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/*
* Copyright (C) 2009 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include "SkCubicClipper.h"
#include "SkGeometry.h"
SkCubicClipper::SkCubicClipper() {}
void SkCubicClipper::setClip(const SkIRect& clip) {
// conver to scalars, since that's where we'll see the points
fClip.set(clip);
}
static bool chopMonoCubicAtY(SkPoint pts[4], SkScalar y, SkScalar* t) {
SkScalar ycrv[4];
ycrv[0] = pts[0].fY - y;
ycrv[1] = pts[1].fY - y;
ycrv[2] = pts[2].fY - y;
ycrv[3] = pts[3].fY - y;
#ifdef NEWTON_RAPHSON // Quadratic convergence, typically <= 3 iterations.
// Initial guess.
// TODO(turk): Check for zero denominator? Shouldn't happen unless the curve
// is not only monotonic but degenerate.
#ifdef SK_SCALAR_IS_FLOAT
SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]);
#else // !SK_SCALAR_IS_FLOAT
SkScalar t1 = SkDivBits(ycrv[0], ycrv[0] - ycrv[3], 16);
#endif // !SK_SCALAR_IS_FLOAT
// Newton's iterations.
const SkScalar tol = SK_Scalar1 / 16384; // This leaves 2 fixed noise bits.
SkScalar t0;
const int maxiters = 5;
int iters = 0;
bool converged;
do {
t0 = t1;
SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], t0);
SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], t0);
SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], t0);
SkScalar y012 = SkScalarInterp(y01, y12, t0);
SkScalar y123 = SkScalarInterp(y12, y23, t0);
SkScalar y0123 = SkScalarInterp(y012, y123, t0);
SkScalar yder = (y123 - y012) * 3;
// TODO(turk): check for yder==0: horizontal.
#ifdef SK_SCALAR_IS_FLOAT
t1 -= y0123 / yder;
#else // !SK_SCALAR_IS_FLOAT
t1 -= SkDivBits(y0123, yder, 16);
#endif // !SK_SCALAR_IS_FLOAT
converged = SkScalarAbs(t1 - t0) <= tol; // NaN-safe
++iters;
} while (!converged && (iters < maxiters));
*t = t1; // Return the result.
// The result might be valid, even if outside of the range [0, 1], but
// we never evaluate a Bezier outside this interval, so we return false.
if (t1 < 0 || t1 > SK_Scalar1)
return false; // This shouldn't happen, but check anyway.
return converged;
#else // BISECTION // Linear convergence, typically 16 iterations.
// Check that the endpoints straddle zero.
SkScalar tNeg, tPos; // Negative and positive function parameters.
if (ycrv[0] < 0) {
if (ycrv[3] < 0)
return false;
tNeg = 0;
tPos = SK_Scalar1;
} else if (ycrv[0] > 0) {
if (ycrv[3] > 0)
return false;
tNeg = SK_Scalar1;
tPos = 0;
} else {
*t = 0;
return true;
}
const SkScalar tol = SK_Scalar1 / 65536; // 1 for fixed, 1e-5 for float.
int iters = 0;
do {
SkScalar tMid = (tPos + tNeg) / 2;
SkScalar y01 = SkScalarInterp(ycrv[0], ycrv[1], tMid);
SkScalar y12 = SkScalarInterp(ycrv[1], ycrv[2], tMid);
SkScalar y23 = SkScalarInterp(ycrv[2], ycrv[3], tMid);
SkScalar y012 = SkScalarInterp(y01, y12, tMid);
SkScalar y123 = SkScalarInterp(y12, y23, tMid);
SkScalar y0123 = SkScalarInterp(y012, y123, tMid);
if (y0123 == 0) {
*t = tMid;
return true;
}
if (y0123 < 0) tNeg = tMid;
else tPos = tMid;
++iters;
} while (!(SkScalarAbs(tPos - tNeg) <= tol)); // Nan-safe
*t = (tNeg + tPos) / 2;
return true;
#endif // BISECTION
}
bool SkCubicClipper::clipCubic(const SkPoint srcPts[4], SkPoint dst[4]) {
bool reverse;
// we need the data to be monotonically descending in Y
if (srcPts[0].fY > srcPts[3].fY) {
dst[0] = srcPts[3];
dst[1] = srcPts[2];
dst[2] = srcPts[1];
dst[3] = srcPts[0];
reverse = true;
} else {
memcpy(dst, srcPts, 4 * sizeof(SkPoint));
reverse = false;
}
// are we completely above or below
const SkScalar ctop = fClip.fTop;
const SkScalar cbot = fClip.fBottom;
if (dst[3].fY <= ctop || dst[0].fY >= cbot) {
return false;
}
SkScalar t;
SkPoint tmp[7]; // for SkChopCubicAt
// are we partially above
if (dst[0].fY < ctop && chopMonoCubicAtY(dst, ctop, &t)) {
SkChopCubicAt(dst, tmp, t);
dst[0] = tmp[3];
dst[1] = tmp[4];
dst[2] = tmp[5];
}
// are we partially below
if (dst[3].fY > cbot && chopMonoCubicAtY(dst, cbot, &t)) {
SkChopCubicAt(dst, tmp, t);
dst[1] = tmp[1];
dst[2] = tmp[2];
dst[3] = tmp[3];
}
if (reverse) {
SkTSwap<SkPoint>(dst[0], dst[3]);
SkTSwap<SkPoint>(dst[1], dst[2]);
}
return true;
}
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