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968 lines
38 KiB
C#
968 lines
38 KiB
C#
#region --- License ---
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/*
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Copyright (c) 2006 - 2008 The Open Toolkit library.
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Permission is hereby granted, free of charge, to any person obtaining a copy of
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this software and associated documentation files (the "Software"), to deal in
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the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do
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so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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*/
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#endregion
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using System;
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using System.Runtime.InteropServices;
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namespace OpenTK
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{
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/// <summary>
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/// Represents a 4x4 Matrix with double-precision components.
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Matrix4d : IEquatable<Matrix4d>
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{
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#region Fields
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/// <summary>
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/// Top row of the matrix
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/// </summary>
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public Vector4d Row0;
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/// <summary>
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/// 2nd row of the matrix
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/// </summary>
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public Vector4d Row1;
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/// <summary>
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/// 3rd row of the matrix
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/// </summary>
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public Vector4d Row2;
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/// <summary>
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/// Bottom row of the matrix
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/// </summary>
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public Vector4d Row3;
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/// <summary>
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/// The identity matrix
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/// </summary>
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public static Matrix4d Identity = new Matrix4d(Vector4d .UnitX, Vector4d .UnitY, Vector4d .UnitZ, Vector4d .UnitW);
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#endregion
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#region Constructors
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/// <summary>
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/// Constructs a new instance.
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/// </summary>
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/// <param name="row0">Top row of the matrix</param>
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/// <param name="row1">Second row of the matrix</param>
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/// <param name="row2">Third row of the matrix</param>
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/// <param name="row3">Bottom row of the matrix</param>
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public Matrix4d(Vector4d row0, Vector4d row1, Vector4d row2, Vector4d row3)
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{
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Row0 = row0;
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Row1 = row1;
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Row2 = row2;
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Row3 = row3;
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}
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/// <summary>
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/// Constructs a new instance.
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/// </summary>
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/// <param name="m00">First item of the first row.</param>
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/// <param name="m01">Second item of the first row.</param>
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/// <param name="m02">Third item of the first row.</param>
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/// <param name="m03">Fourth item of the first row.</param>
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/// <param name="m10">First item of the second row.</param>
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/// <param name="m11">Second item of the second row.</param>
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/// <param name="m12">Third item of the second row.</param>
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/// <param name="m13">Fourth item of the second row.</param>
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/// <param name="m20">First item of the third row.</param>
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/// <param name="m21">Second item of the third row.</param>
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/// <param name="m22">Third item of the third row.</param>
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/// <param name="m23">First item of the third row.</param>
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/// <param name="m30">Fourth item of the fourth row.</param>
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/// <param name="m31">Second item of the fourth row.</param>
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/// <param name="m32">Third item of the fourth row.</param>
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/// <param name="m33">Fourth item of the fourth row.</param>
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public Matrix4d(
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float m00, float m01, float m02, float m03,
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float m10, float m11, float m12, float m13,
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float m20, float m21, float m22, float m23,
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float m30, float m31, float m32, float m33)
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{
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Row0 = new Vector4d(m00, m01, m02, m03);
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Row1 = new Vector4d(m10, m11, m12, m13);
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Row2 = new Vector4d(m20, m21, m22, m23);
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Row3 = new Vector4d(m30, m31, m32, m33);
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}
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#endregion
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#region Public Members
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#region Properties
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/// <summary>
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/// The determinant of this matrix
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/// </summary>
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public double Determinant
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{
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get
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{
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return
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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
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+ 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
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- 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
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+ 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
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+ 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
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- 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;
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}
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}
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/// <summary>
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/// The first column of this matrix
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/// </summary>
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public Vector4d Column0
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{
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get { return new Vector4d (Row0.X, Row1.X, Row2.X, Row3.X); }
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}
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/// <summary>
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/// The second column of this matrix
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/// </summary>
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public Vector4d Column1
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{
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get { return new Vector4d (Row0.Y, Row1.Y, Row2.Y, Row3.Y); }
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}
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/// <summary>
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/// The third column of this matrix
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/// </summary>
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public Vector4d Column2
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{
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get { return new Vector4d (Row0.Z, Row1.Z, Row2.Z, Row3.Z); }
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}
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/// <summary>
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/// The fourth column of this matrix
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/// </summary>
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public Vector4d Column3
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{
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get { return new Vector4d (Row0.W, Row1.W, Row2.W, Row3.W); }
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}
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public double this[int i, int j]
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{
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get
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{
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if (i < 0 || i > 3)
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throw new ArgumentOutOfRangeException("i");
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if (j < 0 || j > 3)
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throw new ArgumentOutOfRangeException("j");
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unsafe
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{
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fixed (Matrix4d* ptr = &this)
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return *((double*)ptr + i + j * 4);
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}
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}
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set
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{
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if (i < 0 || i > 3)
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throw new ArgumentOutOfRangeException("i");
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if (j < 0 || j > 3)
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throw new ArgumentOutOfRangeException("j");
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unsafe
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{
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fixed (Matrix4d* ptr = &this)
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*((double*)ptr + i + j * 4) = value;
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}
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}
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}
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/// <summary>
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/// Gets or sets the value at row 1, column 1 of this instance.
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/// </summary>
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public double M11 { get { return Row0.X; } set { Row0.X = value; } }
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/// <summary>
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/// Gets or sets the value at row 1, column 2 of this instance.
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/// </summary>
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public double M12 { get { return Row0.Y; } set { Row0.Y = value; } }
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/// <summary>
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/// Gets or sets the value at row 1, column 3 of this instance.
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/// </summary>
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public double M13 { get { return Row0.Z; } set { Row0.Z = value; } }
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/// <summary>
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/// Gets or sets the value at row 1, column 4 of this instance.
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/// </summary>
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public double M14 { get { return Row0.W; } set { Row0.W = value; } }
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/// <summary>
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/// Gets or sets the value at row 2, column 1 of this instance.
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/// </summary>
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public double M21 { get { return Row1.X; } set { Row1.X = value; } }
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/// <summary>
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/// Gets or sets the value at row 2, column 2 of this instance.
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/// </summary>
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public double M22 { get { return Row1.Y; } set { Row1.Y = value; } }
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/// <summary>
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/// Gets or sets the value at row 2, column 3 of this instance.
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/// </summary>
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public double M23 { get { return Row1.Z; } set { Row1.Z = value; } }
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/// <summary>
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/// Gets or sets the value at row 2, column 4 of this instance.
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/// </summary>
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public double M24 { get { return Row1.W; } set { Row1.W = value; } }
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/// <summary>
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/// Gets or sets the value at row 3, column 1 of this instance.
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/// </summary>
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public double M31 { get { return Row2.X; } set { Row2.X = value; } }
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/// <summary>
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/// Gets or sets the value at row 3, column 2 of this instance.
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/// </summary>
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public double M32 { get { return Row2.Y; } set { Row2.Y = value; } }
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/// <summary>
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/// Gets or sets the value at row 3, column 3 of this instance.
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/// </summary>
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public double M33 { get { return Row2.Z; } set { Row2.Z = value; } }
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/// <summary>
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/// Gets or sets the value at row 3, column 4 of this instance.
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/// </summary>
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public double M34 { get { return Row2.W; } set { Row2.W = value; } }
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/// <summary>
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/// Gets or sets the value at row 4, column 1 of this instance.
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/// </summary>
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public double M41 { get { return Row3.X; } set { Row3.X = value; } }
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/// <summary>
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/// Gets or sets the value at row 4, column 3 of this instance.
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/// </summary>
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public double M42 { get { return Row3.Y; } set { Row3.Y = value; } }
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/// <summary>
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/// Gets or sets the value at row 4, column 3 of this instance.
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/// </summary>
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public double M43 { get { return Row3.Z; } set { Row3.Z = value; } }
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/// <summary>
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/// Gets or sets the value at row 4, column 4 of this instance.
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/// </summary>
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public double M44 { get { return Row3.W; } set { Row3.W = value; } }
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#endregion
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#region Instance
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#region public void Invert()
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public void Invert()
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{
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this = Matrix4d.Invert(this);
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}
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#endregion
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#region public void Transpose()
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public void Transpose()
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{
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this = Matrix4d.Transpose(this);
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}
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#endregion
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#endregion
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#region Static
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#region CreateTranslation
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/// <summary>
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/// Creates a translation matrix.
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/// </summary>
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/// <param name="x">X translation.</param>
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/// <param name="y">Y translation.</param>
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/// <param name="z">Z translation.</param>
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/// <param name="result">The resulting Matrix4d instance.</param>
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public static void CreateTranslation(double x, double y, double z, out Matrix4d result)
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{
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result = Identity;
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result.Row3 = new Vector4d(x, y, z, 1);
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}
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/// <summary>
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/// Creates a translation matrix.
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/// </summary>
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/// <param name="vector">The translation vector.</param>
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/// <param name="result">The resulting Matrix4d instance.</param>
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public static void CreateTranslation(ref Vector3d vector, out Matrix4d result)
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{
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result = Identity;
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result.Row3 = new Vector4d(vector.X, vector.Y, vector.Z, 1);
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}
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/// <summary>
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/// Creates a translation matrix.
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/// </summary>
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/// <param name="x">X translation.</param>
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/// <param name="y">Y translation.</param>
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/// <param name="z">Z translation.</param>
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/// <returns>The resulting Matrix4d instance.</returns>
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public static Matrix4d CreateTranslation(double x, double y, double z)
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{
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Matrix4d result;
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CreateTranslation(x, y, z, out result);
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return result;
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}
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/// <summary>
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/// Creates a translation matrix.
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/// </summary>
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/// <param name="vector">The translation vector.</param>
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/// <returns>The resulting Matrix4d instance.</returns>
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public static Matrix4d CreateTranslation(Vector3d vector)
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{
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Matrix4d result;
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CreateTranslation(vector.X, vector.Y, vector.Z, out result);
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return result;
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}
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#endregion
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#region CreateOrthographic
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/// <summary>
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/// Creates an orthographic projection matrix.
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/// </summary>
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/// <param name="width">The width of the projection volume.</param>
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/// <param name="height">The height of the projection volume.</param>
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/// <param name="zNear">The near edge of the projection volume.</param>
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/// <param name="zFar">The far edge of the projection volume.</param>
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/// <param name="result">The resulting Matrix4d instance.</param>
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public static void CreateOrthographic(double width, double height, double zNear, double zFar, out Matrix4d result)
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{
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CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
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}
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/// <summary>
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/// Creates an orthographic projection matrix.
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/// </summary>
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/// <param name="width">The width of the projection volume.</param>
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/// <param name="height">The height of the projection volume.</param>
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/// <param name="zNear">The near edge of the projection volume.</param>
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/// <param name="zFar">The far edge of the projection volume.</param>
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/// <rereturns>The resulting Matrix4d instance.</rereturns>
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public static Matrix4d CreateOrthographic(double width, double height, double zNear, double zFar)
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{
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Matrix4d result;
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CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
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return result;
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}
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#endregion
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#region CreateOrthographicOffCenter
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/// <summary>
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/// Creates an orthographic projection matrix.
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/// </summary>
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/// <param name="left">The left edge of the projection volume.</param>
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/// <param name="right">The right edge of the projection volume.</param>
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/// <param name="bottom">The bottom edge of the projection volume.</param>
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/// <param name="top">The top edge of the projection volume.</param>
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/// <param name="zNear">The near edge of the projection volume.</param>
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/// <param name="zFar">The far edge of the projection volume.</param>
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/// <param name="result">The resulting Matrix4d instance.</param>
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public static void CreateOrthographicOffCenter(double left, double right, double bottom, double top, double zNear, double zFar, out Matrix4d result)
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{
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result = new Matrix4d();
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double invRL = 1 / (right - left);
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double invTB = 1 / (top - bottom);
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double invFN = 1 / (zFar - zNear);
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result.M11 = 2 * invRL;
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result.M22 = 2 * invTB;
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result.M33 = -2 * invFN;
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result.M41 = -(right + left) * invRL;
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result.M42 = -(top + bottom) * invTB;
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result.M43 = -(zFar + zNear) * invFN;
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}
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/// <summary>
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/// Creates an orthographic projection matrix.
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/// </summary>
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/// <param name="left">The left edge of the projection volume.</param>
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/// <param name="right">The right edge of the projection volume.</param>
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/// <param name="bottom">The bottom edge of the projection volume.</param>
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/// <param name="top">The top edge of the projection volume.</param>
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/// <param name="zNear">The near edge of the projection volume.</param>
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/// <param name="zFar">The far edge of the projection volume.</param>
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/// <returns>The resulting Matrix4d instance.</returns>
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public static Matrix4d CreateOrthographicOffCenter(double left, double right, double bottom, double top, double zNear, double zFar)
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{
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Matrix4d result;
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CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);
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return result;
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}
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#endregion
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#region Obsolete Functions
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#region Translation Functions
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/// <summary>
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/// Build a translation matrix with the given translation
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/// </summary>
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/// <param name="trans">The vector to translate along</param>
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/// <returns>A Translation matrix</returns>
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[Obsolete("Use CreateTranslation instead.")]
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public static Matrix4d Translation(Vector3d trans)
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{
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return Translation(trans.X, trans.Y, trans.Z);
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}
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/// <summary>
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/// Build a translation matrix with the given translation
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/// </summary>
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/// <param name="x">X translation</param>
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/// <param name="y">Y translation</param>
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/// <param name="z">Z translation</param>
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/// <returns>A Translation matrix</returns>
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[Obsolete("Use CreateTranslation instead.")]
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public static Matrix4d Translation(double x, double y, double z)
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{
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Matrix4d result = Identity;
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result.Row3 = new Vector4d(x, y, z, 1.0f);
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return result;
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}
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#endregion
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#endregion
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#region Scale Functions
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/// <summary>
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/// Build a scaling matrix
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/// </summary>
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/// <param name="scale">Single scale factor for x,y and z axes</param>
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/// <returns>A scaling matrix</returns>
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public static Matrix4d Scale(double scale)
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{
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return Scale(scale, scale, scale);
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}
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/// <summary>
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/// Build a scaling matrix
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/// </summary>
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/// <param name="scale">Scale factors for x,y and z axes</param>
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/// <returns>A scaling matrix</returns>
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public static Matrix4d Scale(Vector3d scale)
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{
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return Scale(scale.X, scale.Y, scale.Z);
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}
|
|
|
|
/// <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 = (double)System.Math.Cos(angle);
|
|
double sin = (double)System.Math.Sin(angle);
|
|
|
|
Matrix4d result;
|
|
result.Row0 = Vector4d .UnitX;
|
|
result.Row1 = new Vector4d (0.0f, cos, sin, 0.0f);
|
|
result.Row2 = new Vector4d (0.0f, -sin, cos, 0.0f);
|
|
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 = (double)System.Math.Cos(angle);
|
|
double sin = (double)System.Math.Sin(angle);
|
|
|
|
Matrix4d result;
|
|
result.Row0 = new Vector4d (cos, 0.0f, -sin, 0.0f);
|
|
result.Row1 = Vector4d .UnitY;
|
|
result.Row2 = new Vector4d (sin, 0.0f, cos, 0.0f);
|
|
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 = (double)System.Math.Cos(angle);
|
|
double sin = (double)System.Math.Sin(angle);
|
|
|
|
Matrix4d result;
|
|
result.Row0 = new Vector4d (cos, sin, 0.0f, 0.0f);
|
|
result.Row1 = new Vector4d (-sin, cos, 0.0f, 0.0f);
|
|
result.Row2 = Vector4d .UnitZ;
|
|
result.Row3 = Vector4d .UnitW;
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Build a rotation matrix to rotate about the given axis
|
|
/// </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 rotation matrix</returns>
|
|
public static Matrix4d Rotate(Vector3d axis, double angle)
|
|
{
|
|
double cos = (double)System.Math.Cos(-angle);
|
|
double sin = (double)System.Math.Sin(-angle);
|
|
double t = 1.0f - cos;
|
|
|
|
axis.Normalize();
|
|
|
|
Matrix4d result;
|
|
result.Row0 = new Vector4d (t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f);
|
|
result.Row1 = new Vector4d (t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f);
|
|
result.Row2 = new Vector4d (t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f);
|
|
result.Row3 = Vector4d .UnitW;
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Build a rotation matrix from a quaternion
|
|
/// </summary>
|
|
/// <param name="q">the quaternion</param>
|
|
/// <returns>A rotation matrix</returns>
|
|
public static Matrix4d Rotate(Quaterniond q)
|
|
{
|
|
Vector3d axis;
|
|
double angle;
|
|
q.ToAxisAngle(out axis, out angle);
|
|
return Rotate(axis, angle);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Camera Helper Functions
|
|
|
|
/// <summary>
|
|
/// Build a world space to camera space matrix
|
|
/// </summary>
|
|
/// <param name="eye">Eye (camera) position in world space</param>
|
|
/// <param name="target">Target position in world space</param>
|
|
/// <param name="up">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
|
|
/// <returns>A Matrix that transforms world space to camera space</returns>
|
|
public static Matrix4d LookAt(Vector3d eye, Vector3d target, Vector3d up)
|
|
{
|
|
Vector3d z = Vector3d.Normalize(eye - target);
|
|
Vector3d x = Vector3d.Normalize(Vector3d.Cross(up, z));
|
|
Vector3d y = Vector3d.Normalize(Vector3d.Cross(z, x));
|
|
|
|
Matrix4d rot = new Matrix4d(new Vector4d (x.X, y.X, z.X, 0.0f),
|
|
new Vector4d (x.Y, y.Y, z.Y, 0.0f),
|
|
new Vector4d (x.Z, y.Z, z.Z, 0.0f),
|
|
Vector4d .UnitW);
|
|
|
|
Matrix4d trans = Matrix4d.CreateTranslation(-eye);
|
|
|
|
return trans * rot;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Build a world space to camera space matrix
|
|
/// </summary>
|
|
/// <param name="eyeX">Eye (camera) position in world space</param>
|
|
/// <param name="eyeY">Eye (camera) position in world space</param>
|
|
/// <param name="eyeZ">Eye (camera) position in world space</param>
|
|
/// <param name="targetX">Target position in world space</param>
|
|
/// <param name="targetY">Target position in world space</param>
|
|
/// <param name="targetZ">Target position in world space</param>
|
|
/// <param name="upX">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
|
|
/// <param name="upY">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
|
|
/// <param name="upZ">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
|
|
/// <returns>A Matrix4 that transforms world space to camera space</returns>
|
|
public static Matrix4d LookAt(double eyeX, double eyeY, double eyeZ, double targetX, double targetY, double targetZ, double upX, double upY, double upZ)
|
|
{
|
|
return LookAt(new Vector3d(eyeX, eyeY, eyeZ), new Vector3d(targetX, targetY, targetZ), new Vector3d(upX, upY, upZ));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Build a 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="near">Distance to the near clip plane</param>
|
|
/// <param name="far">Distance to the far clip plane</param>
|
|
/// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
public static Matrix4d Frustum(double left, double right, double bottom, double top, double near, double far)
|
|
{
|
|
double invRL = 1.0f / (right - left);
|
|
double invTB = 1.0f / (top - bottom);
|
|
double invFN = 1.0f / (far - near);
|
|
return new Matrix4d(new Vector4d (2.0f * near * invRL, 0.0f, 0.0f, 0.0f),
|
|
new Vector4d (0.0f, 2.0f * near * invTB, 0.0f, 0.0f),
|
|
new Vector4d ((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0f),
|
|
new Vector4d (0.0f, 0.0f, -2.0f * far * near * invFN, 0.0f));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Build a 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="near">Distance to the near clip plane</param>
|
|
/// <param name="far">Distance to the far clip plane</param>
|
|
/// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
public static Matrix4d Perspective(double fovy, double aspect, double near, double far)
|
|
{
|
|
double yMax = near * (double)System.Math.Tan(0.5f * fovy);
|
|
double yMin = -yMax;
|
|
double xMin = yMin * aspect;
|
|
double xMax = yMax * aspect;
|
|
|
|
return Frustum(xMin, xMax, yMin, yMax, near, far);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Multiply Functions
|
|
|
|
/// <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 Matrix4d Mult(Matrix4d left, Matrix4d right)
|
|
{
|
|
Matrix4d 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 Matrix4d left, ref Matrix4d right, out Matrix4d result)
|
|
{
|
|
result = new Matrix4d();
|
|
result.M11 = left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41;
|
|
result.M12 = left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42;
|
|
result.M13 = left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43;
|
|
result.M14 = left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44;
|
|
result.M21 = left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41;
|
|
result.M22 = left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42;
|
|
result.M23 = left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43;
|
|
result.M24 = left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44;
|
|
result.M31 = left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41;
|
|
result.M32 = left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42;
|
|
result.M33 = left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43;
|
|
result.M34 = left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44;
|
|
result.M41 = left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41;
|
|
result.M42 = left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42;
|
|
result.M43 = left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43;
|
|
result.M44 = left.M41 * right.M14 + left.M42 * right.M24 + left.M43 * right.M34 + left.M44 * right.M44;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Invert Functions
|
|
|
|
/// <summary>
|
|
/// Calculate the inverse of the given matrix
|
|
/// </summary>
|
|
/// <param name="mat">The matrix to invert</param>
|
|
/// <returns>The inverse of the given matrix if it has one, or the input if it is singular</returns>
|
|
/// <exception cref="InvalidOperationException">Thrown if the Matrix4d is singular.</exception>
|
|
public static Matrix4d Invert(Matrix4d mat)
|
|
{
|
|
int[] colIdx = { 0, 0, 0, 0 };
|
|
int[] rowIdx = { 0, 0, 0, 0 };
|
|
int[] pivotIdx = { -1, -1, -1, -1 };
|
|
|
|
// convert the matrix to an array for easy looping
|
|
double[,] inverse = {{mat.Row0.X, mat.Row0.Y, mat.Row0.Z, mat.Row0.W},
|
|
{mat.Row1.X, mat.Row1.Y, mat.Row1.Z, mat.Row1.W},
|
|
{mat.Row2.X, mat.Row2.Y, mat.Row2.Z, mat.Row2.W},
|
|
{mat.Row3.X, mat.Row3.Y, mat.Row3.Z, mat.Row3.W} };
|
|
int icol = 0;
|
|
int irow = 0;
|
|
for (int i = 0; i < 4; i++)
|
|
{
|
|
// Find the largest pivot value
|
|
double maxPivot = 0.0f;
|
|
for (int j = 0; j < 4; j++)
|
|
{
|
|
if (pivotIdx[j] != 0)
|
|
{
|
|
for (int k = 0; k < 4; ++k)
|
|
{
|
|
if (pivotIdx[k] == -1)
|
|
{
|
|
double absVal = System.Math.Abs(inverse[j, k]);
|
|
if (absVal > maxPivot)
|
|
{
|
|
maxPivot = absVal;
|
|
irow = j;
|
|
icol = k;
|
|
}
|
|
}
|
|
else if (pivotIdx[k] > 0)
|
|
{
|
|
return mat;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
++(pivotIdx[icol]);
|
|
|
|
// Swap rows over so pivot is on diagonal
|
|
if (irow != icol)
|
|
{
|
|
for (int k = 0; k < 4; ++k)
|
|
{
|
|
double f = inverse[irow, k];
|
|
inverse[irow, k] = inverse[icol, k];
|
|
inverse[icol, k] = f;
|
|
}
|
|
}
|
|
|
|
rowIdx[i] = irow;
|
|
colIdx[i] = icol;
|
|
|
|
double pivot = inverse[icol, icol];
|
|
// check for singular matrix
|
|
if (pivot == 0.0f)
|
|
{
|
|
throw new InvalidOperationException("Matrix is singular and cannot be inverted.");
|
|
//return mat;
|
|
}
|
|
|
|
// Scale row so it has a unit diagonal
|
|
double oneOverPivot = 1.0f / pivot;
|
|
inverse[icol, icol] = 1.0f;
|
|
for (int k = 0; k < 4; ++k)
|
|
inverse[icol, k] *= oneOverPivot;
|
|
|
|
// Do elimination of non-diagonal elements
|
|
for (int j = 0; j < 4; ++j)
|
|
{
|
|
// check this isn't on the diagonal
|
|
if (icol != j)
|
|
{
|
|
double f = inverse[j, icol];
|
|
inverse[j, icol] = 0.0f;
|
|
for (int k = 0; k < 4; ++k)
|
|
inverse[j, k] -= inverse[icol, k] * f;
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int j = 3; j >= 0; --j)
|
|
{
|
|
int ir = rowIdx[j];
|
|
int ic = colIdx[j];
|
|
for (int k = 0; k < 4; ++k)
|
|
{
|
|
double f = inverse[k, ir];
|
|
inverse[k, ir] = inverse[k, ic];
|
|
inverse[k, ic] = f;
|
|
}
|
|
}
|
|
|
|
mat.Row0 = new Vector4d (inverse[0, 0], inverse[0, 1], inverse[0, 2], inverse[0, 3]);
|
|
mat.Row1 = new Vector4d (inverse[1, 0], inverse[1, 1], inverse[1, 2], inverse[1, 3]);
|
|
mat.Row2 = new Vector4d (inverse[2, 0], inverse[2, 1], inverse[2, 2], inverse[2, 3]);
|
|
mat.Row3 = new Vector4d (inverse[3, 0], inverse[3, 1], inverse[3, 2], inverse[3, 3]);
|
|
return mat;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Transpose
|
|
|
|
/// <summary>
|
|
/// Calculate the transpose of the given matrix
|
|
/// </summary>
|
|
/// <param name="mat">The matrix to transpose</param>
|
|
/// <returns>The transpose of the given matrix</returns>
|
|
public static Matrix4d Transpose(Matrix4d mat)
|
|
{
|
|
return new Matrix4d(mat.Column0, mat.Column1, mat.Column2, mat.Column3);
|
|
}
|
|
|
|
|
|
/// <summary>
|
|
/// Calculate the transpose of the given matrix
|
|
/// </summary>
|
|
/// <param name="mat">The matrix to transpose</param>
|
|
/// <param name="result">The result of the calculation</param>
|
|
public static void Transpose(ref Matrix4d mat, out Matrix4d result)
|
|
{
|
|
result.Row0 = mat.Column0;
|
|
result.Row1 = mat.Column1;
|
|
result.Row2 = mat.Column2;
|
|
result.Row3 = mat.Column3;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operators
|
|
|
|
/// <summary>
|
|
/// Matrix multiplication
|
|
/// </summary>
|
|
/// <param name="left">left-hand operand</param>
|
|
/// <param name="right">right-hand operand</param>
|
|
/// <returns>A new Matrix44 which holds the result of the multiplication</returns>
|
|
public static Matrix4d operator *(Matrix4d left, Matrix4d right)
|
|
{
|
|
return Matrix4d.Mult(left, right);
|
|
}
|
|
|
|
public static bool operator ==(Matrix4d left, Matrix4d right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
public static bool operator !=(Matrix4d left, Matrix4d right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Matrix44.
|
|
/// </summary>
|
|
/// <returns></returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("{0}\n{1}\n{2}\n{3}", Row0, Row1, Row2, Row3);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override int GetHashCode()
|
|
|
|
/// <summary>
|
|
/// Returns the hashcode for this instance.
|
|
/// </summary>
|
|
/// <returns>A System.Int32 containing the unique hashcode for this instance.</returns>
|
|
public override int GetHashCode()
|
|
{
|
|
return Row0.GetHashCode() ^ Row1.GetHashCode() ^ Row2.GetHashCode() ^ Row3.GetHashCode();
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override bool Equals(object obj)
|
|
|
|
/// <summary>
|
|
/// Indicates whether this instance and a specified object are equal.
|
|
/// </summary>
|
|
/// <param name="obj">The object to compare to.</param>
|
|
/// <returns>True if the instances are equal; false otherwise.</returns>
|
|
public override bool Equals(object obj)
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|
{
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if (!(obj is Matrix4d))
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return false;
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|
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|
return this.Equals((Matrix4d)obj);
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}
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|
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#endregion
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|
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#endregion
|
|
|
|
#endregion
|
|
|
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#region IEquatable<Matrix4d> Members
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|
|
|
/// <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(Matrix4d other)
|
|
{
|
|
return
|
|
Row0 == other.Row0 &&
|
|
Row1 == other.Row1 &&
|
|
Row2 == other.Row2 &&
|
|
Row3 == other.Row3;
|
|
}
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|
|
|
#endregion
|
|
}
|
|
} |