using System;
using System.Numerics;

namespace LinearAlgebra
{

    public class Vector2Of<T> where T : IComparable<T>
    {
        public T x;
        public T y;

        public Vector2Of(T x, T y)
        {
            this.x = x;
            this.y = y;
        }
    }

    public class Vector2Int : Vector2Of<int>
    {
        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<float>
    {
        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;
        }
    }

    /// <summary>
    /// 2-dimensional vectors
    /// </summary>
    public struct Vector2 : IEquatable<Vector2>
    {

        /// <summary>
        /// The right axis of the vector
        /// </summary>
        public float x; // left/right
        /// <summary>
        /// The upward/forward axis of the vector
        /// </summary>
        public float y; // forward/backward
                        // directions are to be inline with Vector3 as much as possible...

        /// <summary>
        /// Create a new 2-dimensional vector
        /// </summary>
        /// <param name="x">x axis value</param>
        /// <param name="y">y axis value</param>
        public Vector2(float x, float y)
        {
            this.x = x;
            this.y = y;
        }

        /// <summary>
        /// A vector with zero for all axis
        /// </summary>
        public static readonly Vector2 zero = new Vector2(0, 0);
        /// <summary>
        /// A vector with values (1, 1)
        /// </summary>
        public static readonly Vector2 one = new Vector2(1, 1);
        /// <summary>
        /// A vector with values (0, 1)
        /// </summary>
        public static readonly Vector2 up = new Vector2(0, 1);
        /// <summary>
        /// A vector with values (0, -1)
        /// </summary>
        public static readonly Vector2 down = new Vector2(0, -1);
        /// <summary>
        /// A vector with values (0, 1)
        /// </summary>
        public static readonly Vector2 forward = new Vector2(0, 1);
        /// <summary>
        /// A vector with values (0, -1)
        /// </summary>
        public static readonly Vector2 back = new Vector2(0, -1);
        /// <summary>
        /// A vector3 with values (-1, 0)
        /// </summary>
        public static readonly Vector2 left = new Vector2(-1, 0);
        /// <summary>
        /// A vector with values (1, 0)
        /// </summary>
        public static readonly Vector2 right = new Vector2(1, 0);

        /// <summary>
        /// The squared length of this vector
        /// </summary>
        /// <returns>The squared length</returns>
        /// 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;
            }
        }

        /// <summary>
        /// The length of this vector
        /// </summary>
        /// <returns>The length of this vector</returns>
        public float magnitude
        {
            get
            {
                float d = (float)Math.Sqrt(x * x + y * y);
                return d;
            }
        }

        /// <summary>
        /// Convert the vector to a length of a 1
        /// </summary>
        /// <returns>The vector with length 1</returns>
        public Vector2 normalized
        {
            get
            {
                float l = magnitude;
                Vector2 v = zero;
                if (l > Float.epsilon)
                    v = this / l;
                return v;
            }
        }

        /// <summary>
        /// Add two vectors
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns>The result of adding the two vectors</returns>
        public static Vector2 operator +(Vector2 v1, Vector2 v2)
        {
            Vector2 v = new Vector2(v1.x + v2.x, v1.y + v2.y);
            return v;
        }

        /// <summary>
        /// Subtract two vectors
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns>The result of adding the two vectors</returns>
        public static Vector2 operator -(Vector2 v1, Vector2 v2)
        {
            Vector2 v = new Vector2(v1.x - v2.x, v1.y - v2.y);
            return v;
        }

        /// <summary>
        /// Negate the vector
        /// </summary>
        /// <param name="v1">The vector to negate</param>
        /// <returns>The negated vector</returns>
        /// 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;
        }

        /// <summary>
        /// Scale a vector uniformly up
        /// </summary>
        /// <param name="v1">The vector to scale</param>
        /// <param name="f">The scaling factor</param>
        /// <returns>The scaled vector</returns>
        /// 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;
        }

        /// <summary>
        /// Scale a vector uniformly up
        /// </summary>
        /// <param name="f">The scaling factor</param>
        /// <param name="v1">The vector to scale</param>
        /// <returns>The scaled vector</returns>
        /// 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;
        }

        /// <summary>
        /// Scale a vector uniformly down
        /// </summary>
        /// <param name="v1">The vector to scale</param>
        /// <param name="f">The scaling factor</param>
        /// <returns>The scaled vector</returns>
        /// 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;
        }

        /// <summary>
        /// Tests if the vector has equal values as the given vector
        /// </summary>
        /// <param name="v1">The vector to compare to</param>
        /// <returns><em>true</em> if the vector values are equal</returns>
        public bool Equals(Vector2 v1) => x == v1.x && y == v1.y;

        /// <summary>
        /// Tests if the vector is equal to the given object
        /// </summary>
        /// <param name="obj">The object to compare to</param>
        /// <returns><em>false</em> when the object is not a Vector2 or does not have equal values</returns>
        public override bool Equals(object obj)
        {
            if (!(obj is Vector2 v))
                return false;

            return (x == v.x && y == v.y);
        }

        /// <summary>
        /// Tests if the two vectors have equal values
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns><em>true</em>when the vectors have equal values</returns>
        /// 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);
        }

        /// <summary>
        /// Tests if two vectors have different values
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns><em>true</em>when the vectors have different values</returns>
        /// 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);
        }

        /// <summary>
        /// Get an hash code for the vector
        /// </summary>
        /// <returns>The hash code</returns>
        public override int GetHashCode()
        {
            return (x, y).GetHashCode();
        }

        /// <summary>
        /// Get the distance between two vectors
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns>The distance between the two vectors</returns>
        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;
        }

        /// <summary>
        /// The dot product of two vectors
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns>The dot product of the two vectors</returns>
        public static float Dot(Vector2 v1, Vector2 v2)
        {
            return v1.x * v2.x + v1.y * v2.y;
        }

        /// <summary>
        /// Lerp between two vectors
        /// </summary>
        /// <param name="v1">The from vector</param>
        /// <param name="v2">The to vector</param>
        /// <param name="f">The interpolation distance [0..1]</param>
        /// <returns>The lerped vector</returns>
        /// 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;
        }

        /// <summary>
        /// Calculate the signed angle between two vectors.
        /// </summary>
        /// <param name="from">The starting vector</param>
        /// <param name="to">The ending vector</param>
        /// <param name="axis">The axis to rotate around</param>
        /// <returns>The signed angle in degrees</returns>
        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;
        }

        /// <summary>
        /// Rotates the vector with the given angle
        /// </summary>
        /// <param name="v1">The vector to rotate</param>
        /// <param name="angle">The angle in degrees</param>
        /// <returns></returns>
        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;
        }

        /// <summary>
        /// Map interval of angles between vectors [0..Pi] to interval [0..1]
        /// </summary>
        /// <param name="v1">The first vector</param>
        /// <param name="v2">The second vector</param>
        /// <returns>The resulting factor in interval [0..1]</returns>
        /// Vectors a and b must be normalized
        public static float ToFactor(Vector2 v1, Vector2 v2)
        {
            return (1 - Vector2.Dot(v1, v2)) / 2;
        }
    }
}