Build ChatListUI

submodules/LegacyComponents/Sources/UnitBezier.h

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+/*
+ * Copyright (C) 2008 Apple Inc. All Rights Reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
+ * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+ * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
+ * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+ * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ */
+
+#ifndef UnitBezier_h
+#define UnitBezier_h
+
+#include <math.h>
+
+namespace WebCore {
+  
+  struct UnitBezier {
+    UnitBezier(double p1x, double p1y, double p2x, double p2y)
+    {
+      // Calculate the polynomial coefficients, implicit first and last control points are (0,0) and (1,1).
+      cx = 3.0 * p1x;
+      bx = 3.0 * (p2x - p1x) - cx;
+      ax = 1.0 - cx -bx;
+      
+      cy = 3.0 * p1y;
+      by = 3.0 * (p2y - p1y) - cy;
+      ay = 1.0 - cy - by;
+    }
+    
+    double sampleCurveX(double t)
+    {
+      // `ax t^3 + bx t^2 + cx t' expanded using Horner's rule.
+      return ((ax * t + bx) * t + cx) * t;
+    }
+    
+    double sampleCurveY(double t)
+    {
+      return ((ay * t + by) * t + cy) * t;
+    }
+    
+    double sampleCurveDerivativeX(double t)
+    {
+      return (3.0 * ax * t + 2.0 * bx) * t + cx;
+    }
+    
+    // Given an x value, find a parametric value it came from.
+    double solveCurveX(double x, double epsilon)
+    {
+      double t0;
+      double t1;
+      double t2;
+      double x2;
+      double d2;
+      int i;
+      
+      // First try a few iterations of Newton's method -- normally very fast.
+      for (t2 = x, i = 0; i < 8; i++) {
+        x2 = sampleCurveX(t2) - x;
+        if (fabs (x2) < epsilon)
+          return t2;
+        d2 = sampleCurveDerivativeX(t2);
+        if (fabs(d2) < 1e-6)
+          break;
+        t2 = t2 - x2 / d2;
+      }
+      
+      // Fall back to the bisection method for reliability.
+      t0 = 0.0;
+      t1 = 1.0;
+      t2 = x;
+      
+      if (t2 < t0)
+        return t0;
+      if (t2 > t1)
+        return t1;
+      
+      while (t0 < t1) {
+        x2 = sampleCurveX(t2);
+        if (fabs(x2 - x) < epsilon)
+          return t2;
+        if (x > x2)
+          t0 = t2;
+        else
+          t1 = t2;
+        t2 = (t1 - t0) * .5 + t0;
+      }
+      
+      // Failure.
+      return t2;
+    }
+    
+    double solve(double x, double epsilon)
+    {
+      return sampleCurveY(solveCurveX(x, epsilon));
+    }
+    
+  private:
+    double ax;
+    double bx;
+    double cx;
+    
+    double ay;
+    double by;
+    double cy;
+  };
+}
+#endif