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#region --- License ---

/*

Copyright (c) 2006 - 2008 The Open Toolkit library.

Permission is hereby granted, free of charge, to any person obtaining a copy of

this software and associated documentation files (the "Software"), to deal in

the Software without restriction, including without limitation the rights to

use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies

of the Software, and to permit persons to whom the Software is furnished to do

so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all

copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR

IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,

FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE

AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER

LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,

OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE

SOFTWARE.

 */

#endregion

using System;

using System.Runtime.InteropServices;

namespace OpenTK

{

    /// <summary>

    /// Represents a 4x4 Matrix with double-precision components.

    /// </summary>

    [Serializable]

    [StructLayout(LayoutKind.Sequential)]

    public struct Matrix4d : IEquatable<Matrix4d>

    {

        #region Fields

        /// <summary>

        /// Top row of the matrix

        /// </summary>

        public Vector4d  Row0;

        /// <summary>

        /// 2nd row of the matrix

        /// </summary>

        public Vector4d  Row1;

        /// <summary>

        /// 3rd row of the matrix

        /// </summary>

        public Vector4d  Row2;

        /// <summary>

        /// Bottom row of the matrix

        /// </summary>

        public Vector4d  Row3;

        /// <summary>

        /// The identity matrix

        /// </summary>

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

        #endregion

        #region Constructors

        /// <summary>

        /// Constructs a new instance.

        /// </summary>

        /// <param name="row0">Top row of the matrix</param>

        /// <param name="row1">Second row of the matrix</param>

        /// <param name="row2">Third row of the matrix</param>

        /// <param name="row3">Bottom row of the matrix</param>

        public Matrix4d(Vector4d row0, Vector4d row1, Vector4d row2, Vector4d row3)

        {

            Row0 = row0;

            Row1 = row1;

            Row2 = row2;

            Row3 = row3;

        }

        /// <summary>

        /// Constructs a new instance.

        /// </summary>

        /// <param name="m00">First item of the first row.</param>

        /// <param name="m01">Second item of the first row.</param>

        /// <param name="m02">Third item of the first row.</param>

        /// <param name="m03">Fourth item of the first row.</param>

        /// <param name="m10">First item of the second row.</param>

        /// <param name="m11">Second item of the second row.</param>

        /// <param name="m12">Third item of the second row.</param>

        /// <param name="m13">Fourth item of the second row.</param>

        /// <param name="m20">First item of the third row.</param>

        /// <param name="m21">Second item of the third row.</param>

        /// <param name="m22">Third item of the third row.</param>

        /// <param name="m23">First item of the third row.</param>

        /// <param name="m30">Fourth item of the fourth row.</param>

        /// <param name="m31">Second item of the fourth row.</param>

        /// <param name="m32">Third item of the fourth row.</param>

        /// <param name="m33">Fourth item of the fourth row.</param>

        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

        /// <summary>

        /// The determinant of this matrix

        /// </summary>

        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;

            }

        }

        /// <summary>

        /// The first column of this matrix

        /// </summary>

        public Vector4d  Column0

        {

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

        }

        /// <summary>

        /// The second column of this matrix

        /// </summary>

        public Vector4d  Column1

        {

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

        }

        /// <summary>

        /// The third column of this matrix

        /// </summary>

        public Vector4d  Column2

        {

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

        }

        /// <summary>

        /// The fourth column of this matrix

        /// </summary>

        public Vector4d  Column3

        {

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

        /// <summary>

        /// Gets or sets the value at row 4, column 1 of this instance.

        /// </summary>

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

        /// <summary>

        /// Gets or sets the value at row 4, column 2 of this instance.

        /// </summary>

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

        /// <summary>

        /// Gets or sets the value at row 4, column 3 of this instance.

        /// </summary>

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

        /// <summary>

        /// Gets or sets the value at row 4, column 4 of this instance.

        /// </summary>

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

        #endregion

        #region Instance

        #region public void Invert()

        /// <summary>

        /// Converts this instance into its inverse.

        /// </summary>

        public void Invert()

        {

            this = Matrix4d.Invert(this);

        }

        #endregion

        #region public void Transpose()

        /// <summary>

        /// Converts this instance into its transpose.

        /// </summary>

        public void Transpose()

        {

            this = Matrix4d.Transpose(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 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);

        }

        /// <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 Matrix4d CreateFromAxisAngle(Vector3d axis, double angle)

        {

            Matrix4d result;

            CreateFromAxisAngle(axis, angle, 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 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;

        }

        /// <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 Matrix4d CreateRotationX(double angle)

        {

            Matrix4d 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 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;

        }

        /// <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 Matrix4d CreateRotationY(double angle)

        {

            Matrix4d 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 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;

        }

        /// <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 Matrix4d CreateRotationZ(double angle)

        {

            Matrix4d 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 Matrix4d instance.</param>

        public static void CreateTranslation(double x, double y, double z, out Matrix4d result)

        {

            result = Identity;

            result.Row3 = new Vector4d(x, y, z, 1);

        }

        /// <summary>

        /// Creates a translation matrix.

        /// </summary>

        /// <param name="vector">The translation vector.</param>

        /// <param name="result">The resulting Matrix4d instance.</param>

        public static void CreateTranslation(ref Vector3d vector, out Matrix4d result)

        {

            result = Identity;

            result.Row3 = new Vector4d(vector.X, vector.Y, vector.Z, 1);

        }

        /// <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 Matrix4d instance.</returns>

        public static Matrix4d CreateTranslation(double x, double y, double z)

        {

            Matrix4d 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 Matrix4d instance.</returns>

        public static Matrix4d CreateTranslation(Vector3d vector)

        {

            Matrix4d result;

            CreateTranslation(vector.X, vector.Y, vector.Z, out result);

            return result;

        }

        #endregion

        #region CreateOrthographic

        /// <summary>

        /// Creates an orthographic projection matrix.

        /// </summary>

        /// <param name="width">The width of the projection volume.</param>

        /// <param name="height">The height of the projection volume.</param>

        /// <param name="zNear">The near edge of the projection volume.</param>

        /// <param name="zFar">The far edge of the projection volume.</param>

        /// <param name="result">The resulting Matrix4d instance.</param>

        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);

        }

        /// <summary>

        /// Creates an orthographic projection matrix.

        /// </summary>

        /// <param name="width">The width of the projection volume.</param>

        /// <param name="height">The height of the projection volume.</param>

        /// <param name="zNear">The near edge of the projection volume.</param>

        /// <param name="zFar">The far edge of the projection volume.</param>

        /// <rereturns>The resulting Matrix4d instance.</rereturns>

        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

        /// <summary>

        /// Creates an orthographic projection matrix.

        /// </summary>

        /// <param name="left">The left edge of the projection volume.</param>

        /// <param name="right">The right edge of the projection volume.</param>

        /// <param name="bottom">The bottom edge of the projection volume.</param>

        /// <param name="top">The top edge of the projection volume.</param>

        /// <param name="zNear">The near edge of the projection volume.</param>

        /// <param name="zFar">The far edge of the projection volume.</param>

        /// <param name="result">The resulting Matrix4d instance.</param>

        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;

        }

        /// <summary>

        /// Creates an orthographic projection matrix.

        /// </summary>

        /// <param name="left">The left edge of the projection volume.</param>

        /// <param name="right">The right edge of the projection volume.</param>

        /// <param name="bottom">The bottom edge of the projection volume.</param>

        /// <param name="top">The top edge of the projection volume.</param>

        /// <param name="zNear">The near edge of the projection volume.</param>

        /// <param name="zFar">The far edge of the projection volume.</param>

        /// <returns>The resulting Matrix4d instance.</returns>

        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

        /// <summary>

        /// Creates a perspective projection matrix.

        /// </summary>

        /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>

        /// <param name="aspect">Aspect ratio of the view (width / height)</param>

        /// <param name="zNear">Distance to the near clip plane</param>

        /// <param name="zFar">Distance to the far clip plane</param>

        /// <param name="result">A projection matrix that transforms camera space to raster space</param>

        /// <exception cref="System.ArgumentOutOfRangeException">

        /// Thrown under the following conditions:

        /// <list type="bullet">

        /// <item>fovy is zero, less than zero or larger than Math.PI</item>

        /// <item>aspect is negative or zero</item>

        /// <item>zNear is negative or zero</item>

        /// <item>zFar is negative or zero</item>

        /// <item>zNear is larger than zFar</item>

        /// </list>

        /// </exception>

        public static void CreatePerspectiveFieldOfView(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);

        }

        /// <summary>

        /// Creates a perspective projection matrix.

        /// </summary>

        /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>

        /// <param name="aspect">Aspect ratio of the view (width / height)</param>

        /// <param name="zNear">Distance to the near clip plane</param>

        /// <param name="zFar">Distance to the far clip plane</param>

        /// <returns>A projection matrix that transforms camera space to raster space</returns>

        /// <exception cref="System.ArgumentOutOfRangeException">

        /// Thrown under the following conditions:

        /// <list type="bullet">

        /// <item>fovy is zero, less than zero or larger than Math.PI</item>

        /// <item>aspect is negative or zero</item>

        /// <item>zNear is negative or zero</item>

        /// <item>zFar is negative or zero</item>

        /// <item>zNear is larger than zFar</item>

        /// </list>

        /// </exception>

        public static Matrix4d CreatePerspectiveFieldOfView(double fovy, double aspect, double zNear, double zFar)

        {

            Matrix4d result;

            CreatePerspectiveFieldOfView(fovy, aspect, zNear, zFar, out result);

            return result;

        }

        #endregion

        #region CreatePerspectiveOffCenter

        /// <summary>

        /// Creates an perspective projection matrix.

        /// </summary>

        /// <param name="left">Left edge of the view frustum</param>

        /// <param name="right">Right edge of the view frustum</param>

        /// <param name="bottom">Bottom edge of the view frustum</param>

        /// <param name="top">Top edge of the view frustum</param>

        /// <param name="zNear">Distance to the near clip plane</param>

        /// <param name="zFar">Distance to the far clip plane</param>

        /// <param name="result">A projection matrix that transforms camera space to raster space</param>

        /// <exception cref="System.ArgumentOutOfRangeException">

        /// Thrown under the following conditions:

        /// <list type="bullet">

        /// <item>zNear is negative or zero</item>

        /// <item>zFar is negative or zero</item>

        /// <item>zNear is larger than zFar</item>

        /// </list>

        /// </exception>

        public static void CreatePerspectiveOffCenter(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);

        }

        /// <summary>

        /// Creates an perspective projection matrix.

        /// </summary>

        /// <param name="left">Left edge of the view frustum</param>

        /// <param name="right">Right edge of the view frustum</param>

        /// <param name="bottom">Bottom edge of the view frustum</param>

        /// <param name="top">Top edge of the view frustum</param>

        /// <param name="zNear">Distance to the near clip plane</param>

        /// <param name="zFar">Distance to the far clip plane</param>

        /// <returns>A projection matrix that transforms camera space to raster space</returns>

        /// <exception cref="System.ArgumentOutOfRangeException">

        /// Thrown under the following conditions:

        /// <list type="bullet">

        /// <item>zNear is negative or zero</item>

        /// <item>zFar is negative or zero</item>

        /// <item>zNear is larger than zFar</item>

        /// </list>

        /// </exception>

        public static 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

        /// <summary>

        /// Build a translation matrix with the given translation

        /// </summary>

        /// <param name="trans">The vector to translate along</param>

        /// <returns>A Translation matrix</returns>

        [Obsolete("Use CreateTranslation instead.")]

        public static Matrix4d Translation(Vector3d trans)

        {

            return Translation(trans.X, trans.Y, trans.Z);

        }

        /// <summary>

        /// Build a translation matrix with the given translation

        /// </summary>

        /// <param name="x">X translation</param>

        /// <param name="y">Y translation</param>

        /// <param name="z">Z translation</param>

        /// <returns>A Translation matrix</returns>

        [Obsolete("Use CreateTranslation instead.")]

        public static 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

        /// <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 Matrix4d Scale(double scale)

        {

            return Scale(scale, scale, scale);

        }

        /// <summary>

        /// Build a scaling matrix

        /// </summary>

        /// <param name="scale">Scale factors for x,y and z axes</param>

        /// <returns>A scaling matrix</returns>

        public static Matrix4d Scale(Vector3d scale)

        {

            return Scale(scale.X, scale.Y, scale.Z);

        }

        /// <summary>

        /// Build a scaling matrix

        /// </summary>

        /// <param name="x">Scale factor for x-axis</param>

        /// <param name="y">Scale factor for y-axis</param>

        /// <param name="z">Scale factor for z-axis</param>

        /// <returns>A scaling matrix</returns>

        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

        /// <summary>

        /// Build a rotation matrix that rotates about the x-axis

        /// </summary>

        /// <param name="angle">angle in radians to rotate counter-clockwise around the x-axis</param>

        /// <returns>A rotation matrix</returns>

        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;

        }

        /// <summary>

        /// Build a rotation matrix that rotates about the y-axis

        /// </summary>

        /// <param name="angle">angle in radians to rotate counter-clockwise around the y-axis</param>

        /// <returns>A rotation matrix</returns>

        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;

        }

        /// <summary>

        /// Build a rotation matrix that rotates about the z-axis

        /// </summary>

        /// <param name="angle">angle in radians to rotate counter-clockwise around the z-axis</param>

        /// <returns>A rotation matrix</returns>

        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);