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21 
22 
23 
24 // MARKER(update_precomp.py): autogen include statement, do not remove
25 #include "precompiled_basegfx.hxx"
26 #include <basegfx/polygon/b2dpolygonclipper.hxx>
27 #include <osl/diagnose.h>
28 #include <basegfx/polygon/b2dpolygontools.hxx>
29 #include <basegfx/numeric/ftools.hxx>
30 #include <basegfx/matrix/b2dhommatrix.hxx>
31 #include <basegfx/polygon/b2dpolypolygoncutter.hxx>
32 #include <basegfx/polygon/b2dpolygoncutandtouch.hxx>
33 #include <basegfx/polygon/b2dpolypolygontools.hxx>
34 #include <basegfx/curve/b2dcubicbezier.hxx>
35 #include <basegfx/tools/rectcliptools.hxx>
36 #include <basegfx/matrix/b2dhommatrixtools.hxx>
37 
38 //////////////////////////////////////////////////////////////////////////////
39 
40 namespace basegfx
41 {
42 	namespace tools
43 	{
44 		B2DPolyPolygon clipPolygonOnParallelAxis(const B2DPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
45 		{
46 			B2DPolyPolygon aRetval;
47 
48 			if(rCandidate.count())
49 			{
50 				const B2DRange aCandidateRange(getRange(rCandidate));
51 
52 				if(bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinY(), fValueOnOtherAxis))
53 				{
54 					// completely above and on the clip line. also true for curves.
55 					if(bAboveAxis)
56 					{
57 						// add completely
58 						aRetval.append(rCandidate);
59 					}
60 				}
61 				else if(bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxY(), fValueOnOtherAxis))
62 				{
63 					// completely below and on the clip line. also true for curves.
64 					if(!bAboveAxis)
65 					{
66 						// add completely
67 						aRetval.append(rCandidate);
68 					}
69 				}
70 				else if(!bParallelToXAxis && fTools::moreOrEqual(aCandidateRange.getMinX(), fValueOnOtherAxis))
71 				{
72 					// completely right of and on the clip line. also true for curves.
73 					if(bAboveAxis)
74 					{
75 						// add completely
76 						aRetval.append(rCandidate);
77 					}
78 				}
79 				else if(!bParallelToXAxis && fTools::lessOrEqual(aCandidateRange.getMaxX(), fValueOnOtherAxis))
80 				{
81 					// completely left of and on the clip line. also true for curves.
82 					if(!bAboveAxis)
83 					{
84 						// add completely
85 						aRetval.append(rCandidate);
86 					}
87 				}
88 				else
89 				{
90                     // add cuts with axis to polygon, including bezier segments
91                     // Build edge to cut with. Make it a little big longer than needed for
92                     // numerical stability. We want to cut against the edge seen as endless
93                     // ray here, but addPointsAtCuts() will limit itself to the
94                     // edge's range ]0.0 .. 1.0[.
95                     const double fSmallExtension((aCandidateRange.getWidth() + aCandidateRange.getHeight()) * (0.5 * 0.1));
96                     const B2DPoint aStart(
97                         bParallelToXAxis ? aCandidateRange.getMinX() - fSmallExtension : fValueOnOtherAxis,
98                         bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMinY() - fSmallExtension);
99                     const B2DPoint aEnd(
100                         bParallelToXAxis ? aCandidateRange.getMaxX() + fSmallExtension : fValueOnOtherAxis,
101                         bParallelToXAxis ? fValueOnOtherAxis : aCandidateRange.getMaxY() + fSmallExtension);
102                     const B2DPolygon aCandidate(addPointsAtCuts(rCandidate, aStart, aEnd));
103     			    const sal_uInt32 nPointCount(aCandidate.count());
104                     const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
105                     B2DCubicBezier aEdge;
106                     B2DPolygon aRun;
107 
108                     for(sal_uInt32 a(0L); a < nEdgeCount; a++)
109                     {
110                         aCandidate.getBezierSegment(a, aEdge);
111                         const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
112 			            const bool bInside(bParallelToXAxis ?
113 				            fTools::moreOrEqual(aTestPoint.getY(), fValueOnOtherAxis) == bAboveAxis :
114 				            fTools::moreOrEqual(aTestPoint.getX(), fValueOnOtherAxis) == bAboveAxis);
115 
116 						if(bInside)
117 						{
118 							if(!aRun.count() || !aRun.getB2DPoint(aRun.count() - 1).equal(aEdge.getStartPoint()))
119 							{
120 								aRun.append(aEdge.getStartPoint());
121 							}
122 
123 							if(aEdge.isBezier())
124 							{
125 								aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
126 							}
127 							else
128 							{
129 								aRun.append(aEdge.getEndPoint());
130 							}
131 						}
132 						else
133 						{
134                             if(bStroke && aRun.count())
135                             {
136 								aRetval.append(aRun);
137 								aRun.clear();
138                             }
139 						}
140                     }
141 
142                     if(aRun.count())
143 					{
144                         if(bStroke)
145                         {
146                             // try to merge this last and first polygon; they may have been
147                             // the former polygon's start/end point
148                             if(aRetval.count())
149                             {
150                                 const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
151 
152                                 if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
153                                 {
154                                     // append start polygon to aRun, remove from result set
155                                     aRun.append(aStartPolygon); aRun.removeDoublePoints();
156                                     aRetval.remove(0);
157                                 }
158                             }
159 
160 							aRetval.append(aRun);
161                         }
162                         else
163                         {
164 			                // set closed flag and correct last point (which is added double now).
165 			                closeWithGeometryChange(aRun);
166                             aRetval.append(aRun);
167                         }
168 					}
169 				}
170 			}
171 
172 			return aRetval;
173 		}
174 
175 		B2DPolyPolygon clipPolyPolygonOnParallelAxis(const B2DPolyPolygon& rCandidate, bool bParallelToXAxis, bool bAboveAxis, double fValueOnOtherAxis, bool bStroke)
176 		{
177 			const sal_uInt32 nPolygonCount(rCandidate.count());
178 			B2DPolyPolygon aRetval;
179 
180 			for(sal_uInt32 a(0L); a < nPolygonCount; a++)
181 			{
182 				const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnParallelAxis(rCandidate.getB2DPolygon(a), bParallelToXAxis, bAboveAxis, fValueOnOtherAxis, bStroke));
183 
184                 if(aClippedPolyPolygon.count())
185                 {
186     				aRetval.append(aClippedPolyPolygon);
187                 }
188 			}
189 
190 			return aRetval;
191 		}
192 
193 		B2DPolyPolygon clipPolygonOnRange(const B2DPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
194 		{
195             const sal_uInt32 nCount(rCandidate.count());
196 			B2DPolyPolygon aRetval;
197 
198             if(!nCount)
199             {
200                 // source is empty
201                 return aRetval;
202             }
203 
204             if(rRange.isEmpty())
205             {
206                 if(bInside)
207                 {
208                     // nothing is inside an empty range
209                     return aRetval;
210                 }
211                 else
212                 {
213                     // everything is outside an empty range
214                     return B2DPolyPolygon(rCandidate);
215                 }
216             }
217 
218 			const B2DRange aCandidateRange(getRange(rCandidate));
219 
220 			if(rRange.isInside(aCandidateRange))
221 			{
222   				// candidate is completely inside given range
223 				if(bInside)
224 				{
225     				// nothing to do
226 					return B2DPolyPolygon(rCandidate);
227 				}
228                 else
229                 {
230                     // nothing is outside, then
231                     return aRetval;
232                 }
233 			}
234 
235             if(!bInside)
236             {
237                 // cutting off the outer parts of filled polygons at parallell
238                 // lines to the axes is only possible for the inner part, not for
239                 // the outer part which means cutting a hole into the original polygon.
240                 // This is because the inner part is a logical AND-operation of
241                 // the four implied half-planes, but the outer part is not.
242                 // It is possible for strokes, but with creating unnecessary extra
243                 // cuts, so using clipPolygonOnPolyPolygon is better there, too.
244                 // This needs to be done with the topology knowlegde and is unfurtunately
245                 // more expensive, too.
246         		const B2DPolygon aClip(createPolygonFromRect(rRange));
247 
248                 return clipPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
249             }
250 
251 			// clip against the four axes of the range
252 			// against X-Axis, lower value
253 			aRetval = clipPolygonOnParallelAxis(rCandidate, true, bInside, rRange.getMinY(), bStroke);
254 
255 			if(aRetval.count())
256 			{
257 				// against Y-Axis, lower value
258 				if(1L == aRetval.count())
259 				{
260 					aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0L), false, bInside, rRange.getMinX(), bStroke);
261 				}
262 				else
263 				{
264 					aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, bInside, rRange.getMinX(), bStroke);
265 				}
266 
267 				if(aRetval.count())
268 				{
269 					// against X-Axis, higher value
270 					if(1L == aRetval.count())
271 					{
272 						aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0L), true, !bInside, rRange.getMaxY(), bStroke);
273 					}
274 					else
275 					{
276 						aRetval = clipPolyPolygonOnParallelAxis(aRetval, true, !bInside, rRange.getMaxY(), bStroke);
277 					}
278 
279 					if(aRetval.count())
280 					{
281 						// against Y-Axis, higher value
282 						if(1L == aRetval.count())
283 						{
284 							aRetval = clipPolygonOnParallelAxis(aRetval.getB2DPolygon(0L), false, !bInside, rRange.getMaxX(), bStroke);
285 						}
286 						else
287 						{
288 							aRetval = clipPolyPolygonOnParallelAxis(aRetval, false, !bInside, rRange.getMaxX(), bStroke);
289 						}
290 					}
291 				}
292 			}
293 
294 			return aRetval;
295 		}
296 
297 		B2DPolyPolygon clipPolyPolygonOnRange(const B2DPolyPolygon& rCandidate, const B2DRange& rRange, bool bInside, bool bStroke)
298 		{
299 			const sal_uInt32 nPolygonCount(rCandidate.count());
300 			B2DPolyPolygon aRetval;
301 
302             if(!nPolygonCount)
303             {
304                 // source is empty
305                 return aRetval;
306             }
307 
308             if(rRange.isEmpty())
309             {
310                 if(bInside)
311                 {
312                     // nothing is inside an empty range
313                     return aRetval;
314                 }
315                 else
316                 {
317                     // everything is outside an empty range
318                     return rCandidate;
319                 }
320             }
321 
322             if(bInside)
323             {
324 			    for(sal_uInt32 a(0L); a < nPolygonCount; a++)
325 			    {
326 				    const B2DPolyPolygon aClippedPolyPolygon(clipPolygonOnRange(rCandidate.getB2DPolygon(a), rRange, bInside, bStroke));
327 
328                     if(aClippedPolyPolygon.count())
329                     {
330     				    aRetval.append(aClippedPolyPolygon);
331                     }
332 			    }
333             }
334             else
335             {
336                 // for details, see comment in clipPolygonOnRange for the "cutting off
337                 // the outer parts of filled polygons at parallell lines" explanations
338         		const B2DPolygon aClip(createPolygonFromRect(rRange));
339 
340                 return clipPolyPolygonOnPolyPolygon(rCandidate, B2DPolyPolygon(aClip), bInside, bStroke);
341             }
342 
343 			return aRetval;
344 		}
345 
346 		B2DPolyPolygon clipPolygonOnEdge(const B2DPolygon& rCandidate, const B2DPoint& rPointA, const B2DPoint& rPointB, bool bAbove, bool bStroke)
347 		{
348 			B2DPolyPolygon aRetval;
349 
350 			if(rPointA.equal(rPointB))
351 			{
352 				// edge has no length, return polygon
353 				aRetval.append(rCandidate);
354 			}
355 			else if(rCandidate.count())
356 			{
357 				const B2DVector aEdge(rPointB - rPointA);
358 				B2DPolygon aCandidate(rCandidate);
359 
360 				// translate and rotate polygon so that given edge is on x axis
361                 B2DHomMatrix aMatrixTransform(basegfx::tools::createTranslateB2DHomMatrix(-rPointA.getX(), -rPointA.getY()));
362 				aMatrixTransform.rotate(-atan2(aEdge.getY(), aEdge.getX()));
363 				aCandidate.transform(aMatrixTransform);
364 
365 				// call clip method on X-Axis
366 				aRetval = clipPolygonOnParallelAxis(aCandidate, true, bAbove, 0.0, bStroke);
367 
368 				if(aRetval.count())
369 				{
370 					// if there is a result, it needs to be transformed back
371 					aMatrixTransform.invert();
372 					aRetval.transform(aMatrixTransform);
373 				}
374 			}
375 
376 			return aRetval;
377 		}
378 
379 		B2DPolyPolygon clipPolyPolygonOnEdge(const B2DPolyPolygon& rCandidate, const B2DPoint& rPointA, const B2DPoint& rPointB, bool bAbove, bool bStroke)
380 		{
381 			B2DPolyPolygon aRetval;
382 
383 			if(rPointA.equal(rPointB))
384 			{
385 				// edge has no length, return polygon
386 				aRetval = rCandidate;
387 			}
388 			else if(rCandidate.count())
389 			{
390 				const B2DVector aEdge(rPointB - rPointA);
391 				B2DPolyPolygon aCandidate(rCandidate);
392 
393 				// translate and rotate polygon so that given edge is on x axis
394                 B2DHomMatrix aMatrixTransform(basegfx::tools::createTranslateB2DHomMatrix(-rPointA.getX(), -rPointA.getY()));
395 				aMatrixTransform.rotate(-atan2(aEdge.getY(), aEdge.getX()));
396 				aCandidate.transform(aMatrixTransform);
397 
398 				// call clip method on X-Axis
399 				aRetval = clipPolyPolygonOnParallelAxis(aCandidate, true, bAbove, 0.0, bStroke);
400 
401 				if(aRetval.count())
402 				{
403 					// if there is a result, it needs to be transformed back
404 					aMatrixTransform.invert();
405 					aRetval.transform(aMatrixTransform);
406 				}
407 			}
408 
409 			return aRetval;
410 		}
411 
412 		//////////////////////////////////////////////////////////////////////////////
413 
414 		B2DPolyPolygon clipPolyPolygonOnPolyPolygon(const B2DPolyPolygon& rCandidate, const B2DPolyPolygon& rClip, bool bInside, bool bStroke)
415 		{
416 			B2DPolyPolygon aRetval;
417 
418 			if(rCandidate.count() && rClip.count())
419 			{
420                 // one or both are no rectangle - go the hard way and clip PolyPolygon
421                 // against PolyPolygon...
422 				if(bStroke)
423 				{
424 					// line clipping, create line snippets by first adding all cut points and
425                     // then marching along the edges and detecting if they are inside or outside
426                     // the clip polygon
427 					for(sal_uInt32 a(0); a < rCandidate.count(); a++)
428 					{
429                         // add cuts with clip to polygon, including bezier segments
430                         const B2DPolygon aCandidate(addPointsAtCuts(rCandidate.getB2DPolygon(a), rClip));
431     			        const sal_uInt32 nPointCount(aCandidate.count());
432                         const sal_uInt32 nEdgeCount(aCandidate.isClosed() ? nPointCount : nPointCount - 1L);
433                         B2DCubicBezier aEdge;
434                         B2DPolygon aRun;
435 
436                         for(sal_uInt32 b(0); b < nEdgeCount; b++)
437                         {
438                             aCandidate.getBezierSegment(b, aEdge);
439                             const B2DPoint aTestPoint(aEdge.interpolatePoint(0.5));
440                             const bool bIsInside(tools::isInside(rClip, aTestPoint) == bInside);
441 
442 						    if(bIsInside)
443 						    {
444 							    if(!aRun.count())
445 							    {
446 								    aRun.append(aEdge.getStartPoint());
447 							    }
448 
449 							    if(aEdge.isBezier())
450 							    {
451 								    aRun.appendBezierSegment(aEdge.getControlPointA(), aEdge.getControlPointB(), aEdge.getEndPoint());
452 							    }
453 							    else
454 							    {
455 								    aRun.append(aEdge.getEndPoint());
456 							    }
457 						    }
458 						    else
459 						    {
460                                 if(aRun.count())
461                                 {
462 								    aRetval.append(aRun);
463 								    aRun.clear();
464                                 }
465 						    }
466                         }
467 
468                         if(aRun.count())
469 					    {
470                             // try to merge this last and first polygon; they may have been
471                             // the former polygon's start/end point
472                             if(aRetval.count())
473                             {
474                                 const B2DPolygon aStartPolygon(aRetval.getB2DPolygon(0));
475 
476                                 if(aStartPolygon.count() && aStartPolygon.getB2DPoint(0).equal(aRun.getB2DPoint(aRun.count() - 1)))
477                                 {
478                                     // append start polygon to aRun, remove from result set
479                                     aRun.append(aStartPolygon); aRun.removeDoublePoints();
480                                     aRetval.remove(0);
481                                 }
482                             }
483 
484 						    aRetval.append(aRun);
485 					    }
486 					}
487 				}
488                 else
489                 {
490                     // check for simplification with ranges if !bStroke (handling as stroke is more simple),
491                     // but also only when bInside, else the simplification may lead to recursive calls (see
492                     // calls to clipPolyPolygonOnPolyPolygon in clipPolyPolygonOnRange and clipPolygonOnRange)
493                     if(bInside)
494                     {
495                         // #125349# detect if both given PolyPolygons are indeed ranges
496                         bool bBothRectangle(false);
497 
498                         if(basegfx::tools::isRectangle(rCandidate))
499                         {
500                             if(basegfx::tools::isRectangle(rClip))
501                             {
502                                 // both are ranges
503                                 bBothRectangle = true;
504                             }
505                             else
506                             {
507                                 // rCandidate is rectangle -> clip rClip on rRectangle, use the much
508                                 // cheaper and numerically more stable clipping against a range
509                                 // This simplification (exchanging content and clip) is valid
510                                 // since we do a logical AND operation
511                                 return clipPolyPolygonOnRange(rClip, rCandidate.getB2DRange(), bInside, bStroke);
512                             }
513                         }
514                         else if(basegfx::tools::isRectangle(rClip))
515                         {
516                             if(basegfx::tools::isRectangle(rCandidate))
517                             {
518                                 // both are ranges
519                                 bBothRectangle = true;
520                             }
521                             else
522                             {
523                                 // rClip is rectangle -> clip rCandidate on rRectangle, use the much
524                                 // cheaper and numerically more stable clipping against a range
525                                 return clipPolyPolygonOnRange(rCandidate, rClip.getB2DRange(), bInside, bStroke);
526                             }
527                         }
528 
529                         if(bBothRectangle)
530                         {
531                             // both are rectangle
532                             if(rCandidate.getB2DRange().equal(rClip.getB2DRange()))
533                             {
534                                 // if both are equal -> no change
535                                 return rCandidate;
536                             }
537                             else
538                             {
539                                 // not equal -> create new intersection from both ranges,
540                                 // but much cheaper based on the ranges
541                                 basegfx::B2DRange aIntersectionRange(rCandidate.getB2DRange());
542 
543                                 aIntersectionRange.intersect(rClip.getB2DRange());
544 
545                                 if(aIntersectionRange.isEmpty())
546                                 {
547                                     // no common IntersectionRange -> the clip will be empty
548                                     return B2DPolyPolygon();
549                                 }
550                                 else
551                                 {
552                                     // use common aIntersectionRange as result, convert
553                                     // to expected PolyPolygon form
554                                     return basegfx::B2DPolyPolygon(
555                                         basegfx::tools::createPolygonFromRect(aIntersectionRange));
556                                 }
557                             }
558                         }
559                     }
560 
561                     // area clipping
562                     B2DPolyPolygon aMergePolyPolygonA(rClip);
563 
564                     // First solve all polygon-self and polygon-polygon intersections.
565                     // Also get rid of some not-needed polygons (neutral, no area -> when
566                     // no intersections, these are tubes).
567                     // Now it is possible to correct the orientations in the cut-free
568                     // polygons to values corresponding to painting the PolyPolygon with
569                     // a XOR-WindingRule.
570                     aMergePolyPolygonA = solveCrossovers(aMergePolyPolygonA);
571 					aMergePolyPolygonA = stripNeutralPolygons(aMergePolyPolygonA);
572                     aMergePolyPolygonA = correctOrientations(aMergePolyPolygonA);
573 
574 					if(!bInside)
575 					{
576                         // if we want to get the outside of the clip polygon, make
577                         // it a 'Hole' in topological sense
578 						aMergePolyPolygonA.flip();
579 					}
580 
581 					B2DPolyPolygon aMergePolyPolygonB(rCandidate);
582 
583                     // prepare 2nd source polygon in same way
584                     aMergePolyPolygonB = solveCrossovers(aMergePolyPolygonB);
585 					aMergePolyPolygonB = stripNeutralPolygons(aMergePolyPolygonB);
586                     aMergePolyPolygonB = correctOrientations(aMergePolyPolygonB);
587 
588                     // to clip against each other, concatenate and solve all
589                     // polygon-polygon crossovers. polygon-self do not need to
590                     // be solved again, they were solved in the preparation.
591 					aRetval.append(aMergePolyPolygonA);
592 					aRetval.append(aMergePolyPolygonB);
593 					aRetval = solveCrossovers(aRetval);
594 
595                     // now remove neutral polygons (closed, but no area). In a last
596                     // step throw away all polygons which have a depth of less than 1
597                     // which means there was no logical AND at their position. For the
598                     // not-inside solution, the clip was flipped to define it as 'Hole',
599                     // so the removal rule is different here; remove all with a depth
600                     // of less than 0 (aka holes).
601 					aRetval = stripNeutralPolygons(aRetval);
602 					aRetval = stripDispensablePolygons(aRetval, bInside);
603 				}
604 			}
605 
606 			return aRetval;
607 		}
608 
609 		//////////////////////////////////////////////////////////////////////////////
610 
611 		B2DPolyPolygon clipPolygonOnPolyPolygon(const B2DPolygon& rCandidate, const B2DPolyPolygon& rClip, bool bInside, bool bStroke)
612 		{
613 			B2DPolyPolygon aRetval;
614 
615 			if(rCandidate.count() && rClip.count())
616 			{
617 				aRetval = clipPolyPolygonOnPolyPolygon(B2DPolyPolygon(rCandidate), rClip, bInside, bStroke);
618 			}
619 
620 			return aRetval;
621 		}
622 
623 		//////////////////////////////////////////////////////////////////////////////
624 
625 		/*
626 		* let a plane be defined as
627 		*
628 		*     v.n+d=0
629 		*
630 		* and a ray be defined as
631 		*
632 		*     a+(b-a)*t=0
633 		*
634 		* substitute and rearranging yields
635 		*
636 		*     t = -(a.n+d)/(n.(b-a))
637 		*
638 		* if the denominator is zero, the line is either
639 		* contained in the plane or parallel to the plane.
640 		* in either case, there is no intersection.
641 		* if numerator and denominator are both zero, the
642 		* ray is contained in the plane.
643 		*
644 		*/
645 		struct scissor_plane {
646 			double nx,ny;			// plane normal
647 			double d;				// [-] minimum distance from origin
648 			sal_uInt32 clipmask;	// clipping mask, e.g. 1000 1000
649 		};
650 
651 		/*
652 		*
653 		* polygon clipping rules  (straight out of Foley and Van Dam)
654 		* ===========================================================
655 		* current	|next		|emit
656 		* ____________________________________
657 		* inside	|inside		|next
658 		* inside	|outside	|intersect with clip plane
659 		* outside	|outside	|nothing
660 		* outside	|inside		|intersect with clip plane follwed by next
661 		*
662 		*/
663 		sal_uInt32 scissorLineSegment( ::basegfx::B2DPoint			 *in_vertex,	// input buffer
664                                        sal_uInt32					  in_count,		// number of verts in input buffer
665                                        ::basegfx::B2DPoint			 *out_vertex,	// output buffer
666                                        scissor_plane				 *pPlane,		// scissoring plane
667                                        const ::basegfx::B2DRectangle &rR )			// clipping rectangle
668 		{
669 			::basegfx::B2DPoint *curr;
670 			::basegfx::B2DPoint *next;
671 
672 			sal_uInt32 out_count=0;
673 
674 			// process all the verts
675 			for(sal_uInt32 i=0; i<in_count; i++) {
676 
677 				// vertices are relative to the coordinate
678 				// system defined by the rectangle.
679 				curr = &in_vertex[i];
680 				next = &in_vertex[(i+1)%in_count];
681 
682 				// perform clipping judgement & mask against current plane.
683 				sal_uInt32 clip = pPlane->clipmask & ((getCohenSutherlandClipFlags(*curr,rR)<<4)|getCohenSutherlandClipFlags(*next,rR));
684 
685 				if(clip==0) { // both verts are inside
686 					out_vertex[out_count++] = *next;
687 				}
688 				else if((clip&0x0f) && (clip&0xf0)) { // both verts are outside
689 				}
690 				else if((clip&0x0f) && (clip&0xf0)==0) { // curr is inside, next is outside
691 
692 					// direction vector from 'current' to 'next', *not* normalized
693 					// to bring 't' into the [0<=x<=1] intervall.
694 					::basegfx::B2DPoint dir((*next)-(*curr));
695 
696 					double denominator = ( pPlane->nx*dir.getX() +
697 										pPlane->ny*dir.getY() );
698 					double numerator = ( pPlane->nx*curr->getX() +
699 										pPlane->ny*curr->getY() +
700 										pPlane->d );
701 					double t = -numerator/denominator;
702 
703 					// calculate the actual point of intersection
704 					::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
705 													curr->getY()+t*dir.getY() );
706 
707 					out_vertex[out_count++] = intersection;
708 				}
709 				else if((clip&0x0f)==0 && (clip&0xf0)) { // curr is outside, next is inside
710 
711 					// direction vector from 'current' to 'next', *not* normalized
712 					// to bring 't' into the [0<=x<=1] intervall.
713 					::basegfx::B2DPoint dir((*next)-(*curr));
714 
715 					double denominator = ( pPlane->nx*dir.getX() +
716 										pPlane->ny*dir.getY() );
717 					double numerator = ( pPlane->nx*curr->getX() +
718 										pPlane->ny*curr->getY() +
719 										pPlane->d );
720 					double t = -numerator/denominator;
721 
722 					// calculate the actual point of intersection
723 					::basegfx::B2DPoint intersection( curr->getX()+t*dir.getX(),
724 													curr->getY()+t*dir.getY() );
725 
726 					out_vertex[out_count++] = intersection;
727 					out_vertex[out_count++] = *next;
728 				}
729 			}
730 
731 			return out_count;
732 		}
733 
734 		B2DPolygon clipTriangleListOnRange( const B2DPolygon& rCandidate,
735                                             const B2DRange&   rRange )
736 		{
737 			B2DPolygon aResult;
738 
739 			if( !(rCandidate.count()%3) )
740 			{
741 				const int scissor_plane_count = 4;
742 
743 				scissor_plane sp[scissor_plane_count];
744 
745 				sp[0].nx = +1.0;
746 				sp[0].ny = +0.0;
747 				sp[0].d = -(rRange.getMinX());
748 				sp[0].clipmask = (RectClipFlags::LEFT << 4) | RectClipFlags::LEFT; // 0001 0001
749 				sp[1].nx = -1.0;
750 				sp[1].ny = +0.0;
751 				sp[1].d = +(rRange.getMaxX());
752 				sp[1].clipmask = (RectClipFlags::RIGHT << 4) | RectClipFlags::RIGHT; // 0010 0010
753 				sp[2].nx = +0.0;
754 				sp[2].ny = +1.0;
755 				sp[2].d = -(rRange.getMinY());
756 				sp[2].clipmask = (RectClipFlags::TOP << 4) | RectClipFlags::TOP; // 0100 0100
757 				sp[3].nx = +0.0;
758 				sp[3].ny = -1.0;
759 				sp[3].d = +(rRange.getMaxY());
760 				sp[3].clipmask = (RectClipFlags::BOTTOM << 4) | RectClipFlags::BOTTOM; // 1000 1000
761 
762 				// retrieve the number of vertices of the triangulated polygon
763 				const sal_uInt32 nVertexCount = rCandidate.count();
764 
765 				if(nVertexCount)
766 				{
767 					////////////////////////////////////////////////////////////////////////
768 					////////////////////////////////////////////////////////////////////////
769 					////////////////////////////////////////////////////////////////////////
770 					//
771 					// Upper bound for the maximal number of vertices when intersecting an
772 					// axis-aligned rectangle with a triangle in E2
773 					//
774 					// The rectangle and the triangle are in general position, and have 4 and 3
775 					// vertices, respectively.
776 					//
777 					//   Lemma: Since the rectangle is a convex polygon ( see
778 					//   http://mathworld.wolfram.com/ConvexPolygon.html for a definition), and
779 					//   has no holes, it follows that any straight line will intersect the
780 					//   rectangle's border line at utmost two times (with the usual
781 					//   tie-breaking rule, if the intersection exactly hits an already existing
782 					//   rectangle vertex, that this intersection is only attributed to one of
783 					//   the adjoining edges). Thus, having a rectangle intersected with
784 					//   a half-plane (one side of a straight line denotes 'inside', the
785 					//   other 'outside') will at utmost add _one_  vertex to the resulting
786 					//   intersection polygon (adding two intersection vertices, and removing at
787 					//   least one rectangle vertex):
788 					//
789 					//         *
790 					//     +--+-----------------+
791 					//     | *                  |
792 					//     |*                   |
793 					//     +                    |
794 					//    *|                    |
795 					//   * |                    |
796 					//     +--------------------+
797 					//
798 					//   Proof: If the straight line intersects the rectangle two
799 					//   times, it does so for distinct edges, i.e. the intersection has
800 					//   minimally one of the rectangle's vertices on either side of the straight
801 					//   line (but maybe more). Thus, the intersection with a half-plane has
802 					//   minimally _one_ rectangle vertex removed from the resulting clip
803 					//   polygon, and therefore, a clip against a half-plane has the net effect
804 					//   of adding at utmost _one_ vertex to the resulting clip polygon.
805 					//
806 					// Theorem: The intersection of a rectangle and a triangle results in a
807 					// polygon with at utmost 7 vertices.
808 					//
809 					// Proof: The inside of the triangle can be described as the consecutive
810 					// intersection with three half-planes. Together with the lemma above, this
811 					// results in at utmost 3 additional vertices added to the already existing 4
812 					// rectangle vertices.
813 					//
814 					// This upper bound is attained with the following example configuration:
815 					//
816 					//                               *
817 					//                             ***
818 					//                           ** *
819 					//                         **  *
820 					//                       **   *
821 					//                     **    *
822 					//                   **     *
823 					//                 **      *
824 					//               **       *
825 					//             **        *
826 					//           **         *
827 					//     ----*2--------3 *
828 					//     | **          |*
829 					//     1*            4
830 					//   **|            *|
831 					// **  |           * |
832 					//   **|          *  |
833 					//     7*        *   |
834 					//     --*6-----5-----
835 					//         **  *
836 					//           **
837 					//
838 					// As we need to scissor all triangles against the
839 					// output rectangle we employ an output buffer for the
840 					// resulting vertices.  the question is how large this
841 					// buffer needs to be compared to the number of
842 					// incoming vertices.  this buffer needs to hold at
843 					// most the number of original vertices times '7'. see
844 					// figure above for an example.  scissoring triangles
845 					// with the cohen-sutherland line clipping algorithm
846 					// as implemented here will result in a triangle fan
847 					// which will be rendered as separate triangles to
848 					// avoid pipeline stalls for each scissored
849 					// triangle. creating separate triangles from a
850 					// triangle fan produces (n-2)*3 vertices where n is
851 					// the number of vertices of the original triangle
852 					// fan.  for the maximum number of 7 vertices of
853 					// resulting triangle fans we therefore need 15 times
854 					// the number of original vertices.
855 					//
856 					////////////////////////////////////////////////////////////////////////
857 					////////////////////////////////////////////////////////////////////////
858 					////////////////////////////////////////////////////////////////////////
859 
860 					//const size_t nBufferSize = sizeof(vertex)*(nVertexCount*16);
861 					//vertex *pVertices = (vertex*)alloca(nBufferSize);
862 					//sal_uInt32 nNumOutput = 0;
863 
864 					// we need to clip this triangle against the output rectangle
865 					// to ensure that the resulting texture coordinates are in
866 					// the valid range from [0<=st<=1]. under normal circustances
867 					// we could use the BORDERCOLOR renderstate but some cards
868 					// seem to ignore this feature.
869 					::basegfx::B2DPoint stack[3];
870 					unsigned int clipflag = 0;
871 
872 					for(sal_uInt32 nIndex=0; nIndex<nVertexCount; ++nIndex)
873 					{
874 						// rotate stack
875 						stack[0] = stack[1];
876 						stack[1] = stack[2];
877 						stack[2] = rCandidate.getB2DPoint(nIndex);
878 
879 						// clipping judgement
880 						clipflag |= !(rRange.isInside(stack[2]));
881 
882 						if(nIndex > 1)
883 						{
884 							// consume vertices until a single separate triangle has been visited.
885 							if(!((nIndex+1)%3))
886 							{
887 								// if any of the last three vertices was outside
888 								// we need to scissor against the destination rectangle
889 								if(clipflag & 7)
890 								{
891 									::basegfx::B2DPoint buf0[16];
892 									::basegfx::B2DPoint buf1[16];
893 
894 									sal_uInt32 vertex_count = 3;
895 
896 									// clip against all 4 planes passing the result of
897 									// each plane as the input to the next using a double buffer
898 									vertex_count = scissorLineSegment(stack,vertex_count,buf1,&sp[0],rRange);
899 									vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[1],rRange);
900 									vertex_count = scissorLineSegment(buf0,vertex_count,buf1,&sp[2],rRange);
901 									vertex_count = scissorLineSegment(buf1,vertex_count,buf0,&sp[3],rRange);
902 
903 									if(vertex_count >= 3)
904 									{
905 										// convert triangle fan back to triangle list.
906 										::basegfx::B2DPoint v0(buf0[0]);
907 										::basegfx::B2DPoint v1(buf0[1]);
908 										for(sal_uInt32 i=2; i<vertex_count; ++i)
909 										{
910 											::basegfx::B2DPoint v2(buf0[i]);
911 											aResult.append(v0);
912 											aResult.append(v1);
913 											aResult.append(v2);
914 											v1 = v2;
915 										}
916 									}
917 								}
918 								else
919 								{
920 									// the last triangle has not been altered, simply copy to result
921 									for(sal_uInt32 i=0; i<3; ++i)
922 										aResult.append(stack[i]);
923 								}
924 							}
925 						}
926 
927 						clipflag <<= 1;
928 					}
929 				}
930 			}
931 
932 			return aResult;
933 		}
934 
935 		//////////////////////////////////////////////////////////////////////////////
936 
937 	} // end of namespace tools
938 } // end of namespace basegfx
939 
940 //////////////////////////////////////////////////////////////////////////////
941 
942 // eof
943