/*
* Copyright 2008 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 "SkPathMeasure.h"
#include "SkGeometry.h"
#include "SkPath.h"
#include "SkTSearch.h"
// these must be 0,1,2,3 since they are in our 2-bit field
enum {
kLine_SegType,
kQuad_SegType,
kCubic_SegType,
kConic_SegType,
};
#define kMaxTValue 0x3FFFFFFF
static inline SkScalar tValue2Scalar(int t) {
SkASSERT((unsigned)t <= kMaxTValue);
const SkScalar kMaxTReciprocal = 1.0f / kMaxTValue;
return t * kMaxTReciprocal;
}
SkScalar SkPathMeasure::Segment::getScalarT() const {
return tValue2Scalar(fTValue);
}
const SkPathMeasure::Segment* SkPathMeasure::NextSegment(const Segment* seg) {
unsigned ptIndex = seg->fPtIndex;
do {
++seg;
} while (seg->fPtIndex == ptIndex);
return seg;
}
///////////////////////////////////////////////////////////////////////////////
static inline int tspan_big_enough(int tspan) {
SkASSERT((unsigned)tspan <= kMaxTValue);
return tspan >> 10;
}
// can't use tangents, since we need [0..1..................2] to be seen
// as definitely not a line (it is when drawn, but not parametrically)
// so we compare midpoints
#define CHEAP_DIST_LIMIT (SK_Scalar1/2) // just made this value up
bool SkPathMeasure::quad_too_curvy(const SkPoint pts[3]) {
// diff = (a/4 + b/2 + c/4) - (a/2 + c/2)
// diff = -a/4 + b/2 - c/4
SkScalar dx = SkScalarHalf(pts[1].fX) -
SkScalarHalf(SkScalarHalf(pts[0].fX + pts[2].fX));
SkScalar dy = SkScalarHalf(pts[1].fY) -
SkScalarHalf(SkScalarHalf(pts[0].fY + pts[2].fY));
SkScalar dist = SkMaxScalar(SkScalarAbs(dx), SkScalarAbs(dy));
return dist > fTolerance;
}
bool SkPathMeasure::conic_too_curvy(const SkPoint& firstPt, const SkPoint& midTPt,
const SkPoint& lastPt) {
SkPoint midEnds = firstPt + lastPt;
midEnds *= 0.5f;
SkVector dxy = midTPt - midEnds;
SkScalar dist = SkMaxScalar(SkScalarAbs(dxy.fX), SkScalarAbs(dxy.fY));
return dist > fTolerance;
}
bool SkPathMeasure::cheap_dist_exceeds_limit(const SkPoint& pt,
SkScalar x, SkScalar y) {
SkScalar dist = SkMaxScalar(SkScalarAbs(x - pt.fX), SkScalarAbs(y - pt.fY));
// just made up the 1/2
return dist > fTolerance;
}
bool SkPathMeasure::cubic_too_curvy(const SkPoint pts[4]) {
return cheap_dist_exceeds_limit(pts[1],
SkScalarInterp(pts[0].fX, pts[3].fX, SK_Scalar1/3),
SkScalarInterp(pts[0].fY, pts[3].fY, SK_Scalar1/3))
||
cheap_dist_exceeds_limit(pts[2],
SkScalarInterp(pts[0].fX, pts[3].fX, SK_Scalar1*2/3),
SkScalarInterp(pts[0].fY, pts[3].fY, SK_Scalar1*2/3));
}
static SkScalar quad_folded_len(const SkPoint pts[3]) {
SkScalar t = SkFindQuadMaxCurvature(pts);
SkPoint pt = SkEvalQuadAt(pts, t);
SkVector a = pts[2] - pt;
SkScalar result = a.length();
if (0 != t) {
SkVector b = pts[0] - pt;
result += b.length();
}
SkASSERT(SkScalarIsFinite(result));
return result;
}
/* from http://www.malczak.linuxpl.com/blog/quadratic-bezier-curve-length/ */
/* This works -- more needs to be done to see if it is performant on all platforms.
To use this to measure parts of quads requires recomputing everything -- perhaps
a chop-like interface can start from a larger measurement and get two new measurements
with one call here.
*/
static SkScalar compute_quad_len(const SkPoint pts[3]) {
SkPoint a,b;
a.fX = pts[0].fX - 2 * pts[1].fX + pts[2].fX;
a.fY = pts[0].fY - 2 * pts[1].fY + pts[2].fY;
SkScalar A = 4 * (a.fX * a.fX + a.fY * a.fY);
if (0 == A) {
a = pts[2] - pts[0];
return a.length();
}
b.fX = 2 * (pts[1].fX - pts[0].fX);
b.fY = 2 * (pts[1].fY - pts[0].fY);
SkScalar B = 4 * (a.fX * b.fX + a.fY * b.fY);
SkScalar C = b.fX * b.fX + b.fY * b.fY;
SkScalar Sabc = 2 * SkScalarSqrt(A + B + C);
SkScalar A_2 = SkScalarSqrt(A);
SkScalar A_32 = 2 * A * A_2;
SkScalar C_2 = 2 * SkScalarSqrt(C);
SkScalar BA = B / A_2;
if (0 == BA + C_2) {
return quad_folded_len(pts);
}
SkScalar J = A_32 * Sabc + A_2 * B * (Sabc - C_2);
SkScalar K = 4 * C * A - B * B;
SkScalar L = (2 * A_2 + BA + Sabc) / (BA + C_2);
if (L <= 0) {
return quad_folded_len(pts);
}
SkScalar M = SkScalarLog(L);
SkScalar result = (J + K * M) / (4 * A_32);
SkASSERT(SkScalarIsFinite(result));
return result;
}
SkScalar SkPathMeasure::compute_quad_segs(const SkPoint pts[3],
SkScalar distance, int mint, int maxt, int ptIndex) {
if (tspan_big_enough(maxt - mint) && quad_too_curvy(pts)) {
SkPoint tmp[5];
int halft = (mint + maxt) >> 1;
SkChopQuadAtHalf(pts, tmp);
distance = this->compute_quad_segs(tmp, distance, mint, halft, ptIndex);
distance = this->compute_quad_segs(&tmp[2], distance, halft, maxt, ptIndex);
} else {
SkScalar d = SkPoint::Distance(pts[0], pts[2]);
SkScalar prevD = distance;
distance += d;
if (distance > prevD) {
Segment* seg = fSegments.append();
seg->fDistance = distance;
seg->fPtIndex = ptIndex;
seg->fType = kQuad_SegType;
seg->fTValue = maxt;
}
}
return distance;
}
SkScalar SkPathMeasure::compute_conic_segs(const SkConic& conic, SkScalar distance,
int mint, const SkPoint& minPt,
int maxt, const SkPoint& maxPt, int ptIndex) {
int halft = (mint + maxt) >> 1;
SkPoint halfPt = conic.evalAt(tValue2Scalar(halft));
if (tspan_big_enough(maxt - mint) && conic_too_curvy(minPt, halfPt, maxPt)) {
distance = this->compute_conic_segs(conic, distance, mint, minPt, halft, halfPt, ptIndex);
distance = this->compute_conic_segs(conic, distance, halft, halfPt, maxt, maxPt, ptIndex);
} else {
SkScalar d = SkPoint::Distance(minPt, maxPt);
SkScalar prevD = distance;
distance += d;
if (distance > prevD) {
Segment* seg = fSegments.append();
seg->fDistance = distance;
seg->fPtIndex = ptIndex;
seg->fType = kConic_SegType;
seg->fTValue = maxt;
}
}
return distance;
}
SkScalar SkPathMeasure::compute_cubic_segs(const SkPoint pts[4],
SkScalar distance, int mint, int maxt, int ptIndex) {
if (tspan_big_enough(maxt - mint) && cubic_too_curvy(pts)) {
SkPoint tmp[7];
int halft = (mint + maxt) >> 1;
SkChopCubicAtHalf(pts, tmp);
distance = this->compute_cubic_segs(tmp, distance, mint, halft, ptIndex);
distance = this->compute_cubic_segs(&tmp[3], distance, halft, maxt, ptIndex);
} else {
SkScalar d = SkPoint::Distance(pts[0], pts[3]);
SkScalar prevD = distance;
distance += d;
if (distance > prevD) {
Segment* seg = fSegments.append();
seg->fDistance = distance;
seg->fPtIndex = ptIndex;
seg->fType = kCubic_SegType;
seg->fTValue = maxt;
}
}
return distance;
}
void SkPathMeasure::buildSegments() {
SkPoint pts[4];
int ptIndex = fFirstPtIndex;
SkScalar distance = 0;
bool isClosed = fForceClosed;
bool firstMoveTo = ptIndex < 0;
Segment* seg;
/* Note:
* as we accumulate distance, we have to check that the result of +=
* actually made it larger, since a very small delta might be > 0, but
* still have no effect on distance (if distance >>> delta).
*
* We do this check below, and in compute_quad_segs and compute_cubic_segs
*/
fSegments.reset();
bool done = false;
do {
switch (fIter.next(pts)) {
case SkPath::kMove_Verb:
ptIndex += 1;
fPts.append(1, pts);
if (!firstMoveTo) {
done = true;
break;
}
firstMoveTo = false;
break;
case SkPath::kLine_Verb: {
SkScalar d = SkPoint::Distance(pts[0], pts[1]);
SkASSERT(d >= 0);
SkScalar prevD = distance;
distance += d;
if (distance > prevD) {
seg = fSegments.append();
seg->fDistance = distance;
seg->fPtIndex = ptIndex;
seg->fType = kLine_SegType;
seg->fTValue = kMaxTValue;
fPts.append(1, pts + 1);
ptIndex++;
}
} break;
case SkPath::kQuad_Verb: {
SkScalar prevD = distance;
if (false) {
SkScalar length = compute_quad_len(pts);
if (length) {
distance += length;
Segment* seg = fSegments.append();
seg->fDistance = distance;
seg->fPtIndex = ptIndex;
seg->fType = kQuad_SegType;
seg->fTValue = kMaxTValue;
}
} else {
distance = this->compute_quad_segs(pts, distance, 0, kMaxTValue, ptIndex);
}
if (distance > prevD) {
fPts.append(2, pts + 1);
ptIndex += 2;
}
} break;
case SkPath::kConic_Verb: {
const SkConic conic(pts, fIter.conicWeight());
SkScalar prevD = distance;
distance = this->compute_conic_segs(conic, distance, 0, conic.fPts[0],
kMaxTValue, conic.fPts[2], ptIndex);
if (distance > prevD) {
// we store the conic weight in our next point, followed by the last 2 pts
// thus to reconstitue a conic, you'd need to say
// SkConic(pts[0], pts[2], pts[3], weight = pts[1].fX)
fPts.append()->set(conic.fW, 0);
fPts.append(2, pts + 1);
ptIndex += 3;
}
} break;
case SkPath::kCubic_Verb: {
SkScalar prevD = distance;
distance = this->compute_cubic_segs(pts, distance, 0, kMaxTValue, ptIndex);
if (distance > prevD) {
fPts.append(3, pts + 1);
ptIndex += 3;
}
} break;
case SkPath::kClose_Verb:
isClosed = true;
break;
case SkPath::kDone_Verb:
done = true;
break;
}
} while (!done);
fLength = distance;
fIsClosed = isClosed;
fFirstPtIndex = ptIndex;
#ifdef SK_DEBUG
{
const Segment* seg = fSegments.begin();
const Segment* stop = fSegments.end();
unsigned ptIndex = 0;
SkScalar distance = 0;
while (seg < stop) {
SkASSERT(seg->fDistance > distance);
SkASSERT(seg->fPtIndex >= ptIndex);
SkASSERT(seg->fTValue > 0);
const Segment* s = seg;
while (s < stop - 1 && s[0].fPtIndex == s[1].fPtIndex) {
SkASSERT(s[0].fType == s[1].fType);
SkASSERT(s[0].fTValue < s[1].fTValue);
s += 1;
}
distance = seg->fDistance;
ptIndex = seg->fPtIndex;
seg += 1;
}
// SkDebugf("\n");
}
#endif
}
static void compute_pos_tan(const SkPoint pts[], int segType,
SkScalar t, SkPoint* pos, SkVector* tangent) {
switch (segType) {
case kLine_SegType:
if (pos) {
pos->set(SkScalarInterp(pts[0].fX, pts[1].fX, t),
SkScalarInterp(pts[0].fY, pts[1].fY, t));
}
if (tangent) {
tangent->setNormalize(pts[1].fX - pts[0].fX, pts[1].fY - pts[0].fY);
}
break;
case kQuad_SegType:
SkEvalQuadAt(pts, t, pos, tangent);
if (tangent) {
tangent->normalize();
}
break;
case kConic_SegType: {
SkConic(pts[0], pts[2], pts[3], pts[1].fX).evalAt(t, pos, tangent);
if (tangent) {
tangent->normalize();
}
} break;
case kCubic_SegType:
SkEvalCubicAt(pts, t, pos, tangent, nullptr);
if (tangent) {
tangent->normalize();
}
break;
default:
SkDEBUGFAIL("unknown segType");
}
}
static void seg_to(const SkPoint pts[], int segType,
SkScalar startT, SkScalar stopT, SkPath* dst) {
SkASSERT(startT >= 0 && startT <= SK_Scalar1);
SkASSERT(stopT >= 0 && stopT <= SK_Scalar1);
SkASSERT(startT <= stopT);
if (startT == stopT) {
/* if the dash as a zero-length on segment, add a corresponding zero-length line.
The stroke code will add end caps to zero length lines as appropriate */
SkPoint lastPt;
SkAssertResult(dst->getLastPt(&lastPt));
dst->lineTo(lastPt);
return;
}
SkPoint tmp0[7], tmp1[7];
switch (segType) {
case kLine_SegType:
if (SK_Scalar1 == stopT) {
dst->lineTo(pts[1]);
} else {
dst->lineTo(SkScalarInterp(pts[0].fX, pts[1].fX, stopT),
SkScalarInterp(pts[0].fY, pts[1].fY, stopT));
}
break;
case kQuad_SegType:
if (0 == startT) {
if (SK_Scalar1 == stopT) {
dst->quadTo(pts[1], pts[2]);
} else {
SkChopQuadAt(pts, tmp0, stopT);
dst->quadTo(tmp0[1], tmp0[2]);
}
} else {
SkChopQuadAt(pts, tmp0, startT);
if (SK_Scalar1 == stopT) {
dst->quadTo(tmp0[3], tmp0[4]);
} else {
SkChopQuadAt(&tmp0[2], tmp1, (stopT - startT) / (1 - startT));
dst->quadTo(tmp1[1], tmp1[2]);
}
}
break;
case kConic_SegType: {
SkConic conic(pts[0], pts[2], pts[3], pts[1].fX);
if (0 == startT) {
if (SK_Scalar1 == stopT) {
dst->conicTo(conic.fPts[1], conic.fPts[2], conic.fW);
} else {
SkConic tmp[2];
conic.chopAt(stopT, tmp);
dst->conicTo(tmp[0].fPts[1], tmp[0].fPts[2], tmp[0].fW);
}
} else {
if (SK_Scalar1 == stopT) {
SkConic tmp1[2];
conic.chopAt(startT, tmp1);
dst->conicTo(tmp1[1].fPts[1], tmp1[1].fPts[2], tmp1[1].fW);
} else {
SkConic tmp;
conic.chopAt(startT, stopT, &tmp);
dst->conicTo(tmp.fPts[1], tmp.fPts[2], tmp.fW);
}
}
} break;
case kCubic_SegType:
if (0 == startT) {
if (SK_Scalar1 == stopT) {
dst->cubicTo(pts[1], pts[2], pts[3]);
} else {
SkChopCubicAt(pts, tmp0, stopT);
dst->cubicTo(tmp0[1], tmp0[2], tmp0[3]);
}
} else {
SkChopCubicAt(pts, tmp0, startT);
if (SK_Scalar1 == stopT) {
dst->cubicTo(tmp0[4], tmp0[5], tmp0[6]);
} else {
SkChopCubicAt(&tmp0[3], tmp1, (stopT - startT) / (1 - startT));
dst->cubicTo(tmp1[1], tmp1[2], tmp1[3]);
}
}
break;
default:
SkDEBUGFAIL("unknown segType");
sk_throw();
}
}
////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////
SkPathMeasure::SkPathMeasure() {
fPath = nullptr;
fTolerance = CHEAP_DIST_LIMIT;
fLength = -1; // signal we need to compute it
fForceClosed = false;
fFirstPtIndex = -1;
}
SkPathMeasure::SkPathMeasure(const SkPath& path, bool forceClosed, SkScalar resScale) {
fPath = &path;
fTolerance = CHEAP_DIST_LIMIT * SkScalarInvert(resScale);
fLength = -1; // signal we need to compute it
fForceClosed = forceClosed;
fFirstPtIndex = -1;
fIter.setPath(path, forceClosed);
}
SkPathMeasure::~SkPathMeasure() {}
/** Assign a new path, or null to have none.
*/
void SkPathMeasure::setPath(const SkPath* path, bool forceClosed) {
fPath = path;
fLength = -1; // signal we need to compute it
fForceClosed = forceClosed;
fFirstPtIndex = -1;
if (path) {
fIter.setPath(*path, forceClosed);
}
fSegments.reset();
fPts.reset();
}
SkScalar SkPathMeasure::getLength() {
if (fPath == nullptr) {
return 0;
}
if (fLength < 0) {
this->buildSegments();
}
SkASSERT(fLength >= 0);
return fLength;
}
template <typename T, typename K>
int SkTKSearch(const T base[], int count, const K& key) {
SkASSERT(count >= 0);
if (count <= 0) {
return ~0;
}
SkASSERT(base != nullptr); // base may be nullptr if count is zero
int lo = 0;
int hi = count - 1;
while (lo < hi) {
int mid = (hi + lo) >> 1;
if (base[mid].fDistance < key) {
lo = mid + 1;
} else {
hi = mid;
}
}
if (base[hi].fDistance < key) {
hi += 1;
hi = ~hi;
} else if (key < base[hi].fDistance) {
hi = ~hi;
}
return hi;
}
const SkPathMeasure::Segment* SkPathMeasure::distanceToSegment(
SkScalar distance, SkScalar* t) {
SkDEBUGCODE(SkScalar length = ) this->getLength();
SkASSERT(distance >= 0 && distance <= length);
const Segment* seg = fSegments.begin();
int count = fSegments.count();
int index = SkTKSearch<Segment, SkScalar>(seg, count, distance);
// don't care if we hit an exact match or not, so we xor index if it is negative
index ^= (index >> 31);
seg = &seg[index];
// now interpolate t-values with the prev segment (if possible)
SkScalar startT = 0, startD = 0;
// check if the prev segment is legal, and references the same set of points
if (index > 0) {
startD = seg[-1].fDistance;
if (seg[-1].fPtIndex == seg->fPtIndex) {
SkASSERT(seg[-1].fType == seg->fType);
startT = seg[-1].getScalarT();
}
}
SkASSERT(seg->getScalarT() > startT);
SkASSERT(distance >= startD);
SkASSERT(seg->fDistance > startD);
*t = startT + SkScalarMulDiv(seg->getScalarT() - startT,
distance - startD,
seg->fDistance - startD);
return seg;
}
bool SkPathMeasure::getPosTan(SkScalar distance, SkPoint* pos,
SkVector* tangent) {
if (nullptr == fPath) {
return false;
}
SkScalar length = this->getLength(); // call this to force computing it
int count = fSegments.count();
if (count == 0 || length == 0) {
return false;
}
// pin the distance to a legal range
if (distance < 0) {
distance = 0;
} else if (distance > length) {
distance = length;
}
SkScalar t;
const Segment* seg = this->distanceToSegment(distance, &t);
compute_pos_tan(&fPts[seg->fPtIndex], seg->fType, t, pos, tangent);
return true;
}
bool SkPathMeasure::getMatrix(SkScalar distance, SkMatrix* matrix,
MatrixFlags flags) {
if (nullptr == fPath) {
return false;
}
SkPoint position;
SkVector tangent;
if (this->getPosTan(distance, &position, &tangent)) {
if (matrix) {
if (flags & kGetTangent_MatrixFlag) {
matrix->setSinCos(tangent.fY, tangent.fX, 0, 0);
} else {
matrix->reset();
}
if (flags & kGetPosition_MatrixFlag) {
matrix->postTranslate(position.fX, position.fY);
}
}
return true;
}
return false;
}
bool SkPathMeasure::getSegment(SkScalar startD, SkScalar stopD, SkPath* dst,
bool startWithMoveTo) {
SkASSERT(dst);
SkScalar length = this->getLength(); // ensure we have built our segments
if (startD < 0) {
startD = 0;
}
if (stopD > length) {
stopD = length;
}
if (startD > stopD) {
return false;
}
if (!fSegments.count()) {
return false;
}
SkPoint p;
SkScalar startT, stopT;
const Segment* seg = this->distanceToSegment(startD, &startT);
const Segment* stopSeg = this->distanceToSegment(stopD, &stopT);
SkASSERT(seg <= stopSeg);
if (startWithMoveTo) {
compute_pos_tan(&fPts[seg->fPtIndex], seg->fType, startT, &p, nullptr);
dst->moveTo(p);
}
if (seg->fPtIndex == stopSeg->fPtIndex) {
seg_to(&fPts[seg->fPtIndex], seg->fType, startT, stopT, dst);
} else {
do {
seg_to(&fPts[seg->fPtIndex], seg->fType, startT, SK_Scalar1, dst);
seg = SkPathMeasure::NextSegment(seg);
startT = 0;
} while (seg->fPtIndex < stopSeg->fPtIndex);
seg_to(&fPts[seg->fPtIndex], seg->fType, 0, stopT, dst);
}
return true;
}
bool SkPathMeasure::isClosed() {
(void)this->getLength();
return fIsClosed;
}
/** Move to the next contour in the path. Return true if one exists, or false if
we're done with the path.
*/
bool SkPathMeasure::nextContour() {
fLength = -1;
return this->getLength() > 0;
}
///////////////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////////////
#ifdef SK_DEBUG
void SkPathMeasure::dump() {
SkDebugf("pathmeas: length=%g, segs=%d\n", fLength, fSegments.count());
for (int i = 0; i < fSegments.count(); i++) {
const Segment* seg = &fSegments[i];
SkDebugf("pathmeas: seg[%d] distance=%g, point=%d, t=%g, type=%d\n",
i, seg->fDistance, seg->fPtIndex, seg->getScalarT(),
seg->fType);
}
}
#endif