3(); + Vector3 v2 = s2.ToVector3(); + Vector3 v = v1 + v2; + Spherical r = FromVector3(v); + return r; + } + + } +} \ No newline at end of file diff --git a/LinearAlgebra/src/SwingTwist.cs b/LinearAlgebra/src/SwingTwist.cs new file mode 100644 index 0000000..22eb0bb --- /dev/null +++ b/LinearAlgebra/src/SwingTwist.cs @@ -0,0 +1,41 @@ +using System.Numerics; +#if UNITY_5_3_OR_NEWER +using Quaternion = UnityEngine.Quaternion; +#endif + +namespace LinearAlgebra { + + public class SwingTwist { + public Direction swing; + public float twist; + + public static readonly SwingTwist zero = new SwingTwist(0, 0, 0); + + public SwingTwist(Direction swing, float twist) { + this.swing = swing; + this.twist = twist; + } + public SwingTwist(float horizontalSwing, float verticalSwing, float twist) { + this.swing = Direction.Degrees(horizontalSwing, verticalSwing); + this.swing.Normalize(); + this.twist = twist; + } + public static SwingTwist FromQuat32(Quat32 q32) { + // UnityEngine.Quaternion q = new(q32.x, q32.y, q32.z, q32.w); + // SwingTwist r = new(q.eulerAngles.y, q.eulerAngles.x, q.eulerAngles.z); + q32.ToAngles(out float right, out float up, out float forward); + SwingTwist r = new SwingTwist(up, right, forward); + return r; + } + +#if UNITY_5_3_OR_NEWER + public Quaternion ToQuaternion() { + Quaternion q = Quaternion.Euler(-this.swing.vertical, + this.swing.horizontal, + this.twist); + return q; + } +#endif + } + +} \ No newline at end of file diff --git a/LinearAlgebra/src/Vector2.cs b/LinearAlgebra/src/Vector2.cs new file mode 100644 index 0000000..1840a7a --- /dev/null +++ b/LinearAlgebra/src/Vector2.cs @@ -0,0 +1,363 @@ +using System; +using System.Numerics; + +namespace LinearAlgebra { + + public class Vector2Of where T : IComparable { + public T x; + public T y; + + public Vector2Of(T x, T y) { + this.x = x; + this.y = y; + } + } + + public class Vector2Int : Vector2Of { + public Vector2Int(int x, int y) : base(x, y) { } + + public static Vector2Int operator -(Vector2Int v1, Vector2Int v2) { + return new Vector2Int(v1.x - v2.x, v1.y - v2.y); + } + + public float magnitude { + get { + return (float)Math.Sqrt(this.x * this.x + this.y * this.y); + } + } + + public static float Distance(Vector2Int v1, Vector2Int v2) { + return (v1 - v2).magnitude; + } + } + + public class Vector2Float : Vector2Of { + public Vector2Float(float x, float y) : base(x, y) { } + + public static Vector2Float operator -(Vector2Float v1, Vector2Float v2) { + return new Vector2Float(v1.x - v2.x, v1.y - v2.y); + } + + public float magnitude { + get { + return (float)Math.Sqrt(this.x * this.x + this.y * this.y); + } + } + + public static float Distance(Vector2Float v1, Vector2Float v2) { + return (v1 - v2).magnitude; + } + } + + /// + /// 2-dimensional vectors + /// + public struct Vector2 : IEquatable { + + /// + /// The right axis of the vector + /// + public float x; // left/right + /// + /// The upward/forward axis of the vector + /// + public float y; // 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 Vector2(float x, float y) { + this.x = x; + this.y = y; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector2 zero = new Vector2(0, 0); + /// + /// A vector with values (1, 1) + /// + public static readonly Vector2 one = new Vector2(1, 1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2 up = new Vector2(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2 down = new Vector2(0, -1); + /// + /// A vector with values (0, 1) + /// + public static readonly Vector2 forward = new Vector2(0, 1); + /// + /// A vector with values (0, -1) + /// + public static readonly Vector2 back = new Vector2(0, -1); + /// + /// A vector3 with values (-1, 0) + /// + public static readonly Vector2 left = new Vector2(-1, 0); + /// + /// A vector with values (1, 0) + /// + public static readonly Vector2 right = new Vector2(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 float sqrMagnitude { + get { + float d = x * x + y * y; + return d; + } + } + + /// + /// The length of this vector + /// + /// The length of this vector + public float magnitude { + get { + float d = (float)Math.Sqrt(x * x + y * y); + return d; + } + } + + /// + /// Convert the vector to a length of a 1 + /// + /// The vector with length 1 + public Vector2 normalized { + get { + float l = magnitude; + Vector2 v = zero; + if (l > Float.epsilon) + v = this / l; + return v; + } + } + + /// + /// Add two vectors + /// + /// The first vector + /// The second vector + /// The result of adding the two vectors + public static Vector2 operator +(Vector2 v1, Vector2 v2) { + Vector2 v = new Vector2(v1.x + v2.x, v1.y + v2.y); + return v; + } + + /// + /// Subtract two vectors + /// + /// The first vector + /// The second vector + /// The result of adding the two vectors + public static Vector2 operator -(Vector2 v1, Vector2 v2) { + Vector2 v = new Vector2(v1.x - v2.x, v1.y - v2.y); + 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 Vector2 operator -(Vector2 v1) { + Vector2 v = new Vector2(-v1.x, -v1.y); + return v; + } + + /// + /// 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 Vector2 operator *(Vector2 v1, float f) { + Vector2 v = new Vector2(v1.x * f, v1.y * 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 Vector2 operator *(float f, Vector2 v1) { + Vector2 v = new Vector2(f * v1.x, f * v1.y); + 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 Vector2 operator /(Vector2 v1, float f) { + Vector2 v = new Vector2(v1.x / f, v1.y / f); + return v; + } + + /// + /// 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(Vector2 v1) => x == v1.x && y == v1.y; + + /// + /// 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 Vector2 v)) + return false; + + return (x == v.x && y == v.y); + } + + /// + /// 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 ==(Vector2 v1, Vector2 v2) { + return (v1.x == v2.x && v1.y == v2.y); + } + + /// + /// 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 !=(Vector2 v1, Vector2 v2) { + return (v1.x != v2.x || v1.y != v2.y); + } + + /// + /// Get an hash code for the vector + /// + /// The hash code + public override int GetHashCode() { + return (x, y).GetHashCode(); + } + + /// + /// Get the distance between two vectors + /// + /// The first vector + /// The second vector + /// The distance between the two vectors + public static float Distance(Vector2 v1, Vector2 v2) { + float x = v1.x - v2.x; + float y = v1.y - v2.y; + 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(Vector2 v1, Vector2 v2) { + return v1.x * v2.x + v1.y * v2.y; + } + + /// + /// 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 Vector2 Lerp(Vector2 v1, Vector2 v2, float f) { + Vector2 v = v1 + (v2 - v1) * f; + return v; + } + + /// + /// 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(Vector2 from, Vector2 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.y, from.x); + float angleTo = (float)Math.Atan2(to.y, to.x); + return (angleTo - angleFrom) * Angle.Rad2Deg; + } + + /// + /// Rotates the vector with the given angle + /// + /// The vector to rotate + /// The angle in degrees + /// + public static Vector2 Rotate(Vector2 v1, float angle) { + float sin = (float)Math.Sin(angle * Angle.Deg2Rad); + float cos = (float)Math.Cos(angle * Angle.Deg2Rad); + + float tx = v1.x; + float ty = v1.y; + Vector2 v = new Vector2() { + x = (cos * tx) - (sin * ty), + y = (sin * tx) + (cos * ty) + }; + 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(Vector2 v1, Vector2 v2) { + return (1 - Vector2.Dot(v1, v2)) / 2; + } + } +} \ No newline at end of file diff --git a/LinearAlgebra/src/Vector3.cs b/LinearAlgebra/src/Vector3.cs new file mode 100644 index 0000000..7994dcb --- /dev/null +++ b/LinearAlgebra/src/Vector3.cs @@ -0,0 +1,179 @@ +#if !UNITY_5_3_OR_NEWER +using System; + +namespace LinearAlgebra { + public class Vector3Of { + public T x; + public T y; + public T z; + + public Vector3Of(T x, T y, T z) { + this.x = x; + this.y = y; + this.z = z; + } + + // public uint magnitude { + // get => (float)Math.Sqrt(this.x * this.x + this.y * this.y + this.z * this.z); + // } + } + + public class Vector3Int : Vector3Of { + public Vector3Int(int x, int y, int z) : base(x, y, z) { } + } + public class Vector3Float : Vector3Of { + public Vector3Float(float x, float y, float z) : base(x, y, z) { } + + public float magnitude { + get => (float)Math.Sqrt(this.x * this.x + this.y * this.y + this.z * this.z); + } + } + + /// + /// 3-dimensional vectors + /// + /// This uses the right-handed coordinate system. + public struct Vector3 : IEquatable { + + /// + /// The right axis of the vector + /// + public float x; //> left/right + /// + /// The upward axis of the vector + /// + public float y; //> up/down + /// + /// The forward axis of the vector + /// + public float z; //> forward/backward + + /// + /// Create a new 3-dimensional vector + /// + /// x axis value + /// y axis value + /// z axis value + public Vector3(float x, float y, float z) { + this.x = x; + this.y = y; + this.z = z; + } + + /// + /// A vector with zero for all axis + /// + public static readonly Vector3 zero = new Vector3(0, 0, 0); + /// + /// A vector with one for all axis + /// + public static readonly Vector3 one = new Vector3(1, 1, 1); + /// + /// A vector3 with values (-1, 0, 0) + /// + public static readonly Vector3 left = new Vector3(-1, 0, 0); + /// + /// A vector with values (1, 0, 0) + /// + public static readonly Vector3 right = new Vector3(1, 0, 0); + /// + /// A vector with values (0, -1, 0) + /// + public static readonly Vector3 down = new Vector3(0, -1, 0); + /// + /// A vector with values (0, 1, 0) + /// + public static readonly Vector3 up = new Vector3(0, 1, 0); + /// + /// A vector with values (0, 0, -1) + /// + public static readonly Vector3 back = new Vector3(0, -1, 0); + /// + /// A vector with values (0, 0, 1) + /// + public static readonly Vector3 forward = new Vector3(0, 1, 0); + + public readonly float magnitude { + get { + float d = (float)Math.Sqrt(x * x + y * y + z * z); + return d; + } + } + + public Vector3 normalized { + get { + float l = magnitude; + Vector3 v = zero; + if (l > Float.epsilon) + v = this / l; + return v; + } + } + + public static Vector3 operator +(Vector3 v1, Vector3 v2) { + Vector3 v = new Vector3(v1.x + v2.x, v1.y + v2.y, v1.z + v2.z); + return v; + } + + public static Vector3 operator -(Vector3 v1, Vector3 v2) { + Vector3 v = new Vector3(v1.x - v2.x, v1.y - v2.y, v1.z - v2.z); + return v; + } + + public static Vector3 operator -(Vector3 v1) { + Vector3 v = new Vector3(-v1.x, -v1.y, -v1.z); + return v; + } + + public static Vector3 operator *(Vector3 v1, float d) { + Vector3 v = new Vector3(v1.x * d, v1.y * d, v1.z * d); + return v; + } + + public static Vector3 operator *(float d, Vector3 v1) { + Vector3 v = new Vector3(d * v1.x, d * v1.y, d * v1.z); + return v; + } + + public static Vector3 operator /(Vector3 v1, float d) { + Vector3 v = new Vector3(v1.x / d, v1.y / d, v1.z / d); + return v; + } + + public bool Equals(Vector3 v) => (x == v.x && y == v.y && z == v.z); + + public override bool Equals(object obj) { + if (!(obj is Vector3 v)) + return false; + + return (x == v.x && y == v.y && z == v.z); + } + + public static bool operator ==(Vector3 v1, Vector3 v2) { + return (v1.x == v2.x && v1.y == v2.y && v1.z == v2.z); + } + + public static bool operator !=(Vector3 v1, Vector3 v2) { + return (v1.x != v2.x || v1.y != v2.y || v1.z != v2.z); + } + + public override int GetHashCode() { + return (x, y, z).GetHashCode(); + } + + public static float Distance(Vector3 v1, Vector3 v2) { + return (v2 - v1).magnitude; + } + + public static float Dot(Vector3 v1, Vector3 v2) { + return v1.x * v2.x + v1.y * v2.y + v1.z * v2.z; + } + + public static Vector3 Lerp(Vector3 v1, Vector3 v2, float f) { + Vector3 v = v1 + (v2 - v1) * f; + return v; + } + + } +} +#endif \ No newline at end of file diff --git a/LinearAlgebra/src/float16.cs b/LinearAlgebra/src/float16.cs new file mode 100644 index 0000000..4b58cdd --- /dev/null +++ b/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/LinearAlgebra/test/AngleTest.cs b/LinearAlgebra/test/AngleTest.cs new file mode 100644 index 0000000..00e4981 --- /dev/null +++ b/LinearAlgebra/test/AngleTest.cs @@ -0,0 +1,209 @@ +#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; + Angle a = Angle.Degrees(angle); + Assert.AreEqual(angle, a.inDegrees); + + angle = -180.0f; + a = Angle.Degrees(angle); + Assert.AreEqual(angle, a.inDegrees); + + angle = 270.0f; + a = Angle.Degrees(angle); + Assert.AreEqual(-90, a.inDegrees); + + // Radians + angle = 0.0f; + a = Angle.Radians(angle); + Assert.AreEqual(angle, a.inRadians); + + angle = (float)-Math.PI; + a = Angle.Radians(angle); + Assert.AreEqual(angle, a.inRadians); + + angle = (float)Math.PI * 1.5f; + a = Angle.Radians(angle); + Assert.AreEqual(-Math.PI * 0.5f, a.inRadians); + + // Revolutions + angle = 0.0f; + a = Angle.Revolutions(angle); + Assert.AreEqual(angle, a.inRevolutions); + + angle = -0.5f; + a = Angle.Revolutions(angle); + Assert.AreEqual(angle, a.inRevolutions); + + angle = 0.75f; + a = Angle.Revolutions(angle); + Assert.AreEqual(-0.25f, a.inRevolutions); + + } + + // [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 = Angle.Clamp(Angle.Degrees(1), Angle.Degrees(0), Angle.Degrees(2)); + Assert.AreEqual(r, 1, "Clamp 1 0 2"); + + r = Angle.Clamp(Angle.Degrees(-1), Angle.Degrees(0), Angle.Degrees(2)); + Assert.AreEqual(r, 0, "Clamp -1 0 2"); + + r = Angle.Clamp(Angle.Degrees(3), Angle.Degrees(0), Angle.Degrees(2)); + Assert.AreEqual(r, 2, "Clamp 3 0 2"); + + r = Angle.Clamp(Angle.Degrees(1), Angle.Degrees(0), Angle.Degrees(0)); + Assert.AreEqual(r, 0, "Clamp 1 0 0"); + + r = Angle.Clamp(Angle.Degrees(0), Angle.Degrees(0), Angle.Degrees(0)); + Assert.AreEqual(r, 0, "Clamp 0 0 0"); + + r = Angle.Clamp(Angle.Degrees(0), Angle.Degrees(1), Angle.Degrees(-1)); + Assert.AreEqual(r, 1, "Clamp 0 1 -1"); + + r = Angle.Clamp(Angle.Degrees(1), Angle.Degrees(0), Angle.Degrees(float.PositiveInfinity)); + Assert.AreEqual(r, 1, "Clamp 1 0 INFINITY"); + + r = Angle.Clamp(Angle.Degrees(1), Angle.Degrees(float.NegativeInfinity), Angle.Degrees(1)); + Assert.AreEqual(r, 1, "Clamp 1 -INFINITY 1"); + } + + // [Test] + // public void Difference() { + // float r = 0; + + // r = Angle.Difference(0, 90); + // Assert.AreEqual(r, 90, "Difference 0 90"); + + // r = Angle.Difference(0, -90); + // Assert.AreEqual(r, -90, "Difference 0 -90"); + + // r = Angle.Difference(0, 270); + // Assert.AreEqual(r, -90, "Difference 0 270"); + + // r = Angle.Difference(0, -270); + // Assert.AreEqual(r, 90, "Difference 0 -270"); + + // r = Angle.Difference(90, 0); + // Assert.AreEqual(r, -90, "Difference 90 0"); + + // r = Angle.Difference(-90, 0); + // Assert.AreEqual(r, 90, "Difference -90 0"); + + // r = Angle.Difference(0, 0); + // Assert.AreEqual(r, 0, "Difference 0 0"); + + // r = Angle.Difference(90, 90); + // Assert.AreEqual(r, 0, "Difference 90 90"); + + // r = Angle.Difference(0, float.PositiveInfinity); + // Assert.AreEqual(r, float.PositiveInfinity, "Difference 0 INFINITY"); + + // r = Angle.Difference(0, float.NegativeInfinity); + // Assert.AreEqual(r, float.NegativeInfinity, "Difference 0 -INFINITY"); + + // r = Angle.Difference(float.NegativeInfinity, float.PositiveInfinity); + // Assert.AreEqual(r, float.PositiveInfinity, "Difference -INFINITY INFINITY"); + // } + + [Test] + public void MoveTowards() { + Angle r = Angle.zero; + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), 30); + Assert.AreEqual(r.inDegrees, 30, "MoveTowards 0 90 30"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), 90); + Assert.AreEqual(r.inDegrees, 90, "MoveTowards 0 90 90"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), 180); + Assert.AreEqual(r.inDegrees, 90, "MoveTowards 0 90 180"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), 270); + Assert.AreEqual(r.inDegrees, 90, "MoveTowrads 0 90 270"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), -30); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 90 -30"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(-90), -30); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 -90 -30"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(-90), -90); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 -90 -90"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(-90), -180); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 -90 -180"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(-90), -270); + Assert.AreEqual(r.inDegrees, 0, "MoveTowrads 0 -90 -270"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), 0); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 90 0"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(0), 0); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 0 0"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(0), 30); + Assert.AreEqual(r.inDegrees, 0, "MoveTowrads 0 0 30"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(90), float.PositiveInfinity); + Assert.AreEqual(r.inDegrees, 90, "MoveTowards 0 90 INFINITY"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(float.PositiveInfinity), 30); + Assert.AreEqual(r.inDegrees, 30, "MoveTowrads 0 INFINITY 30"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(-90), float.NegativeInfinity); + Assert.AreEqual(r.inDegrees, 0, "MoveTowards 0 -90 -INFINITY"); + + r = Angle.MoveTowards(Angle.Degrees(0), Angle.Degrees(float.NegativeInfinity), -30); + Assert.AreEqual(r.inDegrees, 0, "MoveTowrads 0 -INFINITY -30"); + + } + } +} +#endif \ No newline at end of file diff --git a/LinearAlgebra/test/DirectionTest.cs b/LinearAlgebra/test/DirectionTest.cs new file mode 100644 index 0000000..e31af4c --- /dev/null +++ b/LinearAlgebra/test/DirectionTest.cs @@ -0,0 +1,17 @@ +using NUnit.Framework; + +namespace LinearAlgebra.Test { + public class DirectionTest { + [SetUp] + public void Setup() { + } + + [Test] + public void Compare() { + Direction d = Direction.Degrees(45, 135); + bool r; + r = d == new Direction(Angle.Degrees(45), Angle.Degrees(135)); + Assert.True(r); + } + }; +} \ No newline at end of file diff --git a/LinearAlgebra/test/LinearAlgebra_Test.csproj b/LinearAlgebra/test/LinearAlgebra_Test.csproj new file mode 100644 index 0000000..3ee2230 --- /dev/null +++ b/LinearAlgebra/test/LinearAlgebra_Test.csproj @@ -0,0 +1,19 @@ + + + + net5.0 + false + true + + + + + + + + + + + + + diff --git a/LinearAlgebra/test/SphericalTest.cs b/LinearAlgebra/test/SphericalTest.cs new file mode 100644 index 0000000..8539dc0 --- /dev/null +++ b/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() { + Vector3 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, "s.hor 0 0 1"); + Assert.AreEqual(0.0f, s.direction.vertical, 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, "s.hor 0 1 0"); + Assert.AreEqual(90.0f, s.direction.vertical, "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, "s.hor 1 0 0"); + Assert.AreEqual(0.0f, s.direction.vertical, 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, "Addition(1 0 90)"); + Assert.AreEqual(45.0f, r.direction.vertical, "Addition(1 0 90)"); + } + } +} +#endif \ No newline at end of file