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-rw-r--r--src/gui/painting/qbezier.cpp228
1 files changed, 4 insertions, 224 deletions
diff --git a/src/gui/painting/qbezier.cpp b/src/gui/painting/qbezier.cpp
index 7ff2a37..2a9b31a 100644
--- a/src/gui/painting/qbezier.cpp
+++ b/src/gui/painting/qbezier.cpp
@@ -93,7 +93,7 @@ QBezier QBezier::fromPoints(const QPointF &p1, const QPointF &p2,
/*!
\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
@@ -108,7 +108,7 @@ QPolygonF QBezier::toPolygon() const
QPolygonF polygon;
polygon.append(QPointF(x1, y1));
- addToPolygon(&polygon);
+ addToPolygon(&polygon, bezier_flattening_threshold);
return polygon;
}
@@ -117,34 +117,6 @@ QBezier QBezier::mapBy(const QTransform &transform) const
return QBezier::fromPoints(transform.map(pt1()), transform.map(pt2()), transform.map(pt3()), transform.map(pt4()));
}
-//0.05 is really low, but required for scaled-up beziers...
-static const qreal flatness = 0.05;
-
-//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 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());
- }
-}
-
QBezier QBezier::getSubRange(qreal t0, qreal t1) const
{
QBezier result;
@@ -223,7 +195,7 @@ static inline bool findInflections(qreal a, qreal b, qreal c,
}
-void QBezier::addToPolygon(QPolygonF *polygon) const
+void QBezier::addToPolygon(QPolygonF *polygon, qreal bezier_flattening_threshold) const
{
QBezier beziers[32];
beziers[0] = *this;
@@ -243,7 +215,7 @@ void QBezier::addToPolygon(QPolygonF *polygon) const
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;
@@ -255,55 +227,6 @@ void QBezier::addToPolygon(QPolygonF *polygon) const
}
}
-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;
@@ -824,147 +747,4 @@ QBezier QBezier::bezierOnInterval(qreal t0, qreal t1) const
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
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