qbezier.cpp

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32****************************************************************************/-
33-
34#include "qbezier_p.h"-
35#include <qdebug.h>-
36#include <qline.h>-
37#include <qpolygon.h>-
38#include <qvector.h>-
39#include <qlist.h>-
40#include <qmath.h>-
41-
42#include <private/qnumeric_p.h>-
43-
44QT_BEGIN_NAMESPACE-
45-
46//#define QDEBUG_BEZIER-
47-
48/*!-
49 \internal-
50*/-
51QBezier QBezier::fromPoints(const QPointF &p1, const QPointF &p2,-
52 const QPointF &p3, const QPointF &p4)-
53{-
54 QBezier b;-
55 b.x1 = p1.x();-
56 b.y1 = p1.y();-
57 b.x2 = p2.x();-
58 b.y2 = p2.y();-
59 b.x3 = p3.x();-
60 b.y3 = p3.y();-
61 b.x4 = p4.x();-
62 b.y4 = p4.y();-
63 return b;
never executed: return b;
0
64}-
65-
66/*!-
67 \internal-
68*/-
69QPolygonF QBezier::toPolygon(qreal bezier_flattening_threshold) const-
70{-
71 // flattening is done by splitting the bezier until we can replace the segment by a straight-
72 // line. We split further until the control points are close enough to the line connecting the-
73 // boundary points.-
74 //-
75 // the Distance of a point p from a line given by the points (a,b) is given by:-
76 //-
77 // d = abs( (bx - ax)(ay - py) - (by - ay)(ax - px) ) / line_length-
78 //-
79 // We can stop splitting if both control points are close enough to the line.-
80 // To make the algorithm faster we use the manhattan length of the line.-
81-
82 QPolygonF polygon;-
83 polygon.append(QPointF(x1, y1));-
84 addToPolygon(&polygon, bezier_flattening_threshold);-
85 return polygon;
never executed: return polygon;
0
86}-
87-
88QBezier QBezier::mapBy(const QTransform &transform) const-
89{-
90 return QBezier::fromPoints(transform.map(pt1()), transform.map(pt2()), transform.map(pt3()), transform.map(pt4()));
never executed: return QBezier::fromPoints(transform.map(pt1()), transform.map(pt2()), transform.map(pt3()), transform.map(pt4()));
0
91}-
92-
93QBezier QBezier::getSubRange(qreal t0, qreal t1) const-
94{-
95 QBezier result;-
96 QBezier temp;-
97-
98 // cut at t1-
99 if (qFuzzyIsNull(t1 - qreal(1.))) {
qFuzzyIsNull(t1 - qreal(1.))Description
TRUEnever evaluated
FALSEnever evaluated
0
100 result = *this;-
101 } else {
never executed: end of block
0
102 temp = *this;-
103 temp.parameterSplitLeft(t1, &result);-
104 }
never executed: end of block
0
105-
106 // cut at t0-
107 if (!qFuzzyIsNull(t0))
!qFuzzyIsNull(t0)Description
TRUEnever evaluated
FALSEnever evaluated
0
108 result.parameterSplitLeft(t0 / t1, &temp);
never executed: result.parameterSplitLeft(t0 / t1, &temp);
0
109-
110 return result;
never executed: return result;
0
111}-
112-
113void QBezier::addToPolygon(QPolygonF *polygon, qreal bezier_flattening_threshold) const-
114{-
115 QBezier beziers[10];-
116 int levels[10];-
117 beziers[0] = *this;-
118 levels[0] = 9;-
119 QBezier *b = beziers;-
120 int *lvl = levels;-
121-
122 while (b >= beziers) {
b >= beziersDescription
TRUEnever evaluated
FALSEnever evaluated
0
123 // check if we can pop the top bezier curve from the stack-
124 qreal y4y1 = b->y4 - b->y1;-
125 qreal x4x1 = b->x4 - b->x1;-
126 qreal l = qAbs(x4x1) + qAbs(y4y1);-
127 qreal d;-
128 if (l > 1.) {
l > 1.Description
TRUEnever evaluated
FALSEnever evaluated
0
129 d = qAbs( (x4x1)*(b->y1 - b->y2) - (y4y1)*(b->x1 - b->x2) )-
130 + qAbs( (x4x1)*(b->y1 - b->y3) - (y4y1)*(b->x1 - b->x3) );-
131 } else {
never executed: end of block
0
132 d = qAbs(b->x1 - b->x2) + qAbs(b->y1 - b->y2) +-
133 qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);-
134 l = 1.;-
135 }
never executed: end of block
0
136 if (d < bezier_flattening_threshold*l || *lvl == 0) {
d < bezier_fla...ng_threshold*lDescription
TRUEnever evaluated
FALSEnever evaluated
*lvl == 0Description
TRUEnever evaluated
FALSEnever evaluated
0
137 // good enough, we pop it off and add the endpoint-
138 polygon->append(QPointF(b->x4, b->y4));-
139 --b;-
140 --lvl;-
141 } else {
never executed: end of block
0
142 // split, second half of the polygon goes lower into the stack-
143 b->split(b+1, b);-
144 lvl[1] = --lvl[0];-
145 ++b;-
146 ++lvl;-
147 }
never executed: end of block
0
148 }-
149}
never executed: end of block
0
150-
151void QBezier::addToPolygon(QDataBuffer<QPointF> &polygon, qreal bezier_flattening_threshold) const-
152{-
153 QBezier beziers[10];-
154 int levels[10];-
155 beziers[0] = *this;-
156 levels[0] = 9;-
157 QBezier *b = beziers;-
158 int *lvl = levels;-
159-
160 while (b >= beziers) {
b >= beziersDescription
TRUEnever evaluated
FALSEnever evaluated
0
161 // check if we can pop the top bezier curve from the stack-
162 qreal y4y1 = b->y4 - b->y1;-
163 qreal x4x1 = b->x4 - b->x1;-
164 qreal l = qAbs(x4x1) + qAbs(y4y1);-
165 qreal d;-
166 if (l > 1.) {
l > 1.Description
TRUEnever evaluated
FALSEnever evaluated
0
167 d = qAbs( (x4x1)*(b->y1 - b->y2) - (y4y1)*(b->x1 - b->x2) )-
168 + qAbs( (x4x1)*(b->y1 - b->y3) - (y4y1)*(b->x1 - b->x3) );-
169 } else {
never executed: end of block
0
170 d = qAbs(b->x1 - b->x2) + qAbs(b->y1 - b->y2) +-
171 qAbs(b->x1 - b->x3) + qAbs(b->y1 - b->y3);-
172 l = 1.;-
173 }
never executed: end of block
0
174 if (d < bezier_flattening_threshold*l || *lvl == 0) {
d < bezier_fla...ng_threshold*lDescription
TRUEnever evaluated
FALSEnever evaluated
*lvl == 0Description
TRUEnever evaluated
FALSEnever evaluated
0
175 // good enough, we pop it off and add the endpoint-
176 polygon.add(QPointF(b->x4, b->y4));-
177 --b;-
178 --lvl;-
179 } else {
never executed: end of block
0
180 // split, second half of the polygon goes lower into the stack-
181 b->split(b+1, b);-
182 lvl[1] = --lvl[0];-
183 ++b;-
184 ++lvl;-
185 }
never executed: end of block
0
186 }-
187}
never executed: end of block
0
188-
189QRectF QBezier::bounds() const-
190{-
191 qreal xmin = x1;-
192 qreal xmax = x1;-
193 if (x2 < xmin)
x2 < xminDescription
TRUEnever evaluated
FALSEnever evaluated
0
194 xmin = x2;
never executed: xmin = x2;
0
195 else if (x2 > xmax)
x2 > xmaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
196 xmax = x2;
never executed: xmax = x2;
0
197 if (x3 < xmin)
x3 < xminDescription
TRUEnever evaluated
FALSEnever evaluated
0
198 xmin = x3;
never executed: xmin = x3;
0
199 else if (x3 > xmax)
x3 > xmaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
200 xmax = x3;
never executed: xmax = x3;
0
201 if (x4 < xmin)
x4 < xminDescription
TRUEnever evaluated
FALSEnever evaluated
0
202 xmin = x4;
never executed: xmin = x4;
0
203 else if (x4 > xmax)
x4 > xmaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
204 xmax = x4;
never executed: xmax = x4;
0
205-
206 qreal ymin = y1;-
207 qreal ymax = y1;-
208 if (y2 < ymin)
y2 < yminDescription
TRUEnever evaluated
FALSEnever evaluated
0
209 ymin = y2;
never executed: ymin = y2;
0
210 else if (y2 > ymax)
y2 > ymaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
211 ymax = y2;
never executed: ymax = y2;
0
212 if (y3 < ymin)
y3 < yminDescription
TRUEnever evaluated
FALSEnever evaluated
0
213 ymin = y3;
never executed: ymin = y3;
0
214 else if (y3 > ymax)
y3 > ymaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
215 ymax = y3;
never executed: ymax = y3;
0
216 if (y4 < ymin)
y4 < yminDescription
TRUEnever evaluated
FALSEnever evaluated
0
217 ymin = y4;
never executed: ymin = y4;
0
218 else if (y4 > ymax)
y4 > ymaxDescription
TRUEnever evaluated
FALSEnever evaluated
0
219 ymax = y4;
never executed: ymax = y4;
0
220 return QRectF(xmin, ymin, xmax-xmin, ymax-ymin);
never executed: return QRectF(xmin, ymin, xmax-xmin, ymax-ymin);
0
221}-
222-
223-
224enum ShiftResult {-
225 Ok,-
226 Discard,-
227 Split,-
228 Circle-
229};-
230-
231static ShiftResult good_offset(const QBezier *b1, const QBezier *b2, qreal offset, qreal threshold)-
232{-
233 const qreal o2 = offset*offset;-
234 const qreal max_dist_line = threshold*offset*offset;-
235 const qreal max_dist_normal = threshold*offset;-
236 const qreal spacing = qreal(0.25);-
237 for (qreal i = spacing; i < qreal(0.99); i += spacing) {
i < qreal(0.99)Description
TRUEnever evaluated
FALSEnever evaluated
0
238 QPointF p1 = b1->pointAt(i);-
239 QPointF p2 = b2->pointAt(i);-
240 qreal d = (p1.x() - p2.x())*(p1.x() - p2.x()) + (p1.y() - p2.y())*(p1.y() - p2.y());-
241 if (qAbs(d - o2) > max_dist_line)
qAbs(d - o2) > max_dist_lineDescription
TRUEnever evaluated
FALSEnever evaluated
0
242 return Split;
never executed: return Split;
0
243-
244 QPointF normalPoint = b1->normalVector(i);-
245 qreal l = qAbs(normalPoint.x()) + qAbs(normalPoint.y());-
246 if (l != qreal(0.0)) {
l != qreal(0.0)Description
TRUEnever evaluated
FALSEnever evaluated
0
247 d = qAbs( normalPoint.x()*(p1.y() - p2.y()) - normalPoint.y()*(p1.x() - p2.x()) ) / l;-
248 if (d > max_dist_normal)
d > max_dist_normalDescription
TRUEnever evaluated
FALSEnever evaluated
0
249 return Split;
never executed: return Split;
0
250 }
never executed: end of block
0
251 }
never executed: end of block
0
252 return Ok;
never executed: return Ok;
0
253}-
254-
255static ShiftResult shift(const QBezier *orig, QBezier *shifted, qreal offset, qreal threshold)-
256{-
257 int map[4];-
258 bool p1_p2_equal = (orig->x1 == orig->x2 && orig->y1 == orig->y2);
orig->x1 == orig->x2Description
TRUEnever evaluated
FALSEnever evaluated
orig->y1 == orig->y2Description
TRUEnever evaluated
FALSEnever evaluated
0
259 bool p2_p3_equal = (orig->x2 == orig->x3 && orig->y2 == orig->y3);
orig->x2 == orig->x3Description
TRUEnever evaluated
FALSEnever evaluated
orig->y2 == orig->y3Description
TRUEnever evaluated
FALSEnever evaluated
0
260 bool p3_p4_equal = (orig->x3 == orig->x4 && orig->y3 == orig->y4);
orig->x3 == orig->x4Description
TRUEnever evaluated
FALSEnever evaluated
orig->y3 == orig->y4Description
TRUEnever evaluated
FALSEnever evaluated
0
261-
262 QPointF points[4];-
263 int np = 0;-
264 points[np] = QPointF(orig->x1, orig->y1);-
265 map[0] = 0;-
266 ++np;-
267 if (!p1_p2_equal) {
!p1_p2_equalDescription
TRUEnever evaluated
FALSEnever evaluated
0
268 points[np] = QPointF(orig->x2, orig->y2);-
269 ++np;-
270 }
never executed: end of block
0
271 map[1] = np - 1;-
272 if (!p2_p3_equal) {
!p2_p3_equalDescription
TRUEnever evaluated
FALSEnever evaluated
0
273 points[np] = QPointF(orig->x3, orig->y3);-
274 ++np;-
275 }
never executed: end of block
0
276 map[2] = np - 1;-
277 if (!p3_p4_equal) {
!p3_p4_equalDescription
TRUEnever evaluated
FALSEnever evaluated
0
278 points[np] = QPointF(orig->x4, orig->y4);-
279 ++np;-
280 }
never executed: end of block
0
281 map[3] = np - 1;-
282 if (np == 1)
np == 1Description
TRUEnever evaluated
FALSEnever evaluated
0
283 return Discard;
never executed: return Discard;
0
284-
285 QRectF b = orig->bounds();-
286 if (np == 4 && b.width() < .1*offset && b.height() < .1*offset) {
np == 4Description
TRUEnever evaluated
FALSEnever evaluated
b.width() < .1*offsetDescription
TRUEnever evaluated
FALSEnever evaluated
b.height() < .1*offsetDescription
TRUEnever evaluated
FALSEnever evaluated
0
287 qreal l = (orig->x1 - orig->x2)*(orig->x1 - orig->x2) +-
288 (orig->y1 - orig->y2)*(orig->y1 - orig->y2) *-
289 (orig->x3 - orig->x4)*(orig->x3 - orig->x4) +-
290 (orig->y3 - orig->y4)*(orig->y3 - orig->y4);-
291 qreal dot = (orig->x1 - orig->x2)*(orig->x3 - orig->x4) +-
292 (orig->y1 - orig->y2)*(orig->y3 - orig->y4);-
293 if (dot < 0 && dot*dot < 0.8*l)
dot < 0Description
TRUEnever evaluated
FALSEnever evaluated
dot*dot < 0.8*lDescription
TRUEnever evaluated
FALSEnever evaluated
0
294 // the points are close and reverse dirction. Approximate the whole-
295 // thing by a semi circle-
296 return Circle;
never executed: return Circle;
0
297 }
never executed: end of block
0
298-
299 QPointF points_shifted[4];-
300-
301 QLineF prev = QLineF(QPointF(), points[1] - points[0]);-
302 QPointF prev_normal = prev.normalVector().unitVector().p2();-
303-
304 points_shifted[0] = points[0] + offset * prev_normal;-
305-
306 for (int i = 1; i < np - 1; ++i) {
i < np - 1Description
TRUEnever evaluated
FALSEnever evaluated
0
307 QLineF next = QLineF(QPointF(), points[i + 1] - points[i]);-
308 QPointF next_normal = next.normalVector().unitVector().p2();-
309-
310 QPointF normal_sum = prev_normal + next_normal;-
311-
312 qreal r = qreal(1.0) + prev_normal.x() * next_normal.x()-
313 + prev_normal.y() * next_normal.y();-
314-
315 if (qFuzzyIsNull(r)) {
qFuzzyIsNull(r)Description
TRUEnever evaluated
FALSEnever evaluated
0
316 points_shifted[i] = points[i] + offset * prev_normal;-
317 } else {
never executed: end of block
0
318 qreal k = offset / r;-
319 points_shifted[i] = points[i] + k * normal_sum;-
320 }
never executed: end of block
0
321-
322 prev_normal = next_normal;-
323 }
never executed: end of block
0
324-
325 points_shifted[np - 1] = points[np - 1] + offset * prev_normal;-
326-
327 *shifted = QBezier::fromPoints(points_shifted[map[0]], points_shifted[map[1]],-
328 points_shifted[map[2]], points_shifted[map[3]]);-
329-
330 return good_offset(orig, shifted, offset, threshold);
never executed: return good_offset(orig, shifted, offset, threshold);
0
331}-
332-
333// This value is used to determine the length of control point vectors-
334// when approximating arc segments as curves. The factor is multiplied-
335// with the radius of the circle.-
336#define KAPPA qreal(0.5522847498)-
337-
338-
339static bool addCircle(const QBezier *b, qreal offset, QBezier *o)-
340{-
341 QPointF normals[3];-
342-
343 normals[0] = QPointF(b->y2 - b->y1, b->x1 - b->x2);-
344 qreal dist = qSqrt(normals[0].x()*normals[0].x() + normals[0].y()*normals[0].y());-
345 if (qFuzzyIsNull(dist))
qFuzzyIsNull(dist)Description
TRUEnever evaluated
FALSEnever evaluated
0
346 return false;
never executed: return false;
0
347 normals[0] /= dist;-
348 normals[2] = QPointF(b->y4 - b->y3, b->x3 - b->x4);-
349 dist = qSqrt(normals[2].x()*normals[2].x() + normals[2].y()*normals[2].y());-
350 if (qFuzzyIsNull(dist))
qFuzzyIsNull(dist)Description
TRUEnever evaluated
FALSEnever evaluated
0
351 return false;
never executed: return false;
0
352 normals[2] /= dist;-
353-
354 normals[1] = QPointF(b->x1 - b->x2 - b->x3 + b->x4, b->y1 - b->y2 - b->y3 + b->y4);-
355 normals[1] /= -1*qSqrt(normals[1].x()*normals[1].x() + normals[1].y()*normals[1].y());-
356-
357 qreal angles[2];-
358 qreal sign = 1.;-
359 for (int i = 0; i < 2; ++i) {
i < 2Description
TRUEnever evaluated
FALSEnever evaluated
0
360 qreal cos_a = normals[i].x()*normals[i+1].x() + normals[i].y()*normals[i+1].y();-
361 if (cos_a > 1.)
cos_a > 1.Description
TRUEnever evaluated
FALSEnever evaluated
0
362 cos_a = 1.;
never executed: cos_a = 1.;
0
363 if (cos_a < -1.)
cos_a < -1.Description
TRUEnever evaluated
FALSEnever evaluated
0
364 cos_a = -1;
never executed: cos_a = -1;
0
365 angles[i] = qAcos(cos_a) * qreal(M_1_PI);-
366 }
never executed: end of block
0
367-
368 if (angles[0] + angles[1] > 1.) {
angles[0] + angles[1] > 1.Description
TRUEnever evaluated
FALSEnever evaluated
0
369 // more than 180 degrees-
370 normals[1] = -normals[1];-
371 angles[0] = 1. - angles[0];-
372 angles[1] = 1. - angles[1];-
373 sign = -1.;-
374-
375 }
never executed: end of block
0
376-
377 QPointF circle[3];-
378 circle[0] = QPointF(b->x1, b->y1) + normals[0]*offset;-
379 circle[1] = QPointF(qreal(0.5)*(b->x1 + b->x4), qreal(0.5)*(b->y1 + b->y4)) + normals[1]*offset;-
380 circle[2] = QPointF(b->x4, b->y4) + normals[2]*offset;-
381-
382 for (int i = 0; i < 2; ++i) {
i < 2Description
TRUEnever evaluated
FALSEnever evaluated
0
383 qreal kappa = qreal(2.0) * KAPPA * sign * offset * angles[i];-
384-
385 o->x1 = circle[i].x();-
386 o->y1 = circle[i].y();-
387 o->x2 = circle[i].x() - normals[i].y()*kappa;-
388 o->y2 = circle[i].y() + normals[i].x()*kappa;-
389 o->x3 = circle[i+1].x() + normals[i+1].y()*kappa;-
390 o->y3 = circle[i+1].y() - normals[i+1].x()*kappa;-
391 o->x4 = circle[i+1].x();-
392 o->y4 = circle[i+1].y();-
393-
394 ++o;-
395 }
never executed: end of block
0
396 return true;
never executed: return true;
0
397}-
398-
399int QBezier::shifted(QBezier *curveSegments, int maxSegments, qreal offset, float threshold) const-
400{-
401 Q_ASSERT(curveSegments);-
402 Q_ASSERT(maxSegments > 0);-
403-
404 if (qFuzzyCompare(x1, x2) && qFuzzyCompare(x1, x3) && qFuzzyCompare(x1, x4) &&
qFuzzyCompare(x1, x2)Description
TRUEnever evaluated
FALSEnever evaluated
qFuzzyCompare(x1, x3)Description
TRUEnever evaluated
FALSEnever evaluated
qFuzzyCompare(x1, x4)Description
TRUEnever evaluated
FALSEnever evaluated
0
405 qFuzzyCompare(y1, y2) && qFuzzyCompare(y1, y3) && qFuzzyCompare(y1, y4))
qFuzzyCompare(y1, y2)Description
TRUEnever evaluated
FALSEnever evaluated
qFuzzyCompare(y1, y3)Description
TRUEnever evaluated
FALSEnever evaluated
qFuzzyCompare(y1, y4)Description
TRUEnever evaluated
FALSEnever evaluated
0
406 return 0;
never executed: return 0;
0
407-
408 --maxSegments;-
409 QBezier beziers[10];-
410redo:
code before this statement never executed: redo:
0
411 beziers[0] = *this;-
412 QBezier *b = beziers;-
413 QBezier *o = curveSegments;-
414-
415 while (b >= beziers) {
b >= beziersDescription
TRUEnever evaluated
FALSEnever evaluated
0
416 int stack_segments = b - beziers + 1;-
417 if ((stack_segments == 10) || (o - curveSegments == maxSegments - stack_segments)) {
(stack_segments == 10)Description
TRUEnever evaluated
FALSEnever evaluated
(o - curveSegm...tack_segments)Description
TRUEnever evaluated
FALSEnever evaluated
0
418 threshold *= qreal(1.5);-
419 if (threshold > qreal(2.0))
threshold > qreal(2.0)Description
TRUEnever evaluated
FALSEnever evaluated
0
420 goto give_up;
never executed: goto give_up;
0
421 goto redo;
never executed: goto redo;
0
422 }-
423 ShiftResult res = shift(b, o, offset, threshold);-
424 if (res == Discard) {
res == DiscardDescription
TRUEnever evaluated
FALSEnever evaluated
0
425 --b;-
426 } else if (res == Ok) {
never executed: end of block
res == OkDescription
TRUEnever evaluated
FALSEnever evaluated
0
427 ++o;-
428 --b;-
429 continue;
never executed: continue;
0
430 } else if (res == Circle && maxSegments - (o - curveSegments) >= 2) {
res == CircleDescription
TRUEnever evaluated
FALSEnever evaluated
maxSegments - ...Segments) >= 2Description
TRUEnever evaluated
FALSEnever evaluated
0
431 // add semi circle-
432 if (addCircle(b, offset, o))
addCircle(b, offset, o)Description
TRUEnever evaluated
FALSEnever evaluated
0
433 o += 2;
never executed: o += 2;
0
434 --b;-
435 } else {
never executed: end of block
0
436 b->split(b+1, b);-
437 ++b;-
438 }
never executed: end of block
0
439 }-
440-
441give_up:
code before this statement never executed: give_up:
0
442 while (b >= beziers) {
b >= beziersDescription
TRUEnever evaluated
FALSEnever evaluated
0
443 ShiftResult res = shift(b, o, offset, threshold);-
444-
445 // if res isn't Ok or Split then *o is undefined-
446 if (res == Ok || res == Split)
res == OkDescription
TRUEnever evaluated
FALSEnever evaluated
res == SplitDescription
TRUEnever evaluated
FALSEnever evaluated
0
447 ++o;
never executed: ++o;
0
448-
449 --b;-
450 }
never executed: end of block
0
451-
452 Q_ASSERT(o - curveSegments <= maxSegments);-
453 return o - curveSegments;
never executed: return o - curveSegments;
0
454}-
455-
456#ifdef QDEBUG_BEZIER-
457static QDebug operator<<(QDebug dbg, const QBezier &bz)-
458{-
459 dbg << '[' << bz.x1<< ", " << bz.y1 << "], "-
460 << '[' << bz.x2 <<", " << bz.y2 << "], "-
461 << '[' << bz.x3 <<", " << bz.y3 << "], "-
462 << '[' << bz.x4 <<", " << bz.y4 << ']';-
463 return dbg;-
464}-
465#endif-
466-
467qreal QBezier::length(qreal error) const-
468{-
469 qreal length = qreal(0.0);-
470-
471 addIfClose(&length, error);-
472-
473 return length;
never executed: return length;
0
474}-
475-
476void QBezier::addIfClose(qreal *length, qreal error) const-
477{-
478 QBezier left, right; /* bez poly splits */-
479-
480 qreal len = qreal(0.0); /* arc length */-
481 qreal chord; /* chord length */-
482-
483 len = len + QLineF(QPointF(x1, y1),QPointF(x2, y2)).length();-
484 len = len + QLineF(QPointF(x2, y2),QPointF(x3, y3)).length();-
485 len = len + QLineF(QPointF(x3, y3),QPointF(x4, y4)).length();-
486-
487 chord = QLineF(QPointF(x1, y1),QPointF(x4, y4)).length();-
488-
489 if((len-chord) > error) {
(len-chord) > errorDescription
TRUEnever evaluated
FALSEnever evaluated
0
490 split(&left, &right); /* split in two */-
491 left.addIfClose(length, error); /* try left side */-
492 right.addIfClose(length, error); /* try right side */-
493 return;
never executed: return;
0
494 }-
495-
496 *length = *length + len;-
497-
498 return;
never executed: return;
0
499}-
500-
501qreal QBezier::tForY(qreal t0, qreal t1, qreal y) const-
502{-
503 qreal py0 = pointAt(t0).y();-
504 qreal py1 = pointAt(t1).y();-
505-
506 if (py0 > py1) {
py0 > py1Description
TRUEnever evaluated
FALSEnever evaluated
0
507 qSwap(py0, py1);-
508 qSwap(t0, t1);-
509 }
never executed: end of block
0
510-
511 Q_ASSERT(py0 <= py1);-
512-
513 if (py0 >= y)
py0 >= yDescription
TRUEnever evaluated
FALSEnever evaluated
0
514 return t0;
never executed: return t0;
0
515 else if (py1 <= y)
py1 <= yDescription
TRUEnever evaluated
FALSEnever evaluated
0
516 return t1;
never executed: return t1;
0
517-
518 Q_ASSERT(py0 < y && y < py1);-
519-
520 qreal lt = t0;-
521 qreal dt;-
522 do {-
523 qreal t = qreal(0.5) * (t0 + t1);-
524-
525 qreal a, b, c, d;-
526 QBezier::coefficients(t, a, b, c, d);-
527 qreal yt = a * y1 + b * y2 + c * y3 + d * y4;-
528-
529 if (yt < y) {
yt < yDescription
TRUEnever evaluated
FALSEnever evaluated
0
530 t0 = t;-
531 py0 = yt;-
532 } else {
never executed: end of block
0
533 t1 = t;-
534 py1 = yt;-
535 }
never executed: end of block
0
536 dt = lt - t;-
537 lt = t;-
538 } while (qAbs(dt) > qreal(1e-7));
never executed: end of block
qAbs(dt) > qreal(1e-7)Description
TRUEnever evaluated
FALSEnever evaluated
0
539-
540 return t0;
never executed: return t0;
0
541}-
542-
543int QBezier::stationaryYPoints(qreal &t0, qreal &t1) const-
544{-
545 // y(t) = (1 - t)^3 * y1 + 3 * (1 - t)^2 * t * y2 + 3 * (1 - t) * t^2 * y3 + t^3 * y4-
546 // y'(t) = 3 * (-(1-2t+t^2) * y1 + (1 - 4 * t + 3 * t^2) * y2 + (2 * t - 3 * t^2) * y3 + t^2 * y4)-
547 // y'(t) = 3 * ((-y1 + 3 * y2 - 3 * y3 + y4)t^2 + (2 * y1 - 4 * y2 + 2 * y3)t + (-y1 + y2))-
548-
549 const qreal a = -y1 + 3 * y2 - 3 * y3 + y4;-
550 const qreal b = 2 * y1 - 4 * y2 + 2 * y3;-
551 const qreal c = -y1 + y2;-
552-
553 if (qFuzzyIsNull(a)) {
qFuzzyIsNull(a)Description
TRUEnever evaluated
FALSEnever evaluated
0
554 if (qFuzzyIsNull(b))
qFuzzyIsNull(b)Description
TRUEnever evaluated
FALSEnever evaluated
0
555 return 0;
never executed: return 0;
0
556-
557 t0 = -c / b;-
558 return t0 > 0 && t0 < 1;
never executed: return t0 > 0 && t0 < 1;
t0 > 0Description
TRUEnever evaluated
FALSEnever evaluated
t0 < 1Description
TRUEnever evaluated
FALSEnever evaluated
0
559 }-
560-
561 qreal reciprocal = b * b - 4 * a * c;-
562-
563 if (qFuzzyIsNull(reciprocal)) {
qFuzzyIsNull(reciprocal)Description
TRUEnever evaluated
FALSEnever evaluated
0
564 t0 = -b / (2 * a);-
565 return t0 > 0 && t0 < 1;
never executed: return t0 > 0 && t0 < 1;
t0 > 0Description
TRUEnever evaluated
FALSEnever evaluated
t0 < 1Description
TRUEnever evaluated
FALSEnever evaluated
0
566 } else if (reciprocal > 0) {
reciprocal > 0Description
TRUEnever evaluated
FALSEnever evaluated
0
567 qreal temp = qSqrt(reciprocal);-
568-
569 t0 = (-b - temp)/(2*a);-
570 t1 = (-b + temp)/(2*a);-
571-
572 if (t1 < t0)
t1 < t0Description
TRUEnever evaluated
FALSEnever evaluated
0
573 qSwap(t0, t1);
never executed: qSwap(t0, t1);
0
574-
575 int count = 0;-
576 qreal t[2] = { 0, 1 };-
577-
578 if (t0 > 0 && t0 < 1)
t0 > 0Description
TRUEnever evaluated
FALSEnever evaluated
t0 < 1Description
TRUEnever evaluated
FALSEnever evaluated
0
579 t[count++] = t0;
never executed: t[count++] = t0;
0
580 if (t1 > 0 && t1 < 1)
t1 > 0Description
TRUEnever evaluated
FALSEnever evaluated
t1 < 1Description
TRUEnever evaluated
FALSEnever evaluated
0
581 t[count++] = t1;
never executed: t[count++] = t1;
0
582-
583 t0 = t[0];-
584 t1 = t[1];-
585-
586 return count;
never executed: return count;
0
587 }-
588-
589 return 0;
never executed: return 0;
0
590}-
591-
592qreal QBezier::tAtLength(qreal l) const-
593{-
594 qreal len = length();-
595 qreal t = qreal(1.0);-
596 const qreal error = qreal(0.01);-
597 if (l > len || qFuzzyCompare(l, len))
l > lenDescription
TRUEnever evaluated
FALSEnever evaluated
qFuzzyCompare(l, len)Description
TRUEnever evaluated
FALSEnever evaluated
0
598 return t;
never executed: return t;
0
599-
600 t *= qreal(0.5);-
601 //int iters = 0;-
602 //qDebug()<<"LEN is "<<l<<len;-
603 qreal lastBigger = qreal(1.0);-
604 while (1) {-
605 //qDebug()<<"\tt is "<<t;-
606 QBezier right = *this;-
607 QBezier left;-
608 right.parameterSplitLeft(t, &left);-
609 qreal lLen = left.length();-
610 if (qAbs(lLen - l) < error)
qAbs(lLen - l) < errorDescription
TRUEnever evaluated
FALSEnever evaluated
0
611 break;
never executed: break;
0
612-
613 if (lLen < l) {
lLen < lDescription
TRUEnever evaluated
FALSEnever evaluated
0
614 t += (lastBigger - t) * qreal(0.5);-
615 } else {
never executed: end of block
0
616 lastBigger = t;-
617 t -= t * qreal(0.5);-
618 }
never executed: end of block
0
619 //++iters;-
620 }-
621 //qDebug()<<"number of iters is "<<iters;-
622 return t;
never executed: return t;
0
623}-
624-
625QBezier QBezier::bezierOnInterval(qreal t0, qreal t1) const-
626{-
627 if (t0 == 0 && t1 == 1)
t0 == 0Description
TRUEnever evaluated
FALSEnever evaluated
t1 == 1Description
TRUEnever evaluated
FALSEnever evaluated
0
628 return *this;
never executed: return *this;
0
629-
630 QBezier bezier = *this;-
631-
632 QBezier result;-
633 bezier.parameterSplitLeft(t0, &result);-
634 qreal trueT = (t1-t0)/(1-t0);-
635 bezier.parameterSplitLeft(trueT, &result);-
636-
637 return result;
never executed: return result;
0
638}-
639-
640QT_END_NAMESPACE-
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