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/*
* Copyright 2011 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkCubicInterval.h"
static SkScalar eval_cubic(SkScalar c1, SkScalar c2, SkScalar c3,
SkScalar t) {
return SkScalarMul(SkScalarMul(SkScalarMul(c3, t) + c2, t) + c1, t);
}
static SkScalar find_cubic_t(SkScalar c1, SkScalar c2, SkScalar c3,
SkScalar targetX) {
SkScalar minT = 0;
SkScalar maxT = SK_Scalar1;
SkScalar t;
for (;;) {
t = SkScalarAve(minT, maxT);
SkScalar x = eval_cubic(c1, c2, c3, t);
if (SkScalarNearlyZero(x - targetX)) {
break;
}
// subdivide the range and try again
if (x < targetX) {
minT = t;
} else {
maxT = t;
}
}
return t;
}
/*
a(1-t)^3 + 3bt(1-t)^2 + 3ct^2(1-t) + dt^3
a: [0, 0]
d: [1, 1]
3bt - 6bt^2 + 3bt^3 + 3ct^2 - 3ct^3 + t^3
C1 = t^1: 3b
C2 = t^2: 3c - 6b
C3 = t^3: 3b - 3c + 1
((C3*t + C2)*t + C1)*t
*/
SkScalar SkEvalCubicInterval(SkScalar x1, SkScalar y1,
SkScalar x2, SkScalar y2,
SkScalar unitX) {
x1 = SkScalarPin(x1, 0, SK_Scalar1);
x2 = SkScalarPin(x2, 0, SK_Scalar1);
unitX = SkScalarPin(unitX, 0, SK_Scalar1);
// First compute our coefficients in X
x1 *= 3;
x2 *= 3;
// now search for t given unitX
SkScalar t = find_cubic_t(x1, x2 - 2*x1, x1 - x2 + SK_Scalar1, unitX);
// now evaluate the cubic in Y
y1 *= 3;
y2 *= 3;
return eval_cubic(y1, y2 - 2*y1, y1 - y2 + SK_Scalar1, t);
}
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