Deadpikle
7 years ago
1 changed files with 271 additions and 0 deletions
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using System; |
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using System.Collections.Generic; |
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using System.ComponentModel; |
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using System.Globalization; |
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using System.Text; |
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using Avalonia; |
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using Avalonia.Utilities; |
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// From: https://github.com/dotnet/wpf/blob/ae1790531c3b993b56eba8b1f0dd395a3ed7de75/src/Microsoft.DotNet.Wpf/src/PresentationCore/System/Windows/Media/Animation/KeySpline.cs
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namespace Avalonia.Animation |
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{ |
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[TypeConverter(typeof(KeySplineTypeConverter))] |
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public class KeySpline : AvaloniaObject |
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{ |
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// Control points
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private double _controlPointX1; |
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private double _controlPointY1; |
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private double _controlPointX2; |
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private double _controlPointY2; |
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private bool _isSpecified; |
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private bool _isDirty; |
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// The parameter that corresponds to the most recent time
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private double _parameter; |
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// Cached coefficients
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private double _Bx; // 3*points[0].X
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private double _Cx; // 3*points[1].X
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private double _Cx_Bx; // 2*(Cx - Bx)
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private double _three_Cx; // 3 - Cx
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private double _By; // 3*points[0].Y
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private double _Cy; // 3*points[1].Y
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// constants
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private const double _accuracy = .001; // 1/3 the desired accuracy in X
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private const double _fuzz = .000001; // computational zero
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public KeySpline() |
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{ |
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_controlPointX1 = 0.0; |
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_controlPointY1 = 0.0; |
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_controlPointX2 = 1.0; |
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_controlPointY2 = 1.0; |
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_isDirty = true; |
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} |
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public KeySpline(double x1, double y1, double x2, double y2) |
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{ |
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_controlPointX1 = x1; |
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_controlPointY1 = y1; |
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_controlPointX2 = x2; |
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_controlPointY2 = y2; |
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_isDirty = true; |
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} |
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public static KeySpline Parse(string value, CultureInfo culture) |
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{ |
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using (var tokenizer = new StringTokenizer((string)value, CultureInfo.InvariantCulture, exceptionMessage: "Invalid KeySpline.")) |
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{ |
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return new KeySpline(tokenizer.ReadDouble(), tokenizer.ReadDouble(), tokenizer.ReadDouble(), tokenizer.ReadDouble()); |
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} |
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} |
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public double ControlPointX1 |
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{ |
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get => _controlPointX1; |
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set => _controlPointX1 = value; |
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} |
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public double ControlPointY1 |
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{ |
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get => _controlPointY1; |
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set => _controlPointY1 = value; |
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} |
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public double ControlPointX2 |
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{ |
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get => _controlPointX2; |
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set => _controlPointX2 = value; |
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} |
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public double ControlPointY2 |
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{ |
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get => _controlPointY2; |
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set => _controlPointY2 = value; |
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} |
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/// <summary>
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/// Calculates spline progress from a linear progress.
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/// </summary>
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/// <param name="linearProgress">the linear progress</param>
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/// <returns>the spline progress</returns>
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public double GetSplineProgress(double linearProgress) |
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{ |
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//ReadPreamble();
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if (_isDirty) |
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{ |
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Build(); |
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} |
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if (!_isSpecified) |
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{ |
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return linearProgress; |
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} |
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else |
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{ |
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SetParameterFromX(linearProgress); |
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return GetBezierValue(_By, _Cy, _parameter); |
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} |
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} |
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/// <summary>
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/// Compute cached coefficients.
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/// </summary>
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private void Build() |
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{ |
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if (_controlPointX1 == 0 && _controlPointY1 == 0 && _controlPointX2 == 1 && _controlPointY2 == 1) |
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{ |
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// This KeySpline would have no effect on the progress.
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_isSpecified = false; |
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} |
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else |
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{ |
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_isSpecified = true; |
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_parameter = 0; |
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// X coefficients
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_Bx = 3 * _controlPointX1; |
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_Cx = 3 * _controlPointX2; |
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_Cx_Bx = 2 * (_Cx - _Bx); |
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_three_Cx = 3 - _Cx; |
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// Y coefficients
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_By = 3 * _controlPointY1; |
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_Cy = 3 * _controlPointY2; |
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} |
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_isDirty = false; |
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} |
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/// <summary>
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/// Get an X or Y value with the Bezier formula.
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/// </summary>
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/// <param name="b">the second Bezier coefficient</param>
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/// <param name="c">the third Bezier coefficient</param>
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/// <param name="t">the parameter value to evaluate at</param>
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/// <returns>the value of the Bezier function at the given parameter</returns>
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static private double GetBezierValue(double b, double c, double t) |
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{ |
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double s = 1.0 - t; |
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double t2 = t * t; |
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return b * t * s * s + c * t2 * s + t2 * t; |
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} |
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/// <summary>
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/// Get X and dX/dt at a given parameter
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/// </summary>
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/// <param name="t">the parameter value to evaluate at</param>
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/// <param name="x">the value of x there</param>
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/// <param name="dx">the value of dx/dt there</param>
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private void GetXAndDx(double t, out double x, out double dx) |
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{ |
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double s = 1.0 - t; |
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double t2 = t * t; |
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double s2 = s * s; |
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x = _Bx * t * s2 + _Cx * t2 * s + t2 * t; |
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dx = _Bx * s2 + _Cx_Bx * s * t + _three_Cx * t2; |
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} |
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/// <summary>
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/// Compute the parameter value that corresponds to a given X value, using a modified
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/// clamped Newton-Raphson algorithm to solve the equation X(t) - time = 0. We make
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/// use of some known properties of this particular function:
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/// * We are only interested in solutions in the interval [0,1]
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/// * X(t) is increasing, so we can assume that if X(t) > time t > solution. We use
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/// that to clamp down the search interval with every probe.
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/// * The derivative of X and Y are between 0 and 3.
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/// </summary>
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/// <param name="time">the time, scaled to fit in [0,1]</param>
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private void SetParameterFromX(double time) |
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{ |
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// Dynamic search interval to clamp with
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double bottom = 0; |
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double top = 1; |
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if (time == 0) |
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{ |
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_parameter = 0; |
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} |
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else if (time == 1) |
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{ |
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_parameter = 1; |
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} |
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else |
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{ |
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// Loop while improving the guess
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while (top - bottom > _fuzz) |
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{ |
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double x, dx, absdx; |
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// Get x and dx/dt at the current parameter
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GetXAndDx(_parameter, out x, out dx); |
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absdx = Math.Abs(dx); |
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// Clamp down the search interval, relying on the monotonicity of X(t)
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if (x > time) |
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{ |
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top = _parameter; // because parameter > solution
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} |
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else |
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{ |
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bottom = _parameter; // because parameter < solution
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} |
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// The desired accuracy is in ultimately in y, not in x, so the
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// accuracy needs to be multiplied by dx/dy = (dx/dt) / (dy/dt).
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// But dy/dt <=3, so we omit that
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if (Math.Abs(x - time) < _accuracy * absdx) |
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{ |
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break; // We're there
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} |
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if (absdx > _fuzz) |
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{ |
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// Nonzero derivative, use Newton-Raphson to obtain the next guess
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double next = _parameter - (x - time) / dx; |
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// If next guess is out of the search interval then clamp it in
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if (next >= top) |
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{ |
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_parameter = (_parameter + top) / 2; |
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} |
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else if (next <= bottom) |
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{ |
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_parameter = (_parameter + bottom) / 2; |
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} |
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else |
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{ |
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// Next guess is inside the search interval, accept it
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_parameter = next; |
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} |
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} |
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else // Zero derivative, halve the search interval
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{ |
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_parameter = (bottom + top) / 2; |
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} |
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} |
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} |
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} |
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} |
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public class KeySplineTypeConverter : TypeConverter |
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{ |
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public override bool CanConvertFrom(ITypeDescriptorContext context, Type sourceType) |
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{ |
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return sourceType == typeof(string); |
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} |
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public override object ConvertFrom(ITypeDescriptorContext context, CultureInfo culture, object value) |
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{ |
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return KeySpline.Parse((string)value, culture); |
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} |
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} |
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} |
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