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703 lines
23 KiB
C#
703 lines
23 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 3x3 Matrix
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Matrix3d : IEquatable<Matrix3d>
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{
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#region Fields
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/// <summary>
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/// First row of the matrix.
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/// </summary>
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public Vector3d Row0;
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/// <summary>
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/// Second row of the matrix.
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/// </summary>
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public Vector3d Row1;
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/// <summary>
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/// Third row of the matrix.
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/// </summary>
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public Vector3d Row2;
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/// <summary>
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/// The identity matrix.
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/// </summary>
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public static Matrix3d Identity = new Matrix3d(Vector3d.UnitX, Vector3d.UnitY, Vector3d.UnitZ);
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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">Bottom row of the matrix</param>
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public Matrix3d(Vector3d row0, Vector3d row1, Vector3d row2)
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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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}
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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 of the matrix.</param>
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/// <param name="m01">Second item of the first row of the matrix.</param>
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/// <param name="m02">Third item of the first row of the matrix.</param>
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/// <param name="m10">First item of the second row of the matrix.</param>
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/// <param name="m11">Second item of the second row of the matrix.</param>
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/// <param name="m12">Third item of the second row of the matrix.</param>
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/// <param name="m20">First item of the third row of the matrix.</param>
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/// <param name="m21">Second item of the third row of the matrix.</param>
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/// <param name="m22">Third item of the third row of the matrix.</param>
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public Matrix3d(
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double m00, double m01, double m02,
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double m10, double m11, double m12,
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double m20, double m21, double m22)
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{
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Row0 = new Vector3d(m00, m01, m02);
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Row1 = new Vector3d(m10, m11, m12);
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Row2 = new Vector3d(m20, m21, m22);
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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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/// Gets 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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double m11 = Row0.X, m12 = Row0.Y, m13 = Row0.Z,
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m21 = Row1.X, m22 = Row1.Y, m23 = Row1.Z,
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m31 = Row2.X, m32 = Row2.Y, m33 = Row2.Z;
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return
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m11 * m22 * m33 + m12 * m23 * m31 + m13 * m21 * m32
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- m13 * m22 * m31 - m11 * m23 * m32 - m12 * m21 * m33;
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}
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}
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/// <summary>
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/// Gets the first column of this matrix.
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/// </summary>
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public Vector3d Column0
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{
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get { return new Vector3d(Row0.X, Row1.X, Row2.X); }
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}
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/// <summary>
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/// Gets the second column of this matrix.
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/// </summary>
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public Vector3d Column1
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{
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get { return new Vector3d(Row0.Y, Row1.Y, Row2.Y); }
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}
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/// <summary>
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/// Gets the third column of this matrix.
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/// </summary>
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public Vector3d Column2
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{
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get { return new Vector3d(Row0.Z, Row1.Z, Row2.Z); }
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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 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 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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#endregion
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#region Indexers
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/// <summary>
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/// Gets or sets the value at a specified row and column.
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/// </summary>
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public double this[int rowIndex, int columnIndex]
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{
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get
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{
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if (rowIndex == 0) return Row0[columnIndex];
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else if (rowIndex == 1) return Row1[columnIndex];
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else if (rowIndex == 2) return Row2[columnIndex];
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throw new IndexOutOfRangeException("You tried to access this matrix at: (" + rowIndex + ", " + columnIndex + ")");
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}
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set
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{
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if (rowIndex == 0) Row0[columnIndex] = value;
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else if (rowIndex == 1) Row1[columnIndex] = value;
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else if (rowIndex == 2) Row2[columnIndex] = value;
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throw new IndexOutOfRangeException("You tried to set this matrix at: (" + rowIndex + ", " + columnIndex + ")");
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}
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}
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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 = Matrix3d.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 = Matrix3d.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 CreateFromAxisAngle
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public static void CreateFromAxisAngle(Vector3d axis, double angle, out Matrix3d result)
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{
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//normalize and create a local copy of the vector.
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axis.Normalize();
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double axisX = axis.X, axisY = axis.Y, axisZ = axis.Z;
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//calculate angles
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double cos = System.Math.Cos(-angle);
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double sin = System.Math.Sin(-angle);
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double t = 1.0f - cos;
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//do the conversion math once
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double tXX = t * axisX * axisX,
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tXY = t * axisX * axisY,
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tXZ = t * axisX * axisZ,
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tYY = t * axisY * axisY,
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tYZ = t * axisY * axisZ,
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tZZ = t * axisZ * axisZ;
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double sinX = sin * axisX,
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sinY = sin * axisY,
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sinZ = sin * axisZ;
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result.Row0.X = tXX + cos;
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result.Row0.Y = tXY - sinZ;
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result.Row0.Z = tXZ + sinY;
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result.Row1.X = tXY + sinZ;
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result.Row1.Y = tYY + cos;
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result.Row1.Z = tYZ - sinX;
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result.Row2.X = tXZ - sinY;
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result.Row2.Y = tYZ + sinX;
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result.Row2.Z = tZZ + cos;
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}
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public static Matrix3d CreateFromAxisAngle(Vector3d axis, double angle)
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{
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Matrix3d result;
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CreateFromAxisAngle(axis, angle, out result);
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return result;
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}
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#endregion
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#region CreateFromQuaternion
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public static void CreateFromQuaternion(ref Quaterniond q, out Matrix3d result)
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{
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Vector3d axis;
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double angle;
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q.ToAxisAngle(out axis, out angle);
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CreateFromAxisAngle(axis, angle, out result);
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}
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public static Matrix3d CreateFromQuaternion(Quaterniond q)
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{
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Matrix3d result;
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CreateFromQuaternion(ref q, out result);
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return result;
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}
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#endregion
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#region CreateRotation[XYZ]
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public static void CreateRotationX(double angle, out Matrix3d result)
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{
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double cos = System.Math.Cos(angle);
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double sin = System.Math.Sin(angle);
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result = Identity;
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result.Row1.Y = cos;
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result.Row1.Z = sin;
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result.Row2.Y = -sin;
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result.Row2.Z = cos;
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}
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public static Matrix3d CreateRotationX(double angle)
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{
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Matrix3d result;
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CreateRotationX(angle, out result);
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return result;
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}
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public static void CreateRotationY(double angle, out Matrix3d result)
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{
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double cos = System.Math.Cos(angle);
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double sin = System.Math.Sin(angle);
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result = Identity;
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result.Row0.X = cos;
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result.Row0.Z = -sin;
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result.Row2.X = sin;
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result.Row2.Z = cos;
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}
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public static Matrix3d CreateRotationY(double angle)
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{
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Matrix3d result;
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CreateRotationY(angle, out result);
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return result;
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}
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public static void CreateRotationZ(double angle, out Matrix3d result)
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{
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double cos = System.Math.Cos(angle);
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double sin = System.Math.Sin(angle);
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result = Identity;
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result.Row0.X = cos;
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result.Row0.Y = sin;
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result.Row1.X = -sin;
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result.Row1.Y = cos;
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}
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public static Matrix3d CreateRotationZ(double angle)
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{
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Matrix3d result;
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CreateRotationZ(angle, out result);
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return result;
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}
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#endregion
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#region CreateScale
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/// <summary>
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/// Creates a scale matrix.
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/// </summary>
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/// <param name="scale">Single scale factor for the x, y, and z axes.</param>
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/// <returns>A scale matrix.</returns>
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public static Matrix3d CreateScale(double scale)
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{
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Matrix3d result;
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CreateScale(scale, out result);
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return result;
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}
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/// <summary>
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/// Creates a scale matrix.
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/// </summary>
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/// <param name="scale">Scale factors for the x, y, and z axes.</param>
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/// <returns>A scale matrix.</returns>
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public static Matrix3d CreateScale(Vector3d scale)
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{
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Matrix3d result;
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CreateScale(ref scale, out result);
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return result;
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}
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/// <summary>
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/// Creates a scale matrix.
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/// </summary>
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/// <param name="x">Scale factor for the x axis.</param>
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/// <param name="y">Scale factor for the y axis.</param>
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/// <param name="z">Scale factor for the z axis.</param>
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/// <returns>A scale matrix.</returns>
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public static Matrix3d CreateScale(double x, double y, double z)
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{
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Matrix3d result;
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CreateScale(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 scale matrix.
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/// </summary>
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/// <param name="scale">Single scale factor for the x, y, and z axes.</param>
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/// <param name="result">A scale matrix.</param>
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public static void CreateScale(double scale, out Matrix3d result)
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{
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result = Identity;
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result.Row0.X = scale;
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result.Row1.Y = scale;
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result.Row2.Z = scale;
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}
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/// <summary>
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/// Creates a scale matrix.
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/// </summary>
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/// <param name="scale">Scale factors for the x, y, and z axes.</param>
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/// <param name="result">A scale matrix.</param>
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public static void CreateScale(ref Vector3d scale, out Matrix3d result)
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{
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result = Identity;
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result.Row0.X = scale.X;
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result.Row1.Y = scale.Y;
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result.Row2.Z = scale.Z;
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}
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/// <summary>
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/// Creates a scale matrix.
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/// </summary>
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/// <param name="x">Scale factor for the x axis.</param>
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/// <param name="y">Scale factor for the y axis.</param>
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/// <param name="z">Scale factor for the z axis.</param>
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/// <param name="result">A scale matrix.</returns>
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public static void CreateScale(double x, double y, double z, out Matrix3d result)
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{
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result = Identity;
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result.Row0.X = x;
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result.Row1.Y = y;
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result.Row2.Z = z;
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}
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#endregion
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#region Multiply Functions
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public static Matrix3d Mult(Matrix3d left, Matrix3d right)
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{
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Matrix3d result;
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Mult(ref left, ref right, out result);
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return result;
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}
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public static void Mult(ref Matrix3d left, ref Matrix3d right, out Matrix3d result)
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{
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double lM11 = left.Row0.X, lM12 = left.Row0.Y, lM13 = left.Row0.Z,
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lM21 = left.Row1.X, lM22 = left.Row1.Y, lM23 = left.Row1.Z,
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lM31 = left.Row2.X, lM32 = left.Row2.Y, lM33 = left.Row2.Z,
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rM11 = right.Row0.X, rM12 = right.Row0.Y, rM13 = right.Row0.Z,
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rM21 = right.Row1.X, rM22 = right.Row1.Y, rM23 = right.Row1.Z,
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rM31 = right.Row2.X, rM32 = right.Row2.Y, rM33 = right.Row2.Z;
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result.Row0.X = ((lM11 * rM11) + (lM12 * rM21)) + (lM13 * rM31);
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result.Row0.Y = ((lM11 * rM12) + (lM12 * rM22)) + (lM13 * rM32);
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result.Row0.Z = ((lM11 * rM13) + (lM12 * rM23)) + (lM13 * rM33);
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result.Row1.X = ((lM21 * rM11) + (lM22 * rM21)) + (lM23 * rM31);
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result.Row1.Y = ((lM21 * rM12) + (lM22 * rM22)) + (lM23 * rM32);
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result.Row1.Z = ((lM21 * rM13) + (lM22 * rM23)) + (lM23 * rM33);
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result.Row2.X = ((lM31 * rM11) + (lM32 * rM21)) + (lM33 * rM31);
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result.Row2.Y = ((lM31 * rM12) + (lM32 * rM22)) + (lM33 * rM32);
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result.Row2.Z = ((lM31 * rM13) + (lM32 * rM23)) + (lM33 * rM33);
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}
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#endregion
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#region Invert Functions
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/// <summary>
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/// Calculate the inverse of the given matrix
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/// </summary>
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/// <param name="mat">The matrix to invert</param>
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/// <param name="result">The inverse of the given matrix if it has one, or the input if it is singular</param>
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/// <exception cref="InvalidOperationException">Thrown if the Matrix3d is singular.</exception>
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public static void Invert(ref Matrix3d mat, out Matrix3d result)
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{
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int[] colIdx = { 0, 0, 0 };
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int[] rowIdx = { 0, 0, 0 };
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int[] pivotIdx = { -1, -1, -1 };
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double[,] inverse = {{mat.Row0.X, mat.Row0.Y, mat.Row0.Z},
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{mat.Row1.X, mat.Row1.Y, mat.Row1.Z},
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{mat.Row2.X, mat.Row2.Y, mat.Row2.Z}};
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int icol = 0;
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int irow = 0;
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for (int i = 0; i < 3; i++)
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{
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double maxPivot = 0.0;
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for (int j = 0; j < 3; j++)
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{
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if (pivotIdx[j] != 0)
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{
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for (int k = 0; k < 3; ++k)
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{
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if (pivotIdx[k] == -1)
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{
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double absVal = System.Math.Abs(inverse[j, k]);
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if (absVal > maxPivot)
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{
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maxPivot = absVal;
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|
irow = j;
|
|
icol = k;
|
|
}
|
|
}
|
|
else if (pivotIdx[k] > 0)
|
|
{
|
|
result = mat;
|
|
return;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
++(pivotIdx[icol]);
|
|
|
|
if (irow != icol)
|
|
{
|
|
for (int k = 0; k < 3; ++k)
|
|
{
|
|
double f = inverse[irow, k];
|
|
inverse[irow, k] = inverse[icol, k];
|
|
inverse[icol, k] = f;
|
|
}
|
|
}
|
|
|
|
rowIdx[i] = irow;
|
|
colIdx[i] = icol;
|
|
|
|
double pivot = inverse[icol, icol];
|
|
|
|
if (pivot == 0.0)
|
|
{
|
|
throw new InvalidOperationException("Matrix is singular and cannot be inverted.");
|
|
}
|
|
|
|
double oneOverPivot = 1.0 / pivot;
|
|
inverse[icol, icol] = 1.0;
|
|
for (int k = 0; k < 3; ++k)
|
|
inverse[icol, k] *= oneOverPivot;
|
|
|
|
for (int j = 0; j < 3; ++j)
|
|
{
|
|
if (icol != j)
|
|
{
|
|
double f = inverse[j, icol];
|
|
inverse[j, icol] = 0.0;
|
|
for (int k = 0; k < 3; ++k)
|
|
inverse[j, k] -= inverse[icol, k] * f;
|
|
}
|
|
}
|
|
}
|
|
|
|
for (int j = 2; j >= 0; --j)
|
|
{
|
|
int ir = rowIdx[j];
|
|
int ic = colIdx[j];
|
|
for (int k = 0; k < 3; ++k)
|
|
{
|
|
double f = inverse[k, ir];
|
|
inverse[k, ir] = inverse[k, ic];
|
|
inverse[k, ic] = f;
|
|
}
|
|
}
|
|
|
|
result.Row0.X = inverse[0, 0];
|
|
result.Row0.Y = inverse[0, 1];
|
|
result.Row0.Z = inverse[0, 2];
|
|
result.Row1.X = inverse[1, 0];
|
|
result.Row1.Y = inverse[1, 1];
|
|
result.Row1.Z = inverse[1, 2];
|
|
result.Row2.X = inverse[2, 0];
|
|
result.Row2.Y = inverse[2, 1];
|
|
result.Row2.Z = inverse[2, 2];
|
|
}
|
|
|
|
/// <summary>
|
|
/// Calculate the inverse of the given matrix
|
|
/// </summary>
|
|
/// <param name="mat">The matrix to invert</param>
|
|
/// <returns>The inverse of the given matrix if it has one, or the input if it is singular</returns>
|
|
/// <exception cref="InvalidOperationException">Thrown if the Matrix4 is singular.</exception>
|
|
public static Matrix3d Invert(Matrix3d mat)
|
|
{
|
|
Matrix3d result;
|
|
Invert(ref mat, out result);
|
|
return result;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Transpose
|
|
|
|
public static Matrix3d Transpose(Matrix3d mat)
|
|
{
|
|
return new Matrix3d(mat.Column0, mat.Column1, mat.Column2);
|
|
}
|
|
|
|
public static void Transpose(ref Matrix3d mat, out Matrix3d result)
|
|
{
|
|
result.Row0 = mat.Column0;
|
|
result.Row1 = mat.Column1;
|
|
result.Row2 = mat.Column2;
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region Operators
|
|
|
|
public static Matrix3d operator *(Matrix3d left, Matrix3d right)
|
|
{
|
|
return Matrix3d.Mult(left, right);
|
|
}
|
|
|
|
public static bool operator ==(Matrix3d left, Matrix3d right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
public static bool operator !=(Matrix3d left, Matrix3d right)
|
|
{
|
|
return !left.Equals(right);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region Overrides
|
|
|
|
#region public override string ToString()
|
|
|
|
/// <summary>
|
|
/// Returns a System.String that represents the current Matrix3d.
|
|
/// </summary>
|
|
/// <returns>The string representation of the matrix.</returns>
|
|
public override string ToString()
|
|
{
|
|
return String.Format("{0}\n{1}\n{2}", Row0, Row1, Row2);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override int GetHashCode()
|
|
|
|
/// <summary>
|
|
/// Returns the hashcode for this instance.
|
|
/// </summary>
|
|
/// <returns>A System.Int32 containing the unique hashcode for this instance.</returns>
|
|
public override int GetHashCode()
|
|
{
|
|
return Row0.GetHashCode() ^ Row1.GetHashCode() ^ Row2.GetHashCode();
|
|
}
|
|
|
|
#endregion
|
|
|
|
#region public override bool Equals(object obj)
|
|
|
|
/// <summary>
|
|
/// Indicates whether this instance and a specified object are equal.
|
|
/// </summary>
|
|
/// <param name="obj">The object to compare to.</param>
|
|
/// <returns>True if the instances are equal; false otherwise.</returns>
|
|
public override bool Equals(object obj)
|
|
{
|
|
if (!(obj is Matrix3d))
|
|
return false;
|
|
|
|
return this.Equals((Matrix3d)obj);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region IEquatable<Matrix3d> Members
|
|
|
|
public bool Equals(Matrix3d other)
|
|
{
|
|
return
|
|
Row0 == other.Row0 &&
|
|
Row1 == other.Row1 &&
|
|
Row2 == other.Row2;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
} |