Opentk/Source/OpenTK/Math/Matrix4.cs

#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;

namespace OpenTK
{
    /// <summary>
    /// Represents a 4x4 matrix containing 3D rotation, scale, transform, and projection.
    /// </summary>
    /// <seealso cref="Matrix4d"/>
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    public struct Matrix4 : IEquatable<Matrix4>
    {
        #region Fields

        /// <summary>
        /// Top row of the matrix.
        /// </summary>
        public Vector4 Row0;

        /// <summary>
        /// 2nd row of the matrix.
        /// </summary>
        public Vector4 Row1;

        /// <summary>
        /// 3rd row of the matrix.
        /// </summary>
        public Vector4 Row2;

        /// <summary>
        /// Bottom row of the matrix.
        /// </summary>
        public Vector4 Row3;
 
        /// <summary>
        /// The identity matrix.
        /// </summary>
        public static readonly Matrix4 Identity = new Matrix4(Vector4.UnitX, Vector4.UnitY, Vector4.UnitZ, Vector4.UnitW);

        /// <summary>
        /// The zero matrix.
        /// </summary>
        public static readonly Matrix4 Zero = new Matrix4(Vector4.Zero, Vector4.Zero, Vector4.Zero, Vector4.Zero);

        #endregion

        #region Constructors

        /// <summary>
        /// Constructs a new instance.
        /// </summary>
        /// <param name="row0">Top row of the matrix.</param>
        /// <param name="row1">Second row of the matrix.</param>
        /// <param name="row2">Third row of the matrix.</param>
        /// <param name="row3">Bottom row of the matrix.</param>
        public Matrix4(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 row3)
        {
            Row0 = row0;
            Row1 = row1;
            Row2 = row2;
            Row3 = row3;
        }

        /// <summary>
        /// Constructs a new instance.
        /// </summary>
        /// <param name="m00">First item of the first row of the matrix.</param>
        /// <param name="m01">Second item of the first row of the matrix.</param>
        /// <param name="m02">Third item of the first row of the matrix.</param>
        /// <param name="m03">Fourth item of the first row of the matrix.</param>
        /// <param name="m10">First item of the second row of the matrix.</param>
        /// <param name="m11">Second item of the second row of the matrix.</param>
        /// <param name="m12">Third item of the second row of the matrix.</param>
        /// <param name="m13">Fourth item of the second row of the matrix.</param>
        /// <param name="m20">First item of the third row of the matrix.</param>
        /// <param name="m21">Second item of the third row of the matrix.</param>
        /// <param name="m22">Third item of the third row of the matrix.</param>
        /// <param name="m23">First item of the third row of the matrix.</param>
        /// <param name="m30">Fourth item of the fourth row of the matrix.</param>
        /// <param name="m31">Second item of the fourth row of the matrix.</param>
        /// <param name="m32">Third item of the fourth row of the matrix.</param>
        /// <param name="m33">Fourth item of the fourth row of the matrix.</param>
        public Matrix4(
            float m00, float m01, float m02, float m03,
            float m10, float m11, float m12, float m13,
            float m20, float m21, float m22, float m23,
            float m30, float m31, float m32, float m33)
        {
            Row0 = new Vector4(m00, m01, m02, m03);
            Row1 = new Vector4(m10, m11, m12, m13);
            Row2 = new Vector4(m20, m21, m22, m23);
            Row3 = new Vector4(m30, m31, m32, m33);
        }

        /// <summary>
        /// Constructs a new instance.
        /// </summary>
        /// <param name="topLeft">The top left 3x3 of the matrix.</param>
        public Matrix4(Matrix3 topLeft)
        {
            Row0.X = topLeft.Row0.X;
            Row0.Y = topLeft.Row0.Y;
            Row0.Z = topLeft.Row0.Z;
            Row0.W = 0;
            Row1.X = topLeft.Row1.X;
            Row1.Y = topLeft.Row1.Y;
            Row1.Z = topLeft.Row1.Z;
            Row1.W = 0;
            Row2.X = topLeft.Row2.X;
            Row2.Y = topLeft.Row2.Y;
            Row2.Z = topLeft.Row2.Z;
            Row2.W = 0;
            Row3.X = 0;
            Row3.Y = 0;
            Row3.Z = 0;
            Row3.W = 1;
        }

        #endregion

        #region Public Members

        #region Properties

        /// <summary>
        /// Gets the determinant of this matrix.
        /// </summary>
        public float Determinant
        {
            get
            {
                float m11 = Row0.X, m12 = Row0.Y, m13 = Row0.Z, m14 = Row0.W,
                      m21 = Row1.X, m22 = Row1.Y, m23 = Row1.Z, m24 = Row1.W,
                      m31 = Row2.X, m32 = Row2.Y, m33 = Row2.Z, m34 = Row2.W,
                      m41 = Row3.X, m42 = Row3.Y, m43 = Row3.Z, m44 = Row3.W;

                return
                    m11 * m22 * m33 * m44 - m11 * m22 * m34 * m43 + m11 * m23 * m34 * m42 - m11 * m23 * m32 * m44
                  + m11 * m24 * m32 * m43 - m11 * m24 * m33 * m42 - m12 * m23 * m34 * m41 + m12 * m23 * m31 * m44
                  - m12 * m24 * m31 * m43 + m12 * m24 * m33 * m41 - m12 * m21 * m33 * m44 + m12 * m21 * m34 * m43
                  + m13 * m24 * m31 * m42 - m13 * m24 * m32 * m41 + m13 * m21 * m32 * m44 - m13 * m21 * m34 * m42
                  + m13 * m22 * m34 * m41 - m13 * m22 * m31 * m44 - m14 * m21 * m32 * m43 + m14 * m21 * m33 * m42
                  - m14 * m22 * m33 * m41 + m14 * m22 * m31 * m43 - m14 * m23 * m31 * m42 + m14 * m23 * m32 * m41;
            }
        }

        /// <summary>
        /// Gets the first column of this matrix.
        /// </summary>
        public Vector4 Column0
        {
            get { return new Vector4(Row0.X, Row1.X, Row2.X, Row3.X); }
            set { Row0.X = value.X; Row1.X = value.Y; Row2.X = value.Z; Row3.X = value.W; }
        }

        /// <summary>
        /// Gets the second column of this matrix.
        /// </summary>
        public Vector4 Column1
        {
            get { return new Vector4(Row0.Y, Row1.Y, Row2.Y, Row3.Y); }
            set { Row0.Y = value.X; Row1.Y = value.Y; Row2.Y = value.Z; Row3.Y = value.W; }
        }

        /// <summary>
        /// Gets the third column of this matrix.
        /// </summary>
        public Vector4 Column2
        {
            get { return new Vector4(Row0.Z, Row1.Z, Row2.Z, Row3.Z); }
            set { Row0.Z = value.X; Row1.Z = value.Y; Row2.Z = value.Z; Row3.Z = value.W; }
        }

        /// <summary>
        /// Gets the fourth column of this matrix.
        /// </summary>
        public Vector4 Column3
        {
            get { return new Vector4(Row0.W, Row1.W, Row2.W, Row3.W); }
            set { Row0.W = value.X; Row1.W = value.Y; Row2.W = value.Z; Row3.W = value.W; }
        }

        /// <summary>
        /// Gets or sets the value at row 1, column 1 of this instance.
        /// </summary>
        public float M11 { get { return Row0.X; } set { Row0.X = value; } }

        /// <summary>
        /// Gets or sets the value at row 1, column 2 of this instance.
        /// </summary>
        public float M12 { get { return Row0.Y; } set { Row0.Y = value; } }

        /// <summary>
        /// Gets or sets the value at row 1, column 3 of this instance.
        /// </summary>
        public float M13 { get { return Row0.Z; } set { Row0.Z = value; } }

        /// <summary>
        /// Gets or sets the value at row 1, column 4 of this instance.
        /// </summary>
        public float M14 { get { return Row0.W; } set { Row0.W = value; } }

        /// <summary>
        /// Gets or sets the value at row 2, column 1 of this instance.
        /// </summary>
        public float M21 { get { return Row1.X; } set { Row1.X = value; } }

        /// <summary>
        /// Gets or sets the value at row 2, column 2 of this instance.
        /// </summary>
        public float M22 { get { return Row1.Y; } set { Row1.Y = value; } }

        /// <summary>
        /// Gets or sets the value at row 2, column 3 of this instance.
        /// </summary>
        public float M23 { get { return Row1.Z; } set { Row1.Z = value; } }

        /// <summary>
        /// Gets or sets the value at row 2, column 4 of this instance.
        /// </summary>
        public float M24 { get { return Row1.W; } set { Row1.W = value; } }

        /// <summary>
        /// Gets or sets the value at row 3, column 1 of this instance.
        /// </summary>
        public float M31 { get { return Row2.X; } set { Row2.X = value; } }

        /// <summary>
        /// Gets or sets the value at row 3, column 2 of this instance.
        /// </summary>
        public float M32 { get { return Row2.Y; } set { Row2.Y = value; } }

        /// <summary>
        /// Gets or sets the value at row 3, column 3 of this instance.
        /// </summary>
        public float M33 { get { return Row2.Z; } set { Row2.Z = value; } }

        /// <summary>
        /// Gets or sets the value at row 3, column 4 of this instance.
        /// </summary>
        public float M34 { get { return Row2.W; } set { Row2.W = value; } }

        /// <summary>
        /// Gets or sets the value at row 4, column 1 of this instance.
        /// </summary>
        public float M41 { get { return Row3.X; } set { Row3.X = value; } }

        /// <summary>
        /// Gets or sets the value at row 4, column 2 of this instance.
        /// </summary>
        public float M42 { get { return Row3.Y; } set { Row3.Y = value; } }

        /// <summary>
        /// Gets or sets the value at row 4, column 3 of this instance.
        /// </summary>
        public float M43 { get { return Row3.Z; } set { Row3.Z = value; } }

        /// <summary>
        /// Gets or sets the value at row 4, column 4 of this instance.
        /// </summary>
        public float M44 { get { return Row3.W; } set { Row3.W = value; } }
        
        /// <summary>
        /// Gets or sets the values along the main diagonal of the matrix.
        /// </summary>
        public Vector4 Diagonal
        {
            get
            {
                return new Vector4(Row0.X, Row1.Y, Row2.Z, Row3.W);
            }
            set
            {
                Row0.X = value.X;
                Row1.Y = value.Y;
                Row2.Z = value.Z;
                Row3.W = value.W;
            }
        }

        /// <summary>
        /// Gets the trace of the matrix, the sum of the values along the diagonal.
        /// </summary>
        public float Trace { get { return Row0.X + Row1.Y + Row2.Z + Row3.W; } }

        #endregion

        #region Indexers

        /// <summary>
        /// Gets or sets the value at a specified row and column.
        /// </summary>
        public float this[int rowIndex, int columnIndex]
        {
            get
            {
                if (rowIndex == 0) return Row0[columnIndex];
                else if (rowIndex == 1) return Row1[columnIndex];
                else if (rowIndex == 2) return Row2[columnIndex];
                else if (rowIndex == 3) return Row3[columnIndex];
                throw new IndexOutOfRangeException("You tried to access this matrix at: (" + rowIndex + ", " + columnIndex + ")");
            }
            set
            {
                if (rowIndex == 0) Row0[columnIndex] = value;
                else if (rowIndex == 1) Row1[columnIndex] = value;
                else if (rowIndex == 2) Row2[columnIndex] = value;
                else if (rowIndex == 3) Row3[columnIndex] = value;
                else throw new IndexOutOfRangeException("You tried to set this matrix at: (" + rowIndex + ", " + columnIndex + ")");
            }
        }

        #endregion

        #region Instance

        #region public void Invert()

        /// <summary>
        /// Converts this instance into its inverse.
        /// </summary>
        public void Invert()
        {
            this = Matrix4.Invert(this);
        }

        #endregion

        #region public void Transpose()

        /// <summary>
        /// Converts this instance into its transpose.
        /// </summary>
        public void Transpose()
        {
            this = Matrix4.Transpose(this);
        }

        #endregion

        /// <summary>
        /// Returns a normalised copy of this instance.
        /// </summary>
        public Matrix4 Normalized()
        {
            Matrix4 m = this;
            m.Normalize();
            return m;
        }

        /// <summary>
        /// Divides each element in the Matrix by the <see cref="Determinant"/>.
        /// </summary>
        public void Normalize()
        {
            var determinant = this.Determinant;
            Row0 /= determinant;
            Row1 /= determinant;
            Row2 /= determinant;
            Row3 /= determinant;
        }

        /// <summary>
        /// Returns an inverted copy of this instance.
        /// </summary>
        public Matrix4 Inverted()
        {
            Matrix4 m = this;
            if (m.Determinant != 0)
                m.Invert();
            return m;
        }

        /// <summary>
        /// Returns a copy of this Matrix4 without translation.
        /// </summary>
        public Matrix4 ClearTranslation()
        {
            Matrix4 m = this;
            m.Row3.Xyz = Vector3.Zero;
            return m;
        }
        /// <summary>
        /// Returns a copy of this Matrix4 without scale.
        /// </summary>
        public Matrix4 ClearScale()
        {
            Matrix4 m = this;
            m.Row0.Xyz = m.Row0.Xyz.Normalized();
            m.Row1.Xyz = m.Row1.Xyz.Normalized();
            m.Row2.Xyz = m.Row2.Xyz.Normalized();
            return m;
        }
        /// <summary>
        /// Returns a copy of this Matrix4 without rotation.
        /// </summary>
        public Matrix4 ClearRotation()
        {
            Matrix4 m = this;
            m.Row0.Xyz = new Vector3(m.Row0.Xyz.Length, 0, 0);
            m.Row1.Xyz = new Vector3(0, m.Row1.Xyz.Length, 0);
            m.Row2.Xyz = new Vector3(0, 0, m.Row2.Xyz.Length);
            return m;
        }
        /// <summary>
        /// Returns a copy of this Matrix4 without projection.
        /// </summary>
        public Matrix4 ClearProjection()
        {
            Matrix4 m = this;
            m.Column3 = Vector4.Zero;
            return m;
        }

        /// <summary>
        /// Returns the translation component of this instance.
        /// </summary>
        public Vector3 ExtractTranslation() { return Row3.Xyz; }

        /// <summary>
        /// Returns the scale component of this instance.
        /// </summary>
        public Vector3 ExtractScale() { return new Vector3(Row0.Xyz.Length, Row1.Xyz.Length, Row2.Xyz.Length); }

        /// <summary>
        /// Returns the rotation component of this instance. Quite slow.
        /// </summary>
        /// <param name="row_normalise">Whether the method should row-normalise (i.e. remove scale from) the Matrix. Pass false if you know it's already normalised.</param>
        public Quaternion ExtractRotation(bool row_normalise = true)
        {
            var row0 = Row0.Xyz;
            var row1 = Row1.Xyz;
            var row2 = Row2.Xyz;

            if (row_normalise)
            {
                row0 = row0.Normalized();
                row1 = row1.Normalized();
                row2 = row2.Normalized();
            }

            // code below adapted from Blender

            Quaternion q = new Quaternion();
            double trace = 0.25 * (row0[0] + row1[1] + row2[2] + 1.0);

            if (trace > 0)
            {
                double sq = Math.Sqrt(trace);

                q.W = (float)sq;
                sq = 1.0 / (4.0 * sq);
                q.X = (float)((row1[2] - row2[1]) * sq);
                q.Y = (float)((row2[0] - row0[2]) * sq);
                q.Z = (float)((row0[1] - row1[0]) * sq);
            }
            else if (row0[0] > row1[1] && row0[0] > row2[2])
            {
                double sq = 2.0 * Math.Sqrt(1.0 + row0[0] - row1[1] - row2[2]);

                q.X = (float)(0.25 * sq);
                sq = 1.0 / sq;
                q.W = (float)((row2[1] - row1[2]) * sq);
                q.Y = (float)((row1[0] + row0[1]) * sq);
                q.Z = (float)((row2[0] + row0[2]) * sq);
            }
            else if (row1[1] > row2[2])
            {
                double sq = 2.0 * Math.Sqrt(1.0 + row1[1] - row0[0] - row2[2]);

                q.Y = (float)(0.25 * sq);
                sq = 1.0 / sq;
                q.W = (float)((row2[0] - row0[2]) * sq);
                q.X = (float)((row1[0] + row0[1]) * sq);
                q.Z = (float)((row2[1] + row1[2]) * sq);
            }
            else
            {
                double sq = 2.0 * Math.Sqrt(1.0 + row2[2] - row0[0] - row1[1]);

                q.Z = (float)(0.25 * sq);
                sq = 1.0 / sq;
                q.W = (float)((row1[0] - row0[1]) * sq);
                q.X = (float)((row2[0] + row0[2]) * sq);
                q.Y = (float)((row2[1] + row1[2]) * sq);
            }

            q.Normalize();
            return q;
        }

        /// <summary>
        /// Returns the projection component of this instance.
        /// </summary>
        public Vector4 ExtractProjection()
        {
            return Column3;
        }

        #endregion

        #region Static
        
        #region CreateFromAxisAngle
        
        /// <summary>
        /// Build a rotation matrix from the specified axis/angle rotation.
        /// </summary>
        /// <param name="axis">The axis to rotate about.</param>
        /// <param name="angle">Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).</param>
        /// <param name="result">A matrix instance.</param>
        public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix4 result)
        {
            // normalize and create a local copy of the vector.
            axis.Normalize();
            float axisX = axis.X, axisY = axis.Y, axisZ = axis.Z;

            // calculate angles
            float cos = (float)System.Math.Cos(-angle);
            float sin = (float)System.Math.Sin(-angle);
            float t = 1.0f - cos;

            // do the conversion math once
            float tXX = t * axisX * axisX,
                tXY = t * axisX * axisY,
                tXZ = t * axisX * axisZ,
                tYY = t * axisY * axisY,
                tYZ = t * axisY * axisZ,
                tZZ = t * axisZ * axisZ;

            float sinX = sin * axisX,
                sinY = sin * axisY,
                sinZ = sin * axisZ;

            result.Row0.X = tXX + cos;
            result.Row0.Y = tXY - sinZ;
            result.Row0.Z = tXZ + sinY;
            result.Row0.W = 0;
            result.Row1.X = tXY + sinZ;
            result.Row1.Y = tYY + cos;
            result.Row1.Z = tYZ - sinX;
            result.Row1.W = 0;
            result.Row2.X = tXZ - sinY;
            result.Row2.Y = tYZ + sinX;
            result.Row2.Z = tZZ + cos;
            result.Row2.W = 0;
            result.Row3 = Vector4.UnitW;
        }
        
        /// <summary>
        /// Build a rotation matrix from the specified axis/angle rotation.
        /// </summary>
        /// <param name="axis">The axis to rotate about.</param>
        /// <param name="angle">Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).</param>
        /// <returns>A matrix instance.</returns>
        public static Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)
        {
            Matrix4 result;
            CreateFromAxisAngle(axis, angle, out result);
            return result;
        }
        
        #endregion

        #region CreateFromQuaternion

        /// <summary>
        /// Builds a rotation matrix from a quaternion.
        /// </summary>
        /// <param name="q">The quaternion to rotate by.</param>
        /// <param name="result">A matrix instance.</param>
        public static void CreateFromQuaternion(ref Quaternion q, out Matrix4 result)
        {
            Vector3 axis;
            float angle;
            q.ToAxisAngle(out axis, out angle);
            CreateFromAxisAngle(axis, angle, out result);
        }

        /// <summary>
        /// Builds a rotation matrix from a quaternion.
        /// </summary>
        /// <param name="q">The quaternion to rotate by.</param>
        /// <returns>A matrix instance.</returns>
        public static Matrix4 CreateFromQuaternion(Quaternion q)
        {
            Matrix4 result;
            CreateFromQuaternion(ref q, out result);
            return result;
        }

        #endregion

        #region CreateRotation[XYZ]

        /// <summary>
        /// Builds a rotation matrix for a rotation around the x-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateRotationX(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result = Identity;
            result.Row1.Y = cos;
            result.Row1.Z = sin;
            result.Row2.Y = -sin;
            result.Row2.Z = cos;
        }

        /// <summary>
        /// Builds a rotation matrix for a rotation around the x-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateRotationX(float angle)
        {
            Matrix4 result;
            CreateRotationX(angle, out result);
            return result;
        }

        /// <summary>
        /// Builds a rotation matrix for a rotation around the y-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateRotationY(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result = Identity;
            result.Row0.X = cos;
            result.Row0.Z = -sin;
            result.Row2.X = sin;
            result.Row2.Z = cos;
        }

        /// <summary>
        /// Builds a rotation matrix for a rotation around the y-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateRotationY(float angle)
        {
            Matrix4 result;
            CreateRotationY(angle, out result);
            return result;
        }

        /// <summary>
        /// Builds a rotation matrix for a rotation around the z-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateRotationZ(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result = Identity;
            result.Row0.X = cos;
            result.Row0.Y = sin;
            result.Row1.X = -sin;
            result.Row1.Y = cos;
        }

        /// <summary>
        /// Builds a rotation matrix for a rotation around the z-axis.
        /// </summary>
        /// <param name="angle">The counter-clockwise angle in radians.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateRotationZ(float angle)
        {
            Matrix4 result;
            CreateRotationZ(angle, out result);
            return result;
        }

        #endregion

        #region CreateTranslation

        /// <summary>
        /// Creates a translation matrix.
        /// </summary>
        /// <param name="x">X translation.</param>
        /// <param name="y">Y translation.</param>
        /// <param name="z">Z translation.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateTranslation(float x, float y, float z, out Matrix4 result)
        {
            result = Identity;
            result.Row3.X = x;
            result.Row3.Y = y;
            result.Row3.Z = z;
        }

        /// <summary>
        /// Creates a translation matrix.
        /// </summary>
        /// <param name="vector">The translation vector.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateTranslation(ref Vector3 vector, out Matrix4 result)
        {
            result = Identity;
            result.Row3.X = vector.X;
            result.Row3.Y = vector.Y;
            result.Row3.Z = vector.Z;
        }

        /// <summary>
        /// Creates a translation matrix.
        /// </summary>
        /// <param name="x">X translation.</param>
        /// <param name="y">Y translation.</param>
        /// <param name="z">Z translation.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateTranslation(float x, float y, float z)
        {
            Matrix4 result;
            CreateTranslation(x, y, z, out result);
            return result;
        }

        /// <summary>
        /// Creates a translation matrix.
        /// </summary>
        /// <param name="vector">The translation vector.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateTranslation(Vector3 vector)
        {
            Matrix4 result;
            CreateTranslation(vector.X, vector.Y, vector.Z, out result);
            return result;
        }

        #endregion

        #region CreateScale

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="scale">Single scale factor for the x, y, and z axes.</param>
        /// <returns>A scale matrix.</returns>
        public static Matrix4 CreateScale(float scale)
        {
            Matrix4 result;
            CreateScale(scale, out result);
            return result;
        }

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="scale">Scale factors for the x, y, and z axes.</param>
        /// <returns>A scale matrix.</returns>
        public static Matrix4 CreateScale(Vector3 scale)
        {
            Matrix4 result;
            CreateScale(ref scale, out result);
            return result;
        }

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="x">Scale factor for the x axis.</param>
        /// <param name="y">Scale factor for the y axis.</param>
        /// <param name="z">Scale factor for the z axis.</param>
        /// <returns>A scale matrix.</returns>
        public static Matrix4 CreateScale(float x, float y, float z)
        {
            Matrix4 result;
            CreateScale(x, y, z, out result);
            return result;
        }

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="scale">Single scale factor for the x, y, and z axes.</param>
        /// <param name="result">A scale matrix.</param>
        public static void CreateScale(float scale, out Matrix4 result)
        {
            result = Identity;
            result.Row0.X = scale;
            result.Row1.Y = scale;
            result.Row2.Z = scale;
        }

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="scale">Scale factors for the x, y, and z axes.</param>
        /// <param name="result">A scale matrix.</param>
        public static void CreateScale(ref Vector3 scale, out Matrix4 result)
        {
            result = Identity;
            result.Row0.X = scale.X;
            result.Row1.Y = scale.Y;
            result.Row2.Z = scale.Z;
        }

        /// <summary>
        /// Creates a scale matrix.
        /// </summary>
        /// <param name="x">Scale factor for the x axis.</param>
        /// <param name="y">Scale factor for the y axis.</param>
        /// <param name="z">Scale factor for the z axis.</param>
        /// <param name="result">A scale matrix.</param>
        public static void CreateScale(float x, float y, float z, out Matrix4 result)
        {
            result = Identity;
            result.Row0.X = x;
            result.Row1.Y = y;
            result.Row2.Z = z;
        }

        #endregion

        #region CreateOrthographic

        /// <summary>
        /// Creates an orthographic projection matrix.
        /// </summary>
        /// <param name="width">The width of the projection volume.</param>
        /// <param name="height">The height of the projection volume.</param>
        /// <param name="zNear">The near edge of the projection volume.</param>
        /// <param name="zFar">The far edge of the projection volume.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateOrthographic(float width, float height, float zNear, float zFar, out Matrix4 result)
        {
            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
        }

        /// <summary>
        /// Creates an orthographic projection matrix.
        /// </summary>
        /// <param name="width">The width of the projection volume.</param>
        /// <param name="height">The height of the projection volume.</param>
        /// <param name="zNear">The near edge of the projection volume.</param>
        /// <param name="zFar">The far edge of the projection volume.</param>
        /// <rereturns>The resulting Matrix4 instance.</rereturns>
        public static Matrix4 CreateOrthographic(float width, float height, float zNear, float zFar)
        {
            Matrix4 result;
            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
            return result;
        }

        #endregion

        #region CreateOrthographicOffCenter

        /// <summary>
        /// Creates an orthographic projection matrix.
        /// </summary>
        /// <param name="left">The left edge of the projection volume.</param>
        /// <param name="right">The right edge of the projection volume.</param>
        /// <param name="bottom">The bottom edge of the projection volume.</param>
        /// <param name="top">The top edge of the projection volume.</param>
        /// <param name="zNear">The near edge of the projection volume.</param>
        /// <param name="zFar">The far edge of the projection volume.</param>
        /// <param name="result">The resulting Matrix4 instance.</param>
        public static void CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
        {
            result = Identity;

            float invRL = 1.0f / (right - left);
            float invTB = 1.0f / (top - bottom);
            float invFN = 1.0f / (zFar - zNear);

            result.Row0.X = 2 * invRL;
            result.Row1.Y = 2 * invTB;
            result.Row2.Z = -2 * invFN;

            result.Row3.X = -(right + left) * invRL;
            result.Row3.Y = -(top + bottom) * invTB;
            result.Row3.Z = -(zFar + zNear) * invFN;
        }

        /// <summary>
        /// Creates an orthographic projection matrix.
        /// </summary>
        /// <param name="left">The left edge of the projection volume.</param>
        /// <param name="right">The right edge of the projection volume.</param>
        /// <param name="bottom">The bottom edge of the projection volume.</param>
        /// <param name="top">The top edge of the projection volume.</param>
        /// <param name="zNear">The near edge of the projection volume.</param>
        /// <param name="zFar">The far edge of the projection volume.</param>
        /// <returns>The resulting Matrix4 instance.</returns>
        public static Matrix4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
        {
            Matrix4 result;
            CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);
            return result;
        }

        #endregion
        
        #region CreatePerspectiveFieldOfView
        
        /// <summary>
        /// Creates a perspective projection matrix.
        /// </summary>
        /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
        /// <param name="aspect">Aspect ratio of the view (width / height)</param>
        /// <param name="zNear">Distance to the near clip plane</param>
        /// <param name="zFar">Distance to the far clip plane</param>
        /// <param name="result">A projection matrix that transforms camera space to raster space</param>
        /// <exception cref="System.ArgumentOutOfRangeException">
        /// Thrown under the following conditions:
        /// <list type="bullet">
        /// <item>fovy is zero, less than zero or larger than Math.PI</item>
        /// <item>aspect is negative or zero</item>
        /// <item>zNear is negative or zero</item>
        /// <item>zFar is negative or zero</item>
        /// <item>zNear is larger than zFar</item>
        /// </list>
        /// </exception>
        public static void CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar, out Matrix4 result)
        {
            if (fovy <= 0 || fovy > Math.PI)
                throw new ArgumentOutOfRangeException("fovy");
            if (aspect <= 0)
                throw new ArgumentOutOfRangeException("aspect");
            if (zNear <= 0)
                throw new ArgumentOutOfRangeException("zNear");
            if (zFar <= 0)
                throw new ArgumentOutOfRangeException("zFar");
            
            float yMax = zNear * (float)System.Math.Tan(0.5f * fovy);
            float yMin = -yMax;
            float xMin = yMin * aspect;
            float xMax = yMax * aspect;

            CreatePerspectiveOffCenter(xMin, xMax, yMin, yMax, zNear, zFar, out result);
        }
        
        /// <summary>
        /// Creates a perspective projection matrix.
        /// </summary>
        /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
        /// <param name="aspect">Aspect ratio of the view (width / height)</param>
        /// <param name="zNear">Distance to the near clip plane</param>
        /// <param name="zFar">Distance to the far clip plane</param>
        /// <returns>A projection matrix that transforms camera space to raster space</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">
        /// Thrown under the following conditions:
        /// <list type="bullet">
        /// <item>fovy is zero, less than zero or larger than Math.PI</item>
        /// <item>aspect is negative or zero</item>
        /// <item>zNear is negative or zero</item>
        /// <item>zFar is negative or zero</item>
        /// <item>zNear is larger than zFar</item>
        /// </list>
        /// </exception>
        public static Matrix4 CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar)
        {
            Matrix4 result;
            CreatePerspectiveFieldOfView(fovy, aspect, zNear, zFar, out result);
            return result;
        }
        
        #endregion
        
        #region CreatePerspectiveOffCenter
        
        /// <summary>
        /// Creates an perspective projection matrix.
        /// </summary>
        /// <param name="left">Left edge of the view frustum</param>
        /// <param name="right">Right edge of the view frustum</param>
        /// <param name="bottom">Bottom edge of the view frustum</param>
        /// <param name="top">Top edge of the view frustum</param>
        /// <param name="zNear">Distance to the near clip plane</param>
        /// <param name="zFar">Distance to the far clip plane</param>
        /// <param name="result">A projection matrix that transforms camera space to raster space</param>
        /// <exception cref="System.ArgumentOutOfRangeException">
        /// Thrown under the following conditions:
        /// <list type="bullet">
        /// <item>zNear is negative or zero</item>
        /// <item>zFar is negative or zero</item>
        /// <item>zNear is larger than zFar</item>
        /// </list>
        /// </exception>
        public static void CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
        {
            if (zNear <= 0)
                throw new ArgumentOutOfRangeException("zNear");
            if (zFar <= 0)
                throw new ArgumentOutOfRangeException("zFar");
            if (zNear >= zFar)
                throw new ArgumentOutOfRangeException("zNear");
            
            float x = (2.0f * zNear) / (right - left);
            float y = (2.0f * zNear) / (top - bottom);
            float a = (right + left) / (right - left);
            float b = (top + bottom) / (top - bottom);
            float c = -(zFar + zNear) / (zFar - zNear);
            float d = -(2.0f * zFar * zNear) / (zFar - zNear);

            result.Row0.X = x;
            result.Row0.Y = 0;
            result.Row0.Z = 0;
            result.Row0.W = 0;
            result.Row1.X = 0;
            result.Row1.Y = y;
            result.Row1.Z = 0;
            result.Row1.W = 0;
            result.Row2.X = a;
            result.Row2.Y = b;
            result.Row2.Z = c;
            result.Row2.W = -1;
            result.Row3.X = 0;
            result.Row3.Y = 0;
            result.Row3.Z = d;
            result.Row3.W = 0;
        }
        
        /// <summary>
        /// Creates an perspective projection matrix.
        /// </summary>
        /// <param name="left">Left edge of the view frustum</param>
        /// <param name="right">Right edge of the view frustum</param>
        /// <param name="bottom">Bottom edge of the view frustum</param>
        /// <param name="top">Top edge of the view frustum</param>
        /// <param name="zNear">Distance to the near clip plane</param>
        /// <param name="zFar">Distance to the far clip plane</param>
        /// <returns>A projection matrix that transforms camera space to raster space</returns>
        /// <exception cref="System.ArgumentOutOfRangeException">
        /// Thrown under the following conditions:
        /// <list type="bullet">
        /// <item>zNear is negative or zero</item>
        /// <item>zFar is negative or zero</item>
        /// <item>zNear is larger than zFar</item>
        /// </list>
        /// </exception>
        public static Matrix4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
        {
            Matrix4 result;
            CreatePerspectiveOffCenter(left, right, bottom, top, zNear, zFar, out result);
            return result;
        }

        #endregion

        #region Obsolete Functions

        #region Translation Functions

        /// <summary>
        /// Builds a translation matrix.
        /// </summary>
        /// <param name="trans">The translation vector.</param>
        /// <returns>A new Matrix4 instance.</returns>
        [Obsolete("Use CreateTranslation instead.")]
        public static Matrix4 Translation(Vector3 trans)
        {
            return CreateTranslation(trans);
        }

        /// <summary>
        /// Build a translation matrix with the given translation
        /// </summary>
        /// <param name="x">X translation</param>
        /// <param name="y">Y translation</param>
        /// <param name="z">Z translation</param>
        /// <returns>A Translation matrix</returns>
        [Obsolete("Use CreateTranslation instead.")]
        public static Matrix4 Translation(float x, float y, float z)
        {
            return CreateTranslation(x, y, z);
        }

        #endregion

        #region Rotation Functions

        /// <summary>
        /// Build a rotation matrix that rotates about the x-axis
        /// </summary>
        /// <param name="angle">angle in radians to rotate counter-clockwise around the x-axis</param>
        /// <returns>A rotation matrix</returns>
        [Obsolete("Use CreateRotationX instead.")]
        public static Matrix4 RotateX(float angle)
        {
            return CreateRotationX(angle);
        }

        /// <summary>
        /// Build a rotation matrix that rotates about the y-axis
        /// </summary>
        /// <param name="angle">angle in radians to rotate counter-clockwise around the y-axis</param>
        /// <returns>A rotation matrix</returns>
        [Obsolete("Use CreateRotationY instead.")]
        public static Matrix4 RotateY(float angle)
        {
            return CreateRotationY(angle);
        }

        /// <summary>
        /// Build a rotation matrix that rotates about the z-axis
        /// </summary>
        /// <param name="angle">angle in radians to rotate counter-clockwise around the z-axis</param>
        /// <returns>A rotation matrix</returns>
        [Obsolete("Use CreateRotationZ instead.")]
        public static Matrix4 RotateZ(float angle)
        {
            return CreateRotationZ(angle);
        }

        /// <summary>
        /// Build a rotation matrix to rotate about the given axis
        /// </summary>
        /// <param name="axis">the axis to rotate about</param>
        /// <param name="angle">angle in radians to rotate counter-clockwise (looking in the direction of the given axis)</param>
        /// <returns>A rotation matrix</returns>
        [Obsolete("Use CreateFromAxisAngle instead.")]
        public static Matrix4 Rotate(Vector3 axis, float angle)
        {
            return CreateFromAxisAngle(axis, angle);
        }

        /// <summary>
        /// Build a rotation matrix from a quaternion
        /// </summary>
        /// <param name="q">the quaternion</param>
        /// <returns>A rotation matrix</returns>
        [Obsolete("Use CreateRotation instead.")]
        public static Matrix4 Rotate(Quaternion q)
        {
            return CreateFromQuaternion(q);
        }

        #endregion

        #region Scale Functions

        /// <summary>
        /// Build a scaling matrix
        /// </summary>
        /// <param name="scale">Single scale factor for x,y and z axes</param>
        /// <returns>A scaling matrix</returns>
        [Obsolete("Use CreateScale instead.")]
        public static Matrix4 Scale(float scale)
        {
            return Scale(scale, scale, scale);
        }

        /// <summary>
        /// Build a scaling matrix
        /// </summary>
        /// <param name="scale">Scale factors for x,y and z axes</param>
        /// <returns>A scaling matrix</returns>
        [Obsolete("Use CreateScale instead.")]
        public static Matrix4 Scale(Vector3 scale)
        {
            return Scale(scale.X, scale.Y, scale.Z);
        }

        /// <summary>
        /// Build a scaling matrix
        /// </summary>
        /// <param name="x">Scale factor for x-axis</param>
        /// <param name="y">Scale factor for y-axis</param>
        /// <param name="z">Scale factor for z-axis</param>
        /// <returns>A scaling matrix</returns>
        [Obsolete("Use CreateScale instead.")]
        public static Matrix4 Scale(float x, float y, float z)
        {
            Matrix4 result;
            result.Row0 = Vector4.UnitX * x;
            result.Row1 = Vector4.UnitY * y;
            result.Row2 = Vector4.UnitZ * z;
            result.Row3 = Vector4.UnitW;
            return result;
        }

        #endregion

        #region Camera Helper Functions

        /// <summary>
        /// Build a projection matrix
        /// </summary>
        /// <param name="left">Left edge of the view frustum</param>
        /// <param name="right">Right edge of the view frustum</param>
        /// <param name="bottom">Bottom edge of the view frustum</param>
        /// <param name="top">Top edge of the view frustum</param>
        /// <param name="near">Distance to the near clip plane</param>
        /// <param name="far">Distance to the far clip plane</param>
        /// <returns>A projection matrix that transforms camera space to raster space</returns>
        [Obsolete("Use CreatePerspectiveOffCenter instead.")]
        public static Matrix4 Frustum(float left, float right, float bottom, float top, float near, float far)
        {
            float invRL = 1.0f / (right - left);
            float invTB = 1.0f / (top - bottom);
            float invFN = 1.0f / (far - near);
            return new Matrix4(new Vector4(2.0f * near * invRL, 0.0f, 0.0f, 0.0f),
                               new Vector4(0.0f, 2.0f * near * invTB, 0.0f, 0.0f),
                               new Vector4((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0f),
                               new Vector4(0.0f, 0.0f, -2.0f * far * near * invFN, 0.0f));
        }

        /// <summary>
        /// Build a projection matrix
        /// </summary>
        /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
        /// <param name="aspect">Aspect ratio of the view (width / height)</param>
        /// <param name="near">Distance to the near clip plane</param>
        /// <param name="far">Distance to the far clip plane</param>
        /// <returns>A projection matrix that transforms camera space to raster space</returns>
        [Obsolete("Use CreatePerspectiveFieldOfView instead.")]
        public static Matrix4 Perspective(float fovy, float aspect, float near, float far)
        {
            float yMax = near * (float)System.Math.Tan(0.5f * fovy);
            float yMin = -yMax;
            float xMin = yMin * aspect;
            float xMax = yMax * aspect;

            return Frustum(xMin, xMax, yMin, yMax, near, far);
        }

        #endregion

        #endregion

        #region Camera Helper Functions

        /// <summary>
        /// Build a world space to camera space matrix
        /// </summary>
        /// <param name="eye">Eye (camera) position in world space</param>
        /// <param name="target">Target position in world space</param>
        /// <param name="up">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
        /// <returns>A Matrix4 that transforms world space to camera space</returns>
        public static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)
        {
            Vector3 z = Vector3.Normalize(eye - target);
            Vector3 x = Vector3.Normalize(Vector3.Cross(up, z));
            Vector3 y = Vector3.Normalize(Vector3.Cross(z, x));

            Matrix4 result;

            result.Row0.X = x.X;
            result.Row0.Y = y.X;
            result.Row0.Z = z.X;
            result.Row0.W = 0;
            result.Row1.X = x.Y;
            result.Row1.Y = y.Y;
            result.Row1.Z = z.Y;
            result.Row1.W = 0;
            result.Row2.X = x.Z;
            result.Row2.Y = y.Z;
            result.Row2.Z = z.Z;
            result.Row2.W = 0;
            result.Row3.X = -((x.X * eye.X) + (x.Y * eye.Y) + (x.Z * eye.Z));
            result.Row3.Y = -((y.X * eye.X) + (y.Y * eye.Y) + (y.Z * eye.Z));
            result.Row3.Z = -((z.X * eye.X) + (z.Y * eye.Y) + (z.Z * eye.Z));
            result.Row3.W = 1;

            return result;
        }

        /// <summary>
        /// Build a world space to camera space matrix
        /// </summary>
        /// <param name="eyeX">Eye (camera) position in world space</param>
        /// <param name="eyeY">Eye (camera) position in world space</param>
        /// <param name="eyeZ">Eye (camera) position in world space</param>
        /// <param name="targetX">Target position in world space</param>
        /// <param name="targetY">Target position in world space</param>
        /// <param name="targetZ">Target position in world space</param>
        /// <param name="upX">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
        /// <param name="upY">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
        /// <param name="upZ">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
        /// <returns>A Matrix4 that transforms world space to camera space</returns>
        public static Matrix4 LookAt(float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)
        {
            return LookAt(new Vector3(eyeX, eyeY, eyeZ), new Vector3(targetX, targetY, targetZ), new Vector3(upX, upY, upZ));
        }

        #endregion

        #region Add Functions

        /// <summary>
        /// Adds two instances.
        /// </summary>
        /// <param name="left">The left operand of the addition.</param>
        /// <param name="right">The right operand of the addition.</param>
        /// <returns>A new instance that is the result of the addition.</returns>
        public static Matrix4 Add(Matrix4 left, Matrix4 right)
        {
            Matrix4 result;
            Add(ref left, ref right, out result);
            return result;
        }

        /// <summary>
        /// Adds two instances.
        /// </summary>
        /// <param name="left">The left operand of the addition.</param>
        /// <param name="right">The right operand of the addition.</param>
        /// <param name="result">A new instance that is the result of the addition.</param>
        public static void Add(ref Matrix4 left, ref Matrix4 right, out Matrix4 result)
        {
            result.Row0 = left.Row0 + right.Row0;
            result.Row1 = left.Row1 + right.Row1;
            result.Row2 = left.Row2 + right.Row2;
            result.Row3 = left.Row3 + right.Row3;
        }

        #endregion

        #region Subtract Functions

        /// <summary>
        /// Subtracts one instance from another.
        /// </summary>
        /// <param name="left">The left operand of the subraction.</param>
        /// <param name="right">The right operand of the subraction.</param>
        /// <returns>A new instance that is the result of the subraction.</returns>
        public static Matrix4 Subtract(Matrix4 left, Matrix4 right)
        {
            Matrix4 result;
            Subtract(ref left, ref right, out result);
            return result;
        }

        /// <summary>
        /// Subtracts one instance from another.
        /// </summary>
        /// <param name="left">The left operand of the subraction.</param>
        /// <param name="right">The right operand of the subraction.</param>
        /// <param name="result">A new instance that is the result of the subraction.</param>
        public static void Subtract(ref Matrix4 left, ref Matrix4 right, out Matrix4 result)
        {
            result.Row0 = left.Row0 - right.Row0;
            result.Row1 = left.Row1 - right.Row1;
            result.Row2 = left.Row2 - right.Row2;
            result.Row3 = left.Row3 - right.Row3;
        }

        #endregion

        #region Multiply Functions

        /// <summary>
        /// Multiplies two instances.
        /// </summary>
        /// <param name="left">The left operand of the multiplication.</param>
        /// <param name="right">The right operand of the multiplication.</param>
        /// <returns>A new instance that is the result of the multiplication.</returns>
        public static Matrix4 Mult(Matrix4 left, Matrix4 right)
        {
            Matrix4 result;
            Mult(ref left, ref right, out result);
            return result;
        }

        /// <summary>
        /// Multiplies two instances.
        /// </summary>
        /// <param name="left">The left operand of the multiplication.</param>
        /// <param name="right">The right operand of the multiplication.</param>
        /// <param name="result">A new instance that is the result of the multiplication.</param>
        public static void Mult(ref Matrix4 left, ref Matrix4 right, out Matrix4 result)
        {
            float lM11 = left.Row0.X, lM12 = left.Row0.Y, lM13 = left.Row0.Z, lM14 = left.Row0.W,
                lM21 = left.Row1.X, lM22 = left.Row1.Y, lM23 = left.Row1.Z, lM24 = left.Row1.W,
                lM31 = left.Row2.X, lM32 = left.Row2.Y, lM33 = left.Row2.Z, lM34 = left.Row2.W,
                lM41 = left.Row3.X, lM42 = left.Row3.Y, lM43 = left.Row3.Z, lM44 = left.Row3.W,
                rM11 = right.Row0.X, rM12 = right.Row0.Y, rM13 = right.Row0.Z, rM14 = right.Row0.W,
                rM21 = right.Row1.X, rM22 = right.Row1.Y, rM23 = right.Row1.Z, rM24 = right.Row1.W,
                rM31 = right.Row2.X, rM32 = right.Row2.Y, rM33 = right.Row2.Z, rM34 = right.Row2.W,
                rM41 = right.Row3.X, rM42 = right.Row3.Y, rM43 = right.Row3.Z, rM44 = right.Row3.W;

            result.Row0.X = (((lM11 * rM11) + (lM12 * rM21)) + (lM13 * rM31)) + (lM14 * rM41);
            result.Row0.Y = (((lM11 * rM12) + (lM12 * rM22)) + (lM13 * rM32)) + (lM14 * rM42);
            result.Row0.Z = (((lM11 * rM13) + (lM12 * rM23)) + (lM13 * rM33)) + (lM14 * rM43);
            result.Row0.W = (((lM11 * rM14) + (lM12 * rM24)) + (lM13 * rM34)) + (lM14 * rM44);
            result.Row1.X = (((lM21 * rM11) + (lM22 * rM21)) + (lM23 * rM31)) + (lM24 * rM41);
            result.Row1.Y = (((lM21 * rM12) + (lM22 * rM22)) + (lM23 * rM32)) + (lM24 * rM42);
            result.Row1.Z = (((lM21 * rM13) + (lM22 * rM23)) + (lM23 * rM33)) + (lM24 * rM43);
            result.Row1.W = (((lM21 * rM14) + (lM22 * rM24)) + (lM23 * rM34)) + (lM24 * rM44);
            result.Row2.X = (((lM31 * rM11) + (lM32 * rM21)) + (lM33 * rM31)) + (lM34 * rM41);
            result.Row2.Y = (((lM31 * rM12) + (lM32 * rM22)) + (lM33 * rM32)) + (lM34 * rM42);
            result.Row2.Z = (((lM31 * rM13) + (lM32 * rM23)) + (lM33 * rM33)) + (lM34 * rM43);
            result.Row2.W = (((lM31 * rM14) + (lM32 * rM24)) + (lM33 * rM34)) + (lM34 * rM44);
            result.Row3.X = (((lM41 * rM11) + (lM42 * rM21)) + (lM43 * rM31)) + (lM44 * rM41);
            result.Row3.Y = (((lM41 * rM12) + (lM42 * rM22)) + (lM43 * rM32)) + (lM44 * rM42);
            result.Row3.Z = (((lM41 * rM13) + (lM42 * rM23)) + (lM43 * rM33)) + (lM44 * rM43);
            result.Row3.W = (((lM41 * rM14) + (lM42 * rM24)) + (lM43 * rM34)) + (lM44 * rM44);
        }

        /// <summary>
        /// Multiplies an instance by a scalar.
        /// </summary>
        /// <param name="left">The left operand of the multiplication.</param>
        /// <param name="right">The right operand of the multiplication.</param>
        /// <returns>A new instance that is the result of the multiplication</returns>
        public static Matrix4 Mult(Matrix4 left, float right)
        {
            Matrix4 result;
            Mult(ref left, right, out result);
            return result;
        }

        /// <summary>
        /// Multiplies an instance by a scalar.
        /// </summary>
        /// <param name="left">The left operand of the multiplication.</param>
        /// <param name="right">The right operand of the multiplication.</param>
        /// <param name="result">A new instance that is the result of the multiplication</param>
        public static void Mult(ref Matrix4 left, float right, out Matrix4 result)
        {
            result.Row0 = left.Row0 * right;
            result.Row1 = left.Row1 * right;
            result.Row2 = left.Row2 * right;
            result.Row3 = left.Row3 * right;
        }

        #endregion

        #region Invert Functions

        /// <summary>
        /// Calculate the inverse of the given matrix
        /// </summary>
        /// <param name="mat">The matrix to invert</param>
        /// <param name="result">The inverse of the given matrix if it has one, or the input if it is singular</param>
        /// <exception cref="InvalidOperationException">Thrown if the Matrix4 is singular.</exception>
        public static void Invert(ref Matrix4 mat, out Matrix4 result)
        {
            int[] colIdx = { 0, 0, 0, 0 };
            int[] rowIdx = { 0, 0, 0, 0 };
            int[] pivotIdx = { -1, -1, -1, -1 };

            // convert the matrix to an array for easy looping
            float[,] inverse = {{mat.Row0.X, mat.Row0.Y, mat.Row0.Z, mat.Row0.W}, 
                                {mat.Row1.X, mat.Row1.Y, mat.Row1.Z, mat.Row1.W}, 
                                {mat.Row2.X, mat.Row2.Y, mat.Row2.Z, mat.Row2.W}, 
                                {mat.Row3.X, mat.Row3.Y, mat.Row3.Z, mat.Row3.W} };
            int icol = 0;
            int irow = 0;
            for (int i = 0; i < 4; i++)
            {
                // Find the largest pivot value
                float maxPivot = 0.0f;
                for (int j = 0; j < 4; j++)
                {
                    if (pivotIdx[j] != 0)
                    {
                        for (int k = 0; k < 4; ++k)
                        {
                            if (pivotIdx[k] == -1)
                            {
                                float absVal = System.Math.Abs(inverse[j, k]);
                                if (absVal > maxPivot)
                                {
                                    maxPivot = absVal;
                                    irow = j;
                                    icol = k;
                                }
                            }
                            else if (pivotIdx[k] > 0)
                            {
                                result = mat;
                                return;
                            }
                        }
                    }
                }

                ++(pivotIdx[icol]);

                // Swap rows over so pivot is on diagonal
                if (irow != icol)
                {
                    for (int k = 0; k < 4; ++k)
                    {
                        float f = inverse[irow, k];
                        inverse[irow, k] = inverse[icol, k];
                        inverse[icol, k] = f;
                    }
                }

                rowIdx[i] = irow;
                colIdx[i] = icol;

                float pivot = inverse[icol, icol];
                // check for singular matrix
                if (pivot == 0.0f)
                {
                    throw new InvalidOperationException("Matrix is singular and cannot be inverted.");
                }

                // Scale row so it has a unit diagonal
                float oneOverPivot = 1.0f / pivot;
                inverse[icol, icol] = 1.0f;
                for (int k = 0; k < 4; ++k)
                    inverse[icol, k] *= oneOverPivot;

                // Do elimination of non-diagonal elements
                for (int j = 0; j < 4; ++j)
                {
                    // check this isn't on the diagonal
                    if (icol != j)
                    {
                        float f = inverse[j, icol];
                        inverse[j, icol] = 0.0f;
                        for (int k = 0; k < 4; ++k)
                            inverse[j, k] -= inverse[icol, k] * f;
                    }
                }
            }

            for (int j = 3; j >= 0; --j)
            {
                int ir = rowIdx[j];
                int ic = colIdx[j];
                for (int k = 0; k < 4; ++k)
                {
                    float f = inverse[k, ir];
                    inverse[k, ir] = inverse[k, ic];
                    inverse[k, ic] = f;
                }
            }

            result.Row0.X = inverse[0, 0];
            result.Row0.Y = inverse[0, 1];
            result.Row0.Z = inverse[0, 2];
            result.Row0.W = inverse[0, 3];
            result.Row1.X = inverse[1, 0];
            result.Row1.Y = inverse[1, 1];
            result.Row1.Z = inverse[1, 2];
            result.Row1.W = inverse[1, 3];
            result.Row2.X = inverse[2, 0];
            result.Row2.Y = inverse[2, 1];
            result.Row2.Z = inverse[2, 2];
            result.Row2.W = inverse[2, 3];
            result.Row3.X = inverse[3, 0];
            result.Row3.Y = inverse[3, 1];
            result.Row3.Z = inverse[3, 2];
            result.Row3.W = inverse[3, 3];
        }

        /// <summary>
        /// Calculate the inverse of the given matrix
        /// </summary>
        /// <param name="mat">The matrix to invert</param>
        /// <returns>The inverse of the given matrix if it has one, or the input if it is singular</returns>
        /// <exception cref="InvalidOperationException">Thrown if the Matrix4 is singular.</exception>
        public static Matrix4 Invert(Matrix4 mat)
        {
            Matrix4 result;
            Invert(ref mat, out result);
            return result;
        }

        #endregion

        #region Transpose

        /// <summary>
        /// Calculate the transpose of the given matrix
        /// </summary>
        /// <param name="mat">The matrix to transpose</param>
        /// <returns>The transpose of the given matrix</returns>
        public static Matrix4 Transpose(Matrix4 mat)
        {
            return new Matrix4(mat.Column0, mat.Column1, mat.Column2, mat.Column3);
        }


        /// <summary>
        /// Calculate the transpose of the given matrix
        /// </summary>
        /// <param name="mat">The matrix to transpose</param>
        /// <param name="result">The result of the calculation</param>
        public static void Transpose(ref Matrix4 mat, out Matrix4 result)
        {
            result.Row0 = mat.Column0;
            result.Row1 = mat.Column1;
            result.Row2 = mat.Column2;
            result.Row3 = mat.Column3;
        }

        #endregion

        #endregion

        #region Operators

        /// <summary>
        /// Matrix multiplication
        /// </summary>
        /// <param name="left">left-hand operand</param>
        /// <param name="right">right-hand operand</param>
        /// <returns>A new Matrix4 which holds the result of the multiplication</returns>
        public static Matrix4 operator *(Matrix4 left, Matrix4 right)
        {
            return Matrix4.Mult(left, right);
        }

        /// <summary>
        /// Matrix-scalar multiplication
        /// </summary>
        /// <param name="left">left-hand operand</param>
        /// <param name="right">right-hand operand</param>
        /// <returns>A new Matrix4 which holds the result of the multiplication</returns>
        public static Matrix4 operator *(Matrix4 left, float right)
        {
            return Matrix4.Mult(left, right);
        }

        /// <summary>
        /// Matrix addition
        /// </summary>
        /// <param name="left">left-hand operand</param>
        /// <param name="right">right-hand operand</param>
        /// <returns>A new Matrix4 which holds the result of the addition</returns>
        public static Matrix4 operator +(Matrix4 left, Matrix4 right)
        {
            return Matrix4.Add(left, right);
        }

        /// <summary>
        /// Matrix subtraction
        /// </summary>
        /// <param name="left">left-hand operand</param>
        /// <param name="right">right-hand operand</param>
        /// <returns>A new Matrix4 which holds the result of the subtraction</returns>
        public static Matrix4 operator -(Matrix4 left, Matrix4 right)
        {
            return Matrix4.Subtract(left, right);
        }

        /// <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 ==(Matrix4 left, Matrix4 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 equal right; false otherwise.</returns>
        public static bool operator !=(Matrix4 left, Matrix4 right)
        {
            return !left.Equals(right);
        }

        #endregion

        #region Overrides

        #region public override string ToString()

        /// <summary>
        /// Returns a System.String that represents the current Matrix4.
        /// </summary>
        /// <returns>The string representation of the matrix.</returns>
        public override string ToString()
        {
            return String.Format("{0}\n{1}\n{2}\n{3}", Row0, Row1, Row2, Row3);
        }

        #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 Row0.GetHashCode() ^ Row1.GetHashCode() ^ Row2.GetHashCode() ^ Row3.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 tresult.</param>
        /// <returns>True if the instances are equal; false otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (!(obj is Matrix4))
                return false;

            return this.Equals((Matrix4)obj);
        }

        #endregion

        #endregion

        #endregion

        #region IEquatable<Matrix4> Members

        /// <summary>Indicates whether the current matrix is equal to another matrix.</summary>
        /// <param name="other">An matrix to compare with this matrix.</param>
        /// <returns>true if the current matrix is equal to the matrix parameter; otherwise, false.</returns>
        public bool Equals(Matrix4 other)
        {
            return
                Row0 == other.Row0 &&
                Row1 == other.Row1 &&
                Row2 == other.Row2 &&
                Row3 == other.Row3;
        }

        #endregion
    }
}