Opentk/Source/OpenTK/Math/Matrix3x4d.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 3x4 Matrix
    /// </summary>
    [Serializable]
    [StructLayout(LayoutKind.Sequential)]
    public struct Matrix3x4d : IEquatable<Matrix3x4d>
    {
        #region Fields

        /// <summary>
        /// Top row of the matrix
        /// </summary>
        public Vector4d Row0;

        /// <summary>
        /// 2nd row of the matrix
        /// </summary>
        public Vector4d Row1;

        /// <summary>
        /// Bottom row of the matrix
        /// </summary>
        public Vector4d Row2;

        /// <summary>
        /// The zero matrix
        /// </summary>
        public static Matrix3x4d Zero = new Matrix3x4d(Vector4d.Zero, Vector4d.Zero, Vector4d.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">Bottom row of the matrix</param>
        public Matrix3x4d(Vector4d row0, Vector4d row1, Vector4d 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="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>
        public Matrix3x4d(
            double m00, double m01, double m02, double m03,
            double m10, double m11, double m12, double m13,
            double m20, double m21, double m22, double m23)
        {
            Row0 = new Vector4d(m00, m01, m02, m03);
            Row1 = new Vector4d(m10, m11, m12, m13);
            Row2 = new Vector4d(m20, m21, m22, m23);
        }

        #endregion

        #region Public Members

        #region Properties

        /// <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 the fourth column of this matrix.
        /// </summary>
        public Vector3d Column3
        {
            get { return new Vector3d(Row0.W, Row1.W, Row2.W); }
        }

        /// <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 1, column 4 of this instance.
        /// </summary>
        public double 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 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 2, column 4 of this instance.
        /// </summary>
        public double 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 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 value at row 3, column 4 of this instance.
        /// </summary>
        public double M34 { get { return Row2.W; } set { Row2.W = value; } }

        #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()

        public void Invert()
        {
            this = Matrix3x4d.Invert(this);
        }

        #endregion

        #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 Matrix3x4d result)
        {
            axis.Normalize();
            double axisX = axis.X, axisY = axis.Y, axisZ = axis.Z;

            double cos = (double)System.Math.Cos(angle);
            double sin = (double)System.Math.Sin(angle);
            double t = 1.0f - cos;

            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.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;
        }

        /// <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 Matrix3x4d CreateFromAxisAngle(Vector3d axis, double angle)
        {
            Matrix3x4d 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 Matrix3x4d result)
        {
            double x = q.X, y = q.Y, z = q.Z, w = q.W,
                tx = 2 * x, ty = 2 * y, tz = 2 * z,
                txx = tx * x, tyy = ty * y, tzz = tz * z,
                txy = tx * y, txz = tx * z, tyz = ty * z,
                txw = tx * w, tyw = ty * w, tzw = tz * w;

            result.Row0.X = 1f - (tyy + tzz);
            result.Row0.Y = txy + tzw;
            result.Row0.Z = txz - tyw;
            result.Row0.W = 0f;
            result.Row1.X = txy - tzw;
            result.Row1.Y = 1f - (txx + tzz);
            result.Row1.Z = tyz + txw;
            result.Row1.W = 0f;
            result.Row2.X = txz + tyw;
            result.Row2.Y = tyz - txw;
            result.Row2.Z = 1f - (txx + tyy);
            result.Row2.W = 0f;

            /*Vector3d axis;
            double 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 Matrix3x4d CreateFromQuaternion(Quaternion q)
        {
            Matrix3x4d 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(double angle, out Matrix3x4d result)
        {
            double cos = (double)System.Math.Cos(angle);
            double sin = (double)System.Math.Sin(angle);

            result.Row0.X = 1;
            result.Row0.Y = 0;
            result.Row0.Z = 0;
            result.Row0.W = 0;
            result.Row1.X = 0;
            result.Row1.Y = cos;
            result.Row1.Z = sin;
            result.Row1.W = 0;
            result.Row2.X = 0;
            result.Row2.Y = -sin;
            result.Row2.Z = cos;
            result.Row2.W = 0;
        }

        /// <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 Matrix3x4d CreateRotationX(double angle)
        {
            Matrix3x4d 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(double angle, out Matrix3x4d result)
        {
            double cos = (double)System.Math.Cos(angle);
            double sin = (double)System.Math.Sin(angle);

            result.Row0.X = cos;
            result.Row0.Y = 0;
            result.Row0.Z = -sin;
            result.Row0.W = 0;
            result.Row1.X = 0;
            result.Row1.Y = 1;
            result.Row1.Z = 0;
            result.Row1.W = 0;
            result.Row2.X = sin;
            result.Row2.Y = 0;
            result.Row2.Z = cos;
            result.Row2.W = 0;
        }

        /// <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 Matrix3x4d CreateRotationY(double angle)
        {
            Matrix3x4d 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(double angle, out Matrix3x4d result)
        {
            double cos = (double)System.Math.Cos(angle);
            double sin = (double)System.Math.Sin(angle);

            result.Row0.X = cos;
            result.Row0.Y = sin;
            result.Row0.Z = 0;
            result.Row0.W = 0;
            result.Row1.X = -sin;
            result.Row1.Y = cos;
            result.Row1.Z = 0;
            result.Row1.W = 0;
            result.Row2.X = 0;
            result.Row2.Y = 0;
            result.Row2.Z = 1;
            result.Row2.W = 0;
        }

        /// <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 Matrix3x4d CreateRotationZ(double angle)
        {
            Matrix3x4d 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(double x, double y, double z, out Matrix3x4d result)
        {
            result.Row0.X = 1;
            result.Row0.Y = 0;
            result.Row0.Z = 0;
            result.Row0.W = x;
            result.Row1.X = 0;
            result.Row1.Y = 1;
            result.Row1.Z = 0;
            result.Row1.W = y;
            result.Row2.X = 0;
            result.Row2.Y = 0;
            result.Row2.Z = 1;
            result.Row2.W = 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 Vector3d vector, out Matrix3x4d result)
        {
            result.Row0.X = 1;
            result.Row0.Y = 0;
            result.Row0.Z = 0;
            result.Row0.W = vector.X;
            result.Row1.X = 0;
            result.Row1.Y = 1;
            result.Row1.Z = 0;
            result.Row1.W = vector.Y;
            result.Row2.X = 0;
            result.Row2.Y = 0;
            result.Row2.Z = 1;
            result.Row2.W = 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 Matrix3x4d CreateTranslation(double x, double y, double z)
        {
            Matrix3x4d 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 Matrix3x4d CreateTranslation(Vector3d vector)
        {
            Matrix3x4d result;
            CreateTranslation(vector.X, vector.Y, vector.Z, out result);
            return result;
        }

        #endregion

        #region CreateScale

        /// <summary>
        /// Build a scaling matrix
        /// </summary>
        /// <param name="scale">Single scale factor for x,y and z axes</param>
        /// <returns>A scaling matrix</returns>
        public static Matrix3x4d CreateScale(double scale)
        {
            return CreateScale(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>
        public static Matrix3x4d CreateScale(Vector3d scale)
        {
            return CreateScale(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>
        public static Matrix3x4d CreateScale(double x, double y, double z)
        {
            Matrix3x4d result;
            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 = 0;
            result.Row2.Y = 0;
            result.Row2.Z = z;
            result.Row2.W = 0;
            return result;
        }

        #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(Matrix3x4d left, Matrix4x3d 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 Matrix3x4d left, ref Matrix4x3d right, out Matrix3d result)
        {
            double 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,
                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,
                rM41 = right.Row3.X, rM42 = right.Row3.Y, rM43 = right.Row3.Z;

            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.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.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);
        }

        public static Matrix3x4d Mult(Matrix3x4d left, Matrix3x4d right)
        {
            Matrix3x4d result;
            Mult(ref left, ref right, out result);
            return result;
        }

        public static void Mult(ref Matrix3x4d left, ref Matrix3x4d right, out Matrix3x4d result)
        {
            double 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,
                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;

            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.Row0.W = (lM11 * rM14) + (lM12 * rM24) + (lM13 * rM34) + lM14;
            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.Row1.W = (lM21 * rM14) + (lM22 * rM24) + (lM23 * rM34) + lM24;
            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);
            result.Row2.W = (lM31 * rM14) + (lM32 * rM24) + (lM33 * rM34) + lM34;

            /*result.Row0 = (right.Row0 * lM11 + right.Row1 * lM12 + right.Row2 * lM13);
            result.Row0.W += lM14;

            result.Row1 = (right.Row0 * lM21 + right.Row1 * lM22 + right.Row2 * lM23);
            result.Row1.W += lM24;

            result.Row2 = (right.Row0 * lM31 + right.Row1 * lM32 + right.Row2 * lM33);
            result.Row2.W += lM34;*/
        }

        public static Matrix3x4d Mult(Matrix3x4d left, double right)
        {
            Matrix3x4d result;
            Mult(ref left, right, out result);
            return result;
        }

        public static void Mult(ref Matrix3x4d left, double right, out Matrix3x4d result)
        {
            result.Row0 = left.Row0 * right;
            result.Row1 = left.Row1 * right;
            result.Row2 = left.Row2 * right;
        }

        #endregion

        #region Add Functions

        public static Matrix3x4d Add(Matrix3x4d left, Matrix3x4d right)
        {
            Matrix3x4d result;
            Add(ref left, ref right, out result);
            return result;
        }

        public static void Add(ref Matrix3x4d left, ref Matrix3x4d right, out Matrix3x4d result)
        {
            result.Row0 = left.Row0 + right.Row0;
            result.Row1 = left.Row1 + right.Row1;
            result.Row2 = left.Row2 + right.Row2;
        }

        #endregion

        #region Subtract Functions

        public static Matrix3x4d Subtract(Matrix3x4d left, Matrix3x4d right)
        {
            Matrix3x4d result;
            Subtract(ref left, ref right, out result);
            return result;
        }

        public static void Subtract(ref Matrix3x4d left, ref Matrix3x4d right, out Matrix3x4d result)
        {
            result.Row0 = left.Row0 - right.Row0;
            result.Row1 = left.Row1 - right.Row1;
            result.Row2 = left.Row2 - right.Row2;
        }

        #endregion

        #region Invert Functions

        public static Matrix3x4d Invert(Matrix3x4d mat)
        {
            Matrix3x4d result;
            Invert(ref mat, out result);
            return result;
        }

        public static void Invert(ref Matrix3x4d mat, out Matrix3x4d result)
        {
            Matrix3d inverseRotation = new Matrix3d(mat.Column0, mat.Column1, mat.Column2);
            inverseRotation.Row0 /= inverseRotation.Row0.LengthSquared;
            inverseRotation.Row1 /= inverseRotation.Row1.LengthSquared;
            inverseRotation.Row2 /= inverseRotation.Row2.LengthSquared;

            Vector3d translation = new Vector3d(mat.Row0.W, mat.Row1.W, mat.Row2.W);

            result.Row0 = new Vector4d(inverseRotation.Row0, -Vector3d.Dot(inverseRotation.Row0, translation));
            result.Row1 = new Vector4d(inverseRotation.Row1, -Vector3d.Dot(inverseRotation.Row1, translation));
            result.Row2 = new Vector4d(inverseRotation.Row2, -Vector3d.Dot(inverseRotation.Row2, translation));
        }

        #endregion

        #region Transpose

        public static Matrix4x3d Transpose(Matrix3x4d mat)
        {
            return new Matrix4x3d(mat.Column0, mat.Column1, mat.Column2, mat.Column3);
        }

        public static void Transpose(ref Matrix3x4d mat, out Matrix4x3d result)
        {
            result.Row0 = mat.Column0;
            result.Row1 = mat.Column1;
            result.Row2 = mat.Column2;
            result.Row3 = mat.Column3;
        }

        #endregion

        #endregion

        #region Operators

        public static Matrix3d operator *(Matrix3x4d left, Matrix4x3d right)
        {
            return Matrix3x4d.Mult(left, right);
        }

        public static Matrix3x4d operator *(Matrix3x4d left, Matrix3x4d right)
        {
            return Matrix3x4d.Mult(left, right);
        }

        public static Matrix3x4d operator *(Matrix3x4d left, double right)
        {
            return Matrix3x4d.Mult(left, right);
        }

        public static Matrix3x4d operator +(Matrix3x4d left, Matrix3x4d right)
        {
            return Matrix3x4d.Add(left, right);
        }

        public static Matrix3x4d operator -(Matrix3x4d left, Matrix3x4d right)
        {
            return Matrix3x4d.Subtract(left, right);
        }

        public static bool operator ==(Matrix3x4d left, Matrix3x4d right)
        {
            return left.Equals(right);
        }

        public static bool operator !=(Matrix3x4d left, Matrix3x4d 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}", Row0, Row1, Row2);
        }

        #endregion

        #region public override int GetHashCode()

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

        #endregion

        #region public override bool Equals(object obj)

        public override bool Equals(object obj)
        {
            if (!(obj is Matrix3x4d))
                return false;

            return this.Equals((Matrix3x4d)obj);
        }

        #endregion

        #endregion

        #endregion

        #region IEquatable<Matrix3x4d> 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(Matrix3x4d other)
        {
            return
                Row0 == other.Row0 &&
                Row1 == other.Row1 &&
                Row2 == other.Row2;
        }

        #endregion
    }
}