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659 lines
24 KiB
C#
659 lines
24 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.Math
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{
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/// <summary>
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/// Represents a 4x4 Matrix
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/// </summary>
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[Serializable]
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[StructLayout(LayoutKind.Sequential)]
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public struct Matrix4 : IEquatable<Matrix4>
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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 Vector4 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 Vector4 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 Vector4 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 Vector4 Row3;
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/// <summary>
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/// The identity matrix
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/// </summary>
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public static Matrix4 Identity = new Matrix4(Vector4.UnitX, Vector4.UnitY, Vector4.UnitZ, Vector4.UnitW);
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#endregion
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#region Constructors
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/// <summary>
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/// Construct a new matrix from 4 vectors representing each row
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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">2nd row of the matrix</param>
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/// <param name="row2">3rd row of the matrix</param>
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/// <param name="row3">Bottom row of the matrix</param>
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public Matrix4(Vector4 row0, Vector4 row1, Vector4 row2, Vector4 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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#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 float 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 Vector4 Column0
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{
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get { return new Vector4(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 Vector4 Column1
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{
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get { return new Vector4(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 Vector4 Column2
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{
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get { return new Vector4(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 Vector4 Column3
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{
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get { return new Vector4(Row0.W, Row1.W, Row2.W, Row3.W); }
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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 = Matrix4.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 = Matrix4.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 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 Matrix4 Scale(float 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 Matrix4 Scale(Vector3 scale)
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{
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return Scale(scale.X, scale.Y, scale.Z);
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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="x">Scale factor for x-axis</param>
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/// <param name="y">Scale factor for y-axis</param>
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/// <param name="z">Scale factor for z-axis</param>
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/// <returns>A scaling matrix</returns>
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public static Matrix4 Scale(float x, float y, float z)
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{
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Matrix4 result;
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result.Row0 = Vector4.UnitX * x;
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result.Row1 = Vector4.UnitY * y;
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result.Row2 = Vector4.UnitZ * z;
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result.Row3 = Vector4.UnitW;
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return result;
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}
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#endregion
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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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public static Matrix4 Translation(Vector3 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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public static Matrix4 Translation(float x, float y, float z)
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{
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Matrix4 result = Identity;
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result.Row3 = new Vector4(x, y, z, 1.0f);
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return result;
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}
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#endregion
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#region Rotation Functions
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/// <summary>
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/// Build a rotation matrix that rotates about the x-axis
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/// </summary>
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/// <param name="angle">angle in radians to rotate counter-clockwise around the x-axis</param>
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/// <returns>A rotation matrix</returns>
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public static Matrix4 RotateX(float angle)
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{
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float cos = (float)System.Math.Cos(angle);
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float sin = (float)System.Math.Sin(angle);
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Matrix4 result;
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result.Row0 = Vector4.UnitX;
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result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
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result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
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result.Row3 = Vector4.UnitW;
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return result;
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}
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/// <summary>
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/// Build a rotation matrix that rotates about the y-axis
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/// </summary>
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/// <param name="angle">angle in radians to rotate counter-clockwise around the y-axis</param>
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/// <returns>A rotation matrix</returns>
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public static Matrix4 RotateY(float angle)
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{
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float cos = (float)System.Math.Cos(angle);
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float sin = (float)System.Math.Sin(angle);
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Matrix4 result;
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result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
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result.Row1 = Vector4.UnitY;
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result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
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result.Row3 = Vector4.UnitW;
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return result;
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}
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/// <summary>
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/// Build a rotation matrix that rotates about the z-axis
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/// </summary>
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/// <param name="angle">angle in radians to rotate counter-clockwise around the z-axis</param>
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/// <returns>A rotation matrix</returns>
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public static Matrix4 RotateZ(float angle)
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{
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float cos = (float)System.Math.Cos(angle);
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float sin = (float)System.Math.Sin(angle);
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Matrix4 result;
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result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
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result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
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result.Row2 = Vector4.UnitZ;
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result.Row3 = Vector4.UnitW;
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return result;
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}
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/// <summary>
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/// Build a rotation matrix to rotate about the given axis
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/// </summary>
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/// <param name="axis">the axis to rotate about</param>
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/// <param name="angle">angle in radians to rotate counter-clockwise (looking in the direction of the given axis)</param>
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/// <returns>A rotation matrix</returns>
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public static Matrix4 Rotate(Vector3 axis, float angle)
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{
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float cos = (float)System.Math.Cos(-angle);
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float sin = (float)System.Math.Sin(-angle);
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float t = 1.0f - cos;
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axis.Normalize();
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Matrix4 result;
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result.Row0 = new Vector4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f);
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result.Row1 = new Vector4(t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f);
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result.Row2 = new Vector4(t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f);
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result.Row3 = Vector4.UnitW;
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return result;
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}
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/// <summary>
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/// Build a rotation matrix from a quaternion
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/// </summary>
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/// <param name="q">the quaternion</param>
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/// <returns>A rotation matrix</returns>
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public static Matrix4 Rotate(Quaternion q)
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{
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Vector3 axis;
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float angle;
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q.ToAxisAngle(out axis, out angle);
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return Rotate(axis, angle);
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}
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#endregion
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#region Camera Helper Functions
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/// <summary>
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/// Build a world space to camera space matrix
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/// </summary>
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/// <param name="eye">Eye (camera) position in world space</param>
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/// <param name="target">Target position in world space</param>
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/// <param name="up">Up vector in world space (should not be parallel to the camera direction, that is target - eye)</param>
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/// <returns>A Matrix that transforms world space to camera space</returns>
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public static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)
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{
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Vector3 z = Vector3.Normalize(eye - target);
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Vector3 x = Vector3.Normalize(Vector3.Cross(up, z));
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Vector3 y = Vector3.Normalize(Vector3.Cross(z, x));
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Matrix4 rot = new Matrix4(new Vector4(x.X, y.X, z.X, 0.0f),
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new Vector4(x.Y, y.Y, z.Y, 0.0f),
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new Vector4(x.Z, y.Z, z.Z, 0.0f),
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Vector4.UnitW);
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Matrix4 trans = Matrix4.Translation(-eye);
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return trans * rot;
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}
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/// <summary>
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/// Build a projection matrix
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/// </summary>
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/// <param name="left">Left edge of the view frustum</param>
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/// <param name="right">Right edge of the view frustum</param>
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/// <param name="bottom">Bottom edge of the view frustum</param>
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/// <param name="top">Top edge of the view frustum</param>
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/// <param name="near">Distance to the near clip plane</param>
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/// <param name="far">Distance to the far clip plane</param>
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/// <returns>A projection matrix that transforms camera space to raster space</returns>
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public static Matrix4 Frustum(float left, float right, float bottom, float top, float near, float far)
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{
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float invRL = 1.0f / (right - left);
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float invTB = 1.0f / (top - bottom);
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float invFN = 1.0f / (far - near);
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return new Matrix4(new Vector4(2.0f * near * invRL, 0.0f, 0.0f, 0.0f),
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new Vector4(0.0f, 2.0f * near * invTB, 0.0f, 0.0f),
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new Vector4((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0f),
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new Vector4(0.0f, 0.0f, -2.0f * far * near * invFN, 0.0f));
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}
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/// <summary>
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/// Build a projection matrix
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/// </summary>
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/// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
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/// <param name="aspect">Aspect ratio of the view (width / height)</param>
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/// <param name="near">Distance to the near clip plane</param>
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/// <param name="far">Distance to the far clip plane</param>
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/// <returns>A projection matrix that transforms camera space to raster space</returns>
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public static Matrix4 Perspective(float fovy, float aspect, float near, float far)
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{
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float yMax = near * (float)System.Math.Tan(0.5f * fovy);
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float yMin = -yMax;
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float xMin = yMin * aspect;
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float xMax = yMax * aspect;
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return Frustum(xMin, xMax, yMin, yMax, near, far);
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}
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#endregion
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#region Multiply Functions
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/// <summary>
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/// Post multiply this matrix by another matrix
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/// </summary>
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/// <param name="right">The matrix to multiply</param>
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/// <returns>A new Matrix44 that is the result of the multiplication</returns>
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public static Matrix4 Mult(Matrix4 left, Matrix4 right)
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{
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Vector4 col0 = right.Column0;
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Vector4 col1 = right.Column1;
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Vector4 col2 = right.Column2;
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Vector4 col3 = right.Column3;
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left.Row0 = new Vector4(Vector4.Dot(left.Row0, col0), Vector4.Dot(left.Row0, col1), Vector4.Dot(left.Row0, col2), Vector4.Dot(left.Row0, col3));
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left.Row1 = new Vector4(Vector4.Dot(left.Row1, col0), Vector4.Dot(left.Row1, col1), Vector4.Dot(left.Row1, col2), Vector4.Dot(left.Row1, col3));
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left.Row2 = new Vector4(Vector4.Dot(left.Row2, col0), Vector4.Dot(left.Row2, col1), Vector4.Dot(left.Row2, col2), Vector4.Dot(left.Row2, col3));
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left.Row3 = new Vector4(Vector4.Dot(left.Row3, col0), Vector4.Dot(left.Row3, col1), Vector4.Dot(left.Row3, col2), Vector4.Dot(left.Row3, col3));
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return left;
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}
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public static void Mult(ref Matrix4 left, ref Matrix4 right, out Matrix4 result)
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{
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Vector4 col0 = right.Column0;
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Vector4 col1 = right.Column1;
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Vector4 col2 = right.Column2;
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Vector4 col3 = right.Column3;
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result.Row0 = new Vector4(Vector4.Dot(left.Row0, col0), Vector4.Dot(left.Row0, col1), Vector4.Dot(left.Row0, col2), Vector4.Dot(left.Row0, col3));
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result.Row1 = new Vector4(Vector4.Dot(left.Row1, col0), Vector4.Dot(left.Row1, col1), Vector4.Dot(left.Row1, col2), Vector4.Dot(left.Row1, col3));
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result.Row2 = new Vector4(Vector4.Dot(left.Row2, col0), Vector4.Dot(left.Row2, col1), Vector4.Dot(left.Row2, col2), Vector4.Dot(left.Row2, col3));
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result.Row3 = new Vector4(Vector4.Dot(left.Row3, col0), Vector4.Dot(left.Row3, col1), Vector4.Dot(left.Row3, col2), Vector4.Dot(left.Row3, col3));
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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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/// <returns>The inverse of the given matrix if it has one, or the input if it is singular</returns>
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/// <exception cref="InvalidOperationException">Thrown if the Matrix4 is singular.</exception>
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public static Matrix4 Invert(Matrix4 mat)
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{
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int[] colIdx = { 0, 0, 0, 0 };
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int[] rowIdx = { 0, 0, 0, 0 };
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int[] pivotIdx = { -1, -1, -1, -1 };
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// convert the matrix to an array for easy looping
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float[,] inverse = {{mat.Row0.X, mat.Row0.Y, mat.Row0.Z, mat.Row0.W},
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{mat.Row1.X, mat.Row1.Y, mat.Row1.Z, mat.Row1.W},
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{mat.Row2.X, mat.Row2.Y, mat.Row2.Z, mat.Row2.W},
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{mat.Row3.X, mat.Row3.Y, mat.Row3.Z, mat.Row3.W} };
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int icol = 0;
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int irow = 0;
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for (int i = 0; i < 4; i++)
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{
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// Find the largest pivot value
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float maxPivot = 0.0f;
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for (int j = 0; j < 4; 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 < 4; ++k)
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{
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if (pivotIdx[k] == -1)
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{
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float 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)
|
|
{
|
|
float f = inverse[irow, k];
|
|
inverse[irow, k] = inverse[icol, k];
|
|
inverse[icol, k] = f;
|
|
}
|
|
}
|
|
|
|
rowIdx[i] = irow;
|
|
colIdx[i] = icol;
|
|
|
|
float 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
|
|
float 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)
|
|
{
|
|
float 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)
|
|
{
|
|
float f = inverse[k, ir];
|
|
inverse[k, ir] = inverse[k, ic];
|
|
inverse[k, ic] = f;
|
|
}
|
|
}
|
|
|
|
mat.Row0 = new Vector4(inverse[0, 0], inverse[0, 1], inverse[0, 2], inverse[0, 3]);
|
|
mat.Row1 = new Vector4(inverse[1, 0], inverse[1, 1], inverse[1, 2], inverse[1, 3]);
|
|
mat.Row2 = new Vector4(inverse[2, 0], inverse[2, 1], inverse[2, 2], inverse[2, 3]);
|
|
mat.Row3 = new Vector4(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 Matrix4 Transpose(Matrix4 mat)
|
|
{
|
|
return new Matrix4(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>
|
|
public static void Transpose(ref Matrix4 mat, out Matrix4 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 Matrix4 operator *(Matrix4 left, Matrix4 right)
|
|
{
|
|
return Matrix4.Mult(left, right);
|
|
}
|
|
|
|
public static bool operator ==(Matrix4 left, Matrix4 right)
|
|
{
|
|
return left.Equals(right);
|
|
}
|
|
|
|
public static bool operator !=(Matrix4 left, Matrix4 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)
|
|
{
|
|
if (!(obj is Matrix4))
|
|
return false;
|
|
|
|
return this.Equals((Matrix4)obj);
|
|
}
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#endregion
|
|
|
|
#region IEquatable<Matrix4> Members
|
|
|
|
/// <summary>Indicates whether the current matrix is equal to another matrix.</summary>
|
|
/// <param name="matrix">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(Matrix4 other)
|
|
{
|
|
return
|
|
Row0 == other.Row0 &&
|
|
Row1 == other.Row1 &&
|
|
Row2 == other.Row2 &&
|
|
Row3 == other.Row3;
|
|
}
|
|
|
|
#endregion
|
|
}
|
|
}
|