Vector4.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 4D-vector.
    /// </summary>
    [DebuggerDisplay("{DebugDisplayString,nq}")]
    [DataContract]
    [TypeConverter("Microsoft.Xna.Framework.Design.Vector4Converter, Xna.Framework.Design")]
    public struct Vector4 : IEquatable<Vector4>
    {
        #region Private Fields

        private static readonly Vector4 zero = new Vector4();
        private static readonly Vector4 one = 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 Fields

        /// <summary>
        /// The x coordinate of this <see cref="Vector4"/>.
        /// </summary>
        [DataMember]
        public float X;

        /// <summary>
        /// The y coordinate of this <see cref="Vector4"/>.
        /// </summary>
        [DataMember]
        public float Y;

        /// <summary>
        /// The z coordinate of this <see cref="Vector4"/>.
        /// </summary>
        [DataMember]
        public float Z;

        /// <summary>
        /// The w coordinate of this <see cref="Vector4"/>.
        /// </summary>
        [DataMember]
        public float W;

        #endregion

        #region Public 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 one; }
        }

        /// <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(
                    this.X.ToString(), "  ",
                    this.Y.ToString(), "  ",
                    this.Z.ToString(), "  ",
                    this.W.ToString()
                );
            }
        }

        #endregion

        #region 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>
        /// 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 Vector4 Add(Vector4 left, Vector4 right)
        {
            left.X += right.X;
            left.Y += right.Y;
            left.Z += right.Z;
            left.W += right.W;
            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 Vector4 left, ref Vector4 right, out Vector4 result)
        {
            result.X = left.X + right.X;
            result.Y = left.Y + right.Y;
            result.Z = left.Z + right.Z;
            result.W = left.W + right.W;
        }

        /// <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>
        /// Round the members of this <see cref="Vector4"/> towards positive infinity.
        /// </summary>
        public void Ceiling()
        {
            X = (float)Math.Ceiling(X);
            Y = (float)Math.Ceiling(Y);
            Z = (float)Math.Ceiling(Z);
            W = (float)Math.Ceiling(W);
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded towards positive infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <returns>The rounded <see cref="Vector4"/>.</returns>
        public static Vector4 Ceiling(Vector4 value)
        {
            value.X = (float)Math.Ceiling(value.X);
            value.Y = (float)Math.Ceiling(value.Y);
            value.Z = (float)Math.Ceiling(value.Z);
            value.W = (float)Math.Ceiling(value.W);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded towards positive infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The rounded <see cref="Vector4"/>.</param>
        public static void Ceiling(ref Vector4 value, out Vector4 result)
        {
            result.X = (float)Math.Ceiling(value.X);
            result.Y = (float)Math.Ceiling(value.Y);
            result.Z = (float)Math.Ceiling(value.Z);
            result.W = (float)Math.Ceiling(value.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>
        /// <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="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">Divisor <see cref="Vector4"/>.</param>
        /// <returns>The result of dividing the vectors.</returns>
        public static Vector4 Divide(Vector4 left, Vector4 right)
        {
            left.W /= right.W;
            left.X /= right.X;
            left.Y /= right.Y;
            left.Z /= right.Z;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">Divisor scalar.</param>
        /// <returns>The result of dividing a vector by a scalar.</returns>
        public static Vector4 Divide(Vector4 left, float right)
        {
            float factor = 1f / right;
            left.W *= factor;
            left.X *= factor;
            left.Y *= factor;
            left.Z *= factor;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</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 Vector4 left, float right, out Vector4 result)
        {
            float factor = 1f / right;
            result.W = left.W * factor;
            result.X = left.X * factor;
            result.Y = left.Y * factor;
            result.Z = left.Z * factor;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by the components of another <see cref="Vector4"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">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 left, ref Vector4 right, out Vector4 result)
        {
            result.W = left.W / right.W;
            result.X = left.X / right.X;
            result.Y = left.Y / right.Y;
            result.Z = left.Z / right.Z;
        }

        /// <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(Vector4 left, Vector4 right)
        {
            return left.X * right.X + left.Y * right.Y + left.Z * right.Z + left.W * right.W;
        }

        /// <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 Vector4 left, ref Vector4 right, out float result)
        {
            result = left.X * right.X + left.Y * right.Y + left.Z * right.Z + left.W * right.W;
        }

        /// <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 this.W == other.W
                && this.X == other.X
                && this.Y == other.Y
                && this.Z == other.Z;
        }

        /// <summary>
        /// Round the members of this <see cref="Vector4"/> towards negative infinity.
        /// </summary>
        public void Floor()
        {
            X = (float)Math.Floor(X);
            Y = (float)Math.Floor(Y);
            Z = (float)Math.Floor(Z);
            W = (float)Math.Floor(W);
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded towards negative infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <returns>The rounded <see cref="Vector4"/>.</returns>
        public static Vector4 Floor(Vector4 value)
        {
            value.X = (float)Math.Floor(value.X);
            value.Y = (float)Math.Floor(value.Y);
            value.Z = (float)Math.Floor(value.Z);
            value.W = (float)Math.Floor(value.W);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded towards negative infinity.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The rounded <see cref="Vector4"/>.</param>
        public static void Floor(ref Vector4 value, out Vector4 result)
        {
            result.X = (float)Math.Floor(value.X);
            result.Y = (float)Math.Floor(value.Y);
            result.Z = (float)Math.Floor(value.Z);
            result.W = (float)Math.Floor(value.W);
        }

        /// <summary>
        /// Gets the hash code of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>Hash code of this <see cref="Vector4"/>.</returns>
        public override int GetHashCode()
        {
            unchecked
            {
                var hashCode = W.GetHashCode();
                hashCode = (hashCode * 397) ^ X.GetHashCode();
                hashCode = (hashCode * 397) ^ Y.GetHashCode();
                hashCode = (hashCode * 397) ^ Z.GetHashCode();
                return hashCode;
            }
        }

        /// <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.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),
                               MathHelper.Hermite(value1.W, tangent1.W, value2.W, tangent2.W, 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>
        /// Returns the length of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>The length of this <see cref="Vector4"/>.</returns>
        public float Length()
        {
            return (float)Math.Sqrt((X * X) + (Y * Y) + (Z * Z) + (W * W));
        }

        /// <summary>
        /// Returns the squared length of this <see cref="Vector4"/>.
        /// </summary>
        /// <returns>The squared length of this <see cref="Vector4"/>.</returns>
        public float LengthSquared()
        {
            return (X * X) + (Y * Y) + (Z * Z) + (W * W);
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 Lerp(Vector4 start, Vector4 end, float amount)
        {
            Vector4 result;
            result.X = MathHelper.Lerp(start.X, end.X, amount);
            result.Y = MathHelper.Lerp(start.Y, end.Y, amount);
            result.Z = MathHelper.Lerp(start.Z, end.Z, amount);
            result.W = MathHelper.Lerp(start.W, end.W, amount);
            return result;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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 Vector4 start, ref Vector4 end, float amount, out Vector4 result)
        {
            result.X = MathHelper.Lerp(start.X, end.X, amount);
            result.Y = MathHelper.Lerp(start.Y, end.Y, amount);
            result.Z = MathHelper.Lerp(start.Z, end.Z, amount);
            result.W = MathHelper.Lerp(start.W, end.W, amount);
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4.Lerp(Vector4, Vector4, 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 Vector4 LerpPrecise(Vector4 start, Vector4 end, float amount)
        {
            Vector4 result;
            result.X = MathHelper.LerpPrecise(start.X, end.X, amount);
            result.Y = MathHelper.LerpPrecise(start.Y, end.Y, amount);
            result.Z = MathHelper.LerpPrecise(start.Z, end.Z, amount);
            result.W = MathHelper.LerpPrecise(start.W, end.W, amount);
            return result;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> 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="Vector4.Lerp(ref Vector4, ref Vector4, float, out Vector4)"/>.
        /// 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 Vector4 start, ref Vector4 end, float amount, out Vector4 result)
        {
            result.X = MathHelper.LerpPrecise(start.X, end.X, amount);
            result.Y = MathHelper.LerpPrecise(start.Y, end.Y, amount);
            result.Z = MathHelper.LerpPrecise(start.Z, end.Z, amount);
            result.W = MathHelper.LerpPrecise(start.W, end.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="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">Source <see cref="Vector4"/>.</param>
        /// <returns>The result of the vector multiplication.</returns>
        public static Vector4 Multiply(Vector4 left, Vector4 right)
        {
            left.W *= right.W;
            left.X *= right.X;
            left.Y *= right.Y;
            left.Z *= right.Z;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of <see cref="Vector4"/> and a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">Scalar value.</param>
        /// <returns>The result of the vector multiplication with a scalar.</returns>
        public static Vector4 Multiply(Vector4 left, float right)
        {
            left.W *= right;
            left.X *= right;
            left.Y *= right;
            left.Z *= right;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of <see cref="Vector4"/> and a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</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 Vector4 left, float right, out Vector4 result)
        {
            result.W = left.W * right;
            result.X = left.X * right;
            result.Y = left.Y * right;
            result.Z = left.Z * right;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains a multiplication of two vectors.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">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 left, ref Vector4 right, out Vector4 result)
        {
            result.W = left.W * right.W;
            result.X = left.X * right.X;
            result.Y = left.Y * right.Y;
            result.Z = left.Z * right.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>
        /// Turns this <see cref="Vector4"/> to a unit vector with the same direction.
        /// </summary>
        public void Normalize()
        {
            float factor = (float)Math.Sqrt((X * X) + (Y * Y) + (Z * Z) + (W * W));
            factor = 1f / factor;
            X *= factor;
            Y *= factor;
            Z *= factor;
            W *= factor;
        }

        /// <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 value)
        {
            float factor = (float)Math.Sqrt((value.X * value.X) + (value.Y * value.Y) + (value.Z * value.Z) + (value.W * value.W));
            factor = 1f / factor;
            return new Vector4(value.X*factor,value.Y*factor,value.Z*factor,value.W*factor);
        }

        /// <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 value, out Vector4 result)
        {
            float factor = (float)Math.Sqrt((value.X * value.X) + (value.Y * value.Y) + (value.Z * value.Z) + (value.W * value.W));
            factor = 1f / factor;
            result.W = value.W * factor;
            result.X = value.X * factor;
            result.Y = value.Y * factor;
            result.Z = value.Z * factor;
        }

        /// <summary>
        /// Round the members of this <see cref="Vector4"/> to the nearest integer value.
        /// </summary>
        public void Round()
        {
            X = (float)Math.Round(X);
            Y = (float)Math.Round(Y);
            Z = (float)Math.Round(Z);
            W = (float)Math.Round(W);
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded to the nearest integer value.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <returns>The rounded <see cref="Vector4"/>.</returns>
        public static Vector4 Round(Vector4 value)
        {
            value.X = (float)Math.Round(value.X);
            value.Y = (float)Math.Round(value.Y);
            value.Z = (float)Math.Round(value.Z);
            value.W = (float)Math.Round(value.W);
            return value;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains members from another vector rounded to the nearest integer value.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/>.</param>
        /// <param name="result">The rounded <see cref="Vector4"/>.</param>
        public static void Round(ref Vector4 value, out Vector4 result)
        {
            result.X = (float)Math.Round(value.X);
            result.Y = (float)Math.Round(value.Y);
            result.Z = (float)Math.Round(value.Z);
            result.W = (float)Math.Round(value.W);
        }

        /// <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="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">Source <see cref="Vector4"/>.</param>
        /// <returns>The result of the vector subtraction.</returns>
        public static Vector4 Subtract(Vector4 left, Vector4 right)
        {
            left.W -= right.W;
            left.X -= right.X;
            left.Y -= right.Y;
            left.Z -= right.Z;
            return left;
        }

        /// <summary>
        /// Creates a new <see cref="Vector4"/> that contains subtraction of on <see cref="Vector4"/> from a another.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/>.</param>
        /// <param name="right">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 left, ref Vector4 right, out Vector4 result)
        {
            result.W = left.W - right.W;
            result.X = left.X - right.X;
            result.Y = left.Y - right.Y;
            result.Z = left.Z - right.Z;
        }

        #region Transform

        /// <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 value, Matrix matrix)
        {
            Vector4 result;
            Transform(ref value, ref matrix, 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>
        /// <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="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 value, Matrix matrix)
        {
            Vector4 result;
            Transform(ref value, 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="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="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 value, Matrix matrix)
        {
            Transform(ref value, ref matrix, out value);
            return value;
        }

        /// <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="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 value, ref Matrix matrix, out Vector4 result)
        {
            result.X = (value.X * matrix.M11) + (value.Y * matrix.M21) + matrix.M41;
            result.Y = (value.X * matrix.M12) + (value.Y * matrix.M22) + matrix.M42;
            result.Z = (value.X * matrix.M13) + (value.Y * matrix.M23) + matrix.M43;
            result.W = (value.X * matrix.M14) + (value.Y * matrix.M24) + matrix.M44;
        }

        /// <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 = 1f;
        }

        /// <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 value, ref Matrix matrix, out Vector4 result)
        {
            result.X = (value.X * matrix.M11) + (value.Y * matrix.M21) + (value.Z * matrix.M31) + matrix.M41;
            result.Y = (value.X * matrix.M12) + (value.Y * matrix.M22) + (value.Z * matrix.M32) + matrix.M42;
            result.Z = (value.X * matrix.M13) + (value.Y * matrix.M23) + (value.Z * matrix.M33) + matrix.M43;
            result.W = (value.X * matrix.M14) + (value.Y * matrix.M24) + (value.Z * matrix.M34) + matrix.M44;
        }

        /// <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 = 1f;
        }

        /// <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 value, ref Matrix matrix, out Vector4 result)
        {
            var x = (value.X * matrix.M11) + (value.Y * matrix.M21) + (value.Z * matrix.M31) + (value.W * matrix.M41);
            var y = (value.X * matrix.M12) + (value.Y * matrix.M22) + (value.Z * matrix.M32) + (value.W * matrix.M42);
            var z = (value.X * matrix.M13) + (value.Y * matrix.M23) + (value.Z * matrix.M33) + (value.W * matrix.M43);
            var w = (value.X * matrix.M14) + (value.Y * matrix.M24) + (value.Z * matrix.M34) + (value.W * 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="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 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 (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 (var i = 0; i < length; i++)
            {
                Vector4.Transform(ref sourceArray[sourceIndex + i], ref matrix, out destinationArray[destinationIndex + 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 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 (var i = 0; i < length; i++)
            {
                Vector4.Transform(ref sourceArray[sourceIndex + i], ref rotation, out destinationArray[destinationIndex + i]);
            }
        }

        /// <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)
        {
            Vector4.Transform(sourceArray, 0, ref matrix, destinationArray, 0, sourceArray.Length);
        }

        /// <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)
        {
            Vector4.Transform(sourceArray, 0, ref rotation, destinationArray, 0, sourceArray.Length);
        }

        #endregion

        /// <summary>
        /// Returns a <see cref="String"/> representation of this <see cref="Vector4"/> in the format:
        /// {X:[<see cref="X"/>] Y:[<see cref="Y"/>] Z:[<see cref="Z"/>] W:[<see cref="W"/>]}
        /// </summary>
        /// <returns>A <see cref="String"/> representation of this <see cref="Vector4"/>.</returns>
        public override string ToString()
        {
            return String.Format("{{X: {0}, Y: {1}, Z: {2}, W: {3} }}", X, Y, Z, W);
        }

        /// <summary>
        /// Deconstruction method for <see cref="Vector4"/>.
        /// </summary>
        /// <param name="x"></param>
        /// <param name="y"></param>
        /// <param name="z"></param>
        /// <param name="w"></param>
        public void Deconstruct(out float x, out float y, out float z, out float w)
        {
            x = X;
            y = Y;
            z = Z;
            w = W;
        }

        #endregion

        #region Operators

        /// <summary>
        /// Inverts values in the specified <see cref="Vector4"/>.
        /// </summary>
        /// <param name="value">Source <see cref="Vector4"/> on the right of the sub sign.</param>
        /// <returns>Result of the inversion.</returns>
        public static Vector4 operator -(Vector4 value)
        {
            return new Vector4(-value.X, -value.Y, -value.Z, -value.W);
        }

        /// <summary>
        /// Compares whether two <see cref="Vector4"/> instances are equal.
        /// </summary>
        /// <param name="left"><see cref="Vector4"/> instance on the left of the equal sign.</param>
        /// <param name="right"><see cref="Vector4"/> 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 ==(Vector4 left, Vector4 right)
        {
            return left.W == right.W
                && left.X == right.X
                && left.Y == right.Y
                && left.Z == right.Z;
        }

        /// <summary>
        /// Compares whether two <see cref="Vector4"/> instances are not equal.
        /// </summary>
        /// <param name="left"><see cref="Vector4"/> instance on the left of the not equal sign.</param>
        /// <param name="right"><see cref="Vector4"/> 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 !=(Vector4 left, Vector4 right)
        {
            return !(left == right);
        }

        /// <summary>
        /// Adds two vectors.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> on the left of the add sign.</param>
        /// <param name="right">Source <see cref="Vector4"/> on the right of the add sign.</param>
        /// <returns>Sum of the vectors.</returns>
        public static Vector4 operator +(Vector4 left, Vector4 right)
        {
            left.W += right.W;
            left.X += right.X;
            left.Y += right.Y;
            left.Z += right.Z;
            return left;
        }

        /// <summary>
        /// Subtracts a <see cref="Vector4"/> from a <see cref="Vector4"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> on the left of the sub sign.</param>
        /// <param name="right">Source <see cref="Vector4"/> on the right of the sub sign.</param>
        /// <returns>Result of the vector subtraction.</returns>
        public static Vector4 operator -(Vector4 left, Vector4 right)
        {
            left.W -= right.W;
            left.X -= right.X;
            left.Y -= right.Y;
            left.Z -= right.Z;
            return left;
        }

        /// <summary>
        /// Multiplies the components of two vectors by each other.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> on the left of the mul sign.</param>
        /// <param name="right">Source <see cref="Vector4"/> on the right of the mul sign.</param>
        /// <returns>Result of the vector multiplication.</returns>
        public static Vector4 operator *(Vector4 left, Vector4 right)
        {
            left.W *= right.W;
            left.X *= right.X;
            left.Y *= right.Y;
            left.Z *= right.Z;
            return left;
        }

        /// <summary>
        /// Multiplies the components of vector by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> 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 Vector4 operator *(Vector4 left, float right)
        {
            left.W *= right;
            left.X *= right;
            left.Y *= right;
            left.Z *= 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="Vector4"/> on the right of the mul sign.</param>
        /// <returns>Result of the vector multiplication with a scalar.</returns>
        public static Vector4 operator *(float left, Vector4 right)
        {
            right.W *= left;
            right.X *= left;
            right.Y *= left;
            right.Z *= left;
            return right;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by the components of another <see cref="Vector4"/>.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> on the left of the div sign.</param>
        /// <param name="right">Divisor <see cref="Vector4"/> on the right of the div sign.</param>
        /// <returns>The result of dividing the vectors.</returns>
        public static Vector4 operator /(Vector4 left, Vector4 right)
        {
            left.W /= right.W;
            left.X /= right.X;
            left.Y /= right.Y;
            left.Z /= right.Z;
            return left;
        }

        /// <summary>
        /// Divides the components of a <see cref="Vector4"/> by a scalar.
        /// </summary>
        /// <param name="left">Source <see cref="Vector4"/> 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 Vector4 operator /(Vector4 left, float right)
        {
            float factor = 1f / right;
            left.W *= factor;
            left.X *= factor;
            left.Y *= factor;
            left.Z *= factor;
            return left;
        }

#if NET8_0_OR_GREATER
        public static explicit operator Vector4(SysNumerics.Vector4 value)
        {
            return Unsafe.BitCast<SysNumerics.Vector4, Vector4>(value);
        }

        public static explicit operator SysNumerics.Vector4(Vector4 value)
        {
            return Unsafe.BitCast<Vector4, SysNumerics.Vector4>(value);
        }
#endif

        #endregion
    }
}