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Root/src/Vector4.cs

#region License
/* FNA - XNA4 Reimplementation for Desktop Platforms
 * Copyright 2009-2016 Ethan Lee and the MonoGame Team
 *
 * Released under the Microsoft Public License.
 * See LICENSE for details.
 */
 
/* Derived from code by the Mono.Xna Team (Copyright 2006).
 * Released under the MIT License. See monoxna.LICENSE for details.
 */
#endregion
 
#region Using Statements
using System;
using System.ComponentModel;
using System.Diagnostics;
 
using Microsoft.Xna.Framework.Design;
#endregion
 
namespace Microsoft.Xna.Framework
{
    /// <summary>
    /// Describes a 4D-vector.
    /// </summary>
    [Serializable]
    [TypeConverter(typeof(Vector4Converter))]
    [DebuggerDisplay("{DebugDisplayString,nq}")]
    public struct Vector4 : IEquatable<Vector4>
    {
        #region Public Static Properties
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 0, 0, 0, 0.
        /// </summary>
        public static Vector4 Zero
        {
            get
            {
                return zero;
            }
        }
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 1, 1, 1, 1.
        /// </summary>
        public static Vector4 One
        {
            get
            {
                return unit;
            }
        }
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 1, 0, 0, 0.
        /// </summary>
        public static Vector4 UnitX
        {
            get
            {
                return unitX;
            }
        }
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 0, 1, 0, 0.
        /// </summary>
        public static Vector4 UnitY
        {
            get
            {
                return unitY;
            }
        }
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 0, 0, 1, 0.
        /// </summary>
        public static Vector4 UnitZ
        {
            get
            {
                return unitZ;
            }
        }
 
        /// <summary>
        /// Returns a <see cref="Vector4"/> with components 0, 0, 0, 1.
        /// </summary>
        public static Vector4 UnitW
        {
            get
            {
                return unitW;
            }
        }
 
        #endregion
 
        #region Internal Properties
 
        internal string DebugDisplayString
        {
            get
            {
                return string.Concat(
                    X.ToString(), " ",
                    Y.ToString(), " ",
                    Z.ToString(), " ",
                    W.ToString()
                );
            }
        }
 
        #endregion
 
        #region Public Fields
 
        /// <summary>
        /// The x coordinate of this <see cref="Vector4"/>.
        /// </summary>
        public float X;
 
        /// <summary>
        /// The y coordinate of this <see cref="Vector4"/>.
        /// </summary>
        public float Y;
 
        /// <summary>
        /// The z coordinate of this <see cref="Vector4"/>.
        /// </summary>
        public float Z;
 
        /// <summary>
        /// The w coordinate of this <see cref="Vector4"/>.
        /// </summary>
        public float W;
 
        #endregion
 
        #region Private Static Fields
 
        private static Vector4 zero = new Vector4(); // Not readonly for performance -flibit
        private static readonly Vector4 unit = new Vector4(1f, 1f, 1f, 1f);
        private static readonly Vector4 unitX = new Vector4(1f, 0f, 0f, 0f);
        private static readonly Vector4 unitY = new Vector4(0f, 1f, 0f, 0f);
        private static readonly Vector4 unitZ = new Vector4(0f, 0f, 1f, 0f);
        private static readonly Vector4 unitW = new Vector4(0f, 0f, 0f, 1f);
 
        #endregion
 
        #region Public Constructors
 
        /// <summary>
        /// Constructs a 3d vector with X, Y, Z and W from four values.
        /// </summary>
        /// <param name="x">The x coordinate in 4d-space.</param>
        /// <param name="y">The y coordinate in 4d-space.</param>
        /// <param name="z">The z coordinate in 4d-space.</param>
        /// <param name="w">The w coordinate in 4d-space.</param>
        public Vector4(float x, float y, float z, float w)
        {
            this.X = x;
            this.Y = y;
            this.Z = z;
            this.W = w;
        }
 
        /// <summary>
        /// Constructs a 3d vector with X and Z from <see cref="Vector2"/> and Z and W from the scalars.
        /// </summary>
        /// <param name="value">The x and y coordinates in 4d-space.</param>
        /// <param name="z">The z coordinate in 4d-space.</param>
        /// <param name="w">The w coordinate in 4d-space.</param>
        public Vector4(Vector2 value, float z, float w)
        {
            this.X = value.X;
            this.Y = value.Y;
            this.Z = z;
            this.W = w;
        }
 
        /// <summary>
        /// Constructs a 3d vector with X, Y, Z from <see cref="Vector3"/> and W from a scalar.
        /// </summary>
        /// <param name="value">The x, y and z coordinates in 4d-space.</param>
        /// <param name="w">The w coordinate in 4d-space.</param>
        public Vector4(Vector3 value, float w)
        {
            this.X = value.X;
            this.Y = value.Y;
            this.Z = value.Z;
            this.W = w;
        }
 
        /// <summary>
        /// Constructs a 4d vector with X, Y, Z and W set to the same value.
        /// </summary>
        /// <param name="value">The x, y, z and w coordinates in 4d-space.</param>
        public Vector4(float value)
        {
            this.X = value;
            this.Y = value;
            this.Z = value;
            this.W = value;
        }
 
        #endregion
 
        #region Public Methods
 
        /// <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)
        {
            return (obj is Vector4) ? this == (Vector4) obj : false;
        }
 
        /// <summary>
        /// Compares whether current instance is equal to specified <see cref="Vector4"/>.
        /// </summary>
        /// <param name="other">The <see cref="Vector4"/> to compare.</param>
        /// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
        public bool Equals(Vector4 other)
        {
            return (    (MathHelper.WithinEpsilon(this.W, other.W)) &&
                    (MathHelper.WithinEpsilon(this.X, other.X)) &&
                    (MathHelper.WithinEpsilon(this.Y, other.Y)) &&
                    (MathHelper.WithinEpsilon(this.Z, other.Z)) );
        }
 
        /// <summary>
        /// Gets the hash code of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>Hash code of this <see cref="Vector4"/>.</returns>
        public override int GetHashCode()
        {
            return (int) (this.W + this.X + this.Y + this.Y);
        }
 
        /// <summary>
        /// Returns the length of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>The length of this <see cref="Vector4"/>.</returns>
        public float Length()
        {
            float result;
            DistanceSquared(ref this, ref zero, out result);
            return (float) Math.Sqrt(result);
        }
 
        /// <summary>
        /// Returns the squared length of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>The squared length of this <see cref="Vector4"/>.</returns>
        public float LengthSquared()
        {
            float result;
            DistanceSquared(ref this, ref zero, out result);
            return result;
        }
 
        /// <summary>
        /// Turns this <see cref="Vector4"/> to a unit vector with the same direction.
        /// </summary>
        public void Normalize()
        {
            Normalize(ref this, out this);
        }
 
        public override string ToString()
        {
            return (
                "{X:" + X.ToString() +
                " Y:" + Y.ToString() +
                " Z:" + Z.ToString() +
                " W:" + W.ToString() + "}"
            );
        }
 
        #endregion
 
        #region Public Static Methods
 
        /// <summary>
        /// Performs vector addition on <paramref name="value1"/> and <paramref name="value2"/>.
        /// </summary>
        /// <param name="value1">The first vector to add.</param>
        /// <param name="value2">The second vector to add.</param>
        /// <returns>The result of the vector addition.</returns>
        public static Vector4 Add(Vector4 value1, Vector4 value2)
        {
            value1.W += value2.W;
            value1.X += value2.X;
            value1.Y += value2.Y;
            value1.Z += value2.Z;
            return value1;
        }
 
        /// <summary>
        /// Performs vector addition on <paramref name="value1"/> and
        /// <paramref name="value2"/>, storing the result of the
        /// addition in <paramref name="result"/>.
        /// </summary>
        /// <param name="value1">The first vector to add.</param>
        /// <param name="value2">The second vector to add.</param>
        /// <param name="result">The result of the vector addition.</param>
        public static void Add(ref Vector4 value1, ref Vector4 value2, out Vector4 result)
        {
            result.W = value1.W + value2.W;
            result.X = value1.X + value2.X;
            result.Y = value1.Y + value2.Y;
            result.Z = value1.Z + value2.Z;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 4d-triangle.
        /// </summary>
        /// <param name="value1">The first vector of 4d-triangle.</param>
        /// <param name="value2">The second vector of 4d-triangle.</param>
        /// <param name="value3">The third vector of 4d-triangle.</param>
        /// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 4d-triangle.</param>
        /// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 4d-triangle.</param>
        /// <returns>The cartesian translation of barycentric coordinates.</returns>
        public static Vector4 Barycentric(
            Vector4 value1,
            Vector4 value2,
            Vector4 value3,
            float amount1,
            float amount2
        ) {
            return new Vector4(
                MathHelper.Barycentric(value1.X, value2.X, value3.X, amount1, amount2),
                MathHelper.Barycentric(value1.Y, value2.Y, value3.Y, amount1, amount2),
                MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2),
                MathHelper.Barycentric(value1.W, value2.W, value3.W, amount1, amount2)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 4d-triangle.
        /// </summary>
        /// <param name="value1">The first vector of 4d-triangle.</param>
        /// <param name="value2">The second vector of 4d-triangle.</param>
        /// <param name="value3">The third vector of 4d-triangle.</param>
        /// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 4d-triangle.</param>
        /// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 4d-triangle.</param>
        /// <param name="result">The cartesian translation of barycentric coordinates as an output parameter.</param>
        public static void Barycentric(
            ref Vector4 value1,
            ref Vector4 value2,
            ref Vector4 value3,
            float amount1,
            float amount2,
            out Vector4 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);
            result.Z = MathHelper.Barycentric(value1.Z, value2.Z, value3.Z, amount1, amount2);
            result.W = MathHelper.Barycentric(value1.W, value2.W, value3.W, amount1, amount2);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 CatmullRom(
            Vector4 value1,
            Vector4 value2,
            Vector4 value3,
            Vector4 value4,
            float amount
        ) {
            return new Vector4(
                MathHelper.CatmullRom(value1.X, value2.X, value3.X, value4.X, amount),
                MathHelper.CatmullRom(value1.Y, value2.Y, value3.Y, value4.Y, amount),
                MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount),
                MathHelper.CatmullRom(value1.W, value2.W, value3.W, value4.W, amount)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 value1,
            ref Vector4 value2,
            ref Vector4 value3,
            ref Vector4 value4,
            float amount,
            out Vector4 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);
            result.Z = MathHelper.CatmullRom(value1.Z, value2.Z, value3.Z, value4.Z, amount);
            result.W = MathHelper.CatmullRom(value1.W, value2.W, value3.W, value4.W, amount);
        }
 
        /// <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 Vector4 Clamp(Vector4 value1, Vector4 min, Vector4 max)
        {
            return new Vector4(
                MathHelper.Clamp(value1.X, min.X, max.X),
                MathHelper.Clamp(value1.Y, min.Y, max.Y),
                MathHelper.Clamp(value1.Z, min.Z, max.Z),
                MathHelper.Clamp(value1.W, min.W, max.W)
            );
        }
 
        /// <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 Vector4 value1,
            ref Vector4 min,
            ref Vector4 max,
            out Vector4 result
        ) {
            result.X = MathHelper.Clamp(value1.X, min.X, max.X);
            result.Y = MathHelper.Clamp(value1.Y, min.Y, max.Y);
            result.Z = MathHelper.Clamp(value1.Z, min.Z, max.Z);
            result.W = MathHelper.Clamp(value1.W, min.W, max.W);
        }
 
        /// <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(Vector4 value1, Vector4 value2)
        {
            return (float) Math.Sqrt(DistanceSquared(value1, value2));
        }
 
        /// <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 Vector4 value1, ref Vector4 value2, out float result)
        {
            result = (float) Math.Sqrt(DistanceSquared(value1, value2));
        }
 
        /// <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(Vector4 value1, Vector4 value2)
        {
            return (
                (value1.W - value2.W) * (value1.W - value2.W) +
                (value1.X - value2.X) * (value1.X - value2.X) +
                (value1.Y - value2.Y) * (value1.Y - value2.Y) +
                (value1.Z - value2.Z) * (value1.Z - value2.Z)
            );
        }
 
        /// <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 Vector4 value1,
            ref Vector4 value2,
            out float result
        ) {
            result = (
                (value1.W - value2.W) * (value1.W - value2.W) +
                (value1.X - value2.X) * (value1.X - value2.X) +
                (value1.Y - value2.Y) * (value1.Y - value2.Y) +
                (value1.Z - value2.Z) * (value1.Z - value2.Z)
            );
        }
 
        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by the components of another <see cref="Vector4"/>.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Divisor <see cref="Vector4"/>.</param>
        /// <returns>The result of dividing the vectors.</returns>
        public static Vector4 Divide(Vector4 value1, Vector4 value2)
        {
            value1.W /= value2.W;
            value1.X /= value2.X;
            value1.Y /= value2.Y;
            value1.Z /= value2.Z;
            return value1;
        }
 
        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by a scalar.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="divider">Divisor scalar.</param>
        /// <returns>The result of dividing a vector by a scalar.</returns>
        public static Vector4 Divide(Vector4 value1, float divider)
        {
            float factor = 1f / divider;
            value1.W *= factor;
            value1.X *= factor;
            value1.Y *= factor;
            value1.Z *= factor;
            return value1;
        }
 
        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by a scalar.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="divider">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 Vector4 value1, float divider, out Vector4 result)
        {
            float factor = 1f / divider;
            result.W = value1.W * factor;
            result.X = value1.X * factor;
            result.Y = value1.Y * factor;
            result.Z = value1.Z * factor;
        }
 
        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by the components of another <see cref="Vector4"/>.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Divisor <see cref="Vector4"/>.</param>
        /// <param name="result">The result of dividing the vectors as an output parameter.</param>
        public static void Divide(
            ref Vector4 value1,
            ref Vector4 value2,
            out Vector4 result
        ) {
            result.W = value1.W / value2.W;
            result.X = value1.X / value2.X;
            result.Y = value1.Y / value2.Y;
            result.Z = value1.Z / value2.Z;
        }
 
        /// <summary>
        /// Returns a dot product of two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <returns>The dot product of two vectors.</returns>
        public static float Dot(Vector4 vector1, Vector4 vector2)
        {
            return (
                vector1.X * vector2.X +
                vector1.Y * vector2.Y +
                vector1.Z * vector2.Z +
                vector1.W * vector2.W
            );
        }
 
        /// <summary>
        /// Returns a dot product of two vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">The second vector.</param>
        /// <param name="result">The dot product of two vectors as an output parameter.</param>
        public static void Dot(ref Vector4 vector1, ref Vector4 vector2, out float result)
        {
            result = (
                (vector1.X * vector2.X) +
                (vector1.Y * vector2.Y) +
                (vector1.Z * vector2.Z) +
                (vector1.W * vector2.W)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 Hermite(
            Vector4 value1,
            Vector4 tangent1,
            Vector4 value2,
            Vector4 tangent2,
            float amount
        ) {
            return new Vector4(
                MathHelper.Hermite(value1.W, tangent1.W, value2.W, tangent2.W, amount),
                MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount),
                MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount),
                MathHelper.Hermite(value1.Z, tangent1.Z, value2.Z, tangent2.Z, amount)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 value1,
            ref Vector4 tangent1,
            ref Vector4 value2,
            ref Vector4 tangent2,
            float amount,
            out Vector4 result
        ) {
            result.W = MathHelper.Hermite(value1.W, tangent1.W, value2.W, tangent2.W, amount);
            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);
            result.Z = MathHelper.Hermite(value1.Z, tangent1.Z, value2.Z, tangent2.Z, amount);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains linear interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">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 Vector4 Lerp(Vector4 value1, Vector4 value2, float amount)
        {
            return new Vector4(
                MathHelper.Lerp(value1.X, value2.X, amount),
                MathHelper.Lerp(value1.Y, value2.Y, amount),
                MathHelper.Lerp(value1.Z, value2.Z, amount),
                MathHelper.Lerp(value1.W, value2.W, amount)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains linear interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">The first vector.</param>
        /// <param name="value2">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 Vector4 value1,
            ref Vector4 value2,
            float amount,
            out Vector4 result
        ) {
            result.X = MathHelper.Lerp(value1.X, value2.X, amount);
            result.Y = MathHelper.Lerp(value1.Y, value2.Y, amount);
            result.Z = MathHelper.Lerp(value1.Z, value2.Z, amount);
            result.W = MathHelper.Lerp(value1.W, value2.W, amount);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4"/> with maximal values from the two vectors.</returns>
        public static Vector4 Max(Vector4 value1, Vector4 value2)
        {
            return new Vector4(
                MathHelper.Max(value1.X, value2.X),
                MathHelper.Max(value1.Y, value2.Y),
                MathHelper.Max(value1.Z, value2.Z),
                MathHelper.Max(value1.W, value2.W)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4"/> with maximal values from the two vectors as an output parameter.</param>
        public static void Max(ref Vector4 value1, ref Vector4 value2, out Vector4 result)
        {
            result.X = MathHelper.Max(value1.X, value2.X);
            result.Y = MathHelper.Max(value1.Y, value2.Y);
            result.Z = MathHelper.Max(value1.Z, value2.Z);
            result.W = MathHelper.Max(value1.W, value2.W);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4"/> with minimal values from the two vectors.</returns>
        public static Vector4 Min(Vector4 value1, Vector4 value2)
        {
            return new Vector4(
                MathHelper.Min(value1.X, value2.X),
                MathHelper.Min(value1.Y, value2.Y),
                MathHelper.Min(value1.Z, value2.Z),
                MathHelper.Min(value1.W, value2.W)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4"/> with minimal values from the two vectors as an output parameter.</param>
        public static void Min(ref Vector4 value1, ref Vector4 value2, out Vector4 result)
        {
            result.X = MathHelper.Min(value1.X, value2.X);
            result.Y = MathHelper.Min(value1.Y, value2.Y);
            result.Z = MathHelper.Min(value1.Z, value2.Z);
            result.W = MathHelper.Min(value1.W, value2.W);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of two vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</param>
        /// <returns>The result of the vector multiplication.</returns>
        public static Vector4 Multiply(Vector4 value1, Vector4 value2)
        {
            value1.W *= value2.W;
            value1.X *= value2.X;
            value1.Y *= value2.Y;
            value1.Z *= value2.Z;
            return value1;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of <see cref="Vector4"/> and a scalar.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="scaleFactor">Scalar value.</param>
        /// <returns>The result of the vector multiplication with a scalar.</returns>
        public static Vector4 Multiply(Vector4 value1, float scaleFactor)
        {
            value1.W *= scaleFactor;
            value1.X *= scaleFactor;
            value1.Y *= scaleFactor;
            value1.Z *= scaleFactor;
            return value1;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of <see cref="Vector4"/> and a scalar.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="scaleFactor">Scalar value.</param>
        /// <param name="result">The result of the multiplication with a scalar as an output parameter.</param>
        public static void Multiply(ref Vector4 value1, float scaleFactor, out Vector4 result)
        {
            result.W = value1.W * scaleFactor;
            result.X = value1.X * scaleFactor;
            result.Y = value1.Y * scaleFactor;
            result.Z = value1.Z * scaleFactor;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of two vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The result of the vector multiplication as an output parameter.</param>
        public static void Multiply(ref Vector4 value1, ref Vector4 value2, out Vector4 result)
        {
            result.W = value1.W * value2.W;
            result.X = value1.X * value2.X;
            result.Y = value1.Y * value2.Y;
            result.Z = value1.Z * value2.Z;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains the specified vector inversion.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <returns>The result of the vector inversion.</returns>
        public static Vector4 Negate(Vector4 value)
        {
            value = new Vector4(-value.X, -value.Y, -value.Z, -value.W);
            return value;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains the specified vector inversion.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The result of the vector inversion as an output parameter.</param>
        public static void Negate(ref Vector4 value, out Vector4 result)
        {
            result.X = -value.X;
            result.Y = -value.Y;
            result.Z = -value.Z;
            result.W = -value.W;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a normalized values from another vector.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <returns>Unit vector.</returns>
        public static Vector4 Normalize(Vector4 vector)
        {
            Normalize(ref vector, out vector);
            return vector;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a normalized values from another vector.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="result">Unit vector as an output parameter.</param>
        public static void Normalize(ref Vector4 vector, out Vector4 result)
        {
            float factor;
            DistanceSquared(ref vector, ref zero, out factor);
            factor = 1f / (float) Math.Sqrt(factor);
 
            result.W = vector.W * factor;
            result.X = vector.X * factor;
            result.Y = vector.Y * factor;
            result.Z = vector.Z * factor;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains cubic interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</param>
        /// <param name="amount">Weighting value.</param>
        /// <returns>Cubic interpolation of the specified vectors.</returns>
        public static Vector4 SmoothStep(Vector4 value1, Vector4 value2, float amount)
        {
            return new Vector4(
                MathHelper.SmoothStep(value1.X, value2.X, amount),
                MathHelper.SmoothStep(value1.Y, value2.Y, amount),
                MathHelper.SmoothStep(value1.Z, value2.Z, amount),
                MathHelper.SmoothStep(value1.W, value2.W, amount)
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains cubic interpolation of the specified vectors.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</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 Vector4 value1,
            ref Vector4 value2,
            float amount,
            out Vector4 result
        ) {
            result.X = MathHelper.SmoothStep(value1.X, value2.X, amount);
            result.Y = MathHelper.SmoothStep(value1.Y, value2.Y, amount);
            result.Z = MathHelper.SmoothStep(value1.Z, value2.Z, amount);
            result.W = MathHelper.SmoothStep(value1.W, value2.W, amount);
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains subtraction of on <see cref="Vector4"/> from a another.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</param>
        /// <returns>The result of the vector subtraction.</returns>
        public static Vector4 Subtract(Vector4 value1, Vector4 value2)
        {
            value1.W -= value2.W;
            value1.X -= value2.X;
            value1.Y -= value2.Y;
            value1.Z -= value2.Z;
            return value1;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains subtraction of on <see cref="Vector4"/> from a another.
        /// </summary>
        /// <param name="value1">Source <see cref="Vector4"/>.</param>
        /// <param name="value2">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The result of the vector subtraction as an output parameter.</param>
        public static void Subtract(ref Vector4 value1, ref Vector4 value2, out Vector4 result)
        {
            result.W = value1.W - value2.W;
            result.X = value1.X - value2.X;
            result.Y = value1.Y - value2.Y;
            result.Z = value1.Z - value2.Z;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 2d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <returns>Transformed <see cref="Vector4"/>.</returns>
        public static Vector4 Transform(Vector2 position, Matrix matrix)
        {
            Vector4 result;
            Transform(ref position, ref matrix, out result);
            return result;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector3"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <returns>Transformed <see cref="Vector4"/>.</returns>
        public static Vector4 Transform(Vector3 position, Matrix matrix)
        {
            Vector4 result;
            Transform(ref position, ref matrix, out result);
            return result;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 4d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <returns>Transformed <see cref="Vector4"/>.</returns>
        public static Vector4 Transform(Vector4 vector, Matrix matrix)
        {
            Transform(ref vector, ref matrix, out vector);
            return vector;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 2d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector2"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="result">Transformed <see cref="Vector4"/> as an output parameter.</param>
        public static void Transform(ref Vector2 position, ref Matrix matrix, out Vector4 result)
        {
            result = new Vector4(
                (position.X * matrix.M11) + (position.Y * matrix.M21) + matrix.M41,
                (position.X * matrix.M12) + (position.Y * matrix.M22) + matrix.M42,
                (position.X * matrix.M13) + (position.Y * matrix.M23) + matrix.M43,
                (position.X * matrix.M14) + (position.Y * matrix.M24) + matrix.M44
            );
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector3"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="result">Transformed <see cref="Vector4"/> as an output parameter.</param>
        public static void Transform(ref Vector3 position, ref Matrix matrix, out Vector4 result)
        {
            float x = (
                (position.X * matrix.M11) +
                (position.Y * matrix.M21) +
                (position.Z * matrix.M31) +
                matrix.M41
            );
            float y = (
                (position.X * matrix.M12) +
                (position.Y * matrix.M22) +
                (position.Z * matrix.M32) +
                matrix.M42
            );
            float z = (
                (position.X * matrix.M13) +
                (position.Y * matrix.M23) +
                (position.Z * matrix.M33) +
                matrix.M43
            );
            float w = (
                (position.X * matrix.M14) +
                (position.Y * matrix.M24) +
                (position.Z * matrix.M34) +
                matrix.M44
            );
            result.X = x;
            result.Y = y;
            result.Z = z;
            result.W = w;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 4d-vector by the specified <see cref="Matrix"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
        /// <param name="result">Transformed <see cref="Vector4"/> as an output parameter.</param>
        public static void Transform(ref Vector4 vector, ref Matrix matrix, out Vector4 result)
        {
            float x = (
                (vector.X * matrix.M11) +
                (vector.Y * matrix.M21) +
                (vector.Z * matrix.M31) +
                (vector.W * matrix.M41)
            );
            float y = (
                (vector.X * matrix.M12) +
                (vector.Y * matrix.M22) +
                (vector.Z * matrix.M32) +
                (vector.W * matrix.M42)
            );
            float z = (
                (vector.X * matrix.M13) +
                (vector.Y * matrix.M23) +
                (vector.Z * matrix.M33) +
                (vector.W * matrix.M43)
            );
            float w = (
                (vector.X * matrix.M14) +
                (vector.Y * matrix.M24) +
                (vector.Z * matrix.M34) +
                (vector.W * matrix.M44)
            );
            result.X = x;
            result.Y = y;
            result.Z = z;
            result.W = w;
        }
 
        /// <summary>
        /// Apply transformation on all vectors within array of <see cref="Vector4"/> 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(
            Vector4[] sourceArray,
            ref Matrix matrix,
            Vector4[] destinationArray
        ) {
            if (sourceArray == null)
            {
                throw new ArgumentNullException("sourceArray");
            }
            if (destinationArray == null)
            {
                throw new ArgumentNullException("destinationArray");
            }
            if (destinationArray.Length < sourceArray.Length)
            {
                throw new ArgumentException(
                    "destinationArray is too small to contain the result."
                );
            }
            for (int i = 0; i < sourceArray.Length; i += 1)
            {
                Transform(
                    ref sourceArray[i],
                    ref matrix,
                    out destinationArray[i]
                );
            }
        }
 
        /// <summary>
        /// Apply transformation on vectors within array of <see cref="Vector4"/> 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="Vector4"/> should be written.</param>
        /// <param name="length">The number of vectors to be transformed.</param>
        public static void Transform(
            Vector4[] sourceArray,
            int sourceIndex,
            ref Matrix matrix,
            Vector4[] destinationArray,
            int destinationIndex,
            int length
        ) {
            if (sourceArray == null)
            {
                throw new ArgumentNullException("sourceArray");
            }
            if (destinationArray == null)
            {
                throw new ArgumentNullException("destinationArray");
            }
            if (destinationIndex + length > destinationArray.Length)
            {
                throw new ArgumentException(
                    "destinationArray is too small to contain the result."
                );
            }
            if (sourceIndex + length > sourceArray.Length)
            {
                throw new ArgumentException(
                    "The combination of sourceIndex and length was greater than sourceArray.Length."
                );
            }
            for (int i = 0; i < length; i += 1)
            {
                Transform(
                    ref sourceArray[i + sourceIndex],
                    ref matrix,
                    out destinationArray[i + destinationIndex]
                );
            }
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 2d-vector by the specified <see cref="Quaternion"/>.
        /// </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="Vector4"/>.</returns>
        public static Vector4 Transform(Vector2 value, Quaternion rotation)
        {
            Vector4 result;
            Transform(ref value, ref rotation, out result);
            return result;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector3"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <returns>Transformed <see cref="Vector4"/>.</returns>
        public static Vector4 Transform(Vector3 value, Quaternion rotation)
        {
            Vector4 result;
            Transform(ref value, ref rotation, out result);
            return result;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 4d-vector by the specified <see cref="Quaternion"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <returns>Transformed <see cref="Vector4"/>.</returns>
        public static Vector4 Transform(Vector4 value, Quaternion rotation)
        {
            Vector4 result;
            Transform(ref value, ref rotation, out result);
            return result;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 2d-vector by the specified <see cref="Quaternion"/>.
        /// </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="Vector4"/> as an output parameter.</param>
        public static void Transform(
            ref Vector2 value,
            ref Quaternion rotation,
            out Vector4 result
        ) {
            double xx = rotation.X + rotation.X;
            double yy = rotation.Y + rotation.Y;
            double zz = rotation.Z + rotation.Z;
            double wxx = rotation.W * xx;
            double wyy = rotation.W * yy;
            double wzz = rotation.W * zz;
            double xxx = rotation.X * xx;
            double xyy = rotation.X * yy;
            double xzz = rotation.X * zz;
            double yyy = rotation.Y * yy;
            double yzz = rotation.Y * zz;
            double zzz = rotation.Z * zz;
            result.X = (float) (
                (double) value.X * (1.0 - yyy - zzz) +
                (double) value.Y * (xyy - wzz)
            );
            result.Y = (float) (
                (double) value.X * (xyy + wzz) +
                (double) value.Y * (1.0 - xxx - zzz)
            );
            result.Z = (float) (
                (double) value.X * (xzz - wyy) +
                (double) value.Y * (yzz + wxx)
            );
            result.W = 1.0f;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector3"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <param name="result">Transformed <see cref="Vector4"/> as an output parameter.</param>
        public static void Transform(
            ref Vector3 value,
            ref Quaternion rotation,
            out Vector4 result
        ) {
            double xx = rotation.X + rotation.X;
            double yy = rotation.Y + rotation.Y;
            double zz = rotation.Z + rotation.Z;
            double wxx = rotation.W * xx;
            double wyy = rotation.W * yy;
            double wzz = rotation.W * zz;
            double xxx = rotation.X * xx;
            double xyy = rotation.X * yy;
            double xzz = rotation.X * zz;
            double yyy = rotation.Y * yy;
            double yzz = rotation.Y * zz;
            double zzz = rotation.Z * zz;
            result.X = (float) (
                (double) value.X * (1.0 - yyy - zzz) +
                (double) value.Y * (xyy - wzz) +
                (double) value.Z * (xzz + wyy)
            );
            result.Y = (float) (
                (double) value.X * (xyy + wzz) +
                (double) value.Y * (1.0 - xxx - zzz) +
                (double) value.Z * (yzz - wxx)
            );
            result.Z = (float) (
                (double) value.X * (xzz - wyy) +
                (double) value.Y * (yzz + wxx) +
                (double) value.Z * (1.0 - xxx - yyy)
            );
            result.W = 1.0f;
        }
 
        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a transformation of 4d-vector by the specified <see cref="Quaternion"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="rotation">The <see cref="Quaternion"/> which contains rotation transformation.</param>
        /// <param name="result">Transformed <see cref="Vector4"/> as an output parameter.</param>
        public static void Transform(
            ref Vector4 value,
            ref Quaternion rotation,
            out Vector4 result
        ) {
            double xx = rotation.X + rotation.X;
            double yy = rotation.Y + rotation.Y;
            double zz = rotation.Z + rotation.Z;
            double wxx = rotation.W * xx;
            double wyy = rotation.W * yy;
            double wzz = rotation.W * zz;
            double xxx = rotation.X * xx;
            double xyy = rotation.X * yy;
            double xzz = rotation.X * zz;
            double yyy = rotation.Y * yy;
            double yzz = rotation.Y * zz;
            double zzz = rotation.Z * zz;
            result.X = (float) (
                (double) value.X * (1.0 - yyy - zzz) +
                (double) value.Y * (xyy - wzz) +
                (double) value.Z * (xzz + wyy)
            );
            result.Y = (float) (
                (double) value.X * (xyy + wzz) +
                (double) value.Y * (1.0 - xxx - zzz) +
                (double) value.Z * (yzz - wxx)
            );
            result.Z = (float) (
                (double) value.X * (xzz - wyy) +
                (double) value.Y * (yzz + wxx) +
                (double) value.Z * (1.0 - xxx - yyy)
            );
            result.W = value.W;
        }
 
        /// <summary>
        /// Apply transformation on all vectors within array of <see cref="Vector4"/> 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(
            Vector4[] sourceArray,
            ref Quaternion rotation,
            Vector4[] destinationArray
        ) {
            if (sourceArray == null)
            {
                throw new ArgumentException("sourceArray");
            }
            if (destinationArray == null)
            {
                throw new ArgumentException("destinationArray");
            }
            if (destinationArray.Length < sourceArray.Length)
            {
                throw new ArgumentException(
                    "destinationArray is too small to contain the result."
                );
            }
            for (int i = 0; i < sourceArray.Length; i += 1)
            {
                Transform(
                    ref sourceArray[i],
                    ref rotation,
                    out destinationArray[i]
                );
            }
        }
 
        /// <summary>
        /// Apply transformation on vectors within array of <see cref="Vector4"/> 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="Vector4"/> should be written.</param>
        /// <param name="length">The number of vectors to be transformed.</param>
        public static void Transform(
            Vector4[] sourceArray,
            int sourceIndex,
            ref Quaternion rotation,
            Vector4[] destinationArray,
            int destinationIndex,
            int length
        ) {
            if (sourceArray == null)
            {
                throw new ArgumentException("sourceArray");
            }
            if (destinationArray == null)
            {
                throw new ArgumentException("destinationArray");
            }
            if (destinationIndex + length > destinationArray.Length)
            {
                throw new ArgumentException(
                    "destinationArray is too small to contain the result."
                );
            }
            if (sourceIndex + length > sourceArray.Length)
            {
                throw new ArgumentException(
                    "The combination of sourceIndex and length was greater than sourceArray.Length."
                );
            }
            for (int i = 0; i < length; i += 1)
            {
                Transform(
                    ref sourceArray[i + sourceIndex],
                    ref rotation,
                    out destinationArray[i + destinationIndex]
                );
            }
        }
 
        #endregion
 
        #region Public Static Operators
 
        public static Vector4 operator -(Vector4 value)
        {
            return new Vector4(-value.X, -value.Y, -value.Z, -value.W);
        }
 
        public static bool operator ==(Vector4 value1, Vector4 value2)
        {
            return (    (MathHelper.WithinEpsilon(value1.W, value2.W)) &&
                    (MathHelper.WithinEpsilon(value1.X, value2.X)) &&
                    (MathHelper.WithinEpsilon(value1.Y, value2.Y)) &&
                    (MathHelper.WithinEpsilon(value1.Z, value2.Z))  );
        }
 
        public static bool operator !=(Vector4 value1, Vector4 value2)
        {
            return !(value1 == value2);
        }
 
        public static Vector4 operator +(Vector4 value1, Vector4 value2)
        {
            value1.W += value2.W;
            value1.X += value2.X;
            value1.Y += value2.Y;
            value1.Z += value2.Z;
            return value1;
        }
 
        public static Vector4 operator -(Vector4 value1, Vector4 value2)
        {
            value1.W -= value2.W;
            value1.X -= value2.X;
            value1.Y -= value2.Y;
            value1.Z -= value2.Z;
            return value1;
        }
 
        public static Vector4 operator *(Vector4 value1, Vector4 value2)
        {
            value1.W *= value2.W;
            value1.X *= value2.X;
            value1.Y *= value2.Y;
            value1.Z *= value2.Z;
            return value1;
        }
 
        public static Vector4 operator *(Vector4 value1, float scaleFactor)
        {
            value1.W *= scaleFactor;
            value1.X *= scaleFactor;
            value1.Y *= scaleFactor;
            value1.Z *= scaleFactor;
            return value1;
        }
 
        public static Vector4 operator *(float scaleFactor, Vector4 value1)
        {
            value1.W *= scaleFactor;
            value1.X *= scaleFactor;
            value1.Y *= scaleFactor;
            value1.Z *= scaleFactor;
            return value1;
        }
 
        public static Vector4 operator /(Vector4 value1, Vector4 value2)
        {
            value1.W /= value2.W;
            value1.X /= value2.X;
            value1.Y /= value2.Y;
            value1.Z /= value2.Z;
            return value1;
        }
 
        public static Vector4 operator /(Vector4 value1, float divider)
        {
            float factor = 1f / divider;
            value1.W *= factor;
            value1.X *= factor;
            value1.Y *= factor;
            value1.Z *= factor;
            return value1;
        }
 
        #endregion
    }
}

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