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Fix CubicBezier algorithm.

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PopSlime
2023-04-20 00:15:06 +08:00
parent 29a8ac2136
commit d2b71e41c9
1 changed files with 8 additions and 25 deletions
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33
Assets/Cryville/Common/Math/CubicBezier.cs
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@@ -4,41 +4,24 @@ namespace Cryville.Common.Math {
// Ported from https://github.com/arian/cubic-bezier/blob/master/index.js // Ported from https://github.com/arian/cubic-bezier/blob/master/index.js
public static class CubicBezier { public static class CubicBezier {
public static float Evaluate(float t, float x1, float y1, float x2, float y2, float epsilon) { public static float Evaluate(float t, float x1, float y1, float x2, float y2, float epsilon) {
float x = t, t0, t1, t2, tx, d2, i; float x = t, t0 = 0, t1 = 1, t2 = x;
for (t2 = x, i = 0; i < 8; i++) {
tx = CurveX(t2, x1, x2) - x;
if (SMath.Abs(tx) < epsilon) return CurveY(t2, y1, y2);
d2 = DerivativeCurveX(t2, x1, x2);
if (SMath.Abs(d2) < 1e-6) break;
t2 -= tx / d2;
}
t0 = 0; t1 = 1; t2 = x; if (t2 < t0) return Curve(t0, y1, y2);
if (t2 > t1) return Curve(t1, y1, y2);
if (t2 < t0) return CurveY(t0, y1, y2);
if (t2 > t1) return CurveY(t1, y1, y2);
while (t0 < t1) { while (t0 < t1) {
tx = CurveX(t2, x1, x2); float tx = Curve(t2, x1, x2);
if (SMath.Abs(tx - x) < epsilon) return CurveY(t2, y1, y2); if (SMath.Abs(tx - x) < epsilon) return Curve(t2, y1, y2);
if (x > tx) t0 = t2; if (x > tx) t0 = t2;
else t1 = t2; else t1 = t2;
t2 = (t1 - t0) * .5f + t0; t2 = (t1 - t0) * .5f + t0;
} }
return CurveY(t2, y1, y2); return Curve(t2, y1, y2);
} }
static float CurveX(float t, float x1, float x2) { static float Curve(float t, float p1, float p2) {
float v = 1 - t; float v = 1 - t;
return 3 * v * v * t * x1 + 3 * v * t * t * x2 + t * t * t; return 3 * v * v * t * p1 + 3 * v * t * t * p2 + t * t * t;
}
static float CurveY(float t, float y1, float y2) {
float v = 1 - t;
return 3 * v * v * t * y1 + 3 * v * t * t * y2 + t * t * t;
}
static float DerivativeCurveX(float t, float x1, float x2) {
float v = 1 - t;
return 3 * (2 * (t - 1) * t + v * v) * x1 + 3 * (-t * t * t + 2 * v * t) * x2;
} }
} }
} }