Opentk/Source/OpenTK/Math/Matrix3d.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
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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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
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 */
#endregion

using System;
using System.Runtime.InteropServices;

namespace OpenTK
{
    /// <summary>
    /// Represents a 3x3 matrix containing 3D rotation and scale with double-precision components.
    /// </summary>
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    public struct Matrix3d : IEquatable<Matrix3d>
    {
        #region Fields
        
        /// <summary>
        /// First row of the matrix.
        /// </summary>
        public Vector3d Row0;
        
        /// <summary>
        /// Second row of the matrix.
        /// </summary>
        public Vector3d Row1;
        
        /// <summary>
        /// Third row of the matrix.
        /// </summary>
        public Vector3d Row2;
        
        /// <summary>
        /// The identity matrix.
        /// </summary>
        public static Matrix3d Identity = new Matrix3d(Vector3d.UnitX, Vector3d.UnitY, Vector3d.UnitZ);
        
        #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">Bottom row of the matrix</param>
        public Matrix3d(Vector3d row0, Vector3d row1, Vector3d row2)
        {
            Row0 = row0;
            Row1 = row1;
            Row2 = row2;
        }
        
        /// <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="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="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>
        public Matrix3d(
            double m00, double m01, double m02,
            double m10, double m11, double m12,
            double m20, double m21, double m22)
        {
            Row0 = new Vector3d(m00, m01, m02);
            Row1 = new Vector3d(m10, m11, m12);
            Row2 = new Vector3d(m20, m21, m22);
        }

        /// <summary>
        /// Constructs a new instance.
        /// </summary>
        /// <param name="matrix">A Matrix4d to take the upper-left 3x3 from.</param>
        public Matrix3d(Matrix4d matrix)
        {
            Row0 = matrix.Row0.Xyz;
            Row1 = matrix.Row1.Xyz;
            Row2 = matrix.Row2.Xyz;
        }

        #endregion
        
        #region Public Members
        
        #region Properties
        
        /// <summary>
        /// Gets the determinant of this matrix.
        /// </summary>
        public double Determinant
        {
            get
            {
                double m11 = Row0.X, m12 = Row0.Y, m13 = Row0.Z,
                m21 = Row1.X, m22 = Row1.Y, m23 = Row1.Z,
                m31 = Row2.X, m32 = Row2.Y, m33 = Row2.Z;
                
                return
                    m11 * m22 * m33 + m12 * m23 * m31 + m13 * m21 * m32
                        - m13 * m22 * m31 - m11 * m23 * m32 - m12 * m21 * m33;
            }
        }
        
        /// <summary>
        /// Gets the first column of this matrix.
        /// </summary>
        public Vector3d Column0
        {
            get { return new Vector3d(Row0.X, Row1.X, Row2.X); }
        }
        
        /// <summary>
        /// Gets the second column of this matrix.
        /// </summary>
        public Vector3d Column1
        {
            get { return new Vector3d(Row0.Y, Row1.Y, Row2.Y); }
        }
        
        /// <summary>
        /// Gets the third column of this matrix.
        /// </summary>
        public Vector3d Column2
        {
            get { return new Vector3d(Row0.Z, Row1.Z, Row2.Z); }
        }
        
        /// <summary>
        /// Gets or sets the value at row 1, column 1 of this instance.
        /// </summary>
        public double 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 double 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 double M13 { get { return Row0.Z; } set { Row0.Z = value; } }
        
        /// <summary>
        /// Gets or sets the value at row 2, column 1 of this instance.
        /// </summary>
        public double 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 double 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 double M23 { get { return Row1.Z; } set { Row1.Z = value; } }
        
        /// <summary>
        /// Gets or sets the value at row 3, column 1 of this instance.
        /// </summary>
        public double 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 double 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 double M33 { get { return Row2.Z; } set { Row2.Z = value; } }

        /// <summary>
        /// Gets or sets the values along the main diagonal of the matrix.
        /// </summary>
        public Vector3d Diagonal
        {
            get
            {
                return new Vector3d(Row0.X, Row1.Y, Row2.Z);
            }
            set
            {
                Row0.X = value.X;
                Row1.Y = value.Y;
                Row2.Z = value.Z;
            }
        }

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

        #endregion

        #region Indexers

        /// <summary>
        /// Gets or sets the value at a specified row and column.
        /// </summary>
        public double 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];
                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;
                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 = Matrix3d.Invert(this);
        }
        
        #endregion
        
        #region public void Transpose()

        /// <summary>
        /// Converts this instance into its transpose.
        /// </summary>
        public void Transpose()
        {
            this = Matrix3d.Transpose(this);
        }
        
        #endregion

        /// <summary>
        /// Returns a normalised copy of this instance.
        /// </summary>
        public Matrix3d Normalized()
        {
            Matrix3d 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;
        }

        /// <summary>
        /// Returns an inverted copy of this instance.
        /// </summary>
        public Matrix3d Inverted()
        {
            Matrix3d m = this;
            if (m.Determinant != 0)
                m.Invert();
            return m;
        }


        /// <summary>
        /// Returns a copy of this Matrix3 without scale.
        /// </summary>
        public Matrix3d ClearScale()
        {
            Matrix3d m = this;
            m.Row0 = m.Row0.Normalized();
            m.Row1 = m.Row1.Normalized();
            m.Row2 = m.Row2.Normalized();
            return m;
        }
        /// <summary>
        /// Returns a copy of this Matrix3 without rotation.
        /// </summary>
        public Matrix3d ClearRotation()
        {
            Matrix3d m = this;
            m.Row0 = new Vector3d(m.Row0.Length, 0, 0);
            m.Row1 = new Vector3d(0, m.Row1.Length, 0);
            m.Row2 = new Vector3d(0, 0, m.Row2.Length);
            return m;
        }

        /// <summary>
        /// Returns the scale component of this instance.
        /// </summary>
        public Vector3d ExtractScale() { return new Vector3d(Row0.Length, Row1.Length, Row2.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 Quaterniond ExtractRotation(bool row_normalise = true)
        {
            var row0 = Row0;
            var row1 = Row1;
            var row2 = Row2;

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

            // code below adapted from Blender

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

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

                q.W = sq;
                sq = 1.0 / (4.0 * sq);
                q.X = (row1[2] - row2[1]) * sq;
                q.Y = (row2[0] - row0[2]) * sq;
                q.Z = (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 = 0.25 * sq;
                sq = 1.0 / sq;
                q.W = (row2[1] - row1[2]) * sq;
                q.Y = (row1[0] + row0[1]) * sq;
                q.Z = (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 = 0.25 * sq;
                sq = 1.0 / sq;
                q.W = (row2[0] - row0[2]) * sq;
                q.X = (row1[0] + row0[1]) * sq;
                q.Z = (row2[1] + row1[2]) * sq;
            }
            else
            {
                double sq = 2.0 * Math.Sqrt(1.0 + row2[2] - row0[0] - row1[1]);

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

            q.Normalize();
            return q;
        }

        #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(Vector3d axis, double angle, out Matrix3d result)
        {
            //normalize and create a local copy of the vector.
            axis.Normalize();
            double axisX = axis.X, axisY = axis.Y, axisZ = axis.Z;
            
            //calculate angles
            double cos = System.Math.Cos(-angle);
            double sin = System.Math.Sin(-angle);
            double t = 1.0f - cos;
            
            //do the conversion math once
            double tXX = t * axisX * axisX,
            tXY = t * axisX * axisY,
            tXZ = t * axisX * axisZ,
            tYY = t * axisY * axisY,
            tYZ = t * axisY * axisZ,
            tZZ = t * axisZ * axisZ;
            
            double 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.Row1.X = tXY + sinZ;
            result.Row1.Y = tYY + cos;
            result.Row1.Z = tYZ - sinX;
            result.Row2.X = tXZ - sinY;
            result.Row2.Y = tYZ + sinX;
            result.Row2.Z = tZZ + cos;
        }

        /// <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 Matrix3d CreateFromAxisAngle(Vector3d axis, double angle)
        {
            Matrix3d result;
            CreateFromAxisAngle(axis, angle, out result);
            return result;
        }
        
        #endregion
        
        #region CreateFromQuaternion

        /// <summary>
        /// Build a rotation matrix from the specified quaternion.
        /// </summary>
        /// <param name="q">Quaternion to translate.</param>
        /// <param name="result">Matrix result.</param>
        public static void CreateFromQuaternion(ref Quaterniond q, out Matrix3d result)
        {
            Vector3d axis;
            double angle;
            q.ToAxisAngle(out axis, out angle);
            CreateFromAxisAngle(axis, angle, out result);
        }

        /// <summary>
        /// Build a rotation matrix from the specified quaternion.
        /// </summary>
        /// <param name="q">Quaternion to translate.</param>
        /// <returns>A matrix instance.</returns>
        public static Matrix3d CreateFromQuaternion(Quaterniond q)
        {
            Matrix3d 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 Matrix3d instance.</param>
        public static void CreateRotationX(double angle, out Matrix3d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = 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 Matrix3d instance.</returns>
        public static Matrix3d CreateRotationX(double angle)
        {
            Matrix3d 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 Matrix3d instance.</param>
        public static void CreateRotationY(double angle, out Matrix3d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = 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 Matrix3d instance.</returns>
        public static Matrix3d CreateRotationY(double angle)
        {
            Matrix3d 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 Matrix3d instance.</param>
        public static void CreateRotationZ(double angle, out Matrix3d result)
        {
            double cos = System.Math.Cos(angle);
            double sin = 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 Matrix3d instance.</returns>
        public static Matrix3d CreateRotationZ(double angle)
        {
            Matrix3d result;
            CreateRotationZ(angle, 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 Matrix3d CreateScale(double scale)
        {
            Matrix3d 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 Matrix3d CreateScale(Vector3d scale)
        {
            Matrix3d 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 Matrix3d CreateScale(double x, double y, double z)
        {
            Matrix3d 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(double scale, out Matrix3d 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 Vector3d scale, out Matrix3d 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(double x, double y, double z, out Matrix3d result)
        {
            result = Identity;
            result.Row0.X = x;
            result.Row1.Y = y;
            result.Row2.Z = z;
        }
        
        #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 Matrix3d Mult(Matrix3d left, Matrix3d right)
        {
            Matrix3d 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 Matrix3d left, ref Matrix3d right, out Matrix3d result)
        {
            double lM11 = left.Row0.X, lM12 = left.Row0.Y, lM13 = left.Row0.Z,
            lM21 = left.Row1.X, lM22 = left.Row1.Y, lM23 = left.Row1.Z,
            lM31 = left.Row2.X, lM32 = left.Row2.Y, lM33 = left.Row2.Z,
            rM11 = right.Row0.X, rM12 = right.Row0.Y, rM13 = right.Row0.Z,
            rM21 = right.Row1.X, rM22 = right.Row1.Y, rM23 = right.Row1.Z,
            rM31 = right.Row2.X, rM32 = right.Row2.Y, rM33 = right.Row2.Z;
            
            result.Row0.X = ((lM11 * rM11) + (lM12 * rM21)) + (lM13 * rM31);
            result.Row0.Y = ((lM11 * rM12) + (lM12 * rM22)) + (lM13 * rM32);
            result.Row0.Z = ((lM11 * rM13) + (lM12 * rM23)) + (lM13 * rM33);
            result.Row1.X = ((lM21 * rM11) + (lM22 * rM21)) + (lM23 * rM31);
            result.Row1.Y = ((lM21 * rM12) + (lM22 * rM22)) + (lM23 * rM32);
            result.Row1.Z = ((lM21 * rM13) + (lM22 * rM23)) + (lM23 * rM33);
            result.Row2.X = ((lM31 * rM11) + (lM32 * rM21)) + (lM33 * rM31);
            result.Row2.Y = ((lM31 * rM12) + (lM32 * rM22)) + (lM33 * rM32);
            result.Row2.Z = ((lM31 * rM13) + (lM32 * rM23)) + (lM33 * rM33);
        }
        
        #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 Matrix3d is singular.</exception>
        public static void Invert(ref Matrix3d mat, out Matrix3d result)
        {
            int[] colIdx = { 0, 0, 0 };
            int[] rowIdx = { 0, 0, 0 };
            int[] pivotIdx = { -1, -1, -1 };
            
            double[,] inverse = {{mat.Row0.X, mat.Row0.Y, mat.Row0.Z},
                {mat.Row1.X, mat.Row1.Y, mat.Row1.Z},
                {mat.Row2.X, mat.Row2.Y, mat.Row2.Z}};
            
            int icol = 0;
            int irow = 0;
            for (int i = 0; i < 3; i++)
            {
                double maxPivot = 0.0;
                for (int j = 0; j < 3; j++)
                {
                    if (pivotIdx[j] != 0)
                    {
                        for (int k = 0; k < 3; ++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)
                            {
                                result = mat;
                                return;
                            }
                        }
                    }
                }
                
                ++(pivotIdx[icol]);
                
                if (irow != icol)
                {
                    for (int k = 0; k < 3; ++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];
                
                if (pivot == 0.0)
                {
                    throw new InvalidOperationException("Matrix is singular and cannot be inverted.");
                }
                
                double oneOverPivot = 1.0 / pivot;
                inverse[icol, icol] = 1.0;
                for (int k = 0; k < 3; ++k)
                    inverse[icol, k] *= oneOverPivot;
                
                for (int j = 0; j < 3; ++j)
                {
                    if (icol != j)
                    {
                        double f = inverse[j, icol];
                        inverse[j, icol] = 0.0;
                        for (int k = 0; k < 3; ++k)
                            inverse[j, k] -= inverse[icol, k] * f;
                    }
                }
            }
            
            for (int j = 2; j >= 0; --j)
            {
                int ir = rowIdx[j];
                int ic = colIdx[j];
                for (int k = 0; k < 3; ++k)
                {
                    double 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.Row1.X = inverse[1, 0];
            result.Row1.Y = inverse[1, 1];
            result.Row1.Z = inverse[1, 2];
            result.Row2.X = inverse[2, 0];
            result.Row2.Y = inverse[2, 1];
            result.Row2.Z = inverse[2, 2];
        }
        
        /// <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 Matrix3d Invert(Matrix3d mat)
        {
            Matrix3d 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 Matrix3d Transpose(Matrix3d mat)
        {
            return new Matrix3d(mat.Column0, mat.Column1, mat.Column2);
        }

        /// <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 Matrix3d mat, out Matrix3d result)
        {
            result.Row0 = mat.Column0;
            result.Row1 = mat.Column1;
            result.Row2 = mat.Column2;
        }
        
        #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 Matrix3d which holds the result of the multiplication</returns>
        public static Matrix3d operator *(Matrix3d left, Matrix3d right)
        {
            return Matrix3d.Mult(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 ==(Matrix3d left, Matrix3d 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 !=(Matrix3d left, Matrix3d right)
        {
            return !left.Equals(right);
        }
        
        #endregion
        
        #region Overrides
        
        #region public override string ToString()
        
        /// <summary>
        /// Returns a System.String that represents the current Matrix3d.
        /// </summary>
        /// <returns>The string representation of the matrix.</returns>
        public override string ToString()
        {
            return String.Format("{0}\n{1}\n{2}", Row0, Row1, Row2);
        }
        
        #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();
        }
        
        #endregion
        
        #region public override bool Equals(object obj)
        
        /// <summary>
        /// Indicates whether this instance and a specified object are equal.
        /// </summary>
        /// <param name="obj">The object to compare to.</param>
        /// <returns>True if the instances are equal; false otherwise.</returns>
        public override bool Equals(object obj)
        {
            if (!(obj is Matrix3d))
                return false;
            
            return this.Equals((Matrix3d)obj);
        }
        
        #endregion
        
        #endregion
        
        #endregion
        
        #region IEquatable<Matrix3d> Members

        /// <summary>Indicates whether the current matrix is equal to another matrix.</summary>
        /// <param name="other">A 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(Matrix3d other)
        {
            return
                Row0 == other.Row0 &&
                    Row1 == other.Row1 &&
                    Row2 == other.Row2;
        }
        
        #endregion
    }
}