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
{
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    public struct Matrix4 : IEquatable<Matrix4>
    {
        #region Fields

        public Vector4 Row0;
        public Vector4 Row1;
        public Vector4 Row2;
        public Vector4 Row3;
 
        public static Matrix4 Identity = new Matrix4(Vector4.UnitX, Vector4.UnitY, Vector4.UnitZ, Vector4.UnitW);

        #endregion

        #region Constructors

        public Matrix4(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 row3)
        {
            Row0 = row0;
            Row1 = row1;
            Row2 = row2;
            Row3 = row3;
        }

        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);
        }

        #endregion

        #region Public Members

        #region Properties

        public float Determinant
        {
            get
            {
                return
                    Row0.X * Row1.Y * Row2.Z * Row3.W - Row0.X * Row1.Y * Row2.W * Row3.Z + Row0.X * Row1.Z * Row2.W * Row3.Y - Row0.X * Row1.Z * Row2.Y * Row3.W
                  + Row0.X * Row1.W * Row2.Y * Row3.Z - Row0.X * Row1.W * Row2.Z * Row3.Y - Row0.Y * Row1.Z * Row2.W * Row3.X + Row0.Y * Row1.Z * Row2.X * Row3.W
                  - Row0.Y * Row1.W * Row2.X * Row3.Z + Row0.Y * Row1.W * Row2.Z * Row3.X - Row0.Y * Row1.X * Row2.Z * Row3.W + Row0.Y * Row1.X * Row2.W * Row3.Z
                  + Row0.Z * Row1.W * Row2.X * Row3.Y - Row0.Z * Row1.W * Row2.Y * Row3.X + Row0.Z * Row1.X * Row2.Y * Row3.W - Row0.Z * Row1.X * Row2.W * Row3.Y
                  + Row0.Z * Row1.Y * Row2.W * Row3.X - Row0.Z * Row1.Y * Row2.X * Row3.W - Row0.W * Row1.X * Row2.Y * Row3.Z + Row0.W * Row1.X * Row2.Z * Row3.Y
                  - Row0.W * Row1.Y * Row2.Z * Row3.X + Row0.W * Row1.Y * Row2.X * Row3.Z - Row0.W * Row1.Z * Row2.X * Row3.Y + Row0.W * Row1.Z * Row2.Y * Row3.X;
            }
        }

        public Vector4 Column0
        {
            get { return new Vector4(Row0.X, Row1.X, Row2.X, Row3.X); }
        }

        public Vector4 Column1
        {
            get { return new Vector4(Row0.Y, Row1.Y, Row2.Y, Row3.Y); }
        }

        public Vector4 Column2
        {
            get { return new Vector4(Row0.Z, Row1.Z, Row2.Z, Row3.Z); }
        }

        public Vector4 Column3
        {
            get { return new Vector4(Row0.W, Row1.W, Row2.W, Row3.W); }
        }

        public float M11 { get { return Row0.X; } set { Row0.X = value; } }

        public float M12 { get { return Row0.Y; } set { Row0.Y = value; } }

        public float M13 { get { return Row0.Z; } set { Row0.Z = value; } }

        public float M14 { get { return Row0.W; } set { Row0.W = value; } }

        public float M21 { get { return Row1.X; } set { Row1.X = value; } }

        public float M22 { get { return Row1.Y; } set { Row1.Y = value; } }

        public float M23 { get { return Row1.Z; } set { Row1.Z = value; } }

        public float M24 { get { return Row1.W; } set { Row1.W = value; } }

        public float M31 { get { return Row2.X; } set { Row2.X = value; } }

        public float M32 { get { return Row2.Y; } set { Row2.Y = value; } }

        public float M33 { get { return Row2.Z; } set { Row2.Z = value; } }

        public float M34 { get { return Row2.W; } set { Row2.W = value; } }

        public float M41 { get { return Row3.X; } set { Row3.X = value; } }

        public float M42 { get { return Row3.Y; } set { Row3.Y = value; } }

        public float M43 { get { return Row3.Z; } set { Row3.Z = value; } }

        public float M44 { get { return Row3.W; } set { Row3.W = value; } }

        #endregion

        #region Instance

        #region public void Invert()

        public void Invert()
        {
            this = Matrix4.Invert(this);
        }

        #endregion

        #region public void Transpose()

        public void Transpose()
        {
            this = Matrix4.Transpose(this);
        }

        #endregion

        #endregion

        #region Static
        
        #region CreateFromAxisAngle
        
        public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(-angle);
            float sin = (float)System.Math.Sin(-angle);
            float t = 1.0f - cos;

            axis.Normalize();

            result = new Matrix4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f,
                                 t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f,
                                 t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f,
                                 0, 0, 0, 1);
        }
        
        public static Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)
        {
            Matrix4 result;
            CreateFromAxisAngle(axis, angle, out result);
            return result;
        }
        
        #endregion

        #region CreateRotation[XYZ]

        public static void CreateRotationX(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result.Row0 = Vector4.UnitX;
            result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
            result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
            result.Row3 = Vector4.UnitW;
        }

        public static Matrix4 CreateRotationX(float angle)
        {
            Matrix4 result;
            CreateRotationX(angle, out result);
            return result;
        }

        public static void CreateRotationY(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
            result.Row1 = Vector4.UnitY;
            result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
            result.Row3 = Vector4.UnitW;
        }

        public static Matrix4 CreateRotationY(float angle)
        {
            Matrix4 result;
            CreateRotationY(angle, out result);
            return result;
        }

        public static void CreateRotationZ(float angle, out Matrix4 result)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
            result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
            result.Row2 = Vector4.UnitZ;
            result.Row3 = Vector4.UnitW;
        }

        public static Matrix4 CreateRotationZ(float angle)
        {
            Matrix4 result;
            CreateRotationZ(angle, out result);
            return result;
        }

        #endregion

        #region CreateTranslation

        public static void CreateTranslation(float x, float y, float z, out Matrix4 result)
        {
            result = Identity;
            result.Row3 = new Vector4(x, y, z, 1);
        }

        public static void CreateTranslation(ref Vector3 vector, out Matrix4 result)
        {
            result = Identity;
            result.Row3 = new Vector4(vector.X, vector.Y, vector.Z, 1);
        }

        public static Matrix4 CreateTranslation(float x, float y, float z)
        {
            Matrix4 result;
            CreateTranslation(x, y, z, out result);
            return result;
        }

        public static Matrix4 CreateTranslation(Vector3 vector)
        {
            Matrix4 result;
            CreateTranslation(vector.X, vector.Y, vector.Z, out result);
            return result;
        }

        #endregion

        #region CreateOrthographic

        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);
        }

        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

        public static void CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
        {
            result = new Matrix4();

            float invRL = 1 / (right - left);
            float invTB = 1 / (top - bottom);
            float invFN = 1 / (zFar - zNear);

            result.M11 = 2 * invRL;
            result.M22 = 2 * invTB;
            result.M33 = -2 * invFN;

            result.M41 = -(right + left) * invRL;
            result.M42 = -(top + bottom) * invTB;
            result.M43 = -(zFar + zNear) * invFN;
            result.M44 = 1;
        }

        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
        
        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");
            if (zNear >= zFar)
                throw new ArgumentOutOfRangeException("zNear");
            
            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);
        }
        
        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
        
        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 = new Matrix4(x, 0, 0,  0,
                                 0, y, 0,  0,
                                 a, b, c, -1,
                                 0, 0, d,  0);
        }
        
        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

        [Obsolete("Use CreateTranslation instead.")]
        public static Matrix4 Translation(Vector3 trans)
        {
            return Translation(trans.X, trans.Y, trans.Z);
        }

        [Obsolete("Use CreateTranslation instead.")]
        public static Matrix4 Translation(float x, float y, float z)
        {
            Matrix4 result = Identity;
            result.Row3 = new Vector4(x, y, z, 1.0f);
            return result;
        }

        #endregion

        #endregion

        #region Scale Functions

        public static Matrix4 Scale(float scale)
        {
            return Scale(scale, scale, scale);
        }

        public static Matrix4 Scale(Vector3 scale)
        {
            return Scale(scale.X, scale.Y, scale.Z);
        }

        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 Rotation Functions

        [Obsolete("Use CreateRotationX instead.")]
        public static Matrix4 RotateX(float angle)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            Matrix4 result;
            result.Row0 = Vector4.UnitX;
            result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
            result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
            result.Row3 = Vector4.UnitW;
            return result;
        }

        [Obsolete("Use CreateRotationY instead.")]
        public static Matrix4 RotateY(float angle)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            Matrix4 result;
            result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
            result.Row1 = Vector4.UnitY;
            result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
            result.Row3 = Vector4.UnitW;
            return result;
        }

        [Obsolete("Use CreateRotationZ instead.")]
        public static Matrix4 RotateZ(float angle)
        {
            float cos = (float)System.Math.Cos(angle);
            float sin = (float)System.Math.Sin(angle);

            Matrix4 result;
            result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
            result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
            result.Row2 = Vector4.UnitZ;
            result.Row3 = Vector4.UnitW;
            return result;
        }

        [Obsolete("Use CreateFromAxisAngle instead.")]
        public static Matrix4 Rotate(Vector3 axis, float angle)
        {
            float cos = (float)System.Math.Cos(-angle);
            float sin = (float)System.Math.Sin(-angle);
            float t = 1.0f - cos;

            axis.Normalize();

            Matrix4 result;
            result.Row0 = new Vector4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f);
            result.Row1 = new Vector4(t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f);
            result.Row2 = new Vector4(t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f);
            result.Row3 = Vector4.UnitW;
            return result;
        }

        public static Matrix4 Rotate(Quaternion q)
        {
            Vector3 axis;
            float angle;
            q.ToAxisAngle(out axis, out angle);
            return CreateFromAxisAngle(axis, angle);
        }

        #endregion

        #region Camera Helper Functions

        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 rot = new Matrix4(new Vector4(x.X, y.X, z.X, 0.0f),
                                        new Vector4(x.Y, y.Y, z.Y, 0.0f),
                                        new Vector4(x.Z, y.Z, z.Z, 0.0f),
                                        Vector4.UnitW);

            Matrix4 trans = Matrix4.CreateTranslation(-eye);

            return trans * rot;
        }

        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));
        }

        [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));
        }

        [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

        #region Multiply Functions

        public static Matrix4 Mult(Matrix4 left, Matrix4 right)
        {
            Matrix4 result;
            Mult(ref left, ref right, out result);
            return result;
        }

        public static void Mult(ref Matrix4 left, ref Matrix4 right, out Matrix4 result)
        {
            result = new Matrix4(
                left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41,
                left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42,
                left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43,
                left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44,
                left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41,
                left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42,
                left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43,
                left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44,
                left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41,
                left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42,
                left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43,
                left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44,
                left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41,
                left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42,
                left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43,
                left.M41 * right.M14 + left.M42 * right.M24 + left.M43 * right.M34 + left.M44 * right.M44);
        }

        #endregion

        #region Invert Functions

        public static Matrix4 Invert(Matrix4 mat)
        {
            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)
                            {
                                return mat;
                            }
                        }
                    }
                }

                ++(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.");
                    //return mat;
                }

                // 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;
                }
            }

            mat.Row0 = new Vector4(inverse[0, 0], inverse[0, 1], inverse[0, 2], inverse[0, 3]);
            mat.Row1 = new Vector4(inverse[1, 0], inverse[1, 1], inverse[1, 2], inverse[1, 3]);
            mat.Row2 = new Vector4(inverse[2, 0], inverse[2, 1], inverse[2, 2], inverse[2, 3]);
            mat.Row3 = new Vector4(inverse[3, 0], inverse[3, 1], inverse[3, 2], inverse[3, 3]);
            return mat;
        }

        #endregion

        #region Transpose

        public static Matrix4 Transpose(Matrix4 mat)
        {
            return new Matrix4(mat.Column0, mat.Column1, mat.Column2, mat.Column3);
        }


        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

        public static Matrix4 operator *(Matrix4 left, Matrix4 right)
        {
            return Matrix4.Mult(left, right);
        }

        public static bool operator ==(Matrix4 left, Matrix4 right)
        {
            return left.Equals(right);
        }

        public static bool operator !=(Matrix4 left, Matrix4 right)
        {
            return !left.Equals(right);
        }

        #endregion

        #region Overrides

        #region public override string ToString()

        public override string ToString()
        {
            return String.Format("{0}\n{1}\n{2}\n{3}", Row0, Row1, Row2, Row3);
        }

        #endregion

        #region public override int GetHashCode()

        public override int GetHashCode()
        {
            return Row0.GetHashCode() ^ Row1.GetHashCode() ^ Row2.GetHashCode() ^ Row3.GetHashCode();
        }

        #endregion

        #region public override bool Equals(object obj)

        public override bool Equals(object obj)
        {
            if (!(obj is Matrix4))
                return false;

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

        #endregion

        #endregion

        #endregion

        #region IEquatable<Matrix4> Members

        public bool Equals(Matrix4 other)
        {
            return
                Row0 == other.Row0 &&
                Row1 == other.Row1 &&
                Row2 == other.Row2 &&
                Row3 == other.Row3;
        }

        #endregion
    }
}

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