#region --- License ---
/*
Copyright (c) 2006 - 2008 The Open Toolkit library.

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
 */
#endregion

using System;
using System.Runtime.InteropServices;
using System.Xml.Serialization;
namespace OpenTK
{
    /// <summary>Represents a 4D vector using four single-precision floating-point numbers.</summary>
    /// <remarks>
    /// The Vector4 structure is suitable for interoperation with unmanaged code requiring four consecutive floats.
    /// </remarks>
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    public struct Vector4 : IEquatable<Vector4>
    {
        #region Fields

        /// <summary>
        /// The X component of the Vector4.
        /// </summary>
        public float X;

        /// <summary>
        /// The Y component of the Vector4.
        /// </summary>
        public float Y;

        /// <summary>
        /// The Z component of the Vector4.
        /// </summary>
        public float Z;

        /// <summary>
        /// The W component of the Vector4.
        /// </summary>
        public float W;

        /// <summary>
        /// Defines a unit-length Vector4 that points towards the X-axis.
        /// </summary>
        public static Vector4 UnitX = new Vector4(1, 0, 0, 0);

        /// <summary>
        /// Defines a unit-length Vector4 that points towards the Y-axis.
        /// </summary>
        public static Vector4 UnitY = new Vector4(0, 1, 0, 0);

        /// <summary>
        /// Defines a unit-length Vector4 that points towards the Z-axis.
        /// </summary>
        public static Vector4 UnitZ = new Vector4(0, 0, 1, 0);

        /// <summary>
        /// Defines a unit-length Vector4 that points towards the W-axis.
        /// </summary>
        public static Vector4 UnitW = new Vector4(0, 0, 0, 1);

        /// <summary>
        /// Defines a zero-length Vector4.
        /// </summary>
        public static Vector4 Zero = new Vector4(0, 0, 0, 0);

        /// <summary>
        /// Defines an instance with all components set to 1.
        /// </summary>
        public static readonly Vector4 One = new Vector4(1, 1, 1, 1);

        /// <summary>
        /// Defines the size of the Vector4 struct in bytes.
        /// </summary>
        public static readonly int SizeInBytes = Marshal.SizeOf(new Vector4());

        #endregion

        #region Constructors

        /// <summary>
        /// Constructs a new Vector4.
        /// </summary>
        /// <param name="x">The x component of the Vector4.</param>
        /// <param name="y">The y component of the Vector4.</param>
        /// <param name="z">The z component of the Vector4.</param>
        /// <param name="w">The z component of the Vector4.</param>
        public Vector4(float x, float y, float z, float w)
        {
            X = x;
            Y = y;
            Z = z;
            W = w;
        }

        /// <summary>
        /// Constructs a new Vector4 from the given Vector2.
        /// </summary>
        /// <param name="v">The Vector2 to copy components from.</param>
        public Vector4(Vector2 v)
        {
            X = v.X;
            Y = v.Y;
            Z = 0.0f;
            W = 0.0f;
        }

        /// <summary>
        /// Constructs a new Vector4 from the given Vector3.
        /// </summary>
        /// <param name="v">The Vector3 to copy components from.</param>
        public Vector4(Vector3 v)
        {
            X = v.X;
            Y = v.Y;
            Z = v.Z;
            W = 0.0f;
        }

        /// <summary>
        /// Constructs a new Vector4 from the specified Vector3 and W component.
        /// </summary>
        /// <param name="v">The Vector3 to copy components from.</param>
        /// <param name="w">The W component of the new Vector4.</param>
        public Vector4(Vector3 v, float w)
        {
            X = v.X;
            Y = v.Y;
            Z = v.Z;
            W = w;
        }

        /// <summary>
        /// Constructs a new Vector4 from the given Vector4.
        /// </summary>
        /// <param name="v">The Vector4 to copy components from.</param>
        public Vector4(Vector4 v)
        {
            X = v.X;
            Y = v.Y;
            Z = v.Z;
            W = v.W;
        }

        #endregion

        #region Public Members

        #region Instance

        #region public void Add()

        /// <summary>Add the Vector passed as parameter to this instance.</summary>
        /// <param name="right">Right operand. This parameter is only read from.</param>
        public void Add(Vector4 right)
        {
            this.X += right.X;
            this.Y += right.Y;
            this.Z += right.Z;
            this.W += right.W;
        }

        /// <summary>Add the Vector passed as parameter to this instance.</summary>
        /// <param name="right">Right operand. This parameter is only read from.</param>
        [CLSCompliant(false)]
        public void Add(ref Vector4 right)
        {
            this.X += right.X;
            this.Y += right.Y;
            this.Z += right.Z;
            this.W += right.W;
        }

        #endregion public void Add()

        #region public void Sub()

        /// <summary>Subtract the Vector passed as parameter from this instance.</summary>
        /// <param name="right">Right operand. This parameter is only read from.</param>
        public void Sub(Vector4 right)
        {
            this.X -= right.X;
            this.Y -= right.Y;
            this.Z -= right.Z;
            this.W -= right.W;
        }

        /// <summary>Subtract the Vector passed as parameter from this instance.</summary>
        /// <param name="right">Right operand. This parameter is only read from.</param>
        [CLSCompliant(false)]
        public void Sub(ref Vector4 right)
        {
            this.X -= right.X;
            this.Y -= right.Y;
            this.Z -= right.Z;
            this.W -= right.W;
        }

        #endregion public void Sub()

        #region public void Mult()

        /// <summary>Multiply this instance by a scalar.</summary>
        /// <param name="f">Scalar operand.</param>
        public void Mult(float f)
        {
            this.X *= f;
            this.Y *= f;
            this.Z *= f;
            this.W *= f;
        }

        #endregion public void Mult()

        #region public void Div()

        /// <summary>Divide this instance by a scalar.</summary>
        /// <param name="f">Scalar operand.</param>
        public void Div(float f)
        {
            float mult = 1.0f / f;
            this.X *= mult;
            this.Y *= mult;
            this.Z *= mult;
            this.W *= mult;
        }

        #endregion public void Div()

        #region public float Length

        /// <summary>
        /// Gets the length (magnitude) of the vector.
        /// </summary>
        /// <see cref="LengthFast"/>
        /// <seealso cref="LengthSquared"/>
        public float Length
        {
            get
            {
                return (float)System.Math.Sqrt(X * X + Y * Y + Z * Z + W * W);
            }
        }

        #endregion

        #region public float LengthFast

        /// <summary>
        /// Gets an approximation of the vector length (magnitude).
        /// </summary>
        /// <remarks>
        /// This property uses an approximation of the square root function to calculate vector magnitude, with
        /// an upper error bound of 0.001.
        /// </remarks>
        /// <see cref="Length"/>
        /// <seealso cref="LengthSquared"/>
        public float LengthFast
        {
            get
            {
                return 1.0f / MathHelper.InverseSqrtFast(X * X + Y * Y + Z * Z + W * W);
            }
        }

        #endregion

        #region public float LengthSquared

        /// <summary>
        /// Gets the square of the vector length (magnitude).
        /// </summary>
        /// <remarks>
        /// This property avoids the costly square root operation required by the Length property. This makes it more suitable
        /// for comparisons.
        /// </remarks>
        /// <see cref="Length"/>
        /// <seealso cref="LengthFast"/>
        public float LengthSquared
        {
            get
            {
                return X * X + Y * Y + Z * Z + W * W;
            }
        }

        #endregion

        #region public void Normalize()

        /// <summary>
        /// Scales the Vector4 to unit length.
        /// </summary>
        public void Normalize()
        {
            float scale = 1.0f / this.Length;
            X *= scale;
            Y *= scale;
            Z *= scale;
            W *= scale;
        }

        #endregion

        #region public void NormalizeFast()

        /// <summary>
        /// Scales the Vector4 to approximately unit length.
        /// </summary>
        public void NormalizeFast()
        {
            float scale = MathHelper.InverseSqrtFast(X * X + Y * Y + Z * Z + W * W);
            X *= scale;
            Y *= scale;
            Z *= scale;
            W *= scale;
        }

        #endregion

        #region public void Scale()

        /// <summary>
        /// Scales the current Vector4 by the given amounts.
        /// </summary>
        /// <param name="sx">The scale of the X component.</param>
        /// <param name="sy">The scale of the Y component.</param>
        /// <param name="sz">The scale of the Z component.</param>
        /// <param name="sw">The scale of the Z component.</param>
        public void Scale(float sx, float sy, float sz, float sw)
        {
            this.X = X * sx;
            this.Y = Y * sy;
            this.Z = Z * sz;
            this.W = W * sw;
        }

        /// <summary>Scales this instance by the given parameter.</summary>
        /// <param name="scale">The scaling of the individual components.</param>
        public void Scale(Vector4 scale)
        {
            this.X *= scale.X;
            this.Y *= scale.Y;
            this.Z *= scale.Z;
            this.W *= scale.W;
        }

        /// <summary>Scales this instance by the given parameter.</summary>
        /// <param name="scale">The scaling of the individual components.</param>
        [CLSCompliant(false)]
        public void Scale(ref Vector4 scale)
        {
            this.X *= scale.X;
            this.Y *= scale.Y;
            this.Z *= scale.Z;
            this.W *= scale.W;
        }

        #endregion public void Scale()

        #endregion

        #region Static

        #region Add

        /// <summary>
        /// Add two Vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>Result of addition</returns>
        public static Vector4 Add(Vector4 a, Vector4 b)
        {
            a.X += b.X;
            a.Y += b.Y;
            a.Z += b.Z;
            a.W += b.W;
            return a;
        }

        /// <summary>
        /// Add two Vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">Result of addition</param>
        public static void Add(ref Vector4 a, ref Vector4 b, out Vector4 result)
        {
            result.X = a.X + b.X;
            result.Y = a.Y + b.Y;
            result.Z = a.Z + b.Z;
            result.W = a.W + b.W;
        }

        #endregion

        #region Sub

        /// <summary>
        /// Subtract one Vector from another
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>Result of subtraction</returns>
        public static Vector4 Sub(Vector4 a, Vector4 b)
        {
            a.X -= b.X;
            a.Y -= b.Y;
            a.Z -= b.Z;
            a.W -= b.W;
            return a;
        }

        /// <summary>
        /// Subtract one Vector from another
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">Result of subtraction</param>
        public static void Sub(ref Vector4 a, ref Vector4 b, out Vector4 result)
        {
            result.X = a.X - b.X;
            result.Y = a.Y - b.Y;
            result.Z = a.Z - b.Z;
            result.W = a.W - b.W;
        }

        #endregion

        #region Mult

        /// <summary>
        /// Multiply a vector and a scalar
        /// </summary>
        /// <param name="a">Vector operand</param>
        /// <param name="f">Scalar operand</param>
        /// <returns>Result of the multiplication</returns>
        public static Vector4 Mult(Vector4 a, float f)
        {
            a.X *= f;
            a.Y *= f;
            a.Z *= f;
            a.W *= f;
            return a;
        }

        /// <summary>
        /// Multiply a vector and a scalar
        /// </summary>
        /// <param name="a">Vector operand</param>
        /// <param name="f">Scalar operand</param>
        /// <param name="result">Result of the multiplication</param>
        public static void Mult(ref Vector4 a, float f, out Vector4 result)
        {
            result.X = a.X * f;
            result.Y = a.Y * f;
            result.Z = a.Z * f;
            result.W = a.W * f;
        }

        #endregion

        #region Div

        /// <summary>
        /// Divide a vector by a scalar
        /// </summary>
        /// <param name="a">Vector operand</param>
        /// <param name="f">Scalar operand</param>
        /// <returns>Result of the division</returns>
        public static Vector4 Div(Vector4 a, float f)
        {
            float mult = 1.0f / f;
            a.X *= mult;
            a.Y *= mult;
            a.Z *= mult;
            a.W *= mult;
            return a;
        }

        /// <summary>
        /// Divide a vector by a scalar
        /// </summary>
        /// <param name="a">Vector operand</param>
        /// <param name="f">Scalar operand</param>
        /// <param name="result">Result of the division</param>
        public static void Div(ref Vector4 a, float f, out Vector4 result)
        {
            float mult = 1.0f / f;
            result.X = a.X * mult;
            result.Y = a.Y * mult;
            result.Z = a.Z * mult;
            result.W = a.W * mult;
        }

        #endregion

        #region Min

        /// <summary>
        /// Calculate the component-wise minimum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>The component-wise minimum</returns>
        public static Vector4 Min(Vector4 a, Vector4 b)
        {
            a.X = a.X < b.X ? a.X : b.X;
            a.Y = a.Y < b.Y ? a.Y : b.Y;
            a.Z = a.Z < b.Z ? a.Z : b.Z;
            a.W = a.W < b.W ? a.W : b.W;
            return a;
        }

        /// <summary>
        /// Calculate the component-wise minimum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">The component-wise minimum</param>
        public static void Min(ref Vector4 a, ref Vector4 b, out Vector4 result)
        {
            result.X = a.X < b.X ? a.X : b.X;
            result.Y = a.Y < b.Y ? a.Y : b.Y;
            result.Z = a.Z < b.Z ? a.Z : b.Z;
            result.W = a.W < b.W ? a.W : b.W;
        }

        #endregion

        #region Max

        /// <summary>
        /// Calculate the component-wise maximum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <returns>The component-wise maximum</returns>
        public static Vector4 Max(Vector4 a, Vector4 b)
        {
            a.X = a.X > b.X ? a.X : b.X;
            a.Y = a.Y > b.Y ? a.Y : b.Y;
            a.Z = a.Z > b.Z ? a.Z : b.Z;
            a.W = a.W > b.W ? a.W : b.W;
            return a;
        }

        /// <summary>
        /// Calculate the component-wise maximum of two vectors
        /// </summary>
        /// <param name="a">First operand</param>
        /// <param name="b">Second operand</param>
        /// <param name="result">The component-wise maximum</param>
        public static void Max(ref Vector4 a, ref Vector4 b, out Vector4 result)
        {
            result.X = a.X > b.X ? a.X : b.X;
            result.Y = a.Y > b.Y ? a.Y : b.Y;
            result.Z = a.Z > b.Z ? a.Z : b.Z;
            result.W = a.W > b.W ? a.W : b.W;
        }

        #endregion

        #region Clamp

        /// <summary>
        /// Clamp a vector to the given minimum and maximum vectors
        /// </summary>
        /// <param name="vec">Input vector</param>
        /// <param name="min">Minimum vector</param>
        /// <param name="max">Maximum vector</param>
        /// <returns>The clamped vector</returns>
        public static Vector4 Clamp(Vector4 vec, Vector4 min, Vector4 max)
        {
            vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
            vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
            vec.Z = vec.X < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
            vec.W = vec.Y < min.W ? min.W : vec.W > max.W ? max.W : vec.W;
            return vec;
        }

        /// <summary>
        /// Clamp a vector to the given minimum and maximum vectors
        /// </summary>
        /// <param name="vec">Input vector</param>
        /// <param name="min">Minimum vector</param>
        /// <param name="max">Maximum vector</param>
        /// <param name="result">The clamped vector</param>
        public static void Clamp(ref Vector4 vec, ref Vector4 min, ref Vector4 max, out Vector4 result)
        {
            result.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
            result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
            result.Z = vec.X < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
            result.W = vec.Y < min.W ? min.W : vec.W > max.W ? max.W : vec.W;
        }

        #endregion

        #region Normalize

        /// <summary>
        /// Scale a vector to unit length
        /// </summary>
        /// <param name="vec">The input vector</param>
        /// <returns>The normalized vector</returns>
        public static Vector4 Normalize(Vector4 vec)
        {
            float scale = 1.0f / vec.Length;
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
            vec.W *= scale;
            return vec;
        }

        /// <summary>
        /// Scale a vector to unit length
        /// </summary>
        /// <param name="vec">The input vector</param>
        /// <param name="result">The normalized vector</param>
        public static void Normalize(ref Vector4 vec, out Vector4 result)
        {
            float scale = 1.0f / vec.Length;
            result.X = vec.X * scale;
            result.Y = vec.Y * scale;
            result.Z = vec.Z * scale;
            result.W = vec.W * scale;
        }

        #endregion

        #region NormalizeFast

        /// <summary>
        /// Scale a vector to approximately unit length
        /// </summary>
        /// <param name="vec">The input vector</param>
        /// <returns>The normalized vector</returns>
        public static Vector4 NormalizeFast(Vector4 vec)
        {
            float scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z + vec.W * vec.W);
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
            vec.W *= scale;
            return vec;
        }

        /// <summary>
        /// Scale a vector to approximately unit length
        /// </summary>
        /// <param name="vec">The input vector</param>
        /// <param name="result">The normalized vector</param>
        public static void NormalizeFast(ref Vector4 vec, out Vector4 result)
        {
            float scale = MathHelper.InverseSqrtFast(vec.X * vec.X + vec.Y * vec.Y + vec.Z * vec.Z + vec.W * vec.W);
            result.X = vec.X * scale;
            result.Y = vec.Y * scale;
            result.Z = vec.Z * scale;
            result.W = vec.W * scale;
        }

        #endregion

        #region Dot

        /// <summary>
        /// Calculate the dot product of two vectors
        /// </summary>
        /// <param name="left">First operand</param>
        /// <param name="right">Second operand</param>
        /// <returns>The dot product of the two inputs</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>
        /// Calculate the dot product of two vectors
        /// </summary>
        /// <param name="left">First operand</param>
        /// <param name="right">Second operand</param>
        /// <param name="result">The dot product of the two inputs</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;
        }

        #endregion

        #region Lerp

        /// <summary>
        /// Returns a new Vector that is the linear blend of the 2 given Vectors
        /// </summary>
        /// <param name="a">First input vector</param>
        /// <param name="b">Second input vector</param>
        /// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
        /// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>
        public static Vector4 Lerp(Vector4 a, Vector4 b, float blend)
        {
            a.X = blend * (b.X - a.X) + a.X;
            a.Y = blend * (b.Y - a.Y) + a.Y;
            a.Z = blend * (b.Z - a.Z) + a.Z;
            a.W = blend * (b.W - a.W) + a.W;
            return a;
        }

        /// <summary>
        /// Returns a new Vector that is the linear blend of the 2 given Vectors
        /// </summary>
        /// <param name="a">First input vector</param>
        /// <param name="b">Second input vector</param>
        /// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
        /// <param name="result">a when blend=0, b when blend=1, and a linear combination otherwise</param>
        public static void Lerp(ref Vector4 a, ref Vector4 b, float blend, out Vector4 result)
        {
            result.X = blend * (b.X - a.X) + a.X;
            result.Y = blend * (b.Y - a.Y) + a.Y;
            result.Z = blend * (b.Z - a.Z) + a.Z;
            result.W = blend * (b.W - a.W) + a.W;
        }

        #endregion

        #region Barycentric

        /// <summary>
        /// Interpolate 3 Vectors using Barycentric coordinates
        /// </summary>
        /// <param name="a">First input Vector</param>
        /// <param name="b">Second input Vector</param>
        /// <param name="c">Third input Vector</param>
        /// <param name="u">First Barycentric Coordinate</param>
        /// <param name="v">Second Barycentric Coordinate</param>
        /// <returns>a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise</returns>
        public static Vector4 BaryCentric(Vector4 a, Vector4 b, Vector4 c, float u, float v)
        {
            return a + u * (b - a) + v * (c - a);
        }

        /// <summary>Interpolate 3 Vectors using Barycentric coordinates</summary>
        /// <param name="a">First input Vector.</param>
        /// <param name="b">Second input Vector.</param>
        /// <param name="c">Third input Vector.</param>
        /// <param name="u">First Barycentric Coordinate.</param>
        /// <param name="v">Second Barycentric Coordinate.</param>
        /// <param name="result">Output Vector. a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise</param>
        public static void BaryCentric(ref Vector4 a, ref Vector4 b, ref Vector4 c, float u, float v, out Vector4 result)
        {
            result = a; // copy

            Vector4 temp = b; // copy
            temp.Sub(ref a);
            temp.Mult(u);
            result.Add(ref temp);

            temp = c; // copy
            temp.Sub(ref a);
            temp.Mult(v);
            result.Add(ref temp);
        }

        #endregion

        #region Transform

        /// <summary>Transform a Vector by the given Matrix</summary>
        /// <param name="vec">The vector to transform</param>
        /// <param name="mat">The desired transformation</param>
        /// <returns>The transformed vector</returns>
        public static Vector4 Transform(Vector4 vec, Matrix4 mat)
        {
            Vector4 result;
            result.X = Vector4.Dot(vec, mat.Column0);
            result.Y = Vector4.Dot(vec, mat.Column1);
            result.Z = Vector4.Dot(vec, mat.Column2);
            result.W = Vector4.Dot(vec, mat.Column3);
            return result;
        }

        /// <summary>Transform a Vector by the given Matrix</summary>
        /// <param name="vec">The vector to transform</param>
        /// <param name="mat">The desired transformation</param>
        /// <param name="result">The transformed vector</param>
        public static void Transform(ref Vector4 vec, ref Matrix4 mat, out Vector4 result)
        {
            result.X = vec.X * mat.Row0.X +
                       vec.Y * mat.Row1.X +
                       vec.Z * mat.Row2.X +
                       vec.W * mat.Row3.X;

            result.Y = vec.X * mat.Row0.Y +
                       vec.Y * mat.Row1.Y +
                       vec.Z * mat.Row2.Y +
                       vec.W * mat.Row3.Y;

            result.Z = vec.X * mat.Row0.Z +
                       vec.Y * mat.Row1.Z +
                       vec.Z * mat.Row2.Z +
                       vec.W * mat.Row3.Z;

            result.W = vec.X * mat.Row0.W +
                       vec.Y * mat.Row1.W +
                       vec.Z * mat.Row2.W +
                       vec.W * mat.Row3.W;
        }

        #endregion

        #endregion

        #region Swizzle

        /// <summary>
        /// Gets or sets an OpenTK.Vector2 with the X and Y components of this instance.
        /// </summary>
        [XmlIgnore]
        public Vector2 Xy { get { return new Vector2(X, Y); } set { X = value.X; Y = value.Y; } }

        /// <summary>
        /// Gets or sets an OpenTK.Vector3 with the X, Y and Z components of this instance.
        /// </summary>
        [XmlIgnore]
        public Vector3 Xyz { get { return new Vector3(X, Y, Z); } set { X = value.X; Y = value.Y; Z = value.Z; } }

        #endregion

        #region Operators

        /// <summary>
        /// Adds two instances.
        /// </summary>
        /// <param name="left">The first instance.</param>
        /// <param name="right">The second instance.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator +(Vector4 left, Vector4 right)
        {
            left.X += right.X;
            left.Y += right.Y;
            left.Z += right.Z;
            left.W += right.W;
            return left;
        }

        /// <summary>
        /// Subtracts two instances.
        /// </summary>
        /// <param name="left">The first instance.</param>
        /// <param name="right">The second instance.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator -(Vector4 left, Vector4 right)
        {
            left.X -= right.X;
            left.Y -= right.Y;
            left.Z -= right.Z;
            left.W -= right.W;
            return left;
        }

        /// <summary>
        /// Negates an instance.
        /// </summary>
        /// <param name="vec">The instance.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator -(Vector4 vec)
        {
            vec.X = -vec.X;
            vec.Y = -vec.Y;
            vec.Z = -vec.Z;
            vec.W = -vec.W;
            return vec;
        }

        /// <summary>
        /// Multiplies an instance by a scalar.
        /// </summary>
        /// <param name="vec">The instance.</param>
        /// <param name="scale">The scalar.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator *(Vector4 vec, float scale)
        {
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
            vec.W *= scale;
            return vec;
        }

        /// <summary>
        /// Multiplies an instance by a scalar.
        /// </summary>
        /// <param name="scale">The scalar.</param>
        /// <param name="vec">The instance.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator *(float scale, Vector4 vec)
        {
            vec.X *= scale;
            vec.Y *= scale;
            vec.Z *= scale;
            vec.W *= scale;
            return vec;
        }

        /// <summary>
        /// Divides an instance by a scalar.
        /// </summary>
        /// <param name="vec">The instance.</param>
        /// <param name="scale">The scalar.</param>
        /// <returns>The result of the calculation.</returns>
        public static Vector4 operator /(Vector4 vec, float scale)
        {
            float mult = 1.0f / scale;
            vec.X *= mult;
            vec.Y *= mult;
            vec.Z *= mult;
            vec.W *= mult;
            return vec;
        }

        /// <summary>
        /// Compares two instances for equality.
        /// </summary>
        /// <param name="left">The first instance.</param>
        /// <param name="right">The second instance.</param>
        /// <returns>True, if left equals right; false otherwise.</returns>
        public static bool operator ==(Vector4 left, Vector4 right)
        {
            return left.Equals(right);
        }

        /// <summary>
        /// Compares two instances for inequality.
        /// </summary>
        /// <param name="left">The first instance.</param>
        /// <param name="right">The second instance.</param>
        /// <returns>True, if left does not equa lright; false otherwise.</returns>
        public static bool operator !=(Vector4 left, Vector4 right)
        {
            return !left.Equals(right);
        }

        /// <summary>
        /// Returns a pointer to the first element of the specified instance.
        /// </summary>
        /// <param name="v">The instance.</param>
        /// <returns>A pointer to the first element of v.</returns>
        [CLSCompliant(false)]
        unsafe public static explicit operator float*(Vector4 v)
        {
            return &v.X;
        }

        /// <summary>
        /// Returns a pointer to the first element of the specified instance.
        /// </summary>
        /// <param name="v">The instance.</param>
        /// <returns>A pointer to the first element of v.</returns>
        public static explicit operator IntPtr(Vector4 v)
        {
            unsafe
            {
                return (IntPtr)(&v.X);
            }
        }

        #endregion

        #region Overrides

        #region public override string ToString()

        /// <summary>
        /// Returns a System.String that represents the current Vector4.
        /// </summary>
        /// <returns></returns>
        public override string ToString()
        {
            return String.Format("({0}, {1}, {2}, {3})", X, Y, Z, W);
        }

        #endregion

        #region public override int GetHashCode()

        /// <summary>
        /// Returns the hashcode for this instance.
        /// </summary>
        /// <returns>A System.Int32 containing the unique hashcode for this instance.</returns>
        public override int GetHashCode()
        {
            return X.GetHashCode() ^ Y.GetHashCode() ^ Z.GetHashCode() ^ W.GetHashCode();
        }

        #endregion

        #region public override bool Equals(object obj)

        /// <summary>
        /// Indicates whether this instance and a specified object are equal.
        /// </summary>
        /// <param name="obj">The object to compare to.</param>
        /// <returns>True if the instances are equal; false otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (!(obj is Vector4))
                return false;

            return this.Equals((Vector4)obj);
        }

        #endregion

        #endregion

        #endregion

        #region IEquatable<Vector4> Members

        /// <summary>Indicates whether the current vector is equal to another vector.</summary>
        /// <param name="other">A vector to compare with this vector.</param>
        /// <returns>true if the current vector is equal to the vector parameter; otherwise, false.</returns>
        public bool Equals(Vector4 other)
        {
            return
                X == other.X &&
                Y == other.Y &&
                Z == other.Z &&
                W == other.W;
        }

        #endregion
    }
}