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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

    /// </summary>

    [Serializable]

    [StructLayout(LayoutKind.Sequential)]

    public struct Matrix4 : IEquatable<Matrix4>

    {

        #region Fields

        /// <summary>

        /// Top row of the matrix

        /// </summary>

        public Vector4 Row0;

        /// <summary>

        /// 2nd row of the matrix

        /// </summary>

        public Vector4 Row1;

        /// <summary>

        /// 3rd row of the matrix

        /// </summary>

        public Vector4 Row2;

        /// <summary>

        /// Bottom row of the matrix

        /// </summary>

        public Vector4 Row3;

        /// <summary>

        /// The identity matrix

        /// </summary>

        public static Matrix4 Identity = new Matrix4(Vector4.UnitX, Vector4.UnitY, Vector4.UnitZ, Vector4.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 Matrix4(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 row3)

        {

            Row0 = row0;

            Row1 = row1;

            Row2 = row2;

            Row3 = row3;

        }

        /// <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>

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

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

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

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

        public Matrix4(

            float m00, float m01, float m02, float m03,

            float m10, float m11, float m12, float m13,

            float m20, float m21, float m22, float m23,

            float m30, float m31, float m32, float m33)

        {

            Row0 = new Vector4(m00, m01, m02, m03);

            Row1 = new Vector4(m10, m11, m12, m13);

            Row2 = new Vector4(m20, m21, m22, m23);

            Row3 = new Vector4(m30, m31, m32, m33);

        }

        #endregion

        #region Public Members

        #region Properties

        /// <summary>

        /// The determinant of this matrix

        /// </summary>

        public float Determinant

        {

            get

            {

                return

                    Row0.X * Row1.Y * Row2.Z * Row3.W - Row0.X * Row1.Y * Row2.W * Row3.Z + Row0.X * Row1.Z * Row2.W * Row3.Y - Row0.X * Row1.Z * Row2.Y * Row3.W

                  + Row0.X * Row1.W * Row2.Y * Row3.Z - Row0.X * Row1.W * Row2.Z * Row3.Y - Row0.Y * Row1.Z * Row2.W * Row3.X + Row0.Y * Row1.Z * Row2.X * Row3.W

                  - Row0.Y * Row1.W * Row2.X * Row3.Z + Row0.Y * Row1.W * Row2.Z * Row3.X - Row0.Y * Row1.X * Row2.Z * Row3.W + Row0.Y * Row1.X * Row2.W * Row3.Z

                  + Row0.Z * Row1.W * Row2.X * Row3.Y - Row0.Z * Row1.W * Row2.Y * Row3.X + Row0.Z * Row1.X * Row2.Y * Row3.W - Row0.Z * Row1.X * Row2.W * Row3.Y

                  + Row0.Z * Row1.Y * Row2.W * Row3.X - Row0.Z * Row1.Y * Row2.X * Row3.W - Row0.W * Row1.X * Row2.Y * Row3.Z + Row0.W * Row1.X * Row2.Z * Row3.Y

                  - Row0.W * Row1.Y * Row2.Z * Row3.X + Row0.W * Row1.Y * Row2.X * Row3.Z - Row0.W * Row1.Z * Row2.X * Row3.Y + Row0.W * Row1.Z * Row2.Y * Row3.X;

            }

        }

        /// <summary>

        /// The first column of this matrix

        /// </summary>

        public Vector4 Column0

        {

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

        }

        /// <summary>

        /// The second column of this matrix

        /// </summary>

        public Vector4 Column1

        {

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

        }

        /// <summary>

        /// The third column of this matrix

        /// </summary>

        public Vector4 Column2

        {

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

        }

        /// <summary>

        /// The fourth column of this matrix

        /// </summary>

        public Vector4 Column3

        {

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

        }

        /// <summary>

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

        /// </summary>

        public float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 float 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 = Matrix4.Invert(this);

        }

        #endregion

        #region public void Transpose()

        /// <summary>

        /// Converts this instance into its transpose.

        /// </summary>

        public void Transpose()

        {

            this = Matrix4.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(Vector3 axis, float angle, out Matrix4 result)

        {

            float cos = (float)System.Math.Cos(-angle);

            float sin = (float)System.Math.Sin(-angle);

            float t = 1.0f - cos;

            axis.Normalize();

            result = new Matrix4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f,

                                 t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f,

                                 t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f,

                                 0, 0, 0, 1);

        }

        /// <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 Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)

        {

            Matrix4 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(float angle, out Matrix4 result)

        {

            float cos = (float)System.Math.Cos(angle);

            float sin = (float)System.Math.Sin(angle);

            result.Row0 = Vector4.UnitX;

            result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);

            result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);

            result.Row3 = Vector4.UnitW;

        }

        /// <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 Matrix4 CreateRotationX(float angle)

        {

            Matrix4 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(float angle, out Matrix4 result)

        {

            float cos = (float)System.Math.Cos(angle);

            float sin = (float)System.Math.Sin(angle);

            result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);

            result.Row1 = Vector4.UnitY;

            result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);

            result.Row3 = Vector4.UnitW;

        }

        /// <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 Matrix4 CreateRotationY(float angle)

        {

            Matrix4 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(float angle, out Matrix4 result)

        {

            float cos = (float)System.Math.Cos(angle);

            float sin = (float)System.Math.Sin(angle);

            result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);

            result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);

            result.Row2 = Vector4.UnitZ;

            result.Row3 = Vector4.UnitW;

        }

        /// <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 Matrix4 CreateRotationZ(float angle)

        {

            Matrix4 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(float x, float y, float z, out Matrix4 result)

        {

            result = Identity;

            result.Row3 = new Vector4(x, y, z, 1);

        }

        /// <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 Vector3 vector, out Matrix4 result)

        {

            result = Identity;

            result.Row3 = new Vector4(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 Matrix4 instance.</returns>

        public static Matrix4 CreateTranslation(float x, float y, float z)

        {

            Matrix4 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 Matrix4 CreateTranslation(Vector3 vector)

        {

            Matrix4 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 Matrix4 instance.</param>

        public static void CreateOrthographic(float width, float height, float zNear, float zFar, out Matrix4 result)

        {

            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);

        }

        /// <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 Matrix4 instance.</rereturns>

        public static Matrix4 CreateOrthographic(float width, float height, float zNear, float zFar)

        {

            Matrix4 result;

            CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);

            return result;

        }

        #endregion

        #region CreateOrthographicOffCenter

        /// <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 Matrix4 instance.</param>

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

        {

            result = new Matrix4();

            float invRL = 1 / (right - left);

            float invTB = 1 / (top - bottom);

            float invFN = 1 / (zFar - zNear);

            result.M11 = 2 * invRL;

            result.M22 = 2 * invTB;

            result.M33 = -2 * invFN;

            result.M41 = -(right + left) * invRL;

            result.M42 = -(top + bottom) * invTB;

            result.M43 = -(zFar + zNear) * invFN;

            result.M44 = 1;

        }

        /// <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 Matrix4 instance.</returns>

        public static Matrix4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)

        {

            Matrix4 result;

            CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);

            return result;

        }

        #endregion

        #region CreatePerspectiveFieldOfView

        /// <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(float fovy, float aspect, float zNear, float zFar, out Matrix4 result)

        {

            if (fovy <= 0 || fovy > Math.PI)

                throw new ArgumentOutOfRangeException("fovy");

            if (aspect <= 0)

                throw new ArgumentOutOfRangeException("aspect");

            if (zNear <= 0)

                throw new ArgumentOutOfRangeException("zNear");

            if (zFar <= 0)

                throw new ArgumentOutOfRangeException("zFar");

            if (zNear >= zFar)

                throw new ArgumentOutOfRangeException("zNear");

            float yMax = zNear * (float)System.Math.Tan(0.5f * fovy);

            float yMin = -yMax;

            float xMin = yMin * aspect;

            float xMax = yMax * aspect;

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

        }

        /// <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 Matrix4 CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar)

        {

            Matrix4 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(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)

        {

            if (zNear <= 0)

                throw new ArgumentOutOfRangeException("zNear");

            if (zFar <= 0)

                throw new ArgumentOutOfRangeException("zFar");

            if (zNear >= zFar)

                throw new ArgumentOutOfRangeException("zNear");

            float x = (2.0f * zNear) / (right - left);

            float y = (2.0f * zNear) / (top - bottom);

            float a = (right + left) / (right - left);

            float b = (top + bottom) / (top - bottom);

            float c = -(zFar + zNear) / (zFar - zNear);

            float d = -(2.0f * zFar * zNear) / (zFar - zNear);

            result = new Matrix4(x, 0, 0,  0,

                                 0, y, 0,  0,

                                 a, b, c, -1,

                                 0, 0, d,  0);

        }

        /// <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 Matrix4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)

        {

            Matrix4 result;

            CreatePerspectiveOffCenter(left, right, bottom, top, zNear, zFar, out result);

            return result;

        }

        #endregion

        #region Obsolete Functions

        #region Translation Functions

        /// <summary>

        /// Builds a translation matrix.

        /// </summary>

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

        /// <returns>A new Matrix4 instance.</returns>

        [Obsolete("Use CreateTranslation instead.")]

        public static Matrix4 Translation(Vector3 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 Matrix4 Translation(float x, float y, float z)

        {

            Matrix4 result = Identity;

            result.Row3 = new Vector4(x, y, z, 1.0f);

            return result;

        }

        #endregion

        #endregion

        #region Scale Functions

        /// <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 Matrix4 Scale(float 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 Matrix4 Scale(Vector3 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 Matrix4 Scale(float x, float y, float z)

        {

            Matrix4 result;

            result.Row0 = Vector4.UnitX * x;

            result.Row1 = Vector4.UnitY * y;

            result.Row2 = Vector4.UnitZ * z;

            result.Row3 = Vector4.UnitW;

            return result;

        }

        #endregion

        #region Rotation Functions

        /// <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>

        [Obsolete("Use CreateRotationX instead.")]

        public static Matrix4 RotateX(float angle)

        {

            float cos = (float)System.Math.Cos(angle);

            float sin = (float)System.Math.Sin(angle);

            Matrix4 result;

            result.Row0 = Vector4.UnitX;

            result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);

            result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);

            result.Row3 = Vector4.UnitW;

            return result;

        }

        /// <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>

        [Obsolete("Use CreateRotationY instead.")]

        public static Matrix4 RotateY(float angle)

        {

            float cos = (float)System.Math.Cos(angle);

            float sin = (float)System.Math.Sin(angle);

            Matrix4 result;

            result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);

            result.Row1 = Vector4.UnitY;

            result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);

            result.Row3 = Vector4.UnitW;

            return result;

        }

        /// <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>

        [Obsolete("Use CreateRotationZ instead.")]

        public static Matrix4 RotateZ(float angle)