#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 System.Text;

using Microsoft.Xna.Framework.Design;
#endregion

namespace Microsoft.Xna.Framework
{
	/// <summary>
	/// Describes a 3D-vector.
	/// </summary>
	[Serializable]
	[TypeConverter(typeof(Vector3Converter))]
	[DebuggerDisplay("{DebugDisplayString,nq}")]
	public struct Vector3 : IEquatable<Vector3>
	{
		#region Public Static Properties

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 0, 0.
		/// </summary>
		public static Vector3 Zero
		{
			get
			{
				return zero;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 1, 1, 1.
		/// </summary>
		public static Vector3 One
		{
			get
			{
				return one;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 1, 0, 0.
		/// </summary>
		public static Vector3 UnitX
		{
			get
			{
				return unitX;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 1, 0.
		/// </summary>
		public static Vector3 UnitY
		{
			get
			{
				return unitY;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 0, 1.
		/// </summary>
		public static Vector3 UnitZ
		{
			get
			{
				return unitZ;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 1, 0.
		/// </summary>
		public static Vector3 Up
		{
			get
			{
				return up;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, -1, 0.
		/// </summary>
		public static Vector3 Down
		{
			get
			{
				return down;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 1, 0, 0.
		/// </summary>
		public static Vector3 Right
		{
			get
			{
				return right;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components -1, 0, 0.
		/// </summary>
		public static Vector3 Left
		{
			get
			{
				return left;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 0, -1.
		/// </summary>
		public static Vector3 Forward
		{
			get
			{
				return forward;
			}
		}

		/// <summary>
		/// Returns a <see cref="Vector3"/> with components 0, 0, 1.
		/// </summary>
		public static Vector3 Backward
		{
			get
			{
				return backward;
			}
		}

		#endregion

		#region Internal Properties

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

		#endregion

		#region Private Static Fields

		private static Vector3 zero = new Vector3(0f, 0f, 0f); // Not readonly for performance -flibit
		private static readonly Vector3 one = new Vector3(1f, 1f, 1f);
		private static readonly Vector3 unitX = new Vector3(1f, 0f, 0f);
		private static readonly Vector3 unitY = new Vector3(0f, 1f, 0f);
		private static readonly Vector3 unitZ = new Vector3(0f, 0f, 1f);
		private static readonly Vector3 up = new Vector3(0f, 1f, 0f);
		private static readonly Vector3 down = new Vector3(0f, -1f, 0f);
		private static readonly Vector3 right = new Vector3(1f, 0f, 0f);
		private static readonly Vector3 left = new Vector3(-1f, 0f, 0f);
		private static readonly Vector3 forward = new Vector3(0f, 0f, -1f);
		private static readonly Vector3 backward = new Vector3(0f, 0f, 1f);

		#endregion

		#region Public Fields

		/// <summary>
		/// The x coordinate of this <see cref="Vector3"/>.
		/// </summary>
		public float X;

		/// <summary>
		/// The y coordinate of this <see cref="Vector3"/>.
		/// </summary>
		public float Y;

		/// <summary>
		/// The z coordinate of this <see cref="Vector3"/>.
		/// </summary>
		public float Z;

		#endregion

		#region Public Constructors

		/// <summary>
		/// Constructs a 3d vector with X, Y and Z from three values.
		/// </summary>
		/// <param name="x">The x coordinate in 3d-space.</param>
		/// <param name="y">The y coordinate in 3d-space.</param>
		/// <param name="z">The z coordinate in 3d-space.</param>
		public Vector3(float x, float y, float z)
		{
			this.X = x;
			this.Y = y;
			this.Z = z;
		}

		/// <summary>
		/// Constructs a 3d vector with X, Y and Z set to the same value.
		/// </summary>
		/// <param name="value">The x, y and z coordinates in 3d-space.</param>
		public Vector3(float value)
		{
			this.X = value;
			this.Y = value;
			this.Z = value;
		}

		/// <summary>
		/// Constructs a 3d vector with X, Y from <see cref="Vector2"/> and Z from a scalar.
		/// </summary>
		/// <param name="value">The x and y coordinates in 3d-space.</param>
		/// <param name="z">The z coordinate in 3d-space.</param>
		public Vector3(Vector2 value, float z)
		{
			this.X = value.X;
			this.Y = value.Y;
			this.Z = z;
		}

		#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)
		{
			if (!(obj is Vector3))
			{
				return false;
			}

			Vector3 other = (Vector3) obj;
			return (	(MathHelper.WithinEpsilon(X, other.X)) &&
					(MathHelper.WithinEpsilon(Y, other.Y)) &&
					(MathHelper.WithinEpsilon(Z, other.Z))	);
		}

		/// <summary>
		/// Compares whether current instance is equal to specified <see cref="Vector3"/>.
		/// </summary>
		/// <param name="other">The <see cref="Vector3"/> to compare.</param>
		/// <returns><c>true</c> if the instances are equal; <c>false</c> otherwise.</returns>
		public bool Equals(Vector3 other)
		{
			return (	(MathHelper.WithinEpsilon(X, other.X)) &&
					(MathHelper.WithinEpsilon(Y, other.Y)) &&
					(MathHelper.WithinEpsilon(Z, other.Z))	);
		}

		/// <summary>
		/// Gets the hash code of this <see cref="Vector3"/>.
		/// </summary>
		/// <returns>Hash code of this <see cref="Vector3"/>.</returns>
		public override int GetHashCode()
		{
			return (int) (this.X + this.Y + this.Z);
		}

		/// <summary>
		/// Returns the length of this <see cref="Vector3"/>.
		/// </summary>
		/// <returns>The length of this <see cref="Vector3"/>.</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="Vector3"/>.
		/// </summary>
		/// <returns>The squared length of this <see cref="Vector3"/>.</returns>
		public float LengthSquared()
		{
			float result;
			DistanceSquared(ref this, ref zero, out result);
			return result;
		}

		/// <summary>
		/// Turns this <see cref="Vector3"/> to a unit vector with the same direction.
		/// </summary>
		public void Normalize()
		{
			Normalize(ref this, out this);
		}

		/// <summary>
		/// Returns a <see cref="String"/> representation of this <see cref="Vector3"/> in the format:
		/// {X:[<see cref="X"/>] Y:[<see cref="Y"/>] Z:[<see cref="Z"/>]}
		/// </summary>
		/// <returns>A <see cref="String"/> representation of this <see cref="Vector3"/>.</returns>
		public override string ToString()
		{
			StringBuilder sb = new StringBuilder(32);
			sb.Append("{X:");
			sb.Append(this.X);
			sb.Append(" Y:");
			sb.Append(this.Y);
			sb.Append(" Z:");
			sb.Append(this.Z);
			sb.Append("}");
			return sb.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 Vector3 Add(Vector3 value1, Vector3 value2)
		{
			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 Vector3 value1, ref Vector3 value2, out Vector3 result)
		{
			result.X = value1.X + value2.X;
			result.Y = value1.Y + value2.Y;
			result.Z = value1.Z + value2.Z;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 3d-triangle.
		/// </summary>
		/// <param name="value1">The first vector of 3d-triangle.</param>
		/// <param name="value2">The second vector of 3d-triangle.</param>
		/// <param name="value3">The third vector of 3d-triangle.</param>
		/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 3d-triangle.</param>
		/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 3d-triangle.</param>
		/// <returns>The cartesian translation of barycentric coordinates.</returns>
		public static Vector3 Barycentric(
			Vector3 value1,
			Vector3 value2,
			Vector3 value3,
			float amount1,
			float amount2
		) {
			return new Vector3(
				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)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains the cartesian coordinates of a vector specified in barycentric coordinates and relative to 3d-triangle.
		/// </summary>
		/// <param name="value1">The first vector of 3d-triangle.</param>
		/// <param name="value2">The second vector of 3d-triangle.</param>
		/// <param name="value3">The third vector of 3d-triangle.</param>
		/// <param name="amount1">Barycentric scalar <c>b2</c> which represents a weighting factor towards second vector of 3d-triangle.</param>
		/// <param name="amount2">Barycentric scalar <c>b3</c> which represents a weighting factor towards third vector of 3d-triangle.</param>
		/// <param name="result">The cartesian translation of barycentric coordinates as an output parameter.</param>
		public static void Barycentric(
			ref Vector3 value1,
			ref Vector3 value2,
			ref Vector3 value3,
			float amount1,
			float amount2,
			out Vector3 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);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 CatmullRom(
			Vector3 value1,
			Vector3 value2,
			Vector3 value3,
			Vector3 value4,
			float amount
		) {
			return new Vector3(
				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)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 value1,
			ref Vector3 value2,
			ref Vector3 value3,
			ref Vector3 value4,
			float amount,
			out Vector3 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);
		}

		/// <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 Vector3 Clamp(Vector3 value1, Vector3 min, Vector3 max)
		{
			return new Vector3(
				MathHelper.Clamp(value1.X, min.X, max.X),
				MathHelper.Clamp(value1.Y, min.Y, max.Y),
				MathHelper.Clamp(value1.Z, min.Z, max.Z)
			);
		}

		/// <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 Vector3 value1,
			ref Vector3 min,
			ref Vector3 max,
			out Vector3 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);
		}

		/// <summary>
		/// Computes the cross product of two vectors.
		/// </summary>
		/// <param name="vector1">The first vector.</param>
		/// <param name="vector2">The second vector.</param>
		/// <returns>The cross product of two vectors.</returns>
		public static Vector3 Cross(Vector3 vector1, Vector3 vector2)
		{
			Cross(ref vector1, ref vector2, out vector1);
			return vector1;
		}

		/// <summary>
		/// Computes the cross product of two vectors.
		/// </summary>
		/// <param name="vector1">The first vector.</param>
		/// <param name="vector2">The second vector.</param>
		/// <param name="result">The cross product of two vectors as an output parameter.</param>
		public static void Cross(ref Vector3 vector1, ref Vector3 vector2, out Vector3 result)
		{
			float x = vector1.Y * vector2.Z - vector2.Y * vector1.Z;
			float y = -(vector1.X * vector2.Z - vector2.X * vector1.Z);
			float z = vector1.X * vector2.Y - vector2.X * vector1.Y;
			result.X = x;
			result.Y = y;
			result.Z = z;
		}

		/// <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(Vector3 vector1, Vector3 vector2)
		{
			float result;
			DistanceSquared(ref vector1, ref vector2, out result);
			return (float) Math.Sqrt(result);
		}

		/// <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 Vector3 value1, ref Vector3 value2, out float result)
		{
			DistanceSquared(ref value1, ref value2, out result);
			result = (float) Math.Sqrt(result);
		}

		/// <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(Vector3 value1, Vector3 value2)
		{
			return (
				(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 Vector3 value1,
			ref Vector3 value2,
			out float result
		) {
			result = (
				(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="Vector3"/> by the components of another <see cref="Vector3"/>.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Divisor <see cref="Vector3"/>.</param>
		/// <returns>The result of dividing the vectors.</returns>
		public static Vector3 Divide(Vector3 value1, Vector3 value2)
		{
			value1.X /= value2.X;
			value1.Y /= value2.Y;
			value1.Z /= value2.Z;
			return value1;
		}

		/// <summary>
		/// Divides the components of a <see cref="Vector3"/> by the components of another <see cref="Vector3"/>.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Divisor <see cref="Vector3"/>.</param>
		/// <param name="result">The result of dividing the vectors as an output parameter.</param>
		public static void Divide(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
		{
			result.X = value1.X / value2.X;
			result.Y = value1.Y / value2.Y;
			result.Z = value1.Z / value2.Z;
		}

		/// <summary>
		/// Divides the components of a <see cref="Vector3"/> by a scalar.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Divisor scalar.</param>
		/// <returns>The result of dividing a vector by a scalar.</returns>
		public static Vector3 Divide(Vector3 value1, float value2)
		{
			float factor = 1 / value2;
			value1.X *= factor;
			value1.Y *= factor;
			value1.Z *= factor;
			return value1;
		}

		/// <summary>
		/// Divides the components of a <see cref="Vector3"/> by a scalar.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">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 Vector3 value1, float value2, out Vector3 result)
		{
			float factor = 1 / value2;
			result.X = value1.X * factor;
			result.Y = value1.Y * factor;
			result.Z = value1.Z * factor;
		}

		/// <summary>
		/// Returns a dot product of two vectors.
		/// </summary>
		/// <param name="vector1">The first vector.</param>
		/// <param name="vector2">The second vector.</param>
		/// <returns>The dot product of two vectors.</returns>
		public static float Dot(Vector3 vector1, Vector3 vector2)
		{
			return vector1.X * vector2.X + vector1.Y * vector2.Y + vector1.Z * vector2.Z;
		}

		/// <summary>
		/// Returns a dot product of two vectors.
		/// </summary>
		/// <param name="vector1">The first vector.</param>
		/// <param name="vector2">The second vector.</param>
		/// <param name="result">The dot product of two vectors as an output parameter.</param>
		public static void Dot(ref Vector3 vector1, ref Vector3 vector2, out float result)
		{
			result = (
				(vector1.X * vector2.X) +
				(vector1.Y * vector2.Y) +
				(vector1.Z * vector2.Z)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 Hermite(
			Vector3 value1,
			Vector3 tangent1,
			Vector3 value2,
			Vector3 tangent2,
			float amount
		) {
			Vector3 result = new Vector3();
			Hermite(ref value1, ref tangent1, ref value2, ref tangent2, amount, out result);
			return result;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 value1,
			ref Vector3 tangent1,
			ref Vector3 value2,
			ref Vector3 tangent2,
			float amount,
			out Vector3 result
		) {
			result.X = MathHelper.Hermite(value1.X, tangent1.X, value2.X, tangent2.X, amount);
			result.Y = MathHelper.Hermite(value1.Y, tangent1.Y, value2.Y, tangent2.Y, amount);
			result.Z = MathHelper.Hermite(value1.Z, tangent1.Z, value2.Z, tangent2.Z, amount);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 Lerp(Vector3 value1, Vector3 value2, float amount)
		{
			return new Vector3(
				MathHelper.Lerp(value1.X, value2.X, amount),
				MathHelper.Lerp(value1.Y, value2.Y, amount),
				MathHelper.Lerp(value1.Z, value2.Z, amount)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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 Vector3 value1,
			ref Vector3 value2,
			float amount,
			out Vector3 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);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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="Vector3"/> with maximal values from the two vectors.</returns>
		public static Vector3 Max(Vector3 value1, Vector3 value2)
		{
			return new Vector3(
				MathHelper.Max(value1.X, value2.X),
				MathHelper.Max(value1.Y, value2.Y),
				MathHelper.Max(value1.Z, value2.Z)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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="Vector3"/> with maximal values from the two vectors as an output parameter.</param>
		public static void Max(ref Vector3 value1, ref Vector3 value2, out Vector3 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);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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="Vector3"/> with minimal values from the two vectors.</returns>
		public static Vector3 Min(Vector3 value1, Vector3 value2)
		{
			return new Vector3(
				MathHelper.Min(value1.X, value2.X),
				MathHelper.Min(value1.Y, value2.Y),
				MathHelper.Min(value1.Z, value2.Z)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> 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="Vector3"/> with minimal values from the two vectors as an output parameter.</param>
		public static void Min(ref Vector3 value1, ref Vector3 value2, out Vector3 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);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a multiplication of two vectors.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</param>
		/// <returns>The result of the vector multiplication.</returns>
		public static Vector3 Multiply(Vector3 value1, Vector3 value2)
		{
			value1.X *= value2.X;
			value1.Y *= value2.Y;
			value1.Z *= value2.Z;
			return value1;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a multiplication of <see cref="Vector3"/> and a scalar.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="scaleFactor">Scalar value.</param>
		/// <returns>The result of the vector multiplication with a scalar.</returns>
		public static Vector3 Multiply(Vector3 value1, float scaleFactor)
		{
			value1.X *= scaleFactor;
			value1.Y *= scaleFactor;
			value1.Z *= scaleFactor;
			return value1;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a multiplication of <see cref="Vector3"/> and a scalar.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</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 Vector3 value1, float scaleFactor, out Vector3 result)
		{
			result.X = value1.X * scaleFactor;
			result.Y = value1.Y * scaleFactor;
			result.Z = value1.Z * scaleFactor;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a multiplication of two vectors.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</param>
		/// <param name="result">The result of the vector multiplication as an output parameter.</param>
		public static void Multiply(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
		{
			result.X = value1.X * value2.X;
			result.Y = value1.Y * value2.Y;
			result.Z = value1.Z * value2.Z;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains the specified vector inversion.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/>.</param>
		/// <returns>The result of the vector inversion.</returns>
		public static Vector3 Negate(Vector3 value)
		{
			value = new Vector3(-value.X, -value.Y, -value.Z);
			return value;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains the specified vector inversion.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/>.</param>
		/// <param name="result">The result of the vector inversion as an output parameter.</param>
		public static void Negate(ref Vector3 value, out Vector3 result)
		{
			result.X = -value.X;
			result.Y = -value.Y;
			result.Z = -value.Z;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a normalized values from another vector.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/>.</param>
		/// <returns>Unit vector.</returns>
		public static Vector3 Normalize(Vector3 value)
		{
			Normalize(ref value, out value);
			return value;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a normalized values from another vector.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/>.</param>
		/// <param name="result">Unit vector as an output parameter.</param>
		public static void Normalize(ref Vector3 value, out Vector3 result)
		{
			float factor;
			Distance(ref value, ref zero, out factor);
			factor = 1.0f / factor;
			result.X = value.X * factor;
			result.Y = value.Y * factor;
			result.Z = value.Z * factor;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains reflect vector of the given vector and normal.
		/// </summary>
		/// <param name="vector">Source <see cref="Vector3"/>.</param>
		/// <param name="normal">Reflection normal.</param>
		/// <returns>Reflected vector.</returns>
		public static Vector3 Reflect(Vector3 vector, Vector3 normal)
		{
			/* I is the original array.
			 * N is the normal of the incident plane.
			 * R = I - (2 * N * ( DotProduct[ I,N] ))
			 */
			Vector3 reflectedVector;
			// Inline the dotProduct here instead of calling method
			float dotProduct = ((vector.X * normal.X) + (vector.Y * normal.Y)) +
						(vector.Z * normal.Z);
			reflectedVector.X = vector.X - (2.0f * normal.X) * dotProduct;
			reflectedVector.Y = vector.Y - (2.0f * normal.Y) * dotProduct;
			reflectedVector.Z = vector.Z - (2.0f * normal.Z) * dotProduct;

			return reflectedVector;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains reflect vector of the given vector and normal.
		/// </summary>
		/// <param name="vector">Source <see cref="Vector3"/>.</param>
		/// <param name="normal">Reflection normal.</param>
		/// <param name="result">Reflected vector as an output parameter.</param>
		public static void Reflect(ref Vector3 vector, ref Vector3 normal, out Vector3 result)
		{
			/* I is the original array.
			 * N is the normal of the incident plane.
			 * R = I - (2 * N * ( DotProduct[ I,N] ))
			 */

			// Inline the dotProduct here instead of calling method.
			float dotProduct = ((vector.X * normal.X) + (vector.Y * normal.Y)) +
						(vector.Z * normal.Z);
			result.X = vector.X - (2.0f * normal.X) * dotProduct;
			result.Y = vector.Y - (2.0f * normal.Y) * dotProduct;
			result.Z = vector.Z - (2.0f * normal.Z) * dotProduct;

		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains cubic interpolation of the specified vectors.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</param>
		/// <param name="amount">Weighting value.</param>
		/// <returns>Cubic interpolation of the specified vectors.</returns>
		public static Vector3 SmoothStep(Vector3 value1, Vector3 value2, float amount)
		{
			return new Vector3(
				MathHelper.SmoothStep(value1.X, value2.X, amount),
				MathHelper.SmoothStep(value1.Y, value2.Y, amount),
				MathHelper.SmoothStep(value1.Z, value2.Z, amount)
			);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains cubic interpolation of the specified vectors.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</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 Vector3 value1,
			ref Vector3 value2,
			float amount,
			out Vector3 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);
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains subtraction of on <see cref="Vector3"/> from a another.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</param>
		/// <returns>The result of the vector subtraction.</returns>
		public static Vector3 Subtract(Vector3 value1, Vector3 value2)
		{
			value1.X -= value2.X;
			value1.Y -= value2.Y;
			value1.Z -= value2.Z;
			return value1;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains subtraction of on <see cref="Vector3"/> from a another.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/>.</param>
		/// <param name="value2">Source <see cref="Vector3"/>.</param>
		/// <param name="result">The result of the vector subtraction as an output parameter.</param>
		public static void Subtract(ref Vector3 value1, ref Vector3 value2, out Vector3 result)
		{
			result.X = value1.X - value2.X;
			result.Y = value1.Y - value2.Y;
			result.Z = value1.Z - value2.Z;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix"/>.
		/// </summary>
		/// <param name="position">Source <see cref="Vector3"/>.</param>
		/// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
		/// <returns>Transformed <see cref="Vector3"/>.</returns>
		public static Vector3 Transform(Vector3 position, Matrix matrix)
		{
			Transform(ref position, ref matrix, out position);
			return position;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Matrix"/>.
		/// </summary>
		/// <param name="position">Source <see cref="Vector3"/>.</param>
		/// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
		/// <param name="result">Transformed <see cref="Vector3"/> as an output parameter.</param>
		public static void Transform(
			ref Vector3 position,
			ref Matrix matrix,
			out Vector3 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
			);
			result.X = x;
			result.Y = y;
			result.Z = z;
		}

		/// <summary>
		/// Apply transformation on all vectors within array of <see cref="Vector3"/> 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(
			Vector3[] sourceArray,
			ref Matrix matrix,
			Vector3[] destinationArray
		) {
			Debug.Assert(
				destinationArray.Length >= sourceArray.Length,
				"The destination array is smaller than the source array."
			);

			/* TODO: Are there options on some platforms to implement
			 * a vectorized version of this?
			 */

			for (int i = 0; i < sourceArray.Length; i += 1)
			{
				Vector3 position = sourceArray[i];
				destinationArray[i] = new Vector3(
					(position.X * matrix.M11) + (position.Y * matrix.M21) +
						(position.Z * matrix.M31) + matrix.M41,
					(position.X * matrix.M12) + (position.Y * matrix.M22) +
						(position.Z * matrix.M32) + matrix.M42,
					(position.X * matrix.M13) + (position.Y * matrix.M23) +
						(position.Z * matrix.M33) + matrix.M43
				);
			}
		}

		/// <summary>
		/// Apply transformation on vectors within array of <see cref="Vector3"/> 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="Vector3"/> should be written.</param>
		/// <param name="length">The number of vectors to be transformed.</param>
		public static void Transform(
			Vector3[] sourceArray,
			int sourceIndex,
			ref Matrix matrix,
			Vector3[] destinationArray,
			int destinationIndex,
			int length
		) {
			Debug.Assert(
				sourceArray.Length - sourceIndex >= length,
				"The source array is too small for the given sourceIndex and length."
			);
			Debug.Assert(
				destinationArray.Length - destinationIndex >= length,
				"The destination array is too small for " +
				"the given destinationIndex and length."
			);

			/* TODO: Are there options on some platforms to implement a
			 * vectorized version of this?
			 */

			for (int i = 0; i < length; i += 1)
			{
				Vector3 position = sourceArray[sourceIndex + i];
				destinationArray[destinationIndex + i] = new Vector3(
					(position.X * matrix.M11) + (position.Y * matrix.M21) +
						(position.Z * matrix.M31) + matrix.M41,
					(position.X * matrix.M12) + (position.Y * matrix.M22) +
						(position.Z * matrix.M32) + matrix.M42,
					(position.X * matrix.M13) + (position.Y * matrix.M23) +
						(position.Z * matrix.M33) + matrix.M43
				);
			}
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
		/// </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="Vector3"/>.</returns>
		public static Vector3 Transform(Vector3 value, Quaternion rotation)
		{
			Vector3 result;
			Transform(ref value, ref rotation, out result);
			return result;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of 3d-vector by the specified <see cref="Quaternion"/>, representing the rotation.
		/// </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="Vector3"/> as an output parameter.</param>
		public static void Transform(
			ref Vector3 value,
			ref Quaternion rotation,
			out Vector3 result
		) {
			float x = 2 * (rotation.Y * value.Z - rotation.Z * value.Y);
			float y = 2 * (rotation.Z * value.X - rotation.X * value.Z);
			float z = 2 * (rotation.X * value.Y - rotation.Y * value.X);

			result.X = value.X + x * rotation.W + (rotation.Y * z - rotation.Z * y);
			result.Y = value.Y + y * rotation.W + (rotation.Z * x - rotation.X * z);
			result.Z = value.Z + z * rotation.W + (rotation.X * y - rotation.Y * x);
		}

		/// <summary>
		/// Apply transformation on all vectors within array of <see cref="Vector3"/> 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(
			Vector3[] sourceArray,
			ref Quaternion rotation,
			Vector3[] destinationArray
		) {
			Debug.Assert(
				destinationArray.Length >= sourceArray.Length,
				"The destination array is smaller than the source array."
			);

			/* TODO: Are there options on some platforms to implement
			 * a vectorized version of this?
			 */

			for (int i = 0; i < sourceArray.Length; i += 1)
			{
				Vector3 position = sourceArray[i];

				float x = 2 * (rotation.Y * position.Z - rotation.Z * position.Y);
				float y = 2 * (rotation.Z * position.X - rotation.X * position.Z);
				float z = 2 * (rotation.X * position.Y - rotation.Y * position.X);

				destinationArray[i] = new Vector3(
					position.X + x * rotation.W + (rotation.Y * z - rotation.Z * y),
					position.Y + y * rotation.W + (rotation.Z * x - rotation.X * z),
					position.Z + z * rotation.W + (rotation.X * y - rotation.Y * x)
				);
			}
		}

		/// <summary>

		/// Apply transformation on vectors within array of <see cref="Vector3"/> 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="Vector3"/> should be written.</param>
		/// <param name="length">The number of vectors to be transformed.</param>
		public static void Transform(
			Vector3[] sourceArray,
			int sourceIndex,
			ref Quaternion rotation,
			Vector3[] destinationArray,
			int destinationIndex,
			int length
		) {
			Debug.Assert(
				sourceArray.Length - sourceIndex >= length,
				"The source array is too small for the given sourceIndex and length."
			);
			Debug.Assert(
				destinationArray.Length - destinationIndex >= length,
				"The destination array is too small for the " +
				"given destinationIndex and length."
			);

			/* TODO: Are there options on some platforms to implement
			 * a vectorized version of this?
			 */

			for (int i = 0; i < length; i += 1)
			{
				Vector3 position = sourceArray[sourceIndex + i];

				float x = 2 * (rotation.Y * position.Z - rotation.Z * position.Y);
				float y = 2 * (rotation.Z * position.X - rotation.X * position.Z);
				float z = 2 * (rotation.X * position.Y - rotation.Y * position.X);

				destinationArray[destinationIndex + i] = new Vector3(
					position.X + x * rotation.W + (rotation.Y * z - rotation.Z * y),
					position.Y + y * rotation.W + (rotation.Z * x - rotation.X * z),
					position.Z + z * rotation.W + (rotation.X * y - rotation.Y * x)
				);
			}
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of the specified normal by the specified <see cref="Matrix"/>.
		/// </summary>
		/// <param name="normal">Source <see cref="Vector3"/> which represents a normal vector.</param>
		/// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
		/// <returns>Transformed normal.</returns>
		public static Vector3 TransformNormal(Vector3 normal, Matrix matrix)
		{
			TransformNormal(ref normal, ref matrix, out normal);
			return normal;
		}

		/// <summary>
		/// Creates a new <see cref="Vector3"/> that contains a transformation of the specified normal by the specified <see cref="Matrix"/>.
		/// </summary>
		/// <param name="normal">Source <see cref="Vector3"/> which represents a normal vector.</param>
		/// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
		/// <param name="result">Transformed normal as an output parameter.</param>
		public static void TransformNormal(
			ref Vector3 normal,
			ref Matrix matrix,
			out Vector3 result
		) {
			float x = (normal.X * matrix.M11) + (normal.Y * matrix.M21) + (normal.Z * matrix.M31);
			float y = (normal.X * matrix.M12) + (normal.Y * matrix.M22) + (normal.Z * matrix.M32);
			float z = (normal.X * matrix.M13) + (normal.Y * matrix.M23) + (normal.Z * matrix.M33);
			result.X = x;
			result.Y = y;
			result.Z = z;
		}

		/// <summary>
		/// Apply transformation on all normals within array of <see cref="Vector3"/> by the specified <see cref="Matrix"/> and places the results in an another array.
		/// </summary>
		/// <param name="sourceArray">Source array.</param>
		/// <param name="matrix">The transformation <see cref="Matrix"/>.</param>
		/// <param name="destinationArray">Destination array.</param>
		public static void TransformNormal(
			Vector3[] sourceArray,
			ref Matrix matrix,
			Vector3[] destinationArray
		) {
			Debug.Assert(
				destinationArray.Length >= sourceArray.Length,
				"The destination array is smaller than the source array."
			);

			for (int i = 0; i < sourceArray.Length; i += 1)
			{
				Vector3 normal = sourceArray[i];
				destinationArray[i].X = (normal.X * matrix.M11) + (normal.Y * matrix.M21) + (normal.Z * matrix.M31);
				destinationArray[i].Y = (normal.X * matrix.M12) + (normal.Y * matrix.M22) + (normal.Z * matrix.M32);
				destinationArray[i].Z = (normal.X * matrix.M13) + (normal.Y * matrix.M23) + (normal.Z * matrix.M33);
			}
		}

		/// <summary>
		/// Apply transformation on normals within array of <see cref="Vector3"/> 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="Vector3"/> should be written.</param>
		/// <param name="length">The number of normals to be transformed.</param>
		public static void TransformNormal(
			Vector3[] sourceArray,
			int sourceIndex,
			ref Matrix matrix,
			Vector3[] destinationArray,
			int destinationIndex,
			int length
		) {
			if (sourceArray == null)
			{
				throw new ArgumentNullException("sourceArray");
			}
			if (destinationArray == null)
			{
				throw new ArgumentNullException("destinationArray");
			}
			if ((sourceIndex + length) > sourceArray.Length)
			{
				throw new ArgumentException(
					"the combination of sourceIndex and " +
					"length was greater than sourceArray.Length"
				);
			}
			if ((destinationIndex + length) > destinationArray.Length)
			{
				throw new ArgumentException(
					"destinationArray is too small to " +
					"contain the result"
				);
			}

			for (int i = 0; i < length; i += 1)
			{
				Vector3 normal = sourceArray[i + sourceIndex];
				destinationArray[i + destinationIndex].X = (
					(normal.X * matrix.M11) +
					(normal.Y * matrix.M21) +
					(normal.Z * matrix.M31)
				);
				destinationArray[i + destinationIndex].Y = (
					(normal.X * matrix.M12) +
					(normal.Y * matrix.M22) +
					(normal.Z * matrix.M32)
				);
				destinationArray[i + destinationIndex].Z = (
					(normal.X * matrix.M13) +
					(normal.Y * matrix.M23) +
					(normal.Z * matrix.M33)
				);
			}
		}

		#endregion

		#region Public Static Operators

		/// <summary>
		/// Compares whether two <see cref="Vector3"/> instances are equal.
		/// </summary>
		/// <param name="value1"><see cref="Vector3"/> instance on the left of the equal sign.</param>
		/// <param name="value2"><see cref="Vector3"/> 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 ==(Vector3 value1, Vector3 value2)
		{
			return (	(MathHelper.WithinEpsilon(value1.X, value2.X)) &&
					(MathHelper.WithinEpsilon(value1.Y, value2.Y)) &&
					(MathHelper.WithinEpsilon(value1.Z, value2.Z))	);
		}

		/// <summary>
		/// Compares whether two <see cref="Vector3"/> instances are not equal.
		/// </summary>
		/// <param name="value1"><see cref="Vector3"/> instance on the left of the not equal sign.</param>
		/// <param name="value2"><see cref="Vector3"/> 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 !=(Vector3 value1, Vector3 value2)
		{
			return !(value1 == value2);
		}

		/// <summary>
		/// Adds two vectors.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/> on the left of the add sign.</param>
		/// <param name="value2">Source <see cref="Vector3"/> on the right of the add sign.</param>
		/// <returns>Sum of the vectors.</returns>
		public static Vector3 operator +(Vector3 value1, Vector3 value2)
		{
			value1.X += value2.X;
			value1.Y += value2.Y;
			value1.Z += value2.Z;
			return value1;
		}

		/// <summary>
		/// Inverts values in the specified <see cref="Vector3"/>.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/> on the right of the sub sign.</param>
		/// <returns>Result of the inversion.</returns>
		public static Vector3 operator -(Vector3 value)
		{
			value = new Vector3(-value.X, -value.Y, -value.Z);
			return value;
		}

		/// <summary>
		/// Subtracts a <see cref="Vector3"/> from a <see cref="Vector3"/>.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/> on the left of the sub sign.</param>
		/// <param name="value2">Source <see cref="Vector3"/> on the right of the sub sign.</param>
		/// <returns>Result of the vector subtraction.</returns>
		public static Vector3 operator -(Vector3 value1, Vector3 value2)
		{
			value1.X -= value2.X;
			value1.Y -= value2.Y;
			value1.Z -= value2.Z;
			return value1;
		}

		/// <summary>
		/// Multiplies the components of two vectors by each other.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/> on the left of the mul sign.</param>
		/// <param name="value2">Source <see cref="Vector3"/> on the right of the mul sign.</param>
		/// <returns>Result of the vector multiplication.</returns>
		public static Vector3 operator *(Vector3 value1, Vector3 value2)
		{
			value1.X *= value2.X;
			value1.Y *= value2.Y;
			value1.Z *= value2.Z;
			return value1;
		}

		/// <summary>
		/// Multiplies the components of vector by a scalar.
		/// </summary>
		/// <param name="value">Source <see cref="Vector3"/> on the left of the mul sign.</param>
		/// <param name="scaleFactor">Scalar value on the right of the mul sign.</param>
		/// <returns>Result of the vector multiplication with a scalar.</returns>
		public static Vector3 operator *(Vector3 value, float scaleFactor)
		{
			value.X *= scaleFactor;
			value.Y *= scaleFactor;
			value.Z *= scaleFactor;
			return value;
		}

		/// <summary>
		/// Multiplies the components of vector by a scalar.
		/// </summary>
		/// <param name="scaleFactor">Scalar value on the left of the mul sign.</param>
		/// <param name="value">Source <see cref="Vector3"/> on the right of the mul sign.</param>
		/// <returns>Result of the vector multiplication with a scalar.</returns>
		public static Vector3 operator *(float scaleFactor, Vector3 value)
		{
			value.X *= scaleFactor;
			value.Y *= scaleFactor;
			value.Z *= scaleFactor;
			return value;
		}

		/// <summary>
		/// Divides the components of a <see cref="Vector3"/> by the components of another <see cref="Vector3"/>.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/> on the left of the div sign.</param>
		/// <param name="value2">Divisor <see cref="Vector3"/> on the right of the div sign.</param>
		/// <returns>The result of dividing the vectors.</returns>
		public static Vector3 operator /(Vector3 value1, Vector3 value2)
		{
			value1.X /= value2.X;
			value1.Y /= value2.Y;
			value1.Z /= value2.Z;
			return value1;
		}

		/// <summary>
		/// Divides the components of a <see cref="Vector3"/> by a scalar.
		/// </summary>
		/// <param name="value1">Source <see cref="Vector3"/> on the left of the div sign.</param>
		/// <param name="divider">Divisor scalar on the right of the div sign.</param>
		/// <returns>The result of dividing a vector by a scalar.</returns>
		public static Vector3 operator /(Vector3 value, float divider)
		{
			float factor = 1 / divider;
			value.X *= factor;
			value.Y *= factor;
			value.Z *= factor;
			return value;
		}

		#endregion
	}
}