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- /*
- * 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 "include/private/SkMacros.h"
- #include "src/core/SkEdgeClipper.h"
- #include "src/core/SkGeometry.h"
- #include "src/core/SkLineClipper.h"
- #include <utility>
- static bool quick_reject(const SkRect& bounds, const SkRect& clip) {
- return bounds.fTop >= clip.fBottom || bounds.fBottom <= clip.fTop;
- }
- static inline void clamp_le(SkScalar& value, SkScalar max) {
- if (value > max) {
- value = max;
- }
- }
- static inline void clamp_ge(SkScalar& value, SkScalar min) {
- if (value < min) {
- value = min;
- }
- }
- /* src[] must be monotonic in Y. This routine copies src into dst, and sorts
- it to be increasing in Y. If it had to reverse the order of the points,
- it returns true, otherwise it returns false
- */
- static bool sort_increasing_Y(SkPoint dst[], const SkPoint src[], int count) {
- // we need the data to be monotonically increasing in Y
- if (src[0].fY > src[count - 1].fY) {
- for (int i = 0; i < count; i++) {
- dst[i] = src[count - i - 1];
- }
- return true;
- } else {
- memcpy(dst, src, count * sizeof(SkPoint));
- return false;
- }
- }
- bool SkEdgeClipper::clipLine(SkPoint p0, SkPoint p1, const SkRect& clip) {
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- SkPoint lines[SkLineClipper::kMaxPoints];
- const SkPoint pts[] = { p0, p1 };
- int lineCount = SkLineClipper::ClipLine(pts, clip, lines, fCanCullToTheRight);
- for (int i = 0; i < lineCount; i++) {
- this->appendLine(lines[i], lines[i + 1]);
- }
- *fCurrVerb = SkPath::kDone_Verb;
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- return SkPath::kDone_Verb != fVerbs[0];
- }
- ///////////////////////////////////////////////////////////////////////////////
- static bool chopMonoQuadAt(SkScalar c0, SkScalar c1, SkScalar c2,
- SkScalar target, SkScalar* t) {
- /* Solve F(t) = y where F(t) := [0](1-t)^2 + 2[1]t(1-t) + [2]t^2
- * We solve for t, using quadratic equation, hence we have to rearrange
- * our cooefficents to look like At^2 + Bt + C
- */
- SkScalar A = c0 - c1 - c1 + c2;
- SkScalar B = 2*(c1 - c0);
- SkScalar C = c0 - target;
- SkScalar roots[2]; // we only expect one, but make room for 2 for safety
- int count = SkFindUnitQuadRoots(A, B, C, roots);
- if (count) {
- *t = roots[0];
- return true;
- }
- return false;
- }
- static bool chopMonoQuadAtY(SkPoint pts[3], SkScalar y, SkScalar* t) {
- return chopMonoQuadAt(pts[0].fY, pts[1].fY, pts[2].fY, y, t);
- }
- static bool chopMonoQuadAtX(SkPoint pts[3], SkScalar x, SkScalar* t) {
- return chopMonoQuadAt(pts[0].fX, pts[1].fX, pts[2].fX, x, t);
- }
- // Modify pts[] in place so that it is clipped in Y to the clip rect
- static void chop_quad_in_Y(SkPoint pts[3], const SkRect& clip) {
- SkScalar t;
- SkPoint tmp[5]; // for SkChopQuadAt
- // are we partially above
- if (pts[0].fY < clip.fTop) {
- if (chopMonoQuadAtY(pts, clip.fTop, &t)) {
- // take the 2nd chopped quad
- SkChopQuadAt(pts, tmp, t);
- // clamp to clean up imprecise numerics in the chop
- tmp[2].fY = clip.fTop;
- clamp_ge(tmp[3].fY, clip.fTop);
- pts[0] = tmp[2];
- pts[1] = tmp[3];
- } else {
- // if chopMonoQuadAtY failed, then we may have hit inexact numerics
- // so we just clamp against the top
- for (int i = 0; i < 3; i++) {
- if (pts[i].fY < clip.fTop) {
- pts[i].fY = clip.fTop;
- }
- }
- }
- }
- // are we partially below
- if (pts[2].fY > clip.fBottom) {
- if (chopMonoQuadAtY(pts, clip.fBottom, &t)) {
- SkChopQuadAt(pts, tmp, t);
- // clamp to clean up imprecise numerics in the chop
- clamp_le(tmp[1].fY, clip.fBottom);
- tmp[2].fY = clip.fBottom;
- pts[1] = tmp[1];
- pts[2] = tmp[2];
- } else {
- // if chopMonoQuadAtY failed, then we may have hit inexact numerics
- // so we just clamp against the bottom
- for (int i = 0; i < 3; i++) {
- if (pts[i].fY > clip.fBottom) {
- pts[i].fY = clip.fBottom;
- }
- }
- }
- }
- }
- // srcPts[] must be monotonic in X and Y
- void SkEdgeClipper::clipMonoQuad(const SkPoint srcPts[3], const SkRect& clip) {
- SkPoint pts[3];
- bool reverse = sort_increasing_Y(pts, srcPts, 3);
- // are we completely above or below
- if (pts[2].fY <= clip.fTop || pts[0].fY >= clip.fBottom) {
- return;
- }
- // Now chop so that pts is contained within clip in Y
- chop_quad_in_Y(pts, clip);
- if (pts[0].fX > pts[2].fX) {
- using std::swap;
- swap(pts[0], pts[2]);
- reverse = !reverse;
- }
- SkASSERT(pts[0].fX <= pts[1].fX);
- SkASSERT(pts[1].fX <= pts[2].fX);
- // Now chop in X has needed, and record the segments
- if (pts[2].fX <= clip.fLeft) { // wholly to the left
- this->appendVLine(clip.fLeft, pts[0].fY, pts[2].fY, reverse);
- return;
- }
- if (pts[0].fX >= clip.fRight) { // wholly to the right
- if (!this->canCullToTheRight()) {
- this->appendVLine(clip.fRight, pts[0].fY, pts[2].fY, reverse);
- }
- return;
- }
- SkScalar t;
- SkPoint tmp[5]; // for SkChopQuadAt
- // are we partially to the left
- if (pts[0].fX < clip.fLeft) {
- if (chopMonoQuadAtX(pts, clip.fLeft, &t)) {
- SkChopQuadAt(pts, tmp, t);
- this->appendVLine(clip.fLeft, tmp[0].fY, tmp[2].fY, reverse);
- // clamp to clean up imprecise numerics in the chop
- tmp[2].fX = clip.fLeft;
- clamp_ge(tmp[3].fX, clip.fLeft);
- pts[0] = tmp[2];
- pts[1] = tmp[3];
- } else {
- // if chopMonoQuadAtY failed, then we may have hit inexact numerics
- // so we just clamp against the left
- this->appendVLine(clip.fLeft, pts[0].fY, pts[2].fY, reverse);
- return;
- }
- }
- // are we partially to the right
- if (pts[2].fX > clip.fRight) {
- if (chopMonoQuadAtX(pts, clip.fRight, &t)) {
- SkChopQuadAt(pts, tmp, t);
- // clamp to clean up imprecise numerics in the chop
- clamp_le(tmp[1].fX, clip.fRight);
- tmp[2].fX = clip.fRight;
- this->appendQuad(tmp, reverse);
- this->appendVLine(clip.fRight, tmp[2].fY, tmp[4].fY, reverse);
- } else {
- // if chopMonoQuadAtY failed, then we may have hit inexact numerics
- // so we just clamp against the right
- this->appendVLine(clip.fRight, pts[0].fY, pts[2].fY, reverse);
- }
- } else { // wholly inside the clip
- this->appendQuad(pts, reverse);
- }
- }
- bool SkEdgeClipper::clipQuad(const SkPoint srcPts[3], const SkRect& clip) {
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- SkRect bounds;
- bounds.set(srcPts, 3);
- if (!quick_reject(bounds, clip)) {
- SkPoint monoY[5];
- int countY = SkChopQuadAtYExtrema(srcPts, monoY);
- for (int y = 0; y <= countY; y++) {
- SkPoint monoX[5];
- int countX = SkChopQuadAtXExtrema(&monoY[y * 2], monoX);
- for (int x = 0; x <= countX; x++) {
- this->clipMonoQuad(&monoX[x * 2], clip);
- SkASSERT(fCurrVerb - fVerbs < kMaxVerbs);
- SkASSERT(fCurrPoint - fPoints <= kMaxPoints);
- }
- }
- }
- *fCurrVerb = SkPath::kDone_Verb;
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- return SkPath::kDone_Verb != fVerbs[0];
- }
- ///////////////////////////////////////////////////////////////////////////////
- static SkScalar mono_cubic_closestT(const SkScalar src[], SkScalar x) {
- SkScalar t = 0.5f;
- SkScalar lastT;
- SkScalar bestT SK_INIT_TO_AVOID_WARNING;
- SkScalar step = 0.25f;
- SkScalar D = src[0];
- SkScalar A = src[6] + 3*(src[2] - src[4]) - D;
- SkScalar B = 3*(src[4] - src[2] - src[2] + D);
- SkScalar C = 3*(src[2] - D);
- x -= D;
- SkScalar closest = SK_ScalarMax;
- do {
- SkScalar loc = ((A * t + B) * t + C) * t;
- SkScalar dist = SkScalarAbs(loc - x);
- if (closest > dist) {
- closest = dist;
- bestT = t;
- }
- lastT = t;
- t += loc < x ? step : -step;
- step *= 0.5f;
- } while (closest > 0.25f && lastT != t);
- return bestT;
- }
- static void chop_mono_cubic_at_y(SkPoint src[4], SkScalar y, SkPoint dst[7]) {
- if (SkChopMonoCubicAtY(src, y, dst)) {
- return;
- }
- SkChopCubicAt(src, dst, mono_cubic_closestT(&src->fY, y));
- }
- // Modify pts[] in place so that it is clipped in Y to the clip rect
- static void chop_cubic_in_Y(SkPoint pts[4], const SkRect& clip) {
- // are we partially above
- if (pts[0].fY < clip.fTop) {
- SkPoint tmp[7];
- chop_mono_cubic_at_y(pts, clip.fTop, tmp);
- /*
- * For a large range in the points, we can do a poor job of chopping, such that the t
- * we computed resulted in the lower cubic still being partly above the clip.
- *
- * If just the first or first 2 Y values are above the fTop, we can just smash them
- * down. If the first 3 Ys are above fTop, we can't smash all 3, as that can really
- * distort the cubic. In this case, we take the first output (tmp[3..6] and treat it as
- * a guess, and re-chop against fTop. Then we fall through to checking if we need to
- * smash the first 1 or 2 Y values.
- */
- if (tmp[3].fY < clip.fTop && tmp[4].fY < clip.fTop && tmp[5].fY < clip.fTop) {
- SkPoint tmp2[4];
- memcpy(tmp2, &tmp[3].fX, 4 * sizeof(SkPoint));
- chop_mono_cubic_at_y(tmp2, clip.fTop, tmp);
- }
- // tmp[3, 4].fY should all be to the below clip.fTop.
- // Since we can't trust the numerics of the chopper, we force those conditions now
- tmp[3].fY = clip.fTop;
- clamp_ge(tmp[4].fY, clip.fTop);
- pts[0] = tmp[3];
- pts[1] = tmp[4];
- pts[2] = tmp[5];
- }
- // are we partially below
- if (pts[3].fY > clip.fBottom) {
- SkPoint tmp[7];
- chop_mono_cubic_at_y(pts, clip.fBottom, tmp);
- tmp[3].fY = clip.fBottom;
- clamp_le(tmp[2].fY, clip.fBottom);
- pts[1] = tmp[1];
- pts[2] = tmp[2];
- pts[3] = tmp[3];
- }
- }
- static void chop_mono_cubic_at_x(SkPoint src[4], SkScalar x, SkPoint dst[7]) {
- if (SkChopMonoCubicAtX(src, x, dst)) {
- return;
- }
- SkChopCubicAt(src, dst, mono_cubic_closestT(&src->fX, x));
- }
- // srcPts[] must be monotonic in X and Y
- void SkEdgeClipper::clipMonoCubic(const SkPoint src[4], const SkRect& clip) {
- SkPoint pts[4];
- bool reverse = sort_increasing_Y(pts, src, 4);
- // are we completely above or below
- if (pts[3].fY <= clip.fTop || pts[0].fY >= clip.fBottom) {
- return;
- }
- // Now chop so that pts is contained within clip in Y
- chop_cubic_in_Y(pts, clip);
- if (pts[0].fX > pts[3].fX) {
- using std::swap;
- swap(pts[0], pts[3]);
- swap(pts[1], pts[2]);
- reverse = !reverse;
- }
- // Now chop in X has needed, and record the segments
- if (pts[3].fX <= clip.fLeft) { // wholly to the left
- this->appendVLine(clip.fLeft, pts[0].fY, pts[3].fY, reverse);
- return;
- }
- if (pts[0].fX >= clip.fRight) { // wholly to the right
- if (!this->canCullToTheRight()) {
- this->appendVLine(clip.fRight, pts[0].fY, pts[3].fY, reverse);
- }
- return;
- }
- // are we partially to the left
- if (pts[0].fX < clip.fLeft) {
- SkPoint tmp[7];
- chop_mono_cubic_at_x(pts, clip.fLeft, tmp);
- this->appendVLine(clip.fLeft, tmp[0].fY, tmp[3].fY, reverse);
- // tmp[3, 4].fX should all be to the right of clip.fLeft.
- // Since we can't trust the numerics of
- // the chopper, we force those conditions now
- tmp[3].fX = clip.fLeft;
- clamp_ge(tmp[4].fX, clip.fLeft);
- pts[0] = tmp[3];
- pts[1] = tmp[4];
- pts[2] = tmp[5];
- }
- // are we partially to the right
- if (pts[3].fX > clip.fRight) {
- SkPoint tmp[7];
- chop_mono_cubic_at_x(pts, clip.fRight, tmp);
- tmp[3].fX = clip.fRight;
- clamp_le(tmp[2].fX, clip.fRight);
- this->appendCubic(tmp, reverse);
- this->appendVLine(clip.fRight, tmp[3].fY, tmp[6].fY, reverse);
- } else { // wholly inside the clip
- this->appendCubic(pts, reverse);
- }
- }
- static SkRect compute_cubic_bounds(const SkPoint pts[4]) {
- SkRect r;
- r.set(pts, 4);
- return r;
- }
- static bool too_big_for_reliable_float_math(const SkRect& r) {
- // limit set as the largest float value for which we can still reliably compute things like
- // - chopping at XY extrema
- // - chopping at Y or X values for clipping
- //
- // Current value chosen just by experiment. Larger (and still succeeds) is always better.
- //
- const SkScalar limit = 1 << 22;
- return r.fLeft < -limit || r.fTop < -limit || r.fRight > limit || r.fBottom > limit;
- }
- bool SkEdgeClipper::clipCubic(const SkPoint srcPts[4], const SkRect& clip) {
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- const SkRect bounds = compute_cubic_bounds(srcPts);
- // check if we're clipped out vertically
- if (bounds.fBottom > clip.fTop && bounds.fTop < clip.fBottom) {
- if (too_big_for_reliable_float_math(bounds)) {
- // can't safely clip the cubic, so we give up and draw a line (which we can safely clip)
- //
- // If we rewrote chopcubicat*extrema and chopmonocubic using doubles, we could very
- // likely always handle the cubic safely, but (it seems) at a big loss in speed, so
- // we'd only want to take that alternate impl if needed. Perhaps a TODO to try it.
- //
- return this->clipLine(srcPts[0], srcPts[3], clip);
- } else {
- SkPoint monoY[10];
- int countY = SkChopCubicAtYExtrema(srcPts, monoY);
- for (int y = 0; y <= countY; y++) {
- SkPoint monoX[10];
- int countX = SkChopCubicAtXExtrema(&monoY[y * 3], monoX);
- for (int x = 0; x <= countX; x++) {
- this->clipMonoCubic(&monoX[x * 3], clip);
- SkASSERT(fCurrVerb - fVerbs < kMaxVerbs);
- SkASSERT(fCurrPoint - fPoints <= kMaxPoints);
- }
- }
- }
- }
- *fCurrVerb = SkPath::kDone_Verb;
- fCurrPoint = fPoints;
- fCurrVerb = fVerbs;
- return SkPath::kDone_Verb != fVerbs[0];
- }
- ///////////////////////////////////////////////////////////////////////////////
- void SkEdgeClipper::appendLine(SkPoint p0, SkPoint p1) {
- *fCurrVerb++ = SkPath::kLine_Verb;
- fCurrPoint[0] = p0;
- fCurrPoint[1] = p1;
- fCurrPoint += 2;
- }
- void SkEdgeClipper::appendVLine(SkScalar x, SkScalar y0, SkScalar y1, bool reverse) {
- *fCurrVerb++ = SkPath::kLine_Verb;
- if (reverse) {
- using std::swap;
- swap(y0, y1);
- }
- fCurrPoint[0].set(x, y0);
- fCurrPoint[1].set(x, y1);
- fCurrPoint += 2;
- }
- void SkEdgeClipper::appendQuad(const SkPoint pts[3], bool reverse) {
- *fCurrVerb++ = SkPath::kQuad_Verb;
- if (reverse) {
- fCurrPoint[0] = pts[2];
- fCurrPoint[2] = pts[0];
- } else {
- fCurrPoint[0] = pts[0];
- fCurrPoint[2] = pts[2];
- }
- fCurrPoint[1] = pts[1];
- fCurrPoint += 3;
- }
- void SkEdgeClipper::appendCubic(const SkPoint pts[4], bool reverse) {
- *fCurrVerb++ = SkPath::kCubic_Verb;
- if (reverse) {
- for (int i = 0; i < 4; i++) {
- fCurrPoint[i] = pts[3 - i];
- }
- } else {
- memcpy(fCurrPoint, pts, 4 * sizeof(SkPoint));
- }
- fCurrPoint += 4;
- }
- SkPath::Verb SkEdgeClipper::next(SkPoint pts[]) {
- SkPath::Verb verb = *fCurrVerb;
- switch (verb) {
- case SkPath::kLine_Verb:
- memcpy(pts, fCurrPoint, 2 * sizeof(SkPoint));
- fCurrPoint += 2;
- fCurrVerb += 1;
- break;
- case SkPath::kQuad_Verb:
- memcpy(pts, fCurrPoint, 3 * sizeof(SkPoint));
- fCurrPoint += 3;
- fCurrVerb += 1;
- break;
- case SkPath::kCubic_Verb:
- memcpy(pts, fCurrPoint, 4 * sizeof(SkPoint));
- fCurrPoint += 4;
- fCurrVerb += 1;
- break;
- case SkPath::kDone_Verb:
- break;
- default:
- SkDEBUGFAIL("unexpected verb in quadclippper2 iter");
- break;
- }
- return verb;
- }
- ///////////////////////////////////////////////////////////////////////////////
- #ifdef SK_DEBUG
- static void assert_monotonic(const SkScalar coord[], int count) {
- if (coord[0] > coord[(count - 1) * 2]) {
- for (int i = 1; i < count; i++) {
- SkASSERT(coord[2 * (i - 1)] >= coord[i * 2]);
- }
- } else if (coord[0] < coord[(count - 1) * 2]) {
- for (int i = 1; i < count; i++) {
- SkASSERT(coord[2 * (i - 1)] <= coord[i * 2]);
- }
- } else {
- for (int i = 1; i < count; i++) {
- SkASSERT(coord[2 * (i - 1)] == coord[i * 2]);
- }
- }
- }
- void sk_assert_monotonic_y(const SkPoint pts[], int count) {
- if (count > 1) {
- assert_monotonic(&pts[0].fY, count);
- }
- }
- void sk_assert_monotonic_x(const SkPoint pts[], int count) {
- if (count > 1) {
- assert_monotonic(&pts[0].fX, count);
- }
- }
- #endif
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