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@@ -27,1196 +27,1196 @@ using System.Runtime.InteropServices;
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namespace AtomicEngine
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namespace AtomicEngine
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{
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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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- [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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-
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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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+ /// Represents a 4x4 Matrix
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+ /// </summary>
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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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+
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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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-
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- #endregion
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-
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- #region Constructors
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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="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 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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-
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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="m03">Fourth 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="m13">Fourth 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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- /// <param name="m23">First item of the third row of the matrix.</param>
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- /// <param name="m30">Fourth item of the fourth row of the matrix.</param>
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- /// <param name="m31">Second item of the fourth row of the matrix.</param>
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- /// <param name="m32">Third item of the fourth row of the matrix.</param>
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- /// <param name="m33">Fourth item of the fourth row of the matrix.</param>
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- public Matrix4(
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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 Vector4(m00, m01, m02, m03);
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- Row1 = new Vector4(m10, m11, m12, m13);
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- Row2 = new Vector4(m20, m21, m22, m23);
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- Row3 = new Vector4(m30, m31, m32, m33);
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- }
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-
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- #endregion
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-
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- #region Public Members
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-
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- #region Properties
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-
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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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-
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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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-
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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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-
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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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-
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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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-
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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 float M11 { get { return Row0.X; } set { Row0.X = value; } }
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-
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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 float M12 { get { return Row0.Y; } set { Row0.Y = value; } }
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-
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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 float M13 { get { return Row0.Z; } set { Row0.Z = value; } }
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-
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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 float M14 { get { return Row0.W; } set { Row0.W = value; } }
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-
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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 float M21 { get { return Row1.X; } set { Row1.X = value; } }
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-
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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 float M22 { get { return Row1.Y; } set { Row1.Y = value; } }
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-
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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 float M23 { get { return Row1.Z; } set { Row1.Z = value; } }
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-
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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 float M24 { get { return Row1.W; } set { Row1.W = value; } }
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-
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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 float M31 { get { return Row2.X; } set { Row2.X = value; } }
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-
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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 float M32 { get { return Row2.Y; } set { Row2.Y = value; } }
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-
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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 float M33 { get { return Row2.Z; } set { Row2.Z = value; } }
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-
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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 float M34 { get { return Row2.W; } set { Row2.W = value; } }
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-
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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 float M41 { get { return Row3.X; } set { Row3.X = value; } }
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-
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- /// <summary>
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- /// Gets or sets the value at row 4, column 2 of this instance.
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- /// </summary>
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- public float M42 { get { return Row3.Y; } set { Row3.Y = value; } }
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-
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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 float M43 { get { return Row3.Z; } set { Row3.Z = value; } }
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-
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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 float M44 { get { return Row3.W; } set { Row3.W = value; } }
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-
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- #endregion
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-
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- #region Instance
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-
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- #region public void Invert()
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-
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- /// <summary>
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- /// Converts this instance into its inverse.
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- /// </summary>
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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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-
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- #endregion
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-
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- #region public void Transpose()
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-
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- /// <summary>
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- /// Converts this instance into its transpose.
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- /// </summary>
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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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-
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- #endregion
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-
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- #endregion
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-
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- #region Static
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-
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- #region CreateFromAxisAngle
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-
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- /// <summary>
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- /// Build a rotation matrix from the specified axis/angle rotation.
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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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- /// <param name="result">A matrix instance.</param>
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- public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix4 result)
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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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-
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- axis.Normalize();
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-
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- result = new Matrix4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f,
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- 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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- 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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- 0, 0, 0, 1);
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- }
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-
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- /// <summary>
|
|
|
|
|
- /// Build a rotation matrix from the specified axis/angle rotation.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="axis">The axis to rotate about.</param>
|
|
|
|
|
- /// <param name="angle">Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).</param>
|
|
|
|
|
- /// <returns>A matrix instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateFromAxisAngle(axis, angle, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreateRotation[XYZ]
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the x-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateRotationX(float angle, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- result.Row0 = Vector4.UnitX;
|
|
|
|
|
- result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
|
|
|
|
|
- result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the x-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateRotationX(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateRotationX(angle, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the y-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateRotationY(float angle, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
|
|
|
|
|
- result.Row1 = Vector4.UnitY;
|
|
|
|
|
- result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the y-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateRotationY(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateRotationY(angle, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the z-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateRotationZ(float angle, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
|
|
|
|
|
- result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
|
|
|
|
|
- result.Row2 = Vector4.UnitZ;
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a rotation matrix for a rotation around the z-axis.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateRotationZ(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateRotationZ(angle, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreateTranslation
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a translation matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="x">X translation.</param>
|
|
|
|
|
- /// <param name="y">Y translation.</param>
|
|
|
|
|
- /// <param name="z">Z translation.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateTranslation(float x, float y, float z, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- result = Identity;
|
|
|
|
|
- result.Row3 = new Vector4(x, y, z, 1);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a translation matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="vector">The translation vector.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateTranslation(ref Vector3 vector, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- result = Identity;
|
|
|
|
|
- result.Row3 = new Vector4(vector.X, vector.Y, vector.Z, 1);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a translation matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="x">X translation.</param>
|
|
|
|
|
- /// <param name="y">Y translation.</param>
|
|
|
|
|
- /// <param name="z">Z translation.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateTranslation(float x, float y, float z)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateTranslation(x, y, z, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a translation matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="vector">The translation vector.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateTranslation(Vector3 vector)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateTranslation(vector.X, vector.Y, vector.Z, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreateOrthographic
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an orthographic projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="width">The width of the projection volume.</param>
|
|
|
|
|
- /// <param name="height">The height of the projection volume.</param>
|
|
|
|
|
- /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateOrthographic(float width, float height, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an orthographic projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="width">The width of the projection volume.</param>
|
|
|
|
|
- /// <param name="height">The height of the projection volume.</param>
|
|
|
|
|
- /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
- /// <rereturns>The resulting Matrix4 instance.</rereturns>
|
|
|
|
|
- public static Matrix4 CreateOrthographic(float width, float height, float zNear, float zFar)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreateOrthographicOffCenter
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an orthographic projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">The left edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="right">The right edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="bottom">The bottom edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="top">The top edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
- public static void CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- result = new Matrix4();
|
|
|
|
|
-
|
|
|
|
|
- float invRL = 1 / (right - left);
|
|
|
|
|
- float invTB = 1 / (top - bottom);
|
|
|
|
|
- float invFN = 1 / (zFar - zNear);
|
|
|
|
|
-
|
|
|
|
|
- result.M11 = 2 * invRL;
|
|
|
|
|
- result.M22 = 2 * invTB;
|
|
|
|
|
- result.M33 = -2 * invFN;
|
|
|
|
|
-
|
|
|
|
|
- result.M41 = -(right + left) * invRL;
|
|
|
|
|
- result.M42 = -(top + bottom) * invTB;
|
|
|
|
|
- result.M43 = -(zFar + zNear) * invFN;
|
|
|
|
|
- result.M44 = 1;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an orthographic projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">The left edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="right">The right edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="bottom">The bottom edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="top">The top edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
- /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
- /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
- public static Matrix4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreatePerspectiveFieldOfView
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a perspective projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
|
|
|
|
|
- /// <param name="aspect">Aspect ratio of the view (width / height)</param>
|
|
|
|
|
- /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
- /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
- /// <param name="result">A projection matrix that transforms camera space to raster space</param>
|
|
|
|
|
- /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
- /// Thrown under the following conditions:
|
|
|
|
|
- /// <list type="bullet">
|
|
|
|
|
- /// <item>fovy is zero, less than zero or larger than Math.PI</item>
|
|
|
|
|
- /// <item>aspect is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is negative or zero</item>
|
|
|
|
|
- /// <item>zFar is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is larger than zFar</item>
|
|
|
|
|
- /// </list>
|
|
|
|
|
- /// </exception>
|
|
|
|
|
- public static void CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- if (fovy <= 0 || fovy > Math.PI)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("fovy");
|
|
|
|
|
- if (aspect <= 0)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("aspect");
|
|
|
|
|
- if (zNear <= 0)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
- if (zFar <= 0)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zFar");
|
|
|
|
|
- if (zNear >= zFar)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
-
|
|
|
|
|
- float yMax = zNear * (float)System.Math.Tan(0.5f * fovy);
|
|
|
|
|
- float yMin = -yMax;
|
|
|
|
|
- float xMin = yMin * aspect;
|
|
|
|
|
- float xMax = yMax * aspect;
|
|
|
|
|
-
|
|
|
|
|
- CreatePerspectiveOffCenter(xMin, xMax, yMin, yMax, zNear, zFar, out result);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates a perspective projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
|
|
|
|
|
- /// <param name="aspect">Aspect ratio of the view (width / height)</param>
|
|
|
|
|
- /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
- /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
- /// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
|
|
|
- /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
- /// Thrown under the following conditions:
|
|
|
|
|
- /// <list type="bullet">
|
|
|
|
|
- /// <item>fovy is zero, less than zero or larger than Math.PI</item>
|
|
|
|
|
- /// <item>aspect is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is negative or zero</item>
|
|
|
|
|
- /// <item>zFar is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is larger than zFar</item>
|
|
|
|
|
- /// </list>
|
|
|
|
|
- /// </exception>
|
|
|
|
|
- public static Matrix4 CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreatePerspectiveFieldOfView(fovy, aspect, zNear, zFar, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region CreatePerspectiveOffCenter
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an perspective projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">Left edge of the view frustum</param>
|
|
|
|
|
- /// <param name="right">Right edge of the view frustum</param>
|
|
|
|
|
- /// <param name="bottom">Bottom edge of the view frustum</param>
|
|
|
|
|
- /// <param name="top">Top edge of the view frustum</param>
|
|
|
|
|
- /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
- /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
- /// <param name="result">A projection matrix that transforms camera space to raster space</param>
|
|
|
|
|
- /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
- /// Thrown under the following conditions:
|
|
|
|
|
- /// <list type="bullet">
|
|
|
|
|
- /// <item>zNear is negative or zero</item>
|
|
|
|
|
- /// <item>zFar is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is larger than zFar</item>
|
|
|
|
|
- /// </list>
|
|
|
|
|
- /// </exception>
|
|
|
|
|
- public static void CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- if (zNear <= 0)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
- if (zFar <= 0)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zFar");
|
|
|
|
|
- if (zNear >= zFar)
|
|
|
|
|
- throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
-
|
|
|
|
|
- float x = (2.0f * zNear) / (right - left);
|
|
|
|
|
- float y = (2.0f * zNear) / (top - bottom);
|
|
|
|
|
- float a = (right + left) / (right - left);
|
|
|
|
|
- float b = (top + bottom) / (top - bottom);
|
|
|
|
|
- float c = -(zFar + zNear) / (zFar - zNear);
|
|
|
|
|
- float d = -(2.0f * zFar * zNear) / (zFar - zNear);
|
|
|
|
|
-
|
|
|
|
|
- result = new Matrix4(x, 0, 0, 0,
|
|
|
|
|
- 0, y, 0, 0,
|
|
|
|
|
- a, b, c, -1,
|
|
|
|
|
- 0, 0, d, 0);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Creates an perspective projection matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">Left edge of the view frustum</param>
|
|
|
|
|
- /// <param name="right">Right edge of the view frustum</param>
|
|
|
|
|
- /// <param name="bottom">Bottom edge of the view frustum</param>
|
|
|
|
|
- /// <param name="top">Top edge of the view frustum</param>
|
|
|
|
|
- /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
- /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
- /// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
|
|
|
- /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
- /// Thrown under the following conditions:
|
|
|
|
|
- /// <list type="bullet">
|
|
|
|
|
- /// <item>zNear is negative or zero</item>
|
|
|
|
|
- /// <item>zFar is negative or zero</item>
|
|
|
|
|
- /// <item>zNear is larger than zFar</item>
|
|
|
|
|
- /// </list>
|
|
|
|
|
- /// </exception>
|
|
|
|
|
- public static Matrix4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- CreatePerspectiveOffCenter(left, right, bottom, top, zNear, zFar, out result);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region Obsolete Functions
|
|
|
|
|
-
|
|
|
|
|
- #region Translation Functions
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Builds a translation matrix.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="trans">The translation vector.</param>
|
|
|
|
|
- /// <returns>A new Matrix4 instance.</returns>
|
|
|
|
|
- [Obsolete("Use CreateTranslation instead.")]
|
|
|
|
|
- public static Matrix4 Translation(Vector3 trans)
|
|
|
|
|
- {
|
|
|
|
|
- return Translation(trans.X, trans.Y, trans.Z);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a translation matrix with the given translation
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="x">X translation</param>
|
|
|
|
|
- /// <param name="y">Y translation</param>
|
|
|
|
|
- /// <param name="z">Z translation</param>
|
|
|
|
|
- /// <returns>A Translation matrix</returns>
|
|
|
|
|
- [Obsolete("Use CreateTranslation instead.")]
|
|
|
|
|
- public static Matrix4 Translation(float x, float y, float z)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result = Identity;
|
|
|
|
|
- result.Row3 = new Vector4(x, y, z, 1.0f);
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region Scale Functions
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a scaling matrix
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="scale">Single scale factor for x,y and z axes</param>
|
|
|
|
|
- /// <returns>A scaling matrix</returns>
|
|
|
|
|
- public static Matrix4 Scale(float scale)
|
|
|
|
|
- {
|
|
|
|
|
- return Scale(scale, scale, scale);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a scaling matrix
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="scale">Scale factors for x,y and z axes</param>
|
|
|
|
|
- /// <returns>A scaling matrix</returns>
|
|
|
|
|
- public static Matrix4 Scale(Vector3 scale)
|
|
|
|
|
- {
|
|
|
|
|
- return Scale(scale.X, scale.Y, scale.Z);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a scaling matrix
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="x">Scale factor for x-axis</param>
|
|
|
|
|
- /// <param name="y">Scale factor for y-axis</param>
|
|
|
|
|
- /// <param name="z">Scale factor for z-axis</param>
|
|
|
|
|
- /// <returns>A scaling matrix</returns>
|
|
|
|
|
- public static Matrix4 Scale(float x, float y, float z)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- result.Row0 = Vector4.UnitX * x;
|
|
|
|
|
- result.Row1 = Vector4.UnitY * y;
|
|
|
|
|
- result.Row2 = Vector4.UnitZ * z;
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- #endregion
|
|
|
|
|
-
|
|
|
|
|
- #region Rotation Functions
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a rotation matrix that rotates about the x-axis
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">angle in radians to rotate counter-clockwise around the x-axis</param>
|
|
|
|
|
- /// <returns>A rotation matrix</returns>
|
|
|
|
|
- [Obsolete("Use CreateRotationX instead.")]
|
|
|
|
|
- public static Matrix4 RotateX(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- result.Row0 = Vector4.UnitX;
|
|
|
|
|
- result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
|
|
|
|
|
- result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a rotation matrix that rotates about the y-axis
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">angle in radians to rotate counter-clockwise around the y-axis</param>
|
|
|
|
|
- /// <returns>A rotation matrix</returns>
|
|
|
|
|
- [Obsolete("Use CreateRotationY instead.")]
|
|
|
|
|
- public static Matrix4 RotateY(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
|
|
|
|
|
- result.Row1 = Vector4.UnitY;
|
|
|
|
|
- result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- return result;
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Build a rotation matrix that rotates about the z-axis
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="angle">angle in radians to rotate counter-clockwise around the z-axis</param>
|
|
|
|
|
- /// <returns>A rotation matrix</returns>
|
|
|
|
|
- [Obsolete("Use CreateRotationZ instead.")]
|
|
|
|
|
- public static Matrix4 RotateZ(float angle)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
|
|
|
|
|
- result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
|
|
|
|
|
- result.Row2 = Vector4.UnitZ;
|
|
|
|
|
- result.Row3 = Vector4.UnitW;
|
|
|
|
|
- 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>
|
|
|
|
|
- [Obsolete("Use CreateFromAxisAngle instead.")]
|
|
|
|
|
- public static Matrix4 Rotate(Vector3 axis, float angle)
|
|
|
|
|
- {
|
|
|
|
|
- float cos = (float)System.Math.Cos(-angle);
|
|
|
|
|
- float sin = (float)System.Math.Sin(-angle);
|
|
|
|
|
- float t = 1.0f - cos;
|
|
|
|
|
-
|
|
|
|
|
- axis.Normalize();
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 result;
|
|
|
|
|
- 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);
|
|
|
|
|
- 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);
|
|
|
|
|
- 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);
|
|
|
|
|
- result.Row3 = Vector4.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 Matrix4 Rotate(Quaternion q)
|
|
|
|
|
- {
|
|
|
|
|
- Vector3 axis;
|
|
|
|
|
- float angle;
|
|
|
|
|
- q.ToAxisAngle(out axis, out angle);
|
|
|
|
|
- return CreateFromAxisAngle(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 Matrix4 that transforms world space to camera space</returns>
|
|
|
|
|
- public static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)
|
|
|
|
|
- {
|
|
|
|
|
- Vector3 z = Vector3.Normalize(eye - target);
|
|
|
|
|
- Vector3 x = Vector3.Normalize(Vector3.Cross(up, z));
|
|
|
|
|
- Vector3 y = Vector3.Normalize(Vector3.Cross(z, x));
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 rot = new Matrix4(new Vector4(x.X, y.X, z.X, 0.0f),
|
|
|
|
|
- new Vector4(x.Y, y.Y, z.Y, 0.0f),
|
|
|
|
|
- new Vector4(x.Z, y.Z, z.Z, 0.0f),
|
|
|
|
|
- Vector4.UnitW);
|
|
|
|
|
-
|
|
|
|
|
- Matrix4 trans = Matrix4.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 Matrix4 LookAt(float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)
|
|
|
|
|
- {
|
|
|
|
|
- return LookAt(new Vector3(eyeX, eyeY, eyeZ), new Vector3(targetX, targetY, targetZ), new Vector3(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>
|
|
|
|
|
- [Obsolete("Use CreatePerspectiveOffCenter instead.")]
|
|
|
|
|
- public static Matrix4 Frustum(float left, float right, float bottom, float top, float near, float far)
|
|
|
|
|
- {
|
|
|
|
|
- float invRL = 1.0f / (right - left);
|
|
|
|
|
- float invTB = 1.0f / (top - bottom);
|
|
|
|
|
- float invFN = 1.0f / (far - near);
|
|
|
|
|
- return new Matrix4(new Vector4(2.0f * near * invRL, 0.0f, 0.0f, 0.0f),
|
|
|
|
|
- new Vector4(0.0f, 2.0f * near * invTB, 0.0f, 0.0f),
|
|
|
|
|
- new Vector4((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0f),
|
|
|
|
|
- new Vector4(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>
|
|
|
|
|
- [Obsolete("Use CreatePerspectiveFieldOfView instead.")]
|
|
|
|
|
- public static Matrix4 Perspective(float fovy, float aspect, float near, float far)
|
|
|
|
|
- {
|
|
|
|
|
- float yMax = near * (float)System.Math.Tan(0.5f * fovy);
|
|
|
|
|
- float yMin = -yMax;
|
|
|
|
|
- float xMin = yMin * aspect;
|
|
|
|
|
- float 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 Matrix4 Mult(Matrix4 left, Matrix4 right)
|
|
|
|
|
- {
|
|
|
|
|
- Matrix4 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 Matrix4 left, ref Matrix4 right, out Matrix4 result)
|
|
|
|
|
- {
|
|
|
|
|
- result = new Matrix4(
|
|
|
|
|
- left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41,
|
|
|
|
|
- left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42,
|
|
|
|
|
- left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43,
|
|
|
|
|
- left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44,
|
|
|
|
|
- left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41,
|
|
|
|
|
- left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42,
|
|
|
|
|
- left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43,
|
|
|
|
|
- left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44,
|
|
|
|
|
- left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41,
|
|
|
|
|
- left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42,
|
|
|
|
|
- left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43,
|
|
|
|
|
- left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44,
|
|
|
|
|
- left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41,
|
|
|
|
|
- left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42,
|
|
|
|
|
- left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43,
|
|
|
|
|
- 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 Matrix4 is singular.</exception>
|
|
|
|
|
- public static Matrix4 Invert(Matrix4 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
|
|
|
|
|
- float[,] 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
|
|
|
|
|
- float 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)
|
|
|
|
|
- {
|
|
|
|
|
- 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>
|
|
|
|
|
- /// <param name="result">The result of the calculation</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);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Compares two instances for equality.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">The first instance.</param>
|
|
|
|
|
- /// <param name="right">The second instance.</param>
|
|
|
|
|
- /// <returns>True, if left equals right; false otherwise.</returns>
|
|
|
|
|
- public static bool operator ==(Matrix4 left, Matrix4 right)
|
|
|
|
|
- {
|
|
|
|
|
- return left.Equals(right);
|
|
|
|
|
- }
|
|
|
|
|
-
|
|
|
|
|
- /// <summary>
|
|
|
|
|
- /// Compares two instances for inequality.
|
|
|
|
|
- /// </summary>
|
|
|
|
|
- /// <param name="left">The first instance.</param>
|
|
|
|
|
- /// <param name="right">The second instance.</param>
|
|
|
|
|
- /// <returns>True, if left does not equal right; false otherwise.</returns>
|
|
|
|
|
- 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
|
|
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-
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- #region public override bool Equals(object obj)
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-
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- /// <summary>
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- /// Indicates whether this instance and a specified object are equal.
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- /// </summary>
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- /// <param name="obj">The object to compare tresult.</param>
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- /// <returns>True if the instances are equal; false otherwise.</returns>
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- public override bool Equals(object obj)
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- {
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- if (!(obj is Matrix4))
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- return false;
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-
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- return this.Equals((Matrix4)obj);
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- }
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-
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- #endregion
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-
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- #endregion
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-
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- #endregion
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-
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- #region IEquatable<Matrix4> Members
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-
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- /// <summary>Indicates whether the current matrix is equal to another matrix.</summary>
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- /// <param name="other">An matrix to compare with this matrix.</param>
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- /// <returns>true if the current matrix is equal to the matrix parameter; otherwise, false.</returns>
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- public bool Equals(Matrix4 other)
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- {
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- return
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- Row0 == other.Row0 &&
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- Row1 == other.Row1 &&
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- Row2 == other.Row2 &&
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- Row3 == other.Row3;
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- }
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-
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- #endregion
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- }
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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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+
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+ #endregion
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+
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+ #region Constructors
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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="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 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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+
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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="m03">Fourth 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="m13">Fourth 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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+ /// <param name="m23">First item of the third row of the matrix.</param>
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+ /// <param name="m30">Fourth item of the fourth row of the matrix.</param>
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+ /// <param name="m31">Second item of the fourth row of the matrix.</param>
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+ /// <param name="m32">Third item of the fourth row of the matrix.</param>
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+ /// <param name="m33">Fourth item of the fourth row of the matrix.</param>
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|
+ public Matrix4(
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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 Vector4(m00, m01, m02, m03);
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+ Row1 = new Vector4(m10, m11, m12, m13);
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+ Row2 = new Vector4(m20, m21, m22, m23);
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+ Row3 = new Vector4(m30, m31, m32, m33);
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+ }
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+
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+ #endregion
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+
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+ #region Public Members
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+
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+ #region Properties
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+
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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>
|
|
|
|
|
+ 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>
|
|
|
|
|
+ /// The second column of this matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ 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>
|
|
|
|
|
+ /// The third column of this matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public Vector4 Column2
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|
|
|
|
+ {
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|
|
+ get { return new Vector4(Row0.Z, Row1.Z, Row2.Z, Row3.Z); }
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// The fourth column of this matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public Vector4 Column3
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|
|
|
|
+ {
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|
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|
|
+ get { return new Vector4(Row0.W, Row1.W, Row2.W, Row3.W); }
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 1, column 1 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M11 { get { return Row0.X; } set { Row0.X = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 1, column 2 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M12 { get { return Row0.Y; } set { Row0.Y = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 1, column 3 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M13 { get { return Row0.Z; } set { Row0.Z = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 1, column 4 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M14 { get { return Row0.W; } set { Row0.W = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 2, column 1 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M21 { get { return Row1.X; } set { Row1.X = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 2, column 2 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M22 { get { return Row1.Y; } set { Row1.Y = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 2, column 3 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M23 { get { return Row1.Z; } set { Row1.Z = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 2, column 4 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M24 { get { return Row1.W; } set { Row1.W = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 3, column 1 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M31 { get { return Row2.X; } set { Row2.X = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 3, column 2 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M32 { get { return Row2.Y; } set { Row2.Y = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 3, column 3 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M33 { get { return Row2.Z; } set { Row2.Z = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 3, column 4 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M34 { get { return Row2.W; } set { Row2.W = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 4, column 1 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M41 { get { return Row3.X; } set { Row3.X = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 4, column 2 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M42 { get { return Row3.Y; } set { Row3.Y = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 4, column 3 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M43 { get { return Row3.Z; } set { Row3.Z = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Gets or sets the value at row 4, column 4 of this instance.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public float M44 { get { return Row3.W; } set { Row3.W = value; } }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region Instance
|
|
|
|
|
+
|
|
|
|
|
+ #region public void Invert()
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Converts this instance into its inverse.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public void Invert()
|
|
|
|
|
+ {
|
|
|
|
|
+ this = Matrix4.Invert(this);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region public void Transpose()
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Converts this instance into its transpose.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ public void Transpose()
|
|
|
|
|
+ {
|
|
|
|
|
+ this = Matrix4.Transpose(this);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region Static
|
|
|
|
|
+
|
|
|
|
|
+ #region CreateFromAxisAngle
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a rotation matrix from the specified axis/angle rotation.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="axis">The axis to rotate about.</param>
|
|
|
|
|
+ /// <param name="angle">Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).</param>
|
|
|
|
|
+ /// <param name="result">A matrix instance.</param>
|
|
|
|
|
+ public static void CreateFromAxisAngle(Vector3 axis, float angle, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(-angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(-angle);
|
|
|
|
|
+ float t = 1.0f - cos;
|
|
|
|
|
+
|
|
|
|
|
+ axis.Normalize();
|
|
|
|
|
+
|
|
|
|
|
+ result = new Matrix4(t * axis.X * axis.X + cos, t * axis.X * axis.Y - sin * axis.Z, t * axis.X * axis.Z + sin * axis.Y, 0.0f,
|
|
|
|
|
+ t * axis.X * axis.Y + sin * axis.Z, t * axis.Y * axis.Y + cos, t * axis.Y * axis.Z - sin * axis.X, 0.0f,
|
|
|
|
|
+ t * axis.X * axis.Z - sin * axis.Y, t * axis.Y * axis.Z + sin * axis.X, t * axis.Z * axis.Z + cos, 0.0f,
|
|
|
|
|
+ 0, 0, 0, 1);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a rotation matrix from the specified axis/angle rotation.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="axis">The axis to rotate about.</param>
|
|
|
|
|
+ /// <param name="angle">Angle in radians to rotate counter-clockwise (looking in the direction of the given axis).</param>
|
|
|
|
|
+ /// <returns>A matrix instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateFromAxisAngle(Vector3 axis, float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateFromAxisAngle(axis, angle, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreateRotation[XYZ]
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the x-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateRotationX(float angle, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ result.Row0 = Vector4.UnitX;
|
|
|
|
|
+ result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
|
|
|
|
|
+ result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the x-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateRotationX(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateRotationX(angle, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the y-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateRotationY(float angle, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
|
|
|
|
|
+ result.Row1 = Vector4.UnitY;
|
|
|
|
|
+ result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the y-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateRotationY(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateRotationY(angle, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the z-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateRotationZ(float angle, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
|
|
|
|
|
+ result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
|
|
|
|
|
+ result.Row2 = Vector4.UnitZ;
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a rotation matrix for a rotation around the z-axis.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">The counter-clockwise angle in radians.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateRotationZ(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateRotationZ(angle, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreateTranslation
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a translation matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="x">X translation.</param>
|
|
|
|
|
+ /// <param name="y">Y translation.</param>
|
|
|
|
|
+ /// <param name="z">Z translation.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateTranslation(float x, float y, float z, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ result = Identity;
|
|
|
|
|
+ result.Row3 = new Vector4(x, y, z, 1);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a translation matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="vector">The translation vector.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateTranslation(ref Vector3 vector, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ result = Identity;
|
|
|
|
|
+ result.Row3 = new Vector4(vector.X, vector.Y, vector.Z, 1);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a translation matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="x">X translation.</param>
|
|
|
|
|
+ /// <param name="y">Y translation.</param>
|
|
|
|
|
+ /// <param name="z">Z translation.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateTranslation(float x, float y, float z)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateTranslation(x, y, z, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a translation matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="vector">The translation vector.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateTranslation(Vector3 vector)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateTranslation(vector.X, vector.Y, vector.Z, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreateOrthographic
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an orthographic projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="width">The width of the projection volume.</param>
|
|
|
|
|
+ /// <param name="height">The height of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateOrthographic(float width, float height, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an orthographic projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="width">The width of the projection volume.</param>
|
|
|
|
|
+ /// <param name="height">The height of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
+ /// <rereturns>The resulting Matrix4 instance.</rereturns>
|
|
|
|
|
+ public static Matrix4 CreateOrthographic(float width, float height, float zNear, float zFar)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateOrthographicOffCenter(-width / 2, width / 2, -height / 2, height / 2, zNear, zFar, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreateOrthographicOffCenter
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an orthographic projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">The left edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="right">The right edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="bottom">The bottom edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="top">The top edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="result">The resulting Matrix4 instance.</param>
|
|
|
|
|
+ public static void CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ result = new Matrix4();
|
|
|
|
|
+
|
|
|
|
|
+ float invRL = 1 / (right - left);
|
|
|
|
|
+ float invTB = 1 / (top - bottom);
|
|
|
|
|
+ float invFN = 1 / (zFar - zNear);
|
|
|
|
|
+
|
|
|
|
|
+ result.M11 = 2 * invRL;
|
|
|
|
|
+ result.M22 = 2 * invTB;
|
|
|
|
|
+ result.M33 = -2 * invFN;
|
|
|
|
|
+
|
|
|
|
|
+ result.M41 = -(right + left) * invRL;
|
|
|
|
|
+ result.M42 = -(top + bottom) * invTB;
|
|
|
|
|
+ result.M43 = -(zFar + zNear) * invFN;
|
|
|
|
|
+ result.M44 = 1;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an orthographic projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">The left edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="right">The right edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="bottom">The bottom edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="top">The top edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zNear">The near edge of the projection volume.</param>
|
|
|
|
|
+ /// <param name="zFar">The far edge of the projection volume.</param>
|
|
|
|
|
+ /// <returns>The resulting Matrix4 instance.</returns>
|
|
|
|
|
+ public static Matrix4 CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreateOrthographicOffCenter(left, right, bottom, top, zNear, zFar, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreatePerspectiveFieldOfView
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a perspective projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
|
|
|
|
|
+ /// <param name="aspect">Aspect ratio of the view (width / height)</param>
|
|
|
|
|
+ /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
+ /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
+ /// <param name="result">A projection matrix that transforms camera space to raster space</param>
|
|
|
|
|
+ /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
+ /// Thrown under the following conditions:
|
|
|
|
|
+ /// <list type="bullet">
|
|
|
|
|
+ /// <item>fovy is zero, less than zero or larger than Math.PI</item>
|
|
|
|
|
+ /// <item>aspect is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is negative or zero</item>
|
|
|
|
|
+ /// <item>zFar is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is larger than zFar</item>
|
|
|
|
|
+ /// </list>
|
|
|
|
|
+ /// </exception>
|
|
|
|
|
+ public static void CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ if (fovy <= 0 || fovy > Math.PI)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("fovy");
|
|
|
|
|
+ if (aspect <= 0)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("aspect");
|
|
|
|
|
+ if (zNear <= 0)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
+ if (zFar <= 0)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zFar");
|
|
|
|
|
+ if (zNear >= zFar)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
+
|
|
|
|
|
+ float yMax = zNear * (float)System.Math.Tan(0.5f * fovy);
|
|
|
|
|
+ float yMin = -yMax;
|
|
|
|
|
+ float xMin = yMin * aspect;
|
|
|
|
|
+ float xMax = yMax * aspect;
|
|
|
|
|
+
|
|
|
|
|
+ CreatePerspectiveOffCenter(xMin, xMax, yMin, yMax, zNear, zFar, out result);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates a perspective projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="fovy">Angle of the field of view in the y direction (in radians)</param>
|
|
|
|
|
+ /// <param name="aspect">Aspect ratio of the view (width / height)</param>
|
|
|
|
|
+ /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
+ /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
+ /// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
|
|
|
+ /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
+ /// Thrown under the following conditions:
|
|
|
|
|
+ /// <list type="bullet">
|
|
|
|
|
+ /// <item>fovy is zero, less than zero or larger than Math.PI</item>
|
|
|
|
|
+ /// <item>aspect is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is negative or zero</item>
|
|
|
|
|
+ /// <item>zFar is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is larger than zFar</item>
|
|
|
|
|
+ /// </list>
|
|
|
|
|
+ /// </exception>
|
|
|
|
|
+ public static Matrix4 CreatePerspectiveFieldOfView(float fovy, float aspect, float zNear, float zFar)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreatePerspectiveFieldOfView(fovy, aspect, zNear, zFar, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region CreatePerspectiveOffCenter
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an perspective projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">Left edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="right">Right edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="bottom">Bottom edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="top">Top edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
+ /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
+ /// <param name="result">A projection matrix that transforms camera space to raster space</param>
|
|
|
|
|
+ /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
+ /// Thrown under the following conditions:
|
|
|
|
|
+ /// <list type="bullet">
|
|
|
|
|
+ /// <item>zNear is negative or zero</item>
|
|
|
|
|
+ /// <item>zFar is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is larger than zFar</item>
|
|
|
|
|
+ /// </list>
|
|
|
|
|
+ /// </exception>
|
|
|
|
|
+ public static void CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ if (zNear <= 0)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
+ if (zFar <= 0)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zFar");
|
|
|
|
|
+ if (zNear >= zFar)
|
|
|
|
|
+ throw new ArgumentOutOfRangeException("zNear");
|
|
|
|
|
+
|
|
|
|
|
+ float x = (2.0f * zNear) / (right - left);
|
|
|
|
|
+ float y = (2.0f * zNear) / (top - bottom);
|
|
|
|
|
+ float a = (right + left) / (right - left);
|
|
|
|
|
+ float b = (top + bottom) / (top - bottom);
|
|
|
|
|
+ float c = -(zFar + zNear) / (zFar - zNear);
|
|
|
|
|
+ float d = -(2.0f * zFar * zNear) / (zFar - zNear);
|
|
|
|
|
+
|
|
|
|
|
+ result = new Matrix4(x, 0, 0, 0,
|
|
|
|
|
+ 0, y, 0, 0,
|
|
|
|
|
+ a, b, c, -1,
|
|
|
|
|
+ 0, 0, d, 0);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Creates an perspective projection matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">Left edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="right">Right edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="bottom">Bottom edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="top">Top edge of the view frustum</param>
|
|
|
|
|
+ /// <param name="zNear">Distance to the near clip plane</param>
|
|
|
|
|
+ /// <param name="zFar">Distance to the far clip plane</param>
|
|
|
|
|
+ /// <returns>A projection matrix that transforms camera space to raster space</returns>
|
|
|
|
|
+ /// <exception cref="System.ArgumentOutOfRangeException">
|
|
|
|
|
+ /// Thrown under the following conditions:
|
|
|
|
|
+ /// <list type="bullet">
|
|
|
|
|
+ /// <item>zNear is negative or zero</item>
|
|
|
|
|
+ /// <item>zFar is negative or zero</item>
|
|
|
|
|
+ /// <item>zNear is larger than zFar</item>
|
|
|
|
|
+ /// </list>
|
|
|
|
|
+ /// </exception>
|
|
|
|
|
+ public static Matrix4 CreatePerspectiveOffCenter(float left, float right, float bottom, float top, float zNear, float zFar)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ CreatePerspectiveOffCenter(left, right, bottom, top, zNear, zFar, out result);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region Obsolete Functions
|
|
|
|
|
+
|
|
|
|
|
+ #region Translation Functions
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Builds a translation matrix.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="trans">The translation vector.</param>
|
|
|
|
|
+ /// <returns>A new Matrix4 instance.</returns>
|
|
|
|
|
+ [Obsolete("Use CreateTranslation instead.")]
|
|
|
|
|
+ public static Matrix4 Translation(Vector3 trans)
|
|
|
|
|
+ {
|
|
|
|
|
+ return Translation(trans.X, trans.Y, trans.Z);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a translation matrix with the given translation
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="x">X translation</param>
|
|
|
|
|
+ /// <param name="y">Y translation</param>
|
|
|
|
|
+ /// <param name="z">Z translation</param>
|
|
|
|
|
+ /// <returns>A Translation matrix</returns>
|
|
|
|
|
+ [Obsolete("Use CreateTranslation instead.")]
|
|
|
|
|
+ public static Matrix4 Translation(float x, float y, float z)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result = Identity;
|
|
|
|
|
+ result.Row3 = new Vector4(x, y, z, 1.0f);
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region Scale Functions
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a scaling matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="scale">Single scale factor for x,y and z axes</param>
|
|
|
|
|
+ /// <returns>A scaling matrix</returns>
|
|
|
|
|
+ public static Matrix4 Scale(float scale)
|
|
|
|
|
+ {
|
|
|
|
|
+ return Scale(scale, scale, scale);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a scaling matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="scale">Scale factors for x,y and z axes</param>
|
|
|
|
|
+ /// <returns>A scaling matrix</returns>
|
|
|
|
|
+ public static Matrix4 Scale(Vector3 scale)
|
|
|
|
|
+ {
|
|
|
|
|
+ return Scale(scale.X, scale.Y, scale.Z);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a scaling matrix
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="x">Scale factor for x-axis</param>
|
|
|
|
|
+ /// <param name="y">Scale factor for y-axis</param>
|
|
|
|
|
+ /// <param name="z">Scale factor for z-axis</param>
|
|
|
|
|
+ /// <returns>A scaling matrix</returns>
|
|
|
|
|
+ public static Matrix4 Scale(float x, float y, float z)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ result.Row0 = Vector4.UnitX * x;
|
|
|
|
|
+ result.Row1 = Vector4.UnitY * y;
|
|
|
|
|
+ result.Row2 = Vector4.UnitZ * z;
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+
|
|
|
|
|
+ #region Rotation Functions
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a rotation matrix that rotates about the x-axis
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">angle in radians to rotate counter-clockwise around the x-axis</param>
|
|
|
|
|
+ /// <returns>A rotation matrix</returns>
|
|
|
|
|
+ [Obsolete("Use CreateRotationX instead.")]
|
|
|
|
|
+ public static Matrix4 RotateX(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ result.Row0 = Vector4.UnitX;
|
|
|
|
|
+ result.Row1 = new Vector4(0.0f, cos, sin, 0.0f);
|
|
|
|
|
+ result.Row2 = new Vector4(0.0f, -sin, cos, 0.0f);
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a rotation matrix that rotates about the y-axis
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">angle in radians to rotate counter-clockwise around the y-axis</param>
|
|
|
|
|
+ /// <returns>A rotation matrix</returns>
|
|
|
|
|
+ [Obsolete("Use CreateRotationY instead.")]
|
|
|
|
|
+ public static Matrix4 RotateY(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ result.Row0 = new Vector4(cos, 0.0f, -sin, 0.0f);
|
|
|
|
|
+ result.Row1 = Vector4.UnitY;
|
|
|
|
|
+ result.Row2 = new Vector4(sin, 0.0f, cos, 0.0f);
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ return result;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Build a rotation matrix that rotates about the z-axis
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="angle">angle in radians to rotate counter-clockwise around the z-axis</param>
|
|
|
|
|
+ /// <returns>A rotation matrix</returns>
|
|
|
|
|
+ [Obsolete("Use CreateRotationZ instead.")]
|
|
|
|
|
+ public static Matrix4 RotateZ(float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(angle);
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ result.Row0 = new Vector4(cos, sin, 0.0f, 0.0f);
|
|
|
|
|
+ result.Row1 = new Vector4(-sin, cos, 0.0f, 0.0f);
|
|
|
|
|
+ result.Row2 = Vector4.UnitZ;
|
|
|
|
|
+ result.Row3 = Vector4.UnitW;
|
|
|
|
|
+ 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>
|
|
|
|
|
+ [Obsolete("Use CreateFromAxisAngle instead.")]
|
|
|
|
|
+ public static Matrix4 Rotate(Vector3 axis, float angle)
|
|
|
|
|
+ {
|
|
|
|
|
+ float cos = (float)System.Math.Cos(-angle);
|
|
|
|
|
+ float sin = (float)System.Math.Sin(-angle);
|
|
|
|
|
+ float t = 1.0f - cos;
|
|
|
|
|
+
|
|
|
|
|
+ axis.Normalize();
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 result;
|
|
|
|
|
+ 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);
|
|
|
|
|
+ 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);
|
|
|
|
|
+ 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);
|
|
|
|
|
+ result.Row3 = Vector4.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 Matrix4 Rotate(Quaternion q)
|
|
|
|
|
+ {
|
|
|
|
|
+ Vector3 axis;
|
|
|
|
|
+ float angle;
|
|
|
|
|
+ q.ToAxisAngle(out axis, out angle);
|
|
|
|
|
+ return CreateFromAxisAngle(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 Matrix4 that transforms world space to camera space</returns>
|
|
|
|
|
+ public static Matrix4 LookAt(Vector3 eye, Vector3 target, Vector3 up)
|
|
|
|
|
+ {
|
|
|
|
|
+ Vector3 z = Vector3.Normalize(eye - target);
|
|
|
|
|
+ Vector3 x = Vector3.Normalize(Vector3.Cross(up, z));
|
|
|
|
|
+ Vector3 y = Vector3.Normalize(Vector3.Cross(z, x));
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 rot = new Matrix4(new Vector4(x.X, y.X, z.X, 0.0f),
|
|
|
|
|
+ new Vector4(x.Y, y.Y, z.Y, 0.0f),
|
|
|
|
|
+ new Vector4(x.Z, y.Z, z.Z, 0.0f),
|
|
|
|
|
+ Vector4.UnitW);
|
|
|
|
|
+
|
|
|
|
|
+ Matrix4 trans = Matrix4.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 Matrix4 LookAt(float eyeX, float eyeY, float eyeZ, float targetX, float targetY, float targetZ, float upX, float upY, float upZ)
|
|
|
|
|
+ {
|
|
|
|
|
+ return LookAt(new Vector3(eyeX, eyeY, eyeZ), new Vector3(targetX, targetY, targetZ), new Vector3(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>
|
|
|
|
|
+ [Obsolete("Use CreatePerspectiveOffCenter instead.")]
|
|
|
|
|
+ public static Matrix4 Frustum(float left, float right, float bottom, float top, float near, float far)
|
|
|
|
|
+ {
|
|
|
|
|
+ float invRL = 1.0f / (right - left);
|
|
|
|
|
+ float invTB = 1.0f / (top - bottom);
|
|
|
|
|
+ float invFN = 1.0f / (far - near);
|
|
|
|
|
+ return new Matrix4(new Vector4(2.0f * near * invRL, 0.0f, 0.0f, 0.0f),
|
|
|
|
|
+ new Vector4(0.0f, 2.0f * near * invTB, 0.0f, 0.0f),
|
|
|
|
|
+ new Vector4((right + left) * invRL, (top + bottom) * invTB, -(far + near) * invFN, -1.0f),
|
|
|
|
|
+ new Vector4(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>
|
|
|
|
|
+ [Obsolete("Use CreatePerspectiveFieldOfView instead.")]
|
|
|
|
|
+ public static Matrix4 Perspective(float fovy, float aspect, float near, float far)
|
|
|
|
|
+ {
|
|
|
|
|
+ float yMax = near * (float)System.Math.Tan(0.5f * fovy);
|
|
|
|
|
+ float yMin = -yMax;
|
|
|
|
|
+ float xMin = yMin * aspect;
|
|
|
|
|
+ float 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 Matrix4 Mult(Matrix4 left, Matrix4 right)
|
|
|
|
|
+ {
|
|
|
|
|
+ Matrix4 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 Matrix4 left, ref Matrix4 right, out Matrix4 result)
|
|
|
|
|
+ {
|
|
|
|
|
+ result = new Matrix4(
|
|
|
|
|
+ left.M11 * right.M11 + left.M12 * right.M21 + left.M13 * right.M31 + left.M14 * right.M41,
|
|
|
|
|
+ left.M11 * right.M12 + left.M12 * right.M22 + left.M13 * right.M32 + left.M14 * right.M42,
|
|
|
|
|
+ left.M11 * right.M13 + left.M12 * right.M23 + left.M13 * right.M33 + left.M14 * right.M43,
|
|
|
|
|
+ left.M11 * right.M14 + left.M12 * right.M24 + left.M13 * right.M34 + left.M14 * right.M44,
|
|
|
|
|
+ left.M21 * right.M11 + left.M22 * right.M21 + left.M23 * right.M31 + left.M24 * right.M41,
|
|
|
|
|
+ left.M21 * right.M12 + left.M22 * right.M22 + left.M23 * right.M32 + left.M24 * right.M42,
|
|
|
|
|
+ left.M21 * right.M13 + left.M22 * right.M23 + left.M23 * right.M33 + left.M24 * right.M43,
|
|
|
|
|
+ left.M21 * right.M14 + left.M22 * right.M24 + left.M23 * right.M34 + left.M24 * right.M44,
|
|
|
|
|
+ left.M31 * right.M11 + left.M32 * right.M21 + left.M33 * right.M31 + left.M34 * right.M41,
|
|
|
|
|
+ left.M31 * right.M12 + left.M32 * right.M22 + left.M33 * right.M32 + left.M34 * right.M42,
|
|
|
|
|
+ left.M31 * right.M13 + left.M32 * right.M23 + left.M33 * right.M33 + left.M34 * right.M43,
|
|
|
|
|
+ left.M31 * right.M14 + left.M32 * right.M24 + left.M33 * right.M34 + left.M34 * right.M44,
|
|
|
|
|
+ left.M41 * right.M11 + left.M42 * right.M21 + left.M43 * right.M31 + left.M44 * right.M41,
|
|
|
|
|
+ left.M41 * right.M12 + left.M42 * right.M22 + left.M43 * right.M32 + left.M44 * right.M42,
|
|
|
|
|
+ left.M41 * right.M13 + left.M42 * right.M23 + left.M43 * right.M33 + left.M44 * right.M43,
|
|
|
|
|
+ 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 Matrix4 is singular.</exception>
|
|
|
|
|
+ public static Matrix4 Invert(Matrix4 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
|
|
|
|
|
+ float[,] 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
|
|
|
|
|
+ float 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)
|
|
|
|
|
+ {
|
|
|
|
|
+ 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>
|
|
|
|
|
+ /// <param name="result">The result of the calculation</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);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Compares two instances for equality.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">The first instance.</param>
|
|
|
|
|
+ /// <param name="right">The second instance.</param>
|
|
|
|
|
+ /// <returns>True, if left equals right; false otherwise.</returns>
|
|
|
|
|
+ public static bool operator ==(Matrix4 left, Matrix4 right)
|
|
|
|
|
+ {
|
|
|
|
|
+ return left.Equals(right);
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ /// <summary>
|
|
|
|
|
+ /// Compares two instances for inequality.
|
|
|
|
|
+ /// </summary>
|
|
|
|
|
+ /// <param name="left">The first instance.</param>
|
|
|
|
|
+ /// <param name="right">The second instance.</param>
|
|
|
|
|
+ /// <returns>True, if left does not equal right; false otherwise.</returns>
|
|
|
|
|
+ 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 tresult.</param>
|
|
|
|
|
+ /// <returns>True if the instances are equal; false otherwise.</returns>
|
|
|
|
|
+ public override bool Equals(object obj)
|
|
|
|
|
+ {
|
|
|
|
|
+ if (!(obj is Matrix4))
|
|
|
|
|
+ return false;
|
|
|
|
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+
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+ return this.Equals((Matrix4)obj);
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+ }
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+
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+ #endregion
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+
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+ #endregion
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+
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+ #endregion
|
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+
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+ #region IEquatable<Matrix4> Members
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|
+
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|
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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(Matrix4 other)
|
|
|
|
|
+ {
|
|
|
|
|
+ return
|
|
|
|
|
+ Row0 == other.Row0 &&
|
|
|
|
|
+ Row1 == other.Row1 &&
|
|
|
|
|
+ Row2 == other.Row2 &&
|
|
|
|
|
+ Row3 == other.Row3;
|
|
|
|
|
+ }
|
|
|
|
|
+
|
|
|
|
|
+ #endregion
|
|
|
|
|
+ }
|
|
|
}
|
|
}
|