Vector2.cs

// MIT License - Copyright (C) The Mono.Xna Team
// This file is subject to the terms and conditions defined in
// file 'LICENSE.txt', which is part of this source code package.

using System;
using System.ComponentModel;
using System.Diagnostics;
using System.Runtime.Serialization;

#if NET8_0_OR_GREATER
using System.Runtime.CompilerServices;
using SysNumerics = System.Numerics;
#endif

namespace Microsoft.Xna.Framework
{
    /// <summary>
    /// Describes a 2D-vector.
    /// </summary>
    [DebuggerDisplay("{DebugDisplayString,nq}")]
    [DataContract]
    [TypeConverter("Microsoft.Xna.Framework.Design.Vector2Converter, Xna.Framework.Design")]
    public struct Vector2 : IEquatable<Vector2>
    {
        #region Private Fields

        private static readonly Vector2 zeroVector = new Vector2(0f, 0f);
        private static readonly Vector2 unitVector = new Vector2(1f, 1f);
        private static readonly Vector2 unitXVector = new Vector2(1f, 0f);
        private static readonly Vector2 unitYVector = new Vector2(0f, 1f);

        #endregion

        #region Public Fields

        /// <summary>
        /// The x coordinate of this <see cref="Vector2"/>.
        /// </summary>
        [DataMember]
        public float X;

        /// <summary>
        /// The y coordinate of this <see cref="Vector2"/>.
        /// </summary>
        [DataMember]
        public float Y;

        #endregion

        #region Properties

        /// <summary>
        /// Returns a <see cref="Vector2"/> with components 0, 0.
        /// </summary>
        public static Vector2 Zero
        {
            get { return zeroVector; }
        }

        /// <summary>
        /// Returns a <see cref="Vector2"/> with components 1, 1.
        /// </summary>
        public static Vector2 One
        {
            get { return unitVector; }
        }

        /// <summary>
        /// Returns a <see cref="Vector2"/> with components 1, 0.
        /// </summary>
        public static Vector2 UnitX
        {
            get { return unitXVector; }
        }

        /// <summary>
        /// Returns a <see cref="Vector2"/> with components 0, 1.
        /// </summary>
        public static Vector2 UnitY
        {
            get { return unitYVector; }
        }

        #endregion

        #region Internal Properties

        internal string DebugDisplayString
        {
            get
            {
                return string.Concat(
                    this.X.ToString(), "  ",
                    this.Y.ToString()
                );
            }
        }

        #endregion

        #region Constructors

        /// <summary>
        /// Constructs a 2d vector with X and Y from two values.
        /// </summary>
        /// <param name="x">The x coordinate in 2d-space.</param>
        /// <param name="y">The y coordinate in 2d-space.</param>
        public Vector2(float x, float y)
        {
            this.X = x;
            this.Y = y;
        }

        /// <summary>
        /// Constructs a 2d vector with X and Y set to the same value.
        /// </summary>
        /// <param name="value">The x and y coordinates in 2d-space.</param>
        public Vector2(float value)
        {
            this.X = value;
            this.Y = value;
        }

        #endregion

        #region Operators

        /// <summary>
        /// Inverts values in the specified <see cref="Vector2"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/> on the right of the sub sign.</param>
        /// <returns>Result of the inversion.</returns>
        public static Vector2 operator -(Vector2 value)
        {
            value.X = -value.X;
            value.Y = -value.Y;
            return value;
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the add sign.</param>
        /// <param name="right">Source <see cref="Vector2"/> on the right of the add sign.</param>
        /// <returns>Sum of the vectors.</returns>
        public static Vector2 operator +(Vector2 left, Vector2 right)
        {
            left.X += right.X;
            left.Y += right.Y;
            return left;
        }

        /// <summary>
        /// Subtracts a <see cref="Vector2"/> from a <see cref="Vector2"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the sub sign.</param>
        /// <param name="right">Source <see cref="Vector2"/> on the right of the sub sign.</param>
        /// <returns>Result of the vector subtraction.</returns>
        public static Vector2 operator -(Vector2 left, Vector2 right)
        {
            left.X -= right.X;
            left.Y -= right.Y;
            return left;
        }

        /// <summary>
        /// Multiplies the components of two vectors by each other.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the mul sign.</param>
        /// <param name="right">Source <see cref="Vector2"/> on the right of the mul sign.</param>
        /// <returns>Result of the vector multiplication.</returns>
        public static Vector2 operator *(Vector2 left, Vector2 right)
        {
            left.X *= right.X;
            left.Y *= right.Y;
            return left;
        }

        /// <summary>
        /// Multiplies the components of vector by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the mul sign.</param>
        /// <param name="right">Scalar value on the right of the mul sign.</param>
        /// <returns>Result of the vector multiplication with a scalar.</returns>
        public static Vector2 operator *(Vector2 left, float right)
        {
            left.X *= right;
            left.Y *= right;
            return left;
        }

        /// <summary>
        /// Multiplies the components of vector by a scalar.
        /// </summary>
        /// <param name="left">Scalar value on the left of the mul sign.</param>
        /// <param name="right">Source <see cref="Vector2"/> on the right of the mul sign.</param>
        /// <returns>Result of the vector multiplication with a scalar.</returns>
        public static Vector2 operator *(float left, Vector2 right)
        {
            right.X *= left;
            right.Y *= left;
            return right;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by the components of another <see cref="Vector2"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the div sign.</param>
        /// <param name="right">Divisor <see cref="Vector2"/> on the right of the div sign.</param>
        /// <returns>The result of dividing the vectors.</returns>
        public static Vector2 operator /(Vector2 left, Vector2 right)
        {
            left.X /= right.X;
            left.Y /= right.Y;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/> on the left of the div sign.</param>
        /// <param name="right">Divisor scalar on the right of the div sign.</param>
        /// <returns>The result of dividing a vector by a scalar.</returns>
        public static Vector2 operator /(Vector2 left, float right)
        {
            float factor = 1 / right;
            left.X *= factor;
            left.Y *= factor;
            return left;
        }

        /// <summary>
        /// Compares whether two <see cref="Vector2"/> instances are equal.
        /// </summary>
        /// <param name="left"><see cref="Vector2"/> instance on the left of the equal sign.</param>
        /// <param name="right"><see cref="Vector2"/> instance on the right of the equal sign.</param>
        /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
        public static bool operator ==(Vector2 left, Vector2 right)
        {
            return left.X == right.X && left.Y == right.Y;
        }

        /// <summary>
        /// Compares whether two <see cref="Vector2"/> instances are not equal.
        /// </summary>
        /// <param name="left"><see cref="Vector2"/> instance on the left of the not equal sign.</param>
        /// <param name="right"><see cref="Vector2"/> instance on the right of the not equal sign.</param>
        /// <returns><c>true</c> if the instances are not equal; <c>false</c> otherwise.</returns>	
        public static bool operator !=(Vector2 left, Vector2 right)
        {
            return left.X != right.X || left.Y != right.Y;
        }

#if NET8_0_OR_GREATER
        public static explicit operator Vector2(SysNumerics.Vector2 value)
        {
            return Unsafe.BitCast<SysNumerics.Vector2, Vector2>(value);
        }

        public static explicit operator SysNumerics.Vector2(Vector2 value)
        {
            return Unsafe.BitCast<Vector2, SysNumerics.Vector2>(value);
        }
#endif

        #endregion

        #region Public Methods

        /// <summary>
        /// Performs vector addition on <paramref name="left"/> and <paramref name="right"/>.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <returns>The result of the vector addition.</returns>
        public static Vector2 Add(Vector2 left, Vector2 right)
        {
            left.X += right.X;
            left.Y += right.Y;
            return left;
        }

        /// <summary>
        /// Performs vector addition on <paramref name="left"/> and
        /// <paramref name="right"/>, storing the result of the
        /// addition in <paramref name="result"/>.
        /// </summary>
        /// <param name="left">The first vector to add.</param>
        /// <param name="right">The second vector to add.</param>
        /// <param name="result">The result of the vector addition.</param>
        public static void Add(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X + right.X;
            result.Y = left.Y + right.Y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 2d-triangle.
        /// </summary>
        /// <param name="value1">The first vector of 2d-triangle.</param>
        /// <param name="value2">The second vector of 2d-triangle.</param>
        /// <param name="value3">The third vector of 2d-triangle.</param>
        /// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 2d-triangle.</param>
        /// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 2d-triangle.</param>
        /// <returns>The cartesian translation of barycentric coordinates.</returns>
        public static Vector2 Barycentric(Vector2 value1, Vector2 value2, Vector2 value3, float amount1, float amount2)
        {
            return new Vector2(
                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2));
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 2d-triangle.
        /// </summary>
        /// <param name="value1">The first vector of 2d-triangle.</param>
        /// <param name="value2">The second vector of 2d-triangle.</param>
        /// <param name="value3">The third vector of 2d-triangle.</param>
        /// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 2d-triangle.</param>
        /// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 2d-triangle.</param>
        /// <param name="result">The cartesian translation of barycentric coordinates as an output parameter.</param>
        public static void Barycentric(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, float amount1, float amount2, out Vector2 result)
        {
            result.X = MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2);
            result.Y = MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains CatmullRom interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">The first vector in interpolation.</param>
        /// <param name="value2">The second vector in interpolation.</param>
        /// <param name="value3">The third vector in interpolation.</param>
        /// <param name="value4">The fourth vector in interpolation.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <returns>The result of CatmullRom interpolation.</returns>
        public static Vector2 CatmullRom(Vector2 value1, Vector2 value2, Vector2 value3, Vector2 value4, float amount)
        {
            return new Vector2(
                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount));
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains CatmullRom interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">The first vector in interpolation.</param>
        /// <param name="value2">The second vector in interpolation.</param>
        /// <param name="value3">The third vector in interpolation.</param>
        /// <param name="value4">The fourth vector in interpolation.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <param name="result">The result of CatmullRom interpolation as an output parameter.</param>
        public static void CatmullRom(ref Vector2 value1, ref Vector2 value2, ref Vector2 value3, ref Vector2 value4, float amount, out Vector2 result)
        {
            result.X = MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount);
            result.Y = MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount);
        }

        /// <summary>
        /// Round the members of this <see cref="Vector2"/> towards positive infinity.
        /// </summary>
        public void Ceiling()
        {
            X = (float)Math.Ceiling(X);
            Y = (float)Math.Ceiling(Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded towards positive infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <returns>The rounded <see cref="Vector2"/>.</returns>
        public static Vector2 Ceiling(Vector2 value)
        {
            value.X = (float)Math.Ceiling(value.X);
            value.Y = (float)Math.Ceiling(value.Y);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded towards positive infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The rounded <see cref="Vector2"/>.</param>
        public static void Ceiling(ref Vector2 value, out Vector2 result)
        {
            result.X = (float)Math.Ceiling(value.X);
            result.Y = (float)Math.Ceiling(value.Y);
        }

        /// <summary>
        /// Clamps the specified value within a range.
        /// </summary>
        /// <param name="value1">The value to clamp.</param>
        /// <param name="min">The min value.</param>
        /// <param name="max">The max value.</param>
        /// <returns>The clamped value.</returns>
        public static Vector2 Clamp(Vector2 value1, Vector2 min, Vector2 max)
        {
            return new Vector2(
                MathHelper.Clamp(value1.X, min.X, max.X),
                MathHelper.Clamp(value1.Y, min.Y, max.Y));
        }

        /// <summary>
        /// Clamps the specified value within a range.
        /// </summary>
        /// <param name="value1">The value to clamp.</param>
        /// <param name="min">The min value.</param>
        /// <param name="max">The max value.</param>
        /// <param name="result">The clamped value as an output parameter.</param>
        public static void Clamp(ref Vector2 value1, ref Vector2 min, ref Vector2 max, out Vector2 result)
        {
            result.X = MathHelper.Clamp(value1.X, min.X, max.X);
            result.Y = MathHelper.Clamp(value1.Y, min.Y, max.Y);
        }

        /// <summary>
        /// Returns the distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The distance between two vectors.</returns>
        public static float Distance(Vector2 value1, Vector2 value2)
        {
            float dX = value1.X - value2.X;
            float dY = value1.Y - value2.Y;
            return (float)Math.Sqrt(dX * dX + dY * dY);
        }

        /// <summary>
        /// Returns the distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">The distance between two vectors as an output parameter.</param>
        public static void Distance(ref Vector2 value1, ref Vector2 value2, out float result)
        {
            float v1 = value1.X - value2.X, v2 = value1.Y - value2.Y;
            result = (float)Math.Sqrt((v1 * v1) + (v2 * v2));
        }

        /// <summary>
        /// Returns the squared distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The squared distance between two vectors.</returns>
        public static float DistanceSquared(Vector2 value1, Vector2 value2)
        {
            float dX = value1.X - value2.X;
            float dY = value1.Y - value2.Y;
            return (dX * dX + dY * dY);
        }

        /// <summary>
        /// Returns the squared distance between two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">The squared distance between two vectors as an output parameter.</param>
        public static void DistanceSquared(ref Vector2 value1, ref Vector2 value2, out float result)
        {
            float v1 = value1.X - value2.X, v2 = value1.Y - value2.Y;
            result = (v1 * v1) + (v2 * v2);
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by the components of another <see cref="Vector2"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Divisor <see cref="Vector2"/>.</param>
        /// <returns>The result of dividing the vectors.</returns>
        public static Vector2 Divide(Vector2 left, Vector2 right)
        {
            left.X /= right.X;
            left.Y /= right.Y;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by the components of another <see cref="Vector2"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Divisor <see cref="Vector2"/>.</param>
        /// <param name="result">The result of dividing the vectors as an output parameter.</param>
        public static void Divide(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X / right.X;
            result.Y = left.Y / right.Y;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Divisor scalar.</param>
        /// <returns>The result of dividing a vector by a scalar.</returns>
        public static Vector2 Divide(Vector2 left, float right)
        {
            float factor = 1 / right;
            left.X *= factor;
            left.Y *= factor;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector2"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Divisor scalar.</param>
        /// <param name="result">The result of dividing a vector by a scalar as an output parameter.</param>
        public static void Divide(ref Vector2 left, float right, out Vector2 result)
        {
            float factor = 1 / right;
            result.X = left.X * factor;
            result.Y = left.Y * factor;
        }

        /// <summary>
        /// Returns a dot product of two vectors.
        /// </summary>
        /// <param name="left">The first vector.</param>
        /// <param name="right">The second vector.</param>
        /// <returns>The dot product of two vectors.</returns>
        public static float Dot(Vector2 left, Vector2 right)
        {
            return left.X * right.X + left.Y * right.Y;
        }

        /// <summary>
        /// Returns a dot product of two vectors.
        /// </summary>
        /// <param name="left">The first vector.</param>
        /// <param name="right">The second vector.</param>
        /// <param name="result">The dot product of two vectors as an output parameter.</param>
        public static void Dot(ref Vector2 left, ref Vector2 right, out float result)
        {
            result = left.X * right.X + left.Y * right.Y;
        }

        /// <summary>
        /// Compares whether current instance is equal to specified <see cref="Object"/>.
        /// </summary>
        /// <param name="obj">The <see cref="Object"/> to compare.</param>
        /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (obj is Vector2)
            {
                return Equals((Vector2)obj);
            }

            return false;
        }

        /// <summary>
        /// Compares whether current instance is equal to specified <see cref="Vector2"/>.
        /// </summary>
        /// <param name="other">The <see cref="Vector2"/> to compare.</param>
        /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
        public bool Equals(Vector2 other)
        {
            return (X == other.X) && (Y == other.Y);
        }

        /// <summary>
        /// Round the members of this <see cref="Vector2"/> towards negative infinity.
        /// </summary>
        public void Floor()
        {
            X = (float)Math.Floor(X);
            Y = (float)Math.Floor(Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded towards negative infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <returns>The rounded <see cref="Vector2"/>.</returns>
        public static Vector2 Floor(Vector2 value)
        {
            value.X = (float)Math.Floor(value.X);
            value.Y = (float)Math.Floor(value.Y);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded towards negative infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The rounded <see cref="Vector2"/>.</param>
        public static void Floor(ref Vector2 value, out Vector2 result)
        {
            result.X = (float)Math.Floor(value.X);
            result.Y = (float)Math.Floor(value.Y);
        }

        /// <summary>
        /// Gets the hash code of this <see cref="Vector2"/>.
        /// </summary>
        /// <returns>Hash code of this <see cref="Vector2"/>.</returns>
        public override int GetHashCode()
        {
            unchecked
            {
                return (X.GetHashCode() * 397) ^ Y.GetHashCode();
            }
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains hermite spline interpolation.
        /// </summary>
        /// <param name="value1">The first position vector.</param>
        /// <param name="tangent1">The first tangent vector.</param>
        /// <param name="value2">The second position vector.</param>
        /// <param name="tangent2">The second tangent vector.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <returns>The hermite spline interpolation vector.</returns>
        public static Vector2 Hermite(Vector2 value1, Vector2 tangent1, Vector2 value2, Vector2 tangent2, float amount)
        {
            return new Vector2(MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount), MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount));
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains hermite spline interpolation.
        /// </summary>
        /// <param name="value1">The first position vector.</param>
        /// <param name="tangent1">The first tangent vector.</param>
        /// <param name="value2">The second position vector.</param>
        /// <param name="tangent2">The second tangent vector.</param>
        /// <param name="amount">Weighting factor.</param>
        /// <param name="result">The hermite spline interpolation vector as an output parameter.</param>
        public static void Hermite(ref Vector2 value1, ref Vector2 tangent1, ref Vector2 value2, ref Vector2 tangent2, float amount, out Vector2 result)
        {
            result.X = MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
            result.Y = MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
        }

        /// <summary>
        /// Returns the length of this <see cref="Vector2"/>.
        /// </summary>
        /// <returns>The length of this <see cref="Vector2"/>.</returns>
        public float Length()
        {
            return (float)Math.Sqrt((X * X) + (Y * Y));
        }

        /// <summary>
        /// Returns the squared length of this <see cref="Vector2"/>.
        /// </summary>
        /// <returns>The squared length of this <see cref="Vector2"/>.</returns>
        public float LengthSquared()
        {
            return (X * X) + (Y * Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains linear interpolation of the specified vectors.
        /// </summary>
        /// <param name="start">The first vector.</param>
        /// <param name="end">The second vector.</param>
        /// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
        /// <returns>The result of linear interpolation of the specified vectors.</returns>
        public static Vector2 Lerp(Vector2 start, Vector2 end, float amount)
        {
            Vector2 result;
            result.X = MathHelper.Lerp(start.X, end.X, amount);
            result.Y = MathHelper.Lerp(start.Y, end.Y, amount);
            return result;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains linear interpolation of the specified vectors.
        /// </summary>
        /// <param name="start">The first vector.</param>
        /// <param name="end">The second vector.</param>
        /// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
        /// <param name="result">The result of linear interpolation of the specified vectors as an output parameter.</param>
        public static void Lerp(ref Vector2 start, ref Vector2 end, float amount, out Vector2 result)
        {
            result.X = MathHelper.Lerp(start.X, end.X, amount);
            result.Y = MathHelper.Lerp(start.Y, end.Y, amount);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains linear interpolation of the specified vectors.
        /// Uses <see cref="MathHelper.LerpPrecise"/> on MathHelper for the interpolation.
        /// Less efficient but more precise compared to <see cref="Vector2.Lerp(Vector2, Vector2, float)"/>.
        /// See remarks section of <see cref="MathHelper.LerpPrecise"/> on MathHelper for more info.
        /// </summary>
        /// <param name="start">The first vector.</param>
        /// <param name="end">The second vector.</param>
        /// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
        /// <returns>The result of linear interpolation of the specified vectors.</returns>
        public static Vector2 LerpPrecise(Vector2 start, Vector2 end, float amount)
        {
            Vector2 result;
            result.X = MathHelper.LerpPrecise(start.X, end.X, amount);
            result.Y = MathHelper.LerpPrecise(start.Y, end.Y, amount);
            return result;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains linear interpolation of the specified vectors.
        /// Uses <see cref="MathHelper.LerpPrecise"/> on MathHelper for the interpolation.
        /// Less efficient but more precise compared to <see cref="Vector2.Lerp(ref Vector2, ref Vector2, float, out Vector2)"/>.
        /// See remarks section of <see cref="MathHelper.LerpPrecise"/> on MathHelper for more info.
        /// </summary>
        /// <param name="start">The first vector.</param>
        /// <param name="end">The second vector.</param>
        /// <param name="amount">Weighting value(between 0.0 and 1.0).</param>
        /// <param name="result">The result of linear interpolation of the specified vectors as an output parameter.</param>
        public static void LerpPrecise(ref Vector2 start, ref Vector2 end, float amount, out Vector2 result)
        { 
            result.X = MathHelper.LerpPrecise(start.X, end.X, amount);
            result.Y = MathHelper.LerpPrecise(start.Y, end.Y, amount);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a maximal values from the two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The <see cref="Vector2"/> with maximal values from the two vectors.</returns>
        public static Vector2 Max(Vector2 value1, Vector2 value2)
        {
            return new Vector2(value1.X > value2.X ? value1.X : value2.X,
                               value1.Y > value2.Y ? value1.Y : value2.Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a maximal values from the two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">The <see cref="Vector2"/> with maximal values from the two vectors as an output parameter.</param>
        public static void Max(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
        {
            result.X = value1.X > value2.X ? value1.X : value2.X;
            result.Y = value1.Y > value2.Y ? value1.Y : value2.Y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a minimal values from the two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The <see cref="Vector2"/> with minimal values from the two vectors.</returns>
        public static Vector2 Min(Vector2 value1, Vector2 value2)
        {
            return new Vector2(value1.X < value2.X ? value1.X : value2.X,
                               value1.Y < value2.Y ? value1.Y : value2.Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a minimal values from the two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">The <see cref="Vector2"/> with minimal values from the two vectors as an output parameter.</param>
        public static void Min(ref Vector2 value1, ref Vector2 value2, out Vector2 result)
        {
            result.X = value1.X < value2.X ? value1.X : value2.X;
            result.Y = value1.Y < value2.Y ? value1.Y : value2.Y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a multiplication of two vectors.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Source <see cref="Vector2"/>.</param>
        /// <returns>The result of the vector multiplication.</returns>
        public static Vector2 Multiply(Vector2 left, Vector2 right)
        {
            left.X *= right.X;
            left.Y *= right.Y;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a multiplication of two vectors.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The result of the vector multiplication as an output parameter.</param>
        public static void Multiply(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X * right.X;
            result.Y = left.Y * right.Y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a multiplication of <see cref="Vector2"/> and a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Scalar value.</param>
        /// <returns>The result of the vector multiplication with a scalar.</returns>
        public static Vector2 Multiply(Vector2 left, float right)
        {
            left.X *= right;
            left.Y *= right;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a multiplication of <see cref="Vector2"/> and a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Scalar value.</param>
        /// <param name="result">The result of the multiplication with a scalar as an output parameter.</param>
        public static void Multiply(ref Vector2 left, float right, out Vector2 result)
        {
            result.X = left.X * right;
            result.Y = left.Y * right;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains the specified vector inversion.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <returns>The result of the vector inversion.</returns>
        public static Vector2 Negate(Vector2 value)
        {
            value.X = -value.X;
            value.Y = -value.Y;
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains the specified vector inversion.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The result of the vector inversion as an output parameter.</param>
        public static void Negate(ref Vector2 value, out Vector2 result)
        {
            result.X = -value.X;
            result.Y = -value.Y;
        }

        /// <summary>
        /// Turns this <see cref="Vector2"/> to a unit vector with the same direction.
        /// </summary>
        public void Normalize()
        {
            float val = 1.0f / (float)Math.Sqrt((X * X) + (Y * Y));
            X *= val;
            Y *= val;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a normalized values from another vector.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <returns>Unit vector.</returns>
        public static Vector2 Normalize(Vector2 value)
        {
            float val = 1.0f / (float)Math.Sqrt((value.X * value.X) + (value.Y * value.Y));
            value.X *= val;
            value.Y *= val;
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a normalized values from another vector.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="result">Unit vector as an output parameter.</param>
        public static void Normalize(ref Vector2 value, out Vector2 result)
        {
            float val = 1.0f / (float)Math.Sqrt((value.X * value.X) + (value.Y * value.Y));
            result.X = value.X * val;
            result.Y = value.Y * val;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains reflect vector of the given vector and normal.
        /// </summary>
        /// <param name="vector">Source <see cref="Vector2"/>.</param>
        /// <param name="normal">Reflection normal.</param>
        /// <returns>Reflected vector.</returns>
        public static Vector2 Reflect(Vector2 vector, Vector2 normal)
        {
            Vector2 result;
            float val = 2.0f * ((vector.X * normal.X) + (vector.Y * normal.Y));
            result.X = vector.X - (normal.X * val);
            result.Y = vector.Y - (normal.Y * val);
            return result;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains reflect vector of the given vector and normal.
        /// </summary>
        /// <param name="vector">Source <see cref="Vector2"/>.</param>
        /// <param name="normal">Reflection normal.</param>
        /// <param name="result">Reflected vector as an output parameter.</param>
        public static void Reflect(ref Vector2 vector, ref Vector2 normal, out Vector2 result)
        {
            float val = 2.0f * ((vector.X * normal.X) + (vector.Y * normal.Y));
            result.X = vector.X - (normal.X * val);
            result.Y = vector.Y - (normal.Y * val);
        }

        /// <summary>
        /// Round the members of this <see cref="Vector2"/> to the nearest integer value.
        /// </summary>
        public void Round()
        {
            X = (float)Math.Round(X);
            Y = (float)Math.Round(Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded to the nearest integer value.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <returns>The rounded <see cref="Vector2"/>.</returns>
        public static Vector2 Round(Vector2 value)
        {
            value.X = (float)Math.Round(value.X);
            value.Y = (float)Math.Round(value.Y);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains members from another vector rounded to the nearest integer value.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The rounded <see cref="Vector2"/>.</param>
        public static void Round(ref Vector2 value, out Vector2 result)
        {
            result.X = (float)Math.Round(value.X);
            result.Y = (float)Math.Round(value.Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains cubic interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector2"/>.</param>
        /// <param name="value2">Source <see cref="Vector2"/>.</param>
        /// <param name="amount">Weighting value.</param>
        /// <returns>Cubic interpolation of the specified vectors.</returns>
        public static Vector2 SmoothStep(Vector2 value1, Vector2 value2, float amount)
        {
            return new Vector2(
                MathHelper.SmoothStep(value1.X, value2.X, amount),
                MathHelper.SmoothStep(value1.Y, value2.Y, amount));
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains cubic interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector2"/>.</param>
        /// <param name="value2">Source <see cref="Vector2"/>.</param>
        /// <param name="amount">Weighting value.</param>
        /// <param name="result">Cubic interpolation of the specified vectors as an output parameter.</param>
        public static void SmoothStep(ref Vector2 value1, ref Vector2 value2, float amount, out Vector2 result)
        {
            result.X = MathHelper.SmoothStep(value1.X, value2.X, amount);
            result.Y = MathHelper.SmoothStep(value1.Y, value2.Y, amount);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains subtraction of on <see cref="Vector2"/> from a another.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Source <see cref="Vector2"/>.</param>
        /// <returns>The result of the vector subtraction.</returns>
        public static Vector2 Subtract(Vector2 left, Vector2 right)
        {
            left.X -= right.X;
            left.Y -= right.Y;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains subtraction of on <see cref="Vector2"/> from a another.
        /// </summary>
        /// <param name="left">Source <see cref="Vector2"/>.</param>
        /// <param name="right">Source <see cref="Vector2"/>.</param>
        /// <param name="result">The result of the vector subtraction as an output parameter.</param>
        public static void Subtract(ref Vector2 left, ref Vector2 right, out Vector2 result)
        {
            result.X = left.X - right.X;
            result.Y = left.Y - right.Y;
        }

        /// <summary>
        /// Returns a <see cref="String"/> representation of this <see cref="Vector2"/> in the format:
        /// {X:[<see cref="X"/>] Y:[<see cref="Y"/>]}
        /// </summary>
        /// <returns>A <see cref="String"/> representation of this <see cref="Vector2"/>.</returns>
        public override string ToString()
        {
            return String.Format("{{X: {0}, Y: {1} }}", X, Y);
        }

        /// <summary>
        /// Gets a <see cref="Point"/> representation for this object.
        /// </summary>
        /// <returns>A <see cref="Point"/> representation for this object.</returns>
        public Point ToPoint()
        {
            return new Point((int) X,(int) Y);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="position">Source <see cref="Vector2"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <returns>Transformed <see cref="Vector2"/>.</returns>
        public static Vector2 Transform(Vector2 position, Matrix matrix)
        {
            return new Vector2((position.X * matrix.M11) + (position.Y * matrix.M21) + matrix.M41, (position.X * matrix.M12) + (position.Y * matrix.M22) + matrix.M42);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="position">Source <see cref="Vector2"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="result">Transformed <see cref="Vector2"/> as an output parameter.</param>
        public static void Transform(ref Vector2 position, ref Matrix matrix, out Vector2 result)
        {
            var x = (position.X * matrix.M11) + (position.Y * matrix.M21) + matrix.M41;
            var y = (position.X * matrix.M12) + (position.Y * matrix.M22) + matrix.M42;
            result.X = x;
            result.Y = y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <returns>Transformed <see cref="Vector2"/>.</returns>
        public static Vector2 Transform(Vector2 value, Quaternion rotation)
        {
            Transform(ref value, ref rotation, out value);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <param name="result">Transformed <see cref="Vector2"/> as an output parameter.</param>
        public static void Transform(ref Vector2 value, ref Quaternion rotation, out Vector2 result)
        {
            var rot1 = new Vector3(rotation.X + rotation.X, rotation.Y + rotation.Y, rotation.Z + rotation.Z);
            var rot2 = new Vector3(rotation.X, rotation.X, rotation.W);
            var rot3 = new Vector3(1, rotation.Y, rotation.Z);
            var rot4 = rot1*rot2;
            var rot5 = rot1*rot3;

            var v = new Vector2();
            v.X = (float)((double)value.X * (1.0 - (double)rot5.Y - (double)rot5.Z) + (double)value.Y * ((double)rot4.Y - (double)rot4.Z));
            v.Y = (float)((double)value.X * ((double)rot4.Y + (double)rot4.Z) + (double)value.Y * (1.0 - (double)rot4.X - (double)rot5.Z));
            result.X = v.X;
            result.Y = v.Y;
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Complex"/> number.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="complex">The transformation <see cref="Complex"/> number which contains rotation and magnitude transformation.</param>
        /// <returns>Transformed <see cref="Vector2"/>.</returns>
        public static Vector2 Transform(Vector2 value, Complex complex)
        {
            return new Vector2(value.X * complex.R - value.Y * complex.i,
                               value.Y * complex.R + value.X * complex.i);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Complex"/> number.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="complex">The transformation <see cref="Complex"/> which contains rotation and magnitude transformation.</param>
        /// <param name="result">Transformed <see cref="Vector2"/> as an output parameter.</param>
        public static void Transform(ref Vector2 value, ref Complex complex, out Vector2 result)
        {
            result = new Vector2(value.X * complex.R - value.Y * complex.i,
                                 value.Y * complex.R + value.X * complex.i);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of 2d-vector by the specified <see cref="Pose2"/> number.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="pose">The transformation <see cref="Pose2"/> which contains rotation and translation transformation.</param>
        /// <returns>Transformed <see cref="Vector2"/>.</returns>
        public static Vector2 Transform(Vector2 value, Pose2 pose)
        {
            Vector2 result;
            Vector2.Transform(ref value, ref pose.Orientation, out result);
            Vector2.Add(ref result, ref pose.Translation, out result);
            return result;
        }

        /// <summary>
        /// Apply transformation on vectors within array of <see cref="Vector2"/> by the specified <see cref="Matrix"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="sourceIndex">The starting index of transformation in the source array.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="destinationArray">Destination array.</param>
        /// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector2"/> should be written.</param>
        /// <param name="length">The number of vectors to be transformed.</param>
        public static void Transform
        (
            Vector2[] sourceArray, int sourceIndex,
            ref Matrix matrix,
            Vector2[] destinationArray, int destinationIndex,
            int length
        )
        {
            if (sourceArray == null)
                throw new ArgumentNullException("sourceArray");
            if (destinationArray == null)
                throw new ArgumentNullException("destinationArray");
            if (sourceArray.Length < sourceIndex + length)
                throw new ArgumentException("Source array length is lesser than sourceIndex + length");
            if (destinationArray.Length < destinationIndex + length)
                throw new ArgumentException("Destination array length is lesser than destinationIndex + length");

            for (int x = 0; x < length; x++)
            {
                Vector2.Transform(ref sourceArray[sourceIndex + x], ref matrix, out destinationArray[destinationIndex + x]);
            }
        }

        /// <summary>
        /// Apply transformation on vectors within array of <see cref="Vector2"/> by the specified <see cref="Quaternion"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="sourceIndex">The starting index of transformation in the source array.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <param name="destinationArray">Destination array.</param>
        /// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector2"/> should be written.</param>
        /// <param name="length">The number of vectors to be transformed.</param>
        public static void Transform
        (
            Vector2[] sourceArray, int sourceIndex,
            ref Quaternion rotation,
            Vector2[] destinationArray, int destinationIndex,
            int length
        )
        {
            if (sourceArray == null)
                throw new ArgumentNullException("sourceArray");
            if (destinationArray == null)
                throw new ArgumentNullException("destinationArray");
            if (sourceArray.Length < sourceIndex + length)
                throw new ArgumentException("Source array length is lesser than sourceIndex + length");
            if (destinationArray.Length < destinationIndex + length)
                throw new ArgumentException("Destination array length is lesser than destinationIndex + length");

            for (int x = 0; x < length; x++)
            {
                Vector2.Transform(ref sourceArray[sourceIndex + x], ref rotation, out destinationArray[destinationIndex + x]);
            }
        }

        /// <summary>
        /// Apply transformation on vectors within array of <see cref="Vector2"/> by the specified <see cref="Complex"/> number and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="sourceIndex">The starting index of transformation in the source array.</param>
        /// <param name="complex">The transformation <see cref="Complex"/> number.</param>
        /// <param name="destinationArray">Destination array.</param>
        /// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector2"/> should be written.</param>
        /// <param name="length">The number of vectors to be transformed.</param>
        public static void Transform
        (
            Vector2[] sourceArray, int sourceIndex,
            ref Complex complex,
            Vector2[] destinationArray, int destinationIndex,
            int length
        )
        {
            if (sourceArray == null)
                throw new ArgumentNullException("sourceArray");
            if (destinationArray == null)
                throw new ArgumentNullException("destinationArray");
            if (sourceArray.Length < sourceIndex + length)
                throw new ArgumentException("Source array length is lesser than sourceIndex + length");
            if (destinationArray.Length < destinationIndex + length)
                throw new ArgumentException("Destination array length is lesser than destinationIndex + length");

            for (int x = 0; x < length; x++)
            {
                Vector2.Transform(ref sourceArray[sourceIndex + x], ref complex, out destinationArray[destinationIndex + x]);
            }
        }

        /// <summary>
        /// Apply transformation on all vectors within array of <see cref="Vector2"/> by the specified <see cref="Matrix"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="destinationArray">Destination array.</param>
        public static void Transform(Vector2[] sourceArray, ref Matrix matrix, Vector2[] destinationArray)
        {
            Vector2.Transform(sourceArray, 0, ref matrix, destinationArray, 0, sourceArray.Length);
        }

        /// <summary>
        /// Apply transformation on all vectors within array of <see cref="Vector2"/> by the specified <see cref="Quaternion"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <param name="destinationArray">Destination array.</param>
        public static void Transform(Vector2[] sourceArray, ref Quaternion rotation, Vector2[] destinationArray)
        {
            Vector2.Transform(sourceArray, 0, ref rotation, destinationArray, 0, sourceArray.Length);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of the specified normal by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="normal">Source <see cref="Vector2"/> which represents a normal vector.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <returns>Transformed normal.</returns>
        public static Vector2 TransformNormal(Vector2 normal, Matrix matrix)
        {
            return new Vector2((normal.X * matrix.M11) + (normal.Y * matrix.M21),(normal.X * matrix.M12) + (normal.Y * matrix.M22));
        }

        /// <summary>
        /// Apply transformation on all vectors within array of <see cref="Vector2"/> by the specified <see cref="Complex"/> number and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="complex">The <see cref="Complex"/> number which contains rotation and magnitude transformation.</param>
        /// <param name="destinationArray">Destination array.</param>
        public static void Transform(Vector2[] sourceArray, ref Complex complex, Vector2[] destinationArray)
        {
            Vector2.Transform(sourceArray, 0, ref complex, destinationArray, 0, sourceArray.Length);
        }

        /// <summary>
        /// Creates a new <see cref="Vector2"/> that contains a transformation of the specified normal by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="normal">Source <see cref="Vector2"/> which represents a normal vector.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="result">Transformed normal as an output parameter.</param>
        public static void TransformNormal(ref Vector2 normal, ref Matrix matrix, out Vector2 result)
        {
            var x = (normal.X * matrix.M11) + (normal.Y * matrix.M21);
            var y = (normal.X * matrix.M12) + (normal.Y * matrix.M22);
            result.X = x;
            result.Y = y;
        }

        /// <summary>
        /// Apply transformation on normals within array of <see cref="Vector2"/> by the specified <see cref="Matrix"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="sourceIndex">The starting index of transformation in the source array.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="destinationArray">Destination array.</param>
        /// <param name="destinationIndex">The starting index in the destination array, where the first <see cref="Vector2"/> should be written.</param>
        /// <param name="length">The number of normals to be transformed.</param>
        public static void TransformNormal
        (
            Vector2[] sourceArray, int sourceIndex,
            ref Matrix matrix,
            Vector2[] destinationArray, int destinationIndex,
            int length
        )
        {
            if (sourceArray == null)
                throw new ArgumentNullException("sourceArray");
            if (destinationArray == null)
                throw new ArgumentNullException("destinationArray");
            if (sourceArray.Length < sourceIndex + length)
                throw new ArgumentException("Source array length is lesser than sourceIndex + length");
            if (destinationArray.Length < destinationIndex + length)
                throw new ArgumentException("Destination array length is lesser than destinationIndex + length");

            for (int i = 0; i < length; i++)
            {
                Vector2.TransformNormal(ref sourceArray[sourceIndex + i], ref matrix, out destinationArray[destinationIndex + i]);
            }
        }

        /// <summary>
        /// Apply transformation on all normals within array of <see cref="Vector2"/> by the specified <see cref="Matrix"/> and places the results in an another array.
        /// </summary>
        /// <param name="sourceArray">Source array.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="destinationArray">Destination array.</param>
        public static void TransformNormal(Vector2[] sourceArray, ref Matrix matrix,Vector2[] destinationArray)
        {
            Vector2.TransformNormal(sourceArray, 0, ref matrix, destinationArray, 0, sourceArray.Length);
        }

        /// <summary>
        /// Deconstruction method for <see cref="Vector2"/>.
        /// </summary>
        /// <param name="x"></param>
        /// <param name="y"></param>
        public void Deconstruct(out float x, out float y)
        {
            x = X;
            y = Y;
        }

        #endregion
    }
}