| /* |
| * Copyright 2009 The Android Open Source Project |
| * |
| * Use of this source code is governed by a BSD-style license that can be |
| * found in the LICENSE file. |
| */ |
| |
| |
| #include "src/core/SkCubicClipper.h" |
| #include "src/core/SkGeometry.h" |
| |
| #include <utility> |
| |
| SkCubicClipper::SkCubicClipper() { |
| fClip.setEmpty(); |
| } |
| |
| void SkCubicClipper::setClip(const SkIRect& clip) { |
| // conver to scalars, since that's where we'll see the points |
| fClip.set(clip); |
| } |
| |
| |
| bool SkCubicClipper::ChopMonoAtY(const 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. |
| SkScalar t1 = ycrv[0] / (ycrv[0] - ycrv[3]); |
| |
| // 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. |
| t1 -= y0123 / yder; |
| 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 && ChopMonoAtY(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 && ChopMonoAtY(dst, cbot, &t)) { |
| SkChopCubicAt(dst, tmp, t); |
| dst[1] = tmp[1]; |
| dst[2] = tmp[2]; |
| dst[3] = tmp[3]; |
| } |
| |
| if (reverse) { |
| using std::swap; |
| swap(dst[0], dst[3]); |
| swap(dst[1], dst[2]); |
| } |
| return true; |
| } |