147 lines
3.8 KiB
C#
147 lines
3.8 KiB
C#
using System;
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using System.Linq;
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using Unity.Mathematics;
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using static Unity.Mathematics.math;
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public class BezierCurve
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{
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public float4[] Keys;
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private int2 _cachedIndices;
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private const int STEPS = 64;
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private float? _maximum;
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public float Maximum
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{
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get
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{
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if (_maximum != null) return _maximum ?? 0;
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var samples = Enumerable.Range(0, STEPS).Select(i => (float) i / STEPS).ToArray();
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float max = 0;
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_maximum = 0;
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foreach (var f in samples)
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{
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var p = Evaluate(f);
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if (p > max)
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{
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max = p;
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_maximum = f;
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}
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}
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return _maximum??0;
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}
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}
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// Integrate area under curve between start and end time
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public float IntegrateCurve(float startTime, float endTime, int steps)
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{
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return Integrate(Evaluate, startTime, endTime, steps);
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}
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// Integrate function f(x) using the trapezoidal rule between x=x_low..x_high
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public static float Integrate(Func<float, float> f, float x_low, float x_high, int N_steps)
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{
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float h = (x_high - x_low) / N_steps;
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float res = (f(x_low) + f(x_high)) / 2;
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for (int i = 1; i < N_steps; i++)
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{
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res += f(x_low + i * h);
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}
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return h * res;
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}
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// public static float Screen(float a, float b)
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// {
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// return 1 - (1 - a)*(1 - b);
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// }
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public float Evaluate(float time)
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{
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// Clamp time
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time = clamp(time, Keys[0].x, Keys[Keys.Length - 1].x);
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FindSurroundingKeyframes(time, Keys);
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return HermiteInterpolate(time, Keys[_cachedIndices.x], Keys[_cachedIndices.y]);
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}
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void FindSurroundingKeyframes(float time, float4[] curve)
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{
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// Check that time is within cached keyframe time
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if (time >= curve[_cachedIndices.x].x &&
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time <= curve[_cachedIndices.y].x)
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{
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return;
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}
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// Fall back to using dichotomic search.
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var length = curve.Length;
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int half;
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int middle;
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int first = 0;
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while (length > 0)
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{
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half = length >> 1;
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middle = first + half;
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if (time < curve[middle].x)
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{
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length = half;
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}
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else
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{
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first = middle + 1;
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length = length - half - 1;
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}
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}
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// If not within range, we pick the last element twice.
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var indices = int2(first - 1, min(curve.Length - 1, first));
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_cachedIndices = indices;
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}
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float HermiteInterpolate(float time, in float4 leftKeyframe, in float4 rightKeyframe)
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{
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// Handle stepped curve.
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if (isinf(leftKeyframe.w) || isinf(rightKeyframe.z))
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{
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return leftKeyframe.y;
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}
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float dx = rightKeyframe.x - leftKeyframe.x;
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float m0;
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float m1;
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float t;
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if (dx != 0.0f)
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{
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t = (time - leftKeyframe.x) / dx;
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m0 = leftKeyframe.w * dx;
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m1 = rightKeyframe.z * dx;
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}
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else
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{
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t = 0.0f;
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m0 = 0;
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m1 = 0;
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}
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return HermiteInterpolate(t, leftKeyframe.y, m0, m1, rightKeyframe.y);
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}
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static float HermiteInterpolate(float t, float p0, float m0, float m1, float p1)
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{
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// Unrolled the equations to avoid precision issue.
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// (2 * t^3 -3 * t^2 +1) * p0 + (t^3 - 2 * t^2 + t) * m0 + (-2 * t^3 + 3 * t^2) * p1 + (t^3 - t^2) * m1
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var a = 2.0f * p0 + m0 - 2.0f * p1 + m1;
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var b = -3.0f * p0 - 2.0f * m0 + 3.0f * p1 - m1;
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var c = m0;
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var d = p0;
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return t * (t * (a * t + b) + c) + d;
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}
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}
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