Source/OpenTK/Math/Matrix4d.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 Matrix4d : IEquatable<Matrix4d>
    {
        #region Fields

        public Vector4d  Row0;
        public Vector4d  Row1;
        public Vector4d  Row2;
        public Vector4d  Row3;
 
        public static Matrix4d Identity = new Matrix4d(Vector4d .UnitX, Vector4d .UnitY, Vector4d .UnitZ, Vector4d .UnitW);

        #endregion

        #region Constructors

        public Matrix4d(Vector4d row0, Vector4d row1, Vector4d row2, Vector4d row3)
        {
            Row0 = row0;
            Row1 = row1;
            Row2 = row2;
            Row3 = row3;
        }

        public Matrix4d(
            double m00, double m01, double m02, double m03,
            double m10, double m11, double m12, double m13,
            double m20, double m21, double m22, double m23,
            double m30, double m31, double m32, double m33)
        {
            Row0 = new Vector4d(m00, m01, m02, m03);
            Row1 = new Vector4d(m10, m11, m12, m13);
            Row2 = new Vector4d(m20, m21, m22, m23);
            Row3 = new Vector4d(m30, m31, m32, m33);
        }

        #endregion

        #region Public Members

        #region Properties

        public double 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 Vector4d  Column0
        {
            get { return new Vector4d (Row0.X, Row1.X, Row2.X, Row3.X); }
        }

        public Vector4d  Column1
        {
            get { return new Vector4d (Row0.Y, Row1.Y, Row2.Y, Row3.Y); }
        }

        public Vector4d  Column2
        {
            get { return new Vector4d (Row0.Z, Row1.Z, Row2.Z, Row3.Z); }
        }

        public Vector4d  Column3
        {
            get { return new Vector4d (Row0.W, Row1.W, Row2.W, Row3.W); }
        }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

        #endregion

        #region Instance

        #region public void Invert()

        public void Invert()
        {
            this = Matrix4d.Invert(this);
        }

        #endregion

        #region public void Transpose()

        public void Transpose()
        {
            this = Matrix4d.Transpose(this);
        }

        #endregion

        #endregion

        #region Static

        #region CreateFromAxisAngle

        public static void CreateFromAxisAngle(Vector3d axis, double angle, out Matrix4d result)
        {
            double cos = System.Math.Cos(-angle);
            double sin = System.Math.Sin(-angle);
            double t = 1.0 - cos;

            axis.Normalize();

            result = new Matrix4d(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0,
                                 t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0,
                                 t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0,
                                 0, 0, 0, 1);
        }

        public static Matrix4d CreateFromAxisAngle(Vector3d axis, double angle)
        {
            Matrix4d result;
            CreateFromAxisAngle(axis, angle, out result);
            return result;
        }

        #endregion

        #region CreateRotation[XYZ]

        public static void CreateRotationX(double angle, out Matrix4d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            result.Row0 = Vector4d.UnitX;
            result.Row1 = new Vector4d(0, cos, sin, 0);
            result.Row2 = new Vector4d(0, -sin, cos, 0);
            result.Row3 = Vector4d.UnitW;
        }

        public static Matrix4d CreateRotationX(double angle)
        {
            Matrix4d result;
            CreateRotationX(angle, out result);
            return result;
        }

        public static void CreateRotationY(double angle, out Matrix4d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            result.Row0 = new Vector4d(cos, 0, -sin, 0);
            result.Row1 = Vector4d.UnitY;
            result.Row2 = new Vector4d(sin, 0, cos, 0);
            result.Row3 = Vector4d.UnitW;
        }

        public static Matrix4d CreateRotationY(double angle)
        {
            Matrix4d result;
            CreateRotationY(angle, out result);
            return result;
        }

        public static void CreateRotationZ(double angle, out Matrix4d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            result.Row0 = new Vector4d(cos, sin, 0, 0);
            result.Row1 = new Vector4d(-sin, cos, 0, 0);
            result.Row2 = Vector4d.UnitZ;
            result.Row3 = Vector4d.UnitW;
        }

        public static Matrix4d CreateRotationZ(double angle)
        {
            Matrix4d result;
            CreateRotationZ(angle, out result);
            return result;
        }

        #endregion

        #region CreateTranslation

        public static void CreateTranslation(double x, double y, double z, out Matrix4d result)
        {
            result = Identity;
            result.Row3 = new Vector4d(x, y, z, 1);
        }

        public static void CreateTranslation(ref Vector3d vector, out Matrix4d result)
        {
            result = Identity;
            result.Row3 = new Vector4d(vector.X, vector.Y, vector.Z, 1);
        }

        public static Matrix4d CreateTranslation(double x, double y, double z)
        {
            Matrix4d result;
            CreateTranslation(x, y, z, out result);
            return result;
        }

        public static Matrix4d CreateTranslation(Vector3d vector)
        {
            Matrix4d result;
            CreateTranslation(vector.X, vector.Y, vector.Z, out result);
            return result;
        }

        #endregion

        #region CreateOrthographic

        public static void CreateOrthographic(double width, double height, double zNear, double zFar, out Matrix4d result)
        {
            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
        }

        public static Matrix4d CreateOrthographic(double width, double height, double zNear, double zFar)
        {
            Matrix4d result;
            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
            return result;
        }

        #endregion

        #region CreateOrthographicOffCenter

        public static void CreateOrthographicOffCenter(double left, double right, double bottom, double top, double zNear, double zFar, out Matrix4d result)
        {
            result = new Matrix4d();

            double invRL = 1 / (right - left);
            double invTB = 1 / (top - bottom);
            double 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 Matrix4d CreateOrthographicOffCenter(double left, double right, double bottom, double top, double zNear, double zFar)
        {
            Matrix4d result;
            CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);
            return result;
        }

        #endregion

        #region CreatePerspectiveFieldOfView

        public static void CreatePerspectiveFieldOfView(double fovy, double aspect, double zNear, double zFar, out Matrix4d 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");

            double yMax = zNear * System.Math.Tan(0.5 * fovy);
            double yMin = -yMax;
            double xMin = yMin * aspect;
            double xMax = yMax * aspect;

            CreatePerspectiveOffCenter(xMin, xMax, yMin, yMax, zNear, zFar, out result);
        }

        public static Matrix4d CreatePerspectiveFieldOfView(double fovy, double aspect, double zNear, double zFar)
        {
            Matrix4d result;
            CreatePerspectiveFieldOfView(fovy, aspect, zNear, zFar, out result);
            return result;
        }

        #endregion

        #region CreatePerspectiveOffCenter

        public static void CreatePerspectiveOffCenter(double left, double right, double bottom, double top, double zNear, double zFar, out Matrix4d result)
        {
            if (zNear <= 0)
                throw new ArgumentOutOfRangeException("zNear");
            if (zFar <= 0)
                throw new ArgumentOutOfRangeException("zFar");
            if (zNear >= zFar)
                throw new ArgumentOutOfRangeException("zNear");

            double x = (2.0 * zNear) / (right - left);
            double y = (2.0 * zNear) / (top - bottom);
            double a = (right + left) / (right - left);
            double b = (top + bottom) / (top - bottom);
            double c = -(zFar + zNear) / (zFar - zNear);
            double d = -(2.0 * zFar * zNear) / (zFar - zNear);

            result = new Matrix4d(x, 0, 0, 0,
                                 0, y, 0, 0,
                                 a, b, c, -1,
                                 0, 0, d, 0);
        }

        public static Matrix4d CreatePerspectiveOffCenter(double left, double right, double bottom, double top, double zNear, double zFar)
        {
            Matrix4d 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 Matrix4d Translation(Vector3d trans)
        {
            return Translation(trans.X, trans.Y, trans.Z);
        }

        [Obsolete("Use CreateTranslation instead.")]
        public static Matrix4d Translation(double x, double y, double z)
        {
            Matrix4d result = Identity;
            result.Row3 = new Vector4d(x, y, z, 1.0);
            return result;
        }

        #endregion

        #endregion

        #region Scale Functions

        public static Matrix4d Scale(double scale)
        {
            return Scale(scale, scale, scale);
        }

        public static Matrix4d Scale(Vector3d scale)
        {
            return Scale(scale.X, scale.Y, scale.Z);
        }

        public static Matrix4d Scale(double x, double y, double z)
        {
            Matrix4d result;
            result.Row0 = Vector4d .UnitX * x;
            result.Row1 = Vector4d .UnitY * y;
            result.Row2 = Vector4d .UnitZ * z;
            result.Row3 = Vector4d .UnitW;
            return result;
        }

        #endregion

        #region Rotation Functions

        public static Matrix4d RotateX(double angle)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            Matrix4d result;
            result.Row0 = Vector4d .UnitX;
            result.Row1 = new Vector4d (0.0, cos, sin, 0.0);
            result.Row2 = new Vector4d (0.0, -sin, cos, 0.0);
            result.Row3 = Vector4d .UnitW;
            return result;
        }

        public static Matrix4d RotateY(double angle)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            Matrix4d result;
            result.Row0 = new Vector4d (cos, 0.0, -sin, 0.0);
            result.Row1 = Vector4d .UnitY;
            result.Row2 = new Vector4d (sin, 0.0, cos, 0.0);
            result.Row3 = Vector4d .UnitW;
            return result;
        }

        public static Matrix4d RotateZ(double angle)
        {
            double cos = System.Math.Cos(angle);
            double sin = System.Math.Sin(angle);

            Matrix4d result;
            result.Row0 = new Vector4d (cos, sin, 0.0, 0.0);
            result.Row1 = new Vector4d (-sin, cos, 0.0, 0.0);
            result.Row2 = Vector4d .UnitZ;
            result.Row3 = Vector4d .UnitW;
            return result;
        }

        public static Matrix4d Rotate(Vector3d axis, double angle)
        {
            double cos = System.Math.Cos(-angle);
            double sin = System.Math.Sin(-angle);
            double t = 1.0 - cos;

            axis.Normalize();

            Matrix4d result;
            result.Row0 = new Vector4d (t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0);
            result.Row1 = new Vector4d (t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0);
            result.Row2 = new Vector4d (t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0);
            result.Row3 = Vector4d .UnitW;
            return result;
        }

        public static Matrix4d Rotate(Quaterniond q)
        {
            Vector3d axis;
            double angle;
            q.ToAxisAngle(out axis, out angle);
            return Rotate(axis, angle);
        }

        #endregion

        #region Camera Helper Functions

        public static Matrix4d LookAt(Vector3d eye, Vector3d target, Vector3d up)
        {
            Vector3d z = Vector3d.Normalize(eye - target);
            Vector3d x = Vector3d.Normalize(Vector3d.Cross(up, z));
            Vector3d y = Vector3d.Normalize(Vector3d.Cross(z, x));

            Matrix4d rot = new Matrix4d(new Vector4d (x.X, y.X, z.X, 0.0),
                                        new Vector4d (x.Y, y.Y, z.Y, 0.0),
                                        new Vector4d (x.Z, y.Z, z.Z, 0.0),
                                        Vector4d .UnitW);

            Matrix4d trans = Matrix4d.CreateTranslation(-eye);

            return trans * rot;
        }

        public static Matrix4d LookAt(double eyeX, double eyeY, double eyeZ, double targetX, double targetY, double targetZ, double upX, double upY, double upZ)
        {
            return LookAt(new Vector3d(eyeX, eyeY, eyeZ), new Vector3d(targetX, targetY, targetZ), new Vector3d(upX, upY, upZ));
        }

        public static Matrix4d Frustum(double left, double right, double bottom, double top, double near, double far)
        {
            double invRL = 1.0 / (right - left);
            double invTB = 1.0 / (top - bottom);
            double invFN = 1.0 / (far - near);
            return new Matrix4d(new Vector4d (2.0 * near * invRL, 0.0, 0.0, 0.0),
                               new Vector4d (0.0, 2.0 * near * invTB, 0.0, 0.0),
                               new Vector4d ((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0),
                               new Vector4d (0.0, 0.0, -2.0 * far * near * invFN, 0.0));
        }

        public static Matrix4d Perspective(double fovy, double aspect, double near, double far)
        {
            double yMax = near * System.Math.Tan(0.5f * fovy);
            double yMin = -yMax;
            double xMin = yMin * aspect;
            double xMax = yMax * aspect;

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

        #endregion

        #region Multiply Functions

        public static Matrix4d Mult(Matrix4d left, Matrix4d right)
        {
            Matrix4d result;
            Mult(ref left, ref right, out result);
            return result;
        }

        public static void Mult(ref Matrix4d left, ref Matrix4d right, out Matrix4d result)
        {
            result = new Matrix4d();
            result.M11 = left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41;
            result.M12 = left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42;
            result.M13 = left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43;
            result.M14 = left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44;
            result.M21 = left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41;
            result.M22 = left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42;
            result.M23 = left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43;
            result.M24 = left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44;
            result.M31 = left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41;
            result.M32 = left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42;
            result.M33 = left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43;
            result.M34 = left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44;
            result.M41 = left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41;
            result.M42 = left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42;
            result.M43 = left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43;
            result.M44 = left.M41 * right.M14 + left.M42 * right.M24 + left.M43 * right.M34 + left.M44 * right.M44;
        }

        #endregion

        #region Invert Functions

        public static Matrix4d Invert(Matrix4d 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
            double[,] 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
                double maxPivot = 0.0;
                for (int j = 0; j < 4; j++)
                {
                    if (pivotIdx[j] != 0)
                    {
                        for (int k = 0; k < 4; ++k)
                        {
                            if (pivotIdx[k] == -1)
                            {
                                double 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)
                    {
                        double f = inverse[irow, k];
                        inverse[irow, k] = inverse[icol, k];
                        inverse[icol, k] = f;
                    }
                }

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

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

                // Scale row so it has a unit diagonal
                double oneOverPivot = 1.0 / pivot;
                inverse[icol, icol] = 1.0;
                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)
                    {
                        double f = inverse[j, icol];
                        inverse[j, icol] = 0.0;
                        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)
                {
                    double f = inverse[k, ir];
                    inverse[k, ir] = inverse[k, ic];
                    inverse[k, ic] = f;
                }
            }

            mat.Row0 = new Vector4d (inverse[0, 0], inverse[0, 1], inverse[0, 2], inverse[0, 3]);
            mat.Row1 = new Vector4d (inverse[1, 0], inverse[1, 1], inverse[1, 2], inverse[1, 3]);
            mat.Row2 = new Vector4d (inverse[2, 0], inverse[2, 1], inverse[2, 2], inverse[2, 3]);
            mat.Row3 = new Vector4d (inverse[3, 0], inverse[3, 1], inverse[3, 2], inverse[3, 3]);
            return mat;
        }

        #endregion

        #region Transpose

        public static Matrix4d Transpose(Matrix4d mat)
        {
            return new Matrix4d(mat.Column0, mat.Column1, mat.Column2, mat.Column3);
        }


        public static void Transpose(ref Matrix4d mat, out Matrix4d result)
        {
            result.Row0 = mat.Column0;
            result.Row1 = mat.Column1;
            result.Row2 = mat.Column2;
            result.Row3 = mat.Column3;
        }

        #endregion

        #endregion

        #region Operators

        public static Matrix4d operator *(Matrix4d left, Matrix4d right)
        {
            return Matrix4d.Mult(left, right);
        }

        public static bool operator ==(Matrix4d left, Matrix4d right)
        {
            return left.Equals(right);
        }

        public static bool operator !=(Matrix4d left, Matrix4d 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 Matrix4d))
                return false;

            return this.Equals((Matrix4d)obj);
        }

        #endregion

        #endregion

        #endregion

        #region IEquatable<Matrix4d> Members

        public bool Equals(Matrix4d other)
        {
            return
                Row0 == other.Row0 &&
                Row1 == other.Row1 &&
                Row2 == other.Row2 &&
                Row3 == other.Row3;
        }

        #endregion
    }
}

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