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@@ -1,12 +1,22 @@
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using System;
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using System.Globalization;
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+using System.Linq;
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+using System.Numerics;
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using Avalonia.Utilities;
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namespace Avalonia
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{
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/// <summary>
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- /// A 2x3 matrix.
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+ /// A 3x3 matrix.
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/// </summary>
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+ /// <remakrs>Matrix layout:
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+ /// | 1st col | 2nd col | 3r col |
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+ /// 1st row | scaleX | skrewY | persX |
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+ /// 2nd row | skrewX | scaleY | persY |
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+ /// 3rd row | transX | transY | persZ |
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+ ///
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+ /// Note: Skia.SkMatrix uses a transposed layout (where for example skrewX/skrewY and perspp0/tranX are swapped).
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+ /// </remakrs>
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#if !BUILDTASK
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public
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#endif
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@@ -14,40 +24,76 @@ namespace Avalonia
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{
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private readonly double _m11;
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private readonly double _m12;
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+ private readonly double _m13;
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private readonly double _m21;
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private readonly double _m22;
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+ private readonly double _m23;
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private readonly double _m31;
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private readonly double _m32;
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+ private readonly double _m33;
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+
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+ /// <summary>
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+ /// Initializes a new instance of the <see cref="Matrix"/> struct (equivalent to a 2x3 Matrix without perspective).
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+ /// </summary>
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+ /// <param name="scaleX">The first element of the first row.</param>
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+ /// <param name="skrewY">The second element of the first row.</param>
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+ /// <param name="skrewX">The first element of the second row.</param>
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+ /// <param name="scaleY">The second element of the second row.</param>
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+ /// <param name="offsetX">The first element of the third row.</param>
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+ /// <param name="offsetY">The second element of the third row.</param>
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+ public Matrix(
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+ double scaleX,
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+ double skrewY,
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+ double skrewX,
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+ double scaleY,
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+ double offsetX,
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+ double offsetY) : this( scaleX, skrewY, 0, skrewX, scaleY, 0, offsetX, offsetY, 1)
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+ {
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+ }
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+
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+
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/// <summary>
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/// Initializes a new instance of the <see cref="Matrix"/> struct.
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/// </summary>
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- /// <param name="m11">The first element of the first row.</param>
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- /// <param name="m12">The second element of the first row.</param>
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- /// <param name="m21">The first element of the second row.</param>
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- /// <param name="m22">The second element of the second row.</param>
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+ /// <param name="scaleX">The first element of the first row.</param>
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+ /// <param name="skrewY">The second element of the first row.</param>
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+ /// <param name="persX">The third element of the first row.</param>
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+ /// <param name="skrewX">The first element of the second row.</param>
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+ /// <param name="scaleY">The second element of the second row.</param>
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+ /// <param name="persY">The third element of the second row.</param>
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/// <param name="offsetX">The first element of the third row.</param>
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/// <param name="offsetY">The second element of the third row.</param>
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+ /// <param name="persZ">The third element of the third row.</param>
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public Matrix(
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- double m11,
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- double m12,
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- double m21,
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- double m22,
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+ double scaleX,
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+ double skrewY,
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+ double persX,
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+ double skrewX,
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+ double scaleY,
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+ double persY,
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double offsetX,
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- double offsetY)
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+ double offsetY,
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+ double persZ)
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{
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- _m11 = m11;
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- _m12 = m12;
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- _m21 = m21;
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- _m22 = m22;
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+ _m11 = scaleX;
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+ _m12 = skrewY;
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+ _m13 = persX;
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+ _m21 = skrewX;
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+ _m22 = scaleY;
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+ _m23 = persY;
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_m31 = offsetX;
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_m32 = offsetY;
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+ _m33 = persZ;
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}
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/// <summary>
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/// Returns the multiplicative identity matrix.
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/// </summary>
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- public static Matrix Identity { get; } = new Matrix(1.0, 0.0, 0.0, 1.0, 0.0, 0.0);
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+ public static Matrix Identity { get; } = new Matrix(
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+ 1.0, 0.0, 0.0,
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+ 0.0, 1.0, 0.0,
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+ 0.0, 0.0, 1.0);
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/// <summary>
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/// Returns whether the matrix is the identity matrix.
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@@ -60,35 +106,50 @@ namespace Avalonia
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public bool HasInverse => !MathUtilities.IsZero(GetDeterminant());
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/// <summary>
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- /// The first element of the first row
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+ /// The first element of the first row (scaleX).
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/// </summary>
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public double M11 => _m11;
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/// <summary>
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- /// The second element of the first row
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+ /// The second element of the first row (skrewY).
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/// </summary>
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public double M12 => _m12;
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/// <summary>
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- /// The first element of the second row
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+ /// The third element of the first row (persX: input x-axis perspective factor).
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+ /// </summary>
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+ public double M13 => _m13;
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+
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+ /// <summary>
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+ /// The first element of the second row (skrewX).
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/// </summary>
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public double M21 => _m21;
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/// <summary>
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- /// The second element of the second row
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+ /// The second element of the second row (scaleY).
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/// </summary>
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public double M22 => _m22;
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/// <summary>
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- /// The first element of the third row
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+ /// The third element of the second row (persY: input y-axis perspective factor).
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+ /// </summary>
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+ public double M23 => _m23;
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+
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+ /// <summary>
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+ /// The first element of the third row (offsetX/translateX).
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/// </summary>
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public double M31 => _m31;
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/// <summary>
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- /// The second element of the third row
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+ /// The second element of the third row (offsetY/translateY).
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/// </summary>
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public double M32 => _m32;
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+ /// <summary>
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+ /// The third element of the third row (persZ: perspective scale factor).
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+ /// </summary>
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+ public double M33 => _m33;
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+
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/// <summary>
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/// Multiplies two matrices together and returns the resulting matrix.
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/// </summary>
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@@ -98,12 +159,15 @@ namespace Avalonia
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public static Matrix operator *(Matrix value1, Matrix value2)
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{
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return new Matrix(
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- (value1.M11 * value2.M11) + (value1.M12 * value2.M21),
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- (value1.M11 * value2.M12) + (value1.M12 * value2.M22),
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- (value1.M21 * value2.M11) + (value1.M22 * value2.M21),
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- (value1.M21 * value2.M12) + (value1.M22 * value2.M22),
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- (value1._m31 * value2.M11) + (value1._m32 * value2.M21) + value2._m31,
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- (value1._m31 * value2.M12) + (value1._m32 * value2.M22) + value2._m32);
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+ (value1.M11 * value2.M11) + (value1.M12 * value2.M21) + (value1.M13 * value2.M31),
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+ (value1.M11 * value2.M12) + (value1.M12 * value2.M22) + (value1.M13 * value2.M32),
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+ (value1.M11 * value2.M13) + (value1.M12 * value2.M23) + (value1.M13 * value2.M33),
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+ (value1.M21 * value2.M11) + (value1.M22 * value2.M21) + (value1.M23 * value2.M31),
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+ (value1.M21 * value2.M12) + (value1.M22 * value2.M22) + (value1.M23 * value2.M32),
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+ (value1.M21 * value2.M13) + (value1.M22 * value2.M23) + (value1.M23 * value2.M33),
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+ (value1.M31 * value2.M11) + (value1.M32 * value2.M21) + (value1.M33 * value2.M31),
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+ (value1.M31 * value2.M12) + (value1.M32 * value2.M22) + (value1.M33 * value2.M32),
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+ (value1.M31 * value2.M13) + (value1.M32 * value2.M23) + (value1.M33 * value2.M33));
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}
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/// <summary>
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@@ -171,7 +235,7 @@ namespace Avalonia
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/// <returns>A scaling matrix.</returns>
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public static Matrix CreateScale(double xScale, double yScale)
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{
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- return CreateScale(new Vector(xScale, yScale));
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+ return new Matrix(xScale, 0, 0, yScale, 0, 0);
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}
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/// <summary>
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@@ -181,7 +245,7 @@ namespace Avalonia
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/// <returns>A scaling matrix.</returns>
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public static Matrix CreateScale(Vector scales)
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{
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- return new Matrix(scales.X, 0, 0, scales.Y, 0, 0);
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+ return CreateScale(scales.X, scales.Y);
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}
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/// <summary>
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@@ -214,7 +278,7 @@ namespace Avalonia
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{
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return angle * 0.0174532925;
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}
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-
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+
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/// <summary>
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/// Appends another matrix as post-multiplication operation.
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/// Equivalent to this * value;
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@@ -227,7 +291,7 @@ namespace Avalonia
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}
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/// <summary>
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- /// Prpends another matrix as pre-multiplication operation.
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+ /// Prepends another matrix as pre-multiplication operation.
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/// Equivalent to value * this;
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/// </summary>
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/// <param name="value">A matrix.</param>
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@@ -247,7 +311,49 @@ namespace Avalonia
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/// </remarks>
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public double GetDeterminant()
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{
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- return (_m11 * _m22) - (_m12 * _m21);
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+ // implemented using "Laplace expansion":
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+ return _m11 * (_m22 * _m33 - _m23 * _m32)
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+ - _m12 * (_m21 * _m33 - _m23 * _m31)
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+ + _m13 * (_m21 * _m32 - _m22 * _m31);
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+ }
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+
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+ /// <summary>
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+ /// Transforms the point with the matrix
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+ /// </summary>
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+ /// <param name="p">The point to be transformed</param>
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+ /// <returns>The transformed point</returns>
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+ public Point Transform(Point p)
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+ {
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+ Point transformedResult;
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+
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+ // If this matrix contains a non-affine transform with need to extend
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+ // the point to a 3D vector and flatten it back for 2d display
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+ // by multiplying X and Y with the inverse of the Z axis.
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+ // The code below also works with affine transformations, but for performance (and compatibility)
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+ // reasons we will use the more complex calculation only if necessary
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+ if (ContainsPerspective())
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+ {
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+ var m44 = new Matrix4x4(
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+ (float)M11, (float)M12, (float)M13, 0,
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+ (float)M21, (float)M22, (float)M23, 0,
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+ (float)M31, (float)M32, (float)M33, 0,
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+ 0, 0, 0, 1
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+ );
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+
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+ var vector = new Vector3((float)p.X, (float)p.Y, 1);
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+ var transformedVector = Vector3.Transform(vector, m44);
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+ var z = 1 / transformedVector.Z;
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+
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+ transformedResult = new Point(transformedVector.X * z, transformedVector.Y * z);
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+ }
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+ else
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+ {
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+ return new Point(
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+ (p.X * M11) + (p.Y * M21) + M31,
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+ (p.X * M12) + (p.Y * M22) + M32);
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+ }
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+
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+ return transformedResult;
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}
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/// <summary>
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@@ -260,10 +366,13 @@ namespace Avalonia
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// ReSharper disable CompareOfFloatsByEqualityOperator
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return _m11 == other.M11 &&
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_m12 == other.M12 &&
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+ _m13 == other.M13 &&
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_m21 == other.M21 &&
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_m22 == other.M22 &&
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+ _m23 == other.M23 &&
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_m31 == other.M31 &&
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- _m32 == other.M32;
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+ _m32 == other.M32 &&
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+ _m33 == other.M33;
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// ReSharper restore CompareOfFloatsByEqualityOperator
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}
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@@ -280,9 +389,18 @@ namespace Avalonia
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/// <returns>The hash code.</returns>
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public override int GetHashCode()
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{
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- return M11.GetHashCode() + M12.GetHashCode() +
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- M21.GetHashCode() + M22.GetHashCode() +
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- M31.GetHashCode() + M32.GetHashCode();
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+ return (_m11, _m12, _m13, _m21, _m22, _m23, _m31, _m32, _m33).GetHashCode();
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+ }
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+
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+ /// <summary>
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+ /// Determines if the current matrix contains perspective (non-affine) transforms (true) or only (affine) transforms that could be mapped into an 2x3 matrix (false).
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+ /// </summary>
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+ public bool ContainsPerspective()
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+ {
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+
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+ // ReSharper disable CompareOfFloatsByEqualityOperator
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+ return _m13 != 0 || _m23 != 0 || _m33 != 1;
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+ // ReSharper restore CompareOfFloatsByEqualityOperator
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}
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/// <summary>
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@@ -292,15 +410,25 @@ namespace Avalonia
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public override string ToString()
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{
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CultureInfo ci = CultureInfo.CurrentCulture;
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+
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+ string msg;
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+ double[] values;
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+
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+ if (ContainsPerspective())
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+ {
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+ msg = "{{ {{M11:{0} M12:{1} M13:{2}}} {{M21:{3} M22:{4} M23:{5}}} {{M31:{6} M32:{7} M33:{8}}} }}";
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+ values = new[] { M11, M12, M13, M21, M22, M23, M31, M32, M33 };
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+ }
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+ else
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+ {
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+ msg = "{{ {{M11:{0} M12:{1}}} {{M21:{2} M22:{3}}} {{M31:{4} M32:{5}}} }}";
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+ values = new[] { M11, M12, M21, M22, M31, M32 };
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+ }
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+
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return string.Format(
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ci,
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- "{{ {{M11:{0} M12:{1}}} {{M21:{2} M22:{3}}} {{M31:{4} M32:{5}}} }}",
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- M11.ToString(ci),
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- M12.ToString(ci),
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- M21.ToString(ci),
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- M22.ToString(ci),
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- M31.ToString(ci),
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- M32.ToString(ci));
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+ msg,
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+ values.Select((v) => v.ToString(ci)).ToArray());
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}
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/// <summary>
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@@ -318,14 +446,20 @@ namespace Avalonia
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return false;
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}
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+ var invdet = 1 / d;
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+
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inverted = new Matrix(
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- _m22 / d,
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- -_m12 / d,
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- -_m21 / d,
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- _m11 / d,
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- ((_m21 * _m32) - (_m22 * _m31)) / d,
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- ((_m12 * _m31) - (_m11 * _m32)) / d);
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-
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+ (_m22 * _m33 - _m32 * _m23) * invdet,
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+ (_m13 * _m31 - _m12 * _m33) * invdet,
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+ (_m12 * _m23 - _m13 * _m22) * invdet,
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+ (_m23 * _m31 - _m21 * _m33) * invdet,
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+ (_m11 * _m33 - _m13 * _m31) * invdet,
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+ (_m21 * _m13 - _m11 * _m23) * invdet,
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+ (_m21 * _m32 - _m31 * _m22) * invdet,
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+ (_m21 * _m12 - _m11 * _m32) * invdet,
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+ (_m11 * _m22 - _m21 * _m12) * invdet
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+ );
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+
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return true;
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}
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@@ -336,7 +470,7 @@ namespace Avalonia
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/// <returns>The inverted matrix.</returns>
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public Matrix Invert()
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{
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- if (!TryInvert(out Matrix inverted))
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+ if (!TryInvert(out var inverted))
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{
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throw new InvalidOperationException("Transform is not invertible.");
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}
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@@ -347,20 +481,30 @@ namespace Avalonia
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/// <summary>
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/// Parses a <see cref="Matrix"/> string.
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/// </summary>
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- /// <param name="s">Six comma-delimited double values (m11, m12, m21, m22, offsetX, offsetY) that describe the new <see cref="Matrix"/></param>
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+ /// <param name="s">Six or nine comma-delimited double values (m11, m12, m21, m22, offsetX, offsetY[, persX, persY, persZ]) that describe the new <see cref="Matrix"/></param>
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/// <returns>The <see cref="Matrix"/>.</returns>
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public static Matrix Parse(string s)
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{
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+ // initialize to satisfy compiler - only used when retrieved from string.
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+ double v8 = 0;
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+ double v9 = 0;
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+
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using (var tokenizer = new StringTokenizer(s, CultureInfo.InvariantCulture, exceptionMessage: "Invalid Matrix."))
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{
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- return new Matrix(
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- tokenizer.ReadDouble(),
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- tokenizer.ReadDouble(),
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- tokenizer.ReadDouble(),
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- tokenizer.ReadDouble(),
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- tokenizer.ReadDouble(),
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- tokenizer.ReadDouble()
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- );
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+ var v1 = tokenizer.ReadDouble();
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+ var v2 = tokenizer.ReadDouble();
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+ var v3 = tokenizer.ReadDouble();
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+ var v4 = tokenizer.ReadDouble();
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+ var v5 = tokenizer.ReadDouble();
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+ var v6 = tokenizer.ReadDouble();
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+ var pers = tokenizer.TryReadDouble(out var v7);
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+ pers = pers && tokenizer.TryReadDouble(out v8);
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+ pers = pers && tokenizer.TryReadDouble(out v9);
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+
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+ if (pers)
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+ return new Matrix(v1, v2, v7, v3, v4, v8, v5, v6, v9);
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+ else
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+ return new Matrix(v1, v2, v3, v4, v5, v6);
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}
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}
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@@ -369,14 +513,14 @@ namespace Avalonia
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/// </summary>
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/// <param name="matrix">Matrix to decompose.</param>
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/// <param name="decomposed">Decomposed matrix.</param>
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- /// <returns>The status of the operation.</returns>
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+ /// <returns>The status of the operation.</returns>
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public static bool TryDecomposeTransform(Matrix matrix, out Decomposed decomposed)
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{
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decomposed = default;
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var determinant = matrix.GetDeterminant();
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- if (MathUtilities.IsZero(determinant))
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+ if (MathUtilities.IsZero(determinant) || matrix.ContainsPerspective())
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{
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return false;
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}
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Jumar Macato