--- a/src/gui/painting/qbezier.cpp Wed Jun 23 19:07:03 2010 +0300
+++ b/src/gui/painting/qbezier.cpp Tue Jul 06 15:10:48 2010 +0300
@@ -93,7 +93,7 @@
/*!
\internal
*/
-QPolygonF QBezier::toPolygon() const
+QPolygonF QBezier::toPolygon(qreal bezier_flattening_threshold) const
{
// flattening is done by splitting the bezier until we can replace the segment by a straight
// line. We split further until the control points are close enough to the line connecting the
@@ -108,38 +108,34 @@
QPolygonF polygon;
polygon.append(QPointF(x1, y1));
- addToPolygon(&polygon);
+ addToPolygon(&polygon, bezier_flattening_threshold);
return polygon;
}
-//0.5 is really low
-static const qreal flatness = 0.5;
-
-//based on "Fast, precise flattening of cubic Bezier path and offset curves"
-// by T. F. Hain, A. L. Ahmad, S. V. R. Racherla and D. D. Langan
-static inline void flattenBezierWithoutInflections(QBezier &bez,
- QPolygonF *&p)
+QBezier QBezier::mapBy(const QTransform &transform) const
{
- QBezier left;
-
- while (1) {
- qreal dx = bez.x2 - bez.x1;
- qreal dy = bez.y2 - bez.y1;
-
- qreal normalized = qSqrt(dx * dx + dy * dy);
- if (qFuzzyIsNull(normalized))
- break;
-
- qreal d = qAbs(dx * (bez.y3 - bez.y2) - dy * (bez.x3 - bez.x2));
-
- qreal t = qSqrt(4. / 3. * normalized * flatness / d);
- if (t > 1 || qFuzzyIsNull(t - (qreal)1.))
- break;
- bez.parameterSplitLeft(t, &left);
- p->append(bez.pt1());
- }
+ return QBezier::fromPoints(transform.map(pt1()), transform.map(pt2()), transform.map(pt3()), transform.map(pt4()));
}
+QBezier QBezier::getSubRange(qreal t0, qreal t1) const
+{
+ QBezier result;
+ QBezier temp;
+
+ // cut at t1
+ if (qFuzzyIsNull(t1 - qreal(1.))) {
+ result = *this;
+ } else {
+ temp = *this;
+ temp.parameterSplitLeft(t1, &result);
+ }
+
+ // cut at t0
+ if (!qFuzzyIsNull(t0))
+ result.parameterSplitLeft(t0 / t1, &temp);
+
+ return result;
+}
static inline int quadraticRoots(qreal a, qreal b, qreal c,
qreal *x1, qreal *x2)
@@ -199,7 +195,7 @@
}
-void QBezier::addToPolygon(QPolygonF *polygon) const
+void QBezier::addToPolygon(QPolygonF *polygon, qreal bezier_flattening_threshold) const
{
QBezier beziers[32];
beziers[0] = *this;
@@ -219,7 +215,7 @@
qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);
l = 1.;
}
- if (d < flatness*l || b == beziers + 31) {
+ if (d < bezier_flattening_threshold*l || b == beziers + 31) {
// good enough, we pop it off and add the endpoint
polygon->append(QPointF(b->x4, b->y4));
--b;
@@ -231,55 +227,6 @@
}
}
-void QBezier::addToPolygonMixed(QPolygonF *polygon) const
-{
- qreal ax = -x1 + 3*x2 - 3*x3 + x4;
- qreal ay = -y1 + 3*y2 - 3*y3 + y4;
- qreal bx = 3*x1 - 6*x2 + 3*x3;
- qreal by = 3*y1 - 6*y2 + 3*y3;
- qreal cx = -3*x1 + 3*x2;
- qreal cy = -3*y1 + 2*y2;
- qreal a = 6 * (ay * bx - ax * by);
- qreal b = 6 * (ay * cx - ax * cy);
- qreal c = 2 * (by * cx - bx * cy);
-
- if ((qFuzzyIsNull(a) && qFuzzyIsNull(b)) ||
- (b * b - 4 * a *c) < 0) {
- QBezier bez(*this);
- flattenBezierWithoutInflections(bez, polygon);
- polygon->append(QPointF(x4, y4));
- } else {
- QBezier beziers[32];
- beziers[0] = *this;
- QBezier *b = beziers;
-
- while (b >= beziers) {
- // check if we can pop the top bezier curve from the stack
- qreal y4y1 = b->y4 - b->y1;
- qreal x4x1 = b->x4 - b->x1;
- qreal l = qAbs(x4x1) + qAbs(y4y1);
- qreal d;
- if (l > 1.) {
- d = qAbs( (x4x1)*(b->y1 - b->y2) - (y4y1)*(b->x1 - b->x2) )
- + qAbs( (x4x1)*(b->y1 - b->y3) - (y4y1)*(b->x1 - b->x3) );
- } else {
- d = qAbs(b->x1 - b->x2) + qAbs(b->y1 - b->y2) +
- qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);
- l = 1.;
- }
- if (d < .5*l || b == beziers + 31) {
- // good enough, we pop it off and add the endpoint
- polygon->append(QPointF(b->x4, b->y4));
- --b;
- } else {
- // split, second half of the polygon goes lower into the stack
- b->split(b+1, b);
- ++b;
- }
- }
- }
-}
-
QRectF QBezier::bounds() const
{
qreal xmin = x1;
@@ -588,88 +535,6 @@
return o - curveSegments;
}
-#if 0
-static inline bool IntersectBB(const QBezier &a, const QBezier &b)
-{
- return a.bounds().intersects(b.bounds());
-}
-#else
-static int IntersectBB(const QBezier &a, const QBezier &b)
-{
- // Compute bounding box for a
- qreal minax, maxax, minay, maxay;
- if (a.x1 > a.x4) // These are the most likely to be extremal
- minax = a.x4, maxax = a.x1;
- else
- minax = a.x1, maxax = a.x4;
-
- if (a.x3 < minax)
- minax = a.x3;
- else if (a.x3 > maxax)
- maxax = a.x3;
-
- if (a.x2 < minax)
- minax = a.x2;
- else if (a.x2 > maxax)
- maxax = a.x2;
-
- if (a.y1 > a.y4)
- minay = a.y4, maxay = a.y1;
- else
- minay = a.y1, maxay = a.y4;
-
- if (a.y3 < minay)
- minay = a.y3;
- else if (a.y3 > maxay)
- maxay = a.y3;
-
- if (a.y2 < minay)
- minay = a.y2;
- else if (a.y2 > maxay)
- maxay = a.y2;
-
- // Compute bounding box for b
- qreal minbx, maxbx, minby, maxby;
- if (b.x1 > b.x4)
- minbx = b.x4, maxbx = b.x1;
- else
- minbx = b.x1, maxbx = b.x4;
-
- if (b.x3 < minbx)
- minbx = b.x3;
- else if (b.x3 > maxbx)
- maxbx = b.x3;
-
- if (b.x2 < minbx)
- minbx = b.x2;
- else if (b.x2 > maxbx)
- maxbx = b.x2;
-
- if (b.y1 > b.y4)
- minby = b.y4, maxby = b.y1;
- else
- minby = b.y1, maxby = b.y4;
-
- if (b.y3 < minby)
- minby = b.y3;
- else if (b.y3 > maxby)
- maxby = b.y3;
-
- if (b.y2 < minby)
- minby = b.y2;
- else if (b.y2 > maxby)
- maxby = b.y2;
-
- // Test bounding box of b against bounding box of a
- if ((minax > maxbx) || (minay > maxby) // Not >= : need boundary case
- || (minbx > maxax) || (minby > maxay))
- return 0; // they don't intersect
- else
- return 1; // they intersect
-}
-#endif
-
-
#ifdef QDEBUG_BEZIER
static QDebug operator<<(QDebug dbg, const QBezier &bz)
{
@@ -681,193 +546,6 @@
}
#endif
-static bool RecursivelyIntersect(const QBezier &a, qreal t0, qreal t1, int deptha,
- const QBezier &b, qreal u0, qreal u1, int depthb,
- QVector<QPair<qreal, qreal> > *t)
-{
-#ifdef QDEBUG_BEZIER
- static int I = 0;
- int currentD = I;
- fprintf(stderr, "%d) t0 = %lf, t1 = %lf, deptha = %d\n"
- "u0 = %lf, u1 = %lf, depthb = %d\n", I++, t0, t1, deptha,
- u0, u1, depthb);
-#endif
- if (deptha > 0) {
- QBezier A[2];
- a.split(&A[0], &A[1]);
- qreal tmid = (t0+t1)*0.5;
- //qDebug()<<"\t1)"<<A[0];
- //qDebug()<<"\t2)"<<A[1];
- deptha--;
- if (depthb > 0) {
- QBezier B[2];
- b.split(&B[0], &B[1]);
- //qDebug()<<"\t3)"<<B[0];
- //qDebug()<<"\t4)"<<B[1];
- qreal umid = (u0+u1)*0.5;
- depthb--;
- if (IntersectBB(A[0], B[0])) {
- //fprintf(stderr, "\t 1 from %d\n", currentD);
- if (RecursivelyIntersect(A[0], t0, tmid, deptha,
- B[0], u0, umid, depthb,
- t) && !t)
- return true;
- }
- if (IntersectBB(A[1], B[0])) {
- //fprintf(stderr, "\t 2 from %d\n", currentD);
- if (RecursivelyIntersect(A[1], tmid, t1, deptha,
- B[0], u0, umid, depthb,
- t) && !t)
- return true;
- }
- if (IntersectBB(A[0], B[1])) {
- //fprintf(stderr, "\t 3 from %d\n", currentD);
- if (RecursivelyIntersect(A[0], t0, tmid, deptha,
- B[1], umid, u1, depthb,
- t) && !t)
- return true;
- }
- if (IntersectBB(A[1], B[1])) {
- //fprintf(stderr, "\t 4 from %d\n", currentD);
- if (RecursivelyIntersect(A[1], tmid, t1, deptha,
- B[1], umid, u1, depthb,
- t) && !t)
- return true;
- }
- return t ? !t->isEmpty() : false;
- } else {
- if (IntersectBB(A[0], b)) {
- //fprintf(stderr, "\t 5 from %d\n", currentD);
- if (RecursivelyIntersect(A[0], t0, tmid, deptha,
- b, u0, u1, depthb,
- t) && !t)
- return true;
- }
- if (IntersectBB(A[1], b)) {
- //fprintf(stderr, "\t 6 from %d\n", currentD);
- if (RecursivelyIntersect(A[1], tmid, t1, deptha,
- b, u0, u1, depthb,
- t) && !t)
- return true;
- }
- return t ? !t->isEmpty() : false;
- }
- } else {
- if (depthb > 0) {
- QBezier B[2];
- b.split(&B[0], &B[1]);
- qreal umid = (u0 + u1)*0.5;
- depthb--;
- if (IntersectBB(a, B[0])) {
- //fprintf(stderr, "\t 7 from %d\n", currentD);
- if (RecursivelyIntersect(a, t0, t1, deptha,
- B[0], u0, umid, depthb,
- t) && !t)
- return true;
- }
- if (IntersectBB(a, B[1])) {
- //fprintf(stderr, "\t 8 from %d\n", currentD);
- if (RecursivelyIntersect(a, t0, t1, deptha,
- B[1], umid, u1, depthb,
- t) && !t)
- return true;
- }
- return t ? !t->isEmpty() : false;
- }
- else {
- // Both segments are fully subdivided; now do line segments
- qreal xlk = a.x4 - a.x1;
- qreal ylk = a.y4 - a.y1;
- qreal xnm = b.x4 - b.x1;
- qreal ynm = b.y4 - b.y1;
- qreal xmk = b.x1 - a.x1;
- qreal ymk = b.y1 - a.y1;
- qreal det = xnm * ylk - ynm * xlk;
- if (1.0 + det == 1.0) {
- return false;
- } else {
- qreal detinv = 1.0 / det;
- qreal rs = (xnm * ymk - ynm *xmk) * detinv;
- qreal rt = (xlk * ymk - ylk * xmk) * detinv;
- if ((rs < 0.0) || (rs > 1.0) || (rt < 0.0) || (rt > 1.0))
- return false;
-
- if (t) {
- const qreal alpha_a = t0 + rs * (t1 - t0);
- const qreal alpha_b = u0 + rt * (u1 - u0);
-
- *t << qMakePair(alpha_a, alpha_b);
- }
-
- return true;
- }
- }
- }
-}
-
-QVector< QPair<qreal, qreal> > QBezier::findIntersections(const QBezier &a, const QBezier &b)
-{
- QVector< QPair<qreal, qreal> > v(2);
- findIntersections(a, b, &v);
- return v;
-}
-
-bool QBezier::findIntersections(const QBezier &a, const QBezier &b,
- QVector<QPair<qreal, qreal> > *t)
-{
- if (IntersectBB(a, b)) {
- QPointF la1(qFabs((a.x3 - a.x2) - (a.x2 - a.x1)),
- qFabs((a.y3 - a.y2) - (a.y2 - a.y1)));
- QPointF la2(qFabs((a.x4 - a.x3) - (a.x3 - a.x2)),
- qFabs((a.y4 - a.y3) - (a.y3 - a.y2)));
- QPointF la;
- if (la1.x() > la2.x()) la.setX(la1.x()); else la.setX(la2.x());
- if (la1.y() > la2.y()) la.setY(la1.y()); else la.setY(la2.y());
- QPointF lb1(qFabs((b.x3 - b.x2) - (b.x2 - b.x1)),
- qFabs((b.y3 - b.y2) - (b.y2 - b.y1)));
- QPointF lb2(qFabs((b.x4 - b.x3) - (b.x3 - b.x2)),
- qFabs((b.y4 - b.y3) - (b.y3 - b.y2)));
- QPointF lb;
- if (lb1.x() > lb2.x()) lb.setX(lb1.x()); else lb.setX(lb2.x());
- if (lb1.y() > lb2.y()) lb.setY(lb1.y()); else lb.setY(lb2.y());
- qreal l0;
- if (la.x() > la.y())
- l0 = la.x();
- else
- l0 = la.y();
- int ra;
- if (l0 * 0.75 * M_SQRT2 + 1.0 == 1.0)
- ra = 0;
- else
- ra = qCeil(log4(M_SQRT2 * 6.0 / 8.0 * INV_EPS * l0));
- if (lb.x() > lb.y())
- l0 = lb.x();
- else
- l0 = lb.y();
- int rb;
- if (l0 * 0.75 * M_SQRT2 + 1.0 == 1.0)
- rb = 0;
- else
- rb = qCeil(log4(M_SQRT2 * 6.0 / 8.0 * INV_EPS * l0));
-
- // if qreal is float then halve the number of subdivisions
- if (sizeof(qreal) == 4) {
- ra /= 2;
- rb /= 2;
- }
-
- return RecursivelyIntersect(a, 0., 1., ra, b, 0., 1., rb, t);
- }
-
- //Don't sort here because it breaks the orders of corresponding
- // intersections points. this way t's at the same locations correspond
- // to the same intersection point.
- //qSort(parameters[0].begin(), parameters[0].end(), qLess<qreal>());
- //qSort(parameters[1].begin(), parameters[1].end(), qLess<qreal>());
-
- return false;
-}
-
static inline void splitBezierAt(const QBezier &bez, qreal t,
QBezier *left, QBezier *right)
{
@@ -896,42 +574,6 @@
right->y4 = bez.y4;
}
-QVector< QList<QBezier> > QBezier::splitAtIntersections(QBezier &b)
-{
- QVector< QList<QBezier> > curves(2);
-
- QVector< QPair<qreal, qreal> > allInters = findIntersections(*this, b);
-
- QList<qreal> inters1;
- QList<qreal> inters2;
-
- for (int i = 0; i < allInters.size(); ++i) {
- inters1 << allInters[i].first;
- inters2 << allInters[i].second;
- }
-
- qSort(inters1.begin(), inters1.end(), qLess<qreal>());
- qSort(inters2.begin(), inters2.end(), qLess<qreal>());
-
- Q_ASSERT(inters1.count() == inters2.count());
-
- int i;
- for (i = 0; i < inters1.count(); ++i) {
- qreal t1 = inters1.at(i);
- qreal t2 = inters2.at(i);
-
- QBezier curve1, curve2;
- parameterSplitLeft(t1, &curve1);
- b.parameterSplitLeft(t2, &curve2);
- curves[0].append(curve1);
- curves[0].append(curve2);
- }
- curves[0].append(*this);
- curves[1].append(b);
-
- return curves;
-}
-
qreal QBezier::length(qreal error) const
{
qreal length = 0.0;
@@ -1018,13 +660,19 @@
const qreal b = 2 * y1 - 4 * y2 + 2 * y3;
const qreal c = -y1 + y2;
- qreal reciprocal = b * b - 4 * a * c;
+ if (qFuzzyIsNull(a)) {
+ if (qFuzzyIsNull(b))
+ return 0;
- QList<qreal> result;
+ t0 = -c / b;
+ return t0 > 0 && t0 < 1;
+ }
+
+ qreal reciprocal = b * b - 4 * a * c;
if (qFuzzyIsNull(reciprocal)) {
t0 = -b / (2 * a);
- return 1;
+ return t0 > 0 && t0 < 1;
} else if (reciprocal > 0) {
qreal temp = qSqrt(reciprocal);
@@ -1099,147 +747,4 @@
return result;
}
-
-static inline void bindInflectionPoint(const QBezier &bez, const qreal t,
- qreal *tMinus , qreal *tPlus)
-{
- if (t <= 0) {
- *tMinus = *tPlus = -1;
- return;
- } else if (t >= 1) {
- *tMinus = *tPlus = 2;
- return;
- }
-
- QBezier left, right;
- splitBezierAt(bez, t, &left, &right);
-
- qreal ax = -right.x1 + 3*right.x2 - 3*right.x3 + right.x4;
- qreal ay = -right.y1 + 3*right.y2 - 3*right.y3 + right.y4;
- qreal ex = 3 * (right.x2 - right.x3);
- qreal ey = 3 * (right.y2 - right.y3);
-
- qreal s4 = qAbs(6 * (ey * ax - ex * ay) / qSqrt(ex * ex + ey * ey)) + 0.00001f;
- qreal tf = qPow(qreal(9 * flatness / s4), qreal(1./3.));
- *tMinus = t - (1 - t) * tf;
- *tPlus = t + (1 - t) * tf;
-}
-
-void QBezier::addToPolygonIterative(QPolygonF *p) const
-{
- qreal t1, t2, tcusp;
- qreal t1min, t1plus, t2min, t2plus;
-
- qreal ax = -x1 + 3*x2 - 3*x3 + x4;
- qreal ay = -y1 + 3*y2 - 3*y3 + y4;
- qreal bx = 3*x1 - 6*x2 + 3*x3;
- qreal by = 3*y1 - 6*y2 + 3*y3;
- qreal cx = -3*x1 + 3*x2;
- qreal cy = -3*y1 + 2*y2;
-
- if (findInflections(6 * (ay * bx - ax * by),
- 6 * (ay * cx - ax * cy),
- 2 * (by * cx - bx * cy),
- &t1, &t2, &tcusp)) {
- bindInflectionPoint(*this, t1, &t1min, &t1plus);
- bindInflectionPoint(*this, t2, &t2min, &t2plus);
-
- QBezier tmpBez = *this;
- QBezier left, right, bez1, bez2, bez3;
- if (t1min > 0) {
- if (t1min >= 1) {
- flattenBezierWithoutInflections(tmpBez, p);
- } else {
- splitBezierAt(tmpBez, t1min, &left, &right);
- flattenBezierWithoutInflections(left, p);
- p->append(tmpBez.pointAt(t1min));
-
- if (t2min < t1plus) {
- if (tcusp < 1) {
- p->append(tmpBez.pointAt(tcusp));
- }
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &right);
- flattenBezierWithoutInflections(right, p);
- }
- } else if (t1plus < 1) {
- if (t2min < 1) {
- splitBezierAt(tmpBez, t2min, &bez3, &right);
- splitBezierAt(bez3, t1plus, &left, &bez2);
-
- flattenBezierWithoutInflections(bez2, p);
- p->append(tmpBez.pointAt(t2min));
-
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- } else {
- splitBezierAt(tmpBez, t1plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- }
- }
- } else if (t1plus > 0) {
- p->append(QPointF(x1, y1));
- if (t2min < t1plus) {
- if (tcusp < 1) {
- p->append(tmpBez.pointAt(tcusp));
- }
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- } else if (t1plus < 1) {
- if (t2min < 1) {
- splitBezierAt(tmpBez, t2min, &bez3, &right);
- splitBezierAt(bez3, t1plus, &left, &bez2);
-
- flattenBezierWithoutInflections(bez2, p);
-
- p->append(tmpBez.pointAt(t2min));
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- } else {
- splitBezierAt(tmpBez, t1plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- }
- } else if (t2min > 0) {
- if (t2min < 1) {
- splitBezierAt(tmpBez, t2min, &bez1, &right);
- flattenBezierWithoutInflections(bez1, p);
- p->append(tmpBez.pointAt(t2min));
-
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- } else {
- //### in here we should check whether the area of the
- // triangle formed between pt1/pt2/pt3 is smaller
- // or equal to 0 and then do iterative flattening
- // if not we should fallback and do the recursive
- // flattening.
- flattenBezierWithoutInflections(tmpBez, p);
- }
- } else if (t2plus > 0) {
- p->append(QPointF(x1, y1));
- if (t2plus < 1) {
- splitBezierAt(tmpBez, t2plus, &left, &bez2);
- flattenBezierWithoutInflections(bez2, p);
- }
- } else {
- flattenBezierWithoutInflections(tmpBez, p);
- }
- } else {
- QBezier bez = *this;
- flattenBezierWithoutInflections(bez, p);
- }
-
- p->append(QPointF(x4, y4));
-}
-
QT_END_NAMESPACE