2 ** License Applicability. Except to the extent portions of this file are
3 ** made subject to an alternative license as permitted in the SGI Free
4 ** Software License B, Version 1.1 (the "License"), the contents of this
5 ** file are subject only to the provisions of the License. You may not use
6 ** this file except in compliance with the License. You may obtain a copy
7 ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
8 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
10 ** http://oss.sgi.com/projects/FreeB
12 ** Note that, as provided in the License, the Software is distributed on an
13 ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
14 ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
15 ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
16 ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
18 ** Original Code. The Original Code is: OpenGL Sample Implementation,
19 ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
20 ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
21 ** Copyright in any portions created by third parties is as indicated
22 ** elsewhere herein. All Rights Reserved.
24 ** Additional Notice Provisions: The application programming interfaces
25 ** established by SGI in conjunction with the Original Code are The
26 ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
27 ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
28 ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
29 ** Window System(R) (Version 1.3), released October 19, 1998. This software
30 ** was created using the OpenGL(R) version 1.2.1 Sample Implementation
31 ** published by SGI, but has not been independently verified as being
32 ** compliant with the OpenGL(R) version 1.2.1 Specification.
41 #include "glimports.h"
44 #include "monoTriangulation.h"
45 #include "polyUtil.h" /*for area*/
46 #include "partitionX.h"
47 #include "monoPolyPart.h"
51 extern directedLine* polygonConvert(directedLine* polygon);
55 void monoTriangulationOpt(directedLine* poly, primStream* pStream)
58 Int n_edges = poly->numEdges();
59 directedLine** cusps = (directedLine**) malloc(sizeof(directedLine*)*n_edges);
61 findInteriorCuspsX(poly, n_cusps, cusps);
62 if(n_cusps ==0) //u monotine
64 monoTriangulationFun(poly, compV2InX, pStream);
66 else if(n_cusps == 1) // one interior cusp
68 directedLine* new_polygon = polygonConvert(cusps[0]);
69 directedLine* other = findDiagonal_singleCuspX(new_polygon);
70 //<other> should NOT be null unless there are self-intersecting
71 //trim curves. In that case, we don't want to core dump, instead,
72 //we triangulate anyway, and print out error message.
75 monoTriangulationFun(poly, compV2InX, pStream);
82 new_polygon->connectDiagonal_2slines(new_polygon, other,
87 monoTriangulationFun(ret_p1, compV2InX, pStream);
88 monoTriangulationFun(ret_p2, compV2InX, pStream);
90 ret_p1->deleteSinglePolygonWithSline();
91 ret_p2->deleteSinglePolygonWithSline();
96 //we need a general partitionX funtion (supposed to be in partitionX.C,
97 //not implemented yet. XXX
98 monoTriangulationFun(poly, compV2InY, pStream);
104 void monoTriangulationRecOpt(Real* topVertex, Real* botVertex,
105 vertexArray* left_chain, Int left_current,
106 vertexArray* right_chain, Int right_current,
110 Int n_left = left_chain->getNumElements();
111 Int n_right = right_chain->getNumElements();
112 if(left_current>= n_left-1 ||
113 right_current>= n_right-1)
115 monoTriangulationRec(topVertex, botVertex, left_chain, left_current,
116 right_chain, right_current, pStream);
119 //now both left and right have at least two vertices each.
120 Real left_v = left_chain->getVertex(left_current)[1];
121 Real right_v = right_chain->getVertex(right_current)[1];
123 if(left_v <= right_v) //first left vertex is below right
125 //find the last vertex of right which is above or equal to left
126 for(j=right_current; j<=n_right-1; j++)
128 if(right_chain->getVertex(j)[1] < left_v)
131 monoTriangulationRecGen(topVertex, left_chain->getVertex(left_current),
132 left_chain, left_current, left_current,
133 right_chain, right_current, j-1,
135 monoTriangulationRecOpt(right_chain->getVertex(j-1),
137 left_chain, left_current,
141 else //first right vertex is strictly below left
143 //find the last vertex of left which is strictly above right
144 for(i=left_current; i<=n_left-1; i++)
146 if(left_chain->getVertex(i)[1] <= right_v)
149 monoTriangulationRecGen(topVertex, right_chain->getVertex(right_current),
150 left_chain, left_current, i-1,
151 right_chain, right_current, right_current,
153 monoTriangulationRecOpt(left_chain->getVertex(i-1),
156 right_chain, right_current,
162 void monoTriangulationRecGenTBOpt(Real* topVertex, Real* botVertex,
163 vertexArray* inc_chain, Int inc_current, Int inc_end,
164 vertexArray* dec_chain, Int dec_current, Int dec_end,
167 pStream->triangle(topVertex, inc_chain->getVertex(inc_current), dec_chain->getVertex(dec_current));
169 /*printf("**(%f,%f)\n", inc_chain->getArray()[0][0],inc_chain->getArray()[0][1]);*/
170 triangulateXYMonoTB(inc_end-inc_current+1, inc_chain->getArray()+inc_current, dec_end-dec_current+1, dec_chain->getArray()+dec_current, pStream);
172 pStream->triangle(botVertex, dec_chain->getVertex(dec_end), inc_chain->getVertex(inc_end));
178 *the strip is going top to bottom. compared to the funtion
179 * triangulateXYmono()
181 void triangulateXYMonoTB(Int n_left, Real** leftVerts,
182 Int n_right, Real** rightVerts,
190 assert(n_left>=1 && n_right>=1);
191 if(leftVerts[0][1] >= rightVerts[0][1])
195 topMostV = leftVerts[0];
201 topMostV = rightVerts[0];
206 if(i >= n_left) /*case1: no more in left*/
209 if(j<n_right-1) /*at least two vertices in right*/
212 pStream->insert(topMostV);
213 for(k=n_right-1; k>=j; k--)
214 pStream->insert(rightVerts[j]);
216 pStream->end(PRIMITIVE_STREAM_FAN);
222 else if(j>= n_right) /*case2: no more in right*/
225 if(i<n_left-1) /*at least two vertices in left*/
228 pStream->insert(topMostV);
230 for(k=i; k<n_left; k++)
231 pStream->insert(leftVerts[k]);
233 pStream->end(PRIMITIVE_STREAM_FAN);
238 else /* case3: neither is empty, plus the topMostV, there is at least one triangle to output*/
241 if(leftVerts[i][1] >= rightVerts[j][1])
244 pStream->insert(rightVerts[j]); /*the origin of this fan*/
246 pStream->insert(topMostV);
248 /*find the last k>=i such that
249 *leftverts[k][1] >= rightverts[j][1]
254 if(leftVerts[k][1] < rightVerts[j][1])
261 pStream->insert(leftVerts[l]);
264 pStream->end(PRIMITIVE_STREAM_FAN);
265 //update i for next loop
267 topMostV = leftVerts[k];
270 else /*leftVerts[i][1] < rightVerts[j][1]*/
273 pStream->insert(leftVerts[i]);/*the origion of this fan*/
275 /*find the last k>=j such that
276 *rightverts[k][1] > leftverts[i][1]*/
280 if(rightVerts[k][1] <= leftVerts[i][1])
287 pStream->insert(rightVerts[l]);
289 pStream->insert(topMostV);
290 pStream->end(PRIMITIVE_STREAM_FAN);
292 topMostV = rightVerts[j-1];
298 static int chainConvex(vertexArray* inc_chain, Int inc_current, Int inc_end)
301 //if there are no more than 2 vertices, return 1
302 if(inc_current >= inc_end-1) return 1;
303 for(i=inc_current; i<= inc_end-2; i++)
305 if(area(inc_chain->getVertex(i), inc_chain->getVertex(i+1), inc_chain->getVertex(i+2)) <0)
311 static int chainConcave(vertexArray* dec_chain, Int dec_current, Int dec_end)
314 //if there are no more than 2 vertices, return 1
315 if(dec_current >= dec_end -1) return 1;
316 for(i=dec_current; i<=dec_end-2; i++)
318 if(area(dec_chain->getVertex(i), dec_chain->getVertex(i+1), dec_chain->getVertex(i+2)) >0)
324 void monoTriangulationRecGenInU(Real* topVertex, Real* botVertex,
325 vertexArray* inc_chain, Int inc_current, Int inc_end,
326 vertexArray* dec_chain, Int dec_current, Int dec_end,
332 void monoTriangulationRecGenOpt(Real* topVertex, Real* botVertex,
333 vertexArray* inc_chain, Int inc_current, Int inc_end,
334 vertexArray* dec_chain, Int dec_current, Int dec_end,
338 //copy this to a polygon: directedLine Lioop
343 if(inc_current <= inc_end) //at least one vertex in inc_chain
345 sline = new sampledLine(topVertex, inc_chain->getVertex(inc_current));
346 poly = new directedLine(INCREASING, sline);
347 for(i=inc_current; i<=inc_end-1; i++)
349 sline = new sampledLine(inc_chain->getVertex(i), inc_chain->getVertex(i+1));
350 dline = new directedLine(INCREASING, sline);
353 sline = new sampledLine(inc_chain->getVertex(inc_end), botVertex);
354 dline = new directedLine(INCREASING, sline);
357 else //inc_chian is empty
359 sline = new sampledLine(topVertex, botVertex);
360 dline = new directedLine(INCREASING, sline);
364 assert(poly != NULL);
366 if(dec_current <= dec_end) //at least on vertex in dec_Chain
368 sline = new sampledLine(botVertex, dec_chain->getVertex(dec_end));
369 dline = new directedLine(INCREASING, sline);
371 for(i=dec_end; i>dec_current; i--)
373 sline = new sampledLine(dec_chain->getVertex(i), dec_chain->getVertex(i-1));
374 dline = new directedLine(INCREASING, sline);
377 sline = new sampledLine(dec_chain->getVertex(dec_current), topVertex);
378 dline = new directedLine(INCREASING, sline);
381 else //dec_chain is empty
383 sline = new sampledLine(botVertex, topVertex);
384 dline = new directedLine(INCREASING, sline);
390 Int n_edges = poly->numEdges();
391 directedLine** cusps = (directedLine**) malloc(sizeof(directedLine*)*n_edges);
393 findInteriorCuspsX(poly, n_cusps, cusps);
395 if(n_cusps ==0) //u monotine
397 monoTriangulationFun(poly, compV2InX, pStream);
399 else if(n_cusps == 1) // one interior cusp
401 directedLine* new_polygon = polygonConvert(cusps[0]);
402 directedLine* other = findDiagonal_singleCuspX(new_polygon);
403 //<other> should NOT be null unless there are self-intersecting
404 //trim curves. In that case, we don't want to core dump, instead,
405 //we triangulate anyway, and print out error message.
408 monoTriangulationFun(poly, compV2InX, pStream);
412 directedLine* ret_p1;
413 directedLine* ret_p2;
415 new_polygon->connectDiagonal_2slines(new_polygon, other,
420 monoTriangulationFun(ret_p1, compV2InX, pStream);
421 monoTriangulationFun(ret_p2, compV2InX, pStream);
423 ret_p1->deleteSinglePolygonWithSline();
424 ret_p2->deleteSinglePolygonWithSline();
429 //we need a general partitionX funtion (supposed to be in partitionX.C,
430 //not implemented yet. XXX
431 //monoTriangulationFun(poly, compV2InY, pStream);
433 directedLine* new_polygon = polygonConvert(poly);
434 directedLine* list = monoPolyPart(new_polygon);
435 for(directedLine* temp = list; temp != NULL; temp = temp->getNextPolygon())
437 monoTriangulationFun(temp, compV2InX, pStream);
440 list->deletePolygonListWithSline();
446 if(numInteriorCuspsX(poly) == 0) //is u monotone
447 monoTriangulationFun(poly, compV2InX, pStream);
448 else //it is not u motone
449 monoTriangulationFun(poly, compV2InY, pStream);
452 poly->deleteSinglePolygonWithSline();
456 //apparently the following code is not reachable,
457 //it is for test purpose
458 if(inc_current > inc_end || dec_current>dec_end)
460 monoTriangulationRecGen(topVertex, botVertex, inc_chain, inc_current, inc_end,
461 dec_chain, dec_current, dec_end,
468 area(dec_chain->getVertex(dec_current),
470 inc_chain->getVertex(inc_current)) >=0
471 && chainConvex(inc_chain, inc_current, inc_end)
472 && chainConcave(dec_chain, dec_current, dec_end)
473 && area(inc_chain->getVertex(inc_end), botVertex, dec_chain->getVertex(dec_end)) >=0
476 monoTriangulationRecFunGen(topVertex, botVertex,
477 inc_chain, inc_current, inc_end,
478 dec_chain, dec_current, dec_end,
483 monoTriangulationRecGen(topVertex, botVertex, inc_chain, inc_current, inc_end,
484 dec_chain, dec_current, dec_end,
489 /*if inc_current>inc_end, then inc_chain has no points to be considered
492 void monoTriangulationRecGen(Real* topVertex, Real* botVertex,
493 vertexArray* inc_chain, Int inc_current, Int inc_end,
494 vertexArray* dec_chain, Int dec_current, Int dec_end,
501 if(inc_current > inc_end && dec_current>dec_end)
503 else if(inc_current>inc_end) /*no more vertices on inc_chain*/
505 dec_array = dec_chain->getArray();
506 reflexChain rChain(100,0);
507 /*put the top vertex into the reflex chain*/
508 rChain.processNewVertex(topVertex, pStream);
509 /*process all the vertices on the dec_chain*/
510 for(i=dec_current; i<=dec_end; i++){
511 rChain.processNewVertex(dec_array[i], pStream);
513 /*process the bottom vertex*/
514 rChain.processNewVertex(botVertex, pStream);
516 else if(dec_current> dec_end) /*no more vertices on dec_chain*/
518 inc_array = inc_chain->getArray();
520 reflexChain rChain(100,1);
521 /*put the top vertex into the reflex chain*/
522 rChain.processNewVertex(topVertex, pStream);
523 /*process all the vertices on the inc_chain*/
524 for(i=inc_current; i<=inc_end; i++){
525 rChain.processNewVertex(inc_array[i], pStream);
527 /*process the bottom vertex*/
528 rChain.processNewVertex(botVertex, pStream);
530 else /*neither chain is empty*/
532 inc_array = inc_chain -> getArray();
533 dec_array = dec_chain -> getArray();
535 /*if top of inc_chain is 'lower' than top of dec_chain, process all the
536 *vertices on the dec_chain which are higher than top of inc_chain
538 if(compV2InY(inc_array[inc_current], dec_array[dec_current]) <= 0)
541 reflexChain rChain(100, 0);
542 rChain.processNewVertex(topVertex, pStream);
543 for(i=dec_current; i<=dec_end; i++)
545 if(compV2InY(inc_array[inc_current], dec_array[i]) <= 0)
546 rChain.processNewVertex(dec_array[i], pStream);
550 rChain.outputFan(inc_array[inc_current], pStream);
551 monoTriangulationRecGen(dec_array[i-1], botVertex,
552 inc_chain, inc_current, inc_end,
553 dec_chain, i, dec_end,
556 else /*compV2InY(inc_array[inc_current], dec_array[dec_current]) > 0*/
559 reflexChain rChain(100, 1);
560 rChain.processNewVertex(topVertex, pStream);
561 for(i=inc_current; i<=inc_end; i++)
563 if(compV2InY(inc_array[i], dec_array[dec_current]) >0)
564 rChain.processNewVertex(inc_array[i], pStream);
568 rChain.outputFan(dec_array[dec_current], pStream);
569 monoTriangulationRecGen(inc_array[i-1], botVertex,
570 inc_chain, i, inc_end,
571 dec_chain, dec_current,dec_end,
574 }/*end case neither is empty*/
577 void monoTriangulationFun(directedLine* monoPolygon, Int (*compFun)(Real*, Real*), primStream* pStream)
580 /*find the top vertex, bottom vertex, inccreasing chain, and decreasing chain,
581 *then call monoTriangulationRec
586 topV = botV = monoPolygon;
587 for(tempV = monoPolygon->getNext(); tempV != monoPolygon; tempV = tempV->getNext())
589 if(compFun(topV->head(), tempV->head())<0) {
592 if(compFun(botV->head(), tempV->head())>0) {
597 /*creat increase and decrease chains*/
598 vertexArray inc_chain(20); /*this is a dynamic array*/
599 for(i=1; i<=topV->get_npoints()-2; i++) { /*the first vertex is the top vertex which doesn't belong to inc_chain*/
600 inc_chain.appendVertex(topV->getVertex(i));
602 for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
604 for(i=0; i<=tempV->get_npoints()-2; i++){
605 inc_chain.appendVertex(tempV->getVertex(i));
609 vertexArray dec_chain(20);
610 for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
612 for(i=tempV->get_npoints()-2; i>=0; i--){
613 dec_chain.appendVertex(tempV->getVertex(i));
616 for(i=botV->get_npoints()-2; i>=1; i--){
617 dec_chain.appendVertex(tempV->getVertex(i));
620 if (!(0 == inc_chain.getNumElements() && 0 == dec_chain.getNumElements())) {
621 monoTriangulationRecFun(topV->head(), botV->head(), &inc_chain, 0,
622 &dec_chain, 0, compFun, pStream);
626 void monoTriangulation(directedLine* monoPolygon, primStream* pStream)
629 /*find the top vertex, bottom vertex, inccreasing chain, and decreasing chain,
630 *then call monoTriangulationRec
635 topV = botV = monoPolygon;
636 for(tempV = monoPolygon->getNext(); tempV != monoPolygon; tempV = tempV->getNext())
638 if(compV2InY(topV->head(), tempV->head())<0) {
641 if(compV2InY(botV->head(), tempV->head())>0) {
645 /*creat increase and decrease chains*/
646 vertexArray inc_chain(20); /*this is a dynamic array*/
647 for(i=1; i<=topV->get_npoints()-2; i++) { /*the first vertex is the top vertex which doesn't belong to inc_chain*/
648 inc_chain.appendVertex(topV->getVertex(i));
650 for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
652 for(i=0; i<=tempV->get_npoints()-2; i++){
653 inc_chain.appendVertex(tempV->getVertex(i));
657 vertexArray dec_chain(20);
658 for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
660 for(i=tempV->get_npoints()-2; i>=0; i--){
661 dec_chain.appendVertex(tempV->getVertex(i));
664 for(i=botV->get_npoints()-2; i>=1; i--){
665 dec_chain.appendVertex(tempV->getVertex(i));
668 monoTriangulationRec(topV->head(), botV->head(), &inc_chain, 0, &dec_chain, 0, pStream);
672 /*the chain could be increasing or decreasing, although we use the
674 *the argument is_increase_chain indicates whether this chain
675 *is increasing (left chain in V-monotone case) or decreaing (right chain
676 *in V-monotone case).
678 void monoTriangulation2(Real* topVertex, Real* botVertex,
679 vertexArray* inc_chain, Int inc_smallIndex,
681 Int is_increase_chain,
684 assert( inc_chain != NULL);
687 if(inc_smallIndex > inc_largeIndex)
688 return; //no triangles
689 if(inc_smallIndex == inc_largeIndex)
691 if(is_increase_chain)
692 pStream->triangle(inc_chain->getVertex(inc_smallIndex), botVertex, topVertex);
694 pStream->triangle(inc_chain->getVertex(inc_smallIndex), topVertex, botVertex);
699 if(is_increase_chain && botVertex[1] == inc_chain->getVertex(inc_largeIndex)[1])
701 pStream->triangle(botVertex, inc_chain->getVertex(inc_largeIndex-1),
702 inc_chain->getVertex(inc_largeIndex));
703 monoTriangulation2(topVertex, botVertex, inc_chain, inc_smallIndex,
709 else if( (!is_increase_chain) && topVertex[1] == inc_chain->getVertex(inc_smallIndex)[1])
711 pStream->triangle(topVertex, inc_chain->getVertex(inc_smallIndex+1),
712 inc_chain->getVertex(inc_smallIndex));
713 monoTriangulation2(topVertex, botVertex, inc_chain, inc_smallIndex+1,
714 inc_largeIndex, is_increase_chain, pStream);
718 inc_array = inc_chain->getArray();
720 reflexChain rChain(20,is_increase_chain); /*1 means the chain is increasing*/
722 rChain.processNewVertex(topVertex, pStream);
724 for(i=inc_smallIndex; i<=inc_largeIndex; i++){
725 rChain.processNewVertex(inc_array[i], pStream);
727 rChain.processNewVertex(botVertex, pStream);
731 /*if compFun == compV2InY, top to bottom: V-monotone
732 *if compFun == compV2InX, right to left: U-monotone
734 void monoTriangulationRecFunGen(Real* topVertex, Real* botVertex,
735 vertexArray* inc_chain, Int inc_current, Int inc_end,
736 vertexArray* dec_chain, Int dec_current, Int dec_end,
737 Int (*compFun)(Real*, Real*),
740 assert( inc_chain != NULL && dec_chain != NULL);
741 assert( ! (inc_current> inc_end &&
742 dec_current> dec_end));
750 assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
752 if(inc_current> inc_end) /*no more vertices on inc_chain*/
755 dec_array = dec_chain->getArray();
756 reflexChain rChain(20,0);
757 /*put the top vertex into the reflex chain*/
758 rChain.processNewVertex(topVertex, pStream);
759 /*process all the vertices on the dec_chain*/
760 for(i=dec_current; i<=dec_end; i++){
761 rChain.processNewVertex(dec_array[i], pStream);
763 /*process the bottom vertex*/
764 rChain.processNewVertex(botVertex, pStream);
767 else if(dec_current> dec_end) /*no more vertices on dec_chain*/
769 inc_array = inc_chain->getArray();
770 reflexChain rChain(20,1);
771 /*put the top vertex into the reflex chain*/
772 rChain.processNewVertex(topVertex, pStream);
773 /*process all the vertices on the inc_chain*/
774 for(i=inc_current; i<=inc_end; i++){
775 rChain.processNewVertex(inc_array[i], pStream);
777 /*process the bottom vertex*/
778 rChain.processNewVertex(botVertex, pStream);
780 else /*neither chain is empty*/
782 inc_array = inc_chain -> getArray();
783 dec_array = dec_chain -> getArray();
785 /*if top of inc_chain is 'lower' than top of dec_chain, process all the
786 *vertices on the dec_chain which are higher than top of inc_chain
788 if(compFun(inc_array[inc_current], dec_array[dec_current]) <= 0)
791 reflexChain rChain(20, 0);
792 rChain.processNewVertex(topVertex, pStream);
793 for(i=dec_current; i<=dec_end; i++)
795 if(compFun(inc_array[inc_current], dec_array[i]) <= 0)
796 rChain.processNewVertex(dec_array[i], pStream);
800 rChain.outputFan(inc_array[inc_current], pStream);
801 monoTriangulationRecFunGen(dec_array[i-1], botVertex,
802 inc_chain, inc_current, inc_end,
803 dec_chain, i, dec_end,
807 else /*compFun(inc_array[inc_current], dec_array[dec_current]) > 0*/
810 reflexChain rChain(20, 1);
811 rChain.processNewVertex(topVertex, pStream);
812 for(i=inc_current; i<=inc_end; i++)
814 if(compFun(inc_array[i], dec_array[dec_current]) >0)
815 rChain.processNewVertex(inc_array[i], pStream);
819 rChain.outputFan(dec_array[dec_current], pStream);
820 monoTriangulationRecFunGen(inc_array[i-1], botVertex,
821 inc_chain, i,inc_end,
822 dec_chain, dec_current,dec_end,
826 }/*end case neither is empty*/
829 /*if compFun == compV2InY, top to bottom: V-monotone
830 *if compFun == compV2InX, right to left: U-monotone
832 void monoTriangulationRecFun(Real* topVertex, Real* botVertex,
833 vertexArray* inc_chain, Int inc_current,
834 vertexArray* dec_chain, Int dec_current,
835 Int (*compFun)(Real*, Real*),
838 assert( inc_chain != NULL && dec_chain != NULL);
839 assert( ! (inc_current>=inc_chain->getNumElements() &&
840 dec_current>=dec_chain->getNumElements()));
846 assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
848 if(inc_current>=inc_chain->getNumElements()) /*no more vertices on inc_chain*/
851 dec_array = dec_chain->getArray();
852 dec_nVertices = dec_chain->getNumElements();
853 reflexChain rChain(20,0);
854 /*put the top vertex into the reflex chain*/
855 rChain.processNewVertex(topVertex, pStream);
856 /*process all the vertices on the dec_chain*/
857 for(i=dec_current; i<dec_nVertices; i++){
858 rChain.processNewVertex(dec_array[i], pStream);
860 /*process the bottom vertex*/
861 rChain.processNewVertex(botVertex, pStream);
864 else if(dec_current>= dec_chain->getNumElements()) /*no more vertices on dec_chain*/
866 inc_array = inc_chain->getArray();
867 inc_nVertices= inc_chain->getNumElements();
868 reflexChain rChain(20,1);
869 /*put the top vertex into the reflex chain*/
870 rChain.processNewVertex(topVertex, pStream);
871 /*process all the vertices on the inc_chain*/
872 for(i=inc_current; i<inc_nVertices; i++){
873 rChain.processNewVertex(inc_array[i], pStream);
875 /*process the bottom vertex*/
876 rChain.processNewVertex(botVertex, pStream);
878 else /*neither chain is empty*/
880 inc_array = inc_chain -> getArray();
881 dec_array = dec_chain -> getArray();
882 inc_nVertices= inc_chain->getNumElements();
883 dec_nVertices= dec_chain->getNumElements();
884 /*if top of inc_chain is 'lower' than top of dec_chain, process all the
885 *vertices on the dec_chain which are higher than top of inc_chain
887 if(compFun(inc_array[inc_current], dec_array[dec_current]) <= 0)
890 reflexChain rChain(20, 0);
891 rChain.processNewVertex(topVertex, pStream);
892 for(i=dec_current; i<dec_nVertices; i++)
894 if(compFun(inc_array[inc_current], dec_array[i]) <= 0)
895 rChain.processNewVertex(dec_array[i], pStream);
899 rChain.outputFan(inc_array[inc_current], pStream);
900 monoTriangulationRecFun(dec_array[i-1], botVertex,
901 inc_chain, inc_current,
906 else /*compFun(inc_array[inc_current], dec_array[dec_current]) > 0*/
909 reflexChain rChain(20, 1);
910 rChain.processNewVertex(topVertex, pStream);
911 for(i=inc_current; i<inc_nVertices; i++)
913 if(compFun(inc_array[i], dec_array[dec_current]) >0)
914 rChain.processNewVertex(inc_array[i], pStream);
918 rChain.outputFan(dec_array[dec_current], pStream);
919 monoTriangulationRecFun(inc_array[i-1], botVertex,
921 dec_chain, dec_current,
925 }/*end case neither is empty*/
929 void monoTriangulationRec(Real* topVertex, Real* botVertex,
930 vertexArray* inc_chain, Int inc_current,
931 vertexArray* dec_chain, Int dec_current,
934 assert( inc_chain != NULL && dec_chain != NULL);
935 assert( ! (inc_current>=inc_chain->getNumElements() &&
936 dec_current>=dec_chain->getNumElements()));
942 assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
944 if(inc_current>=inc_chain->getNumElements()) /*no more vertices on inc_chain*/
947 dec_array = dec_chain->getArray();
948 dec_nVertices = dec_chain->getNumElements();
949 reflexChain rChain(20,0);
950 /*put the top vertex into the reflex chain*/
951 rChain.processNewVertex(topVertex, pStream);
952 /*process all the vertices on the dec_chain*/
953 for(i=dec_current; i<dec_nVertices; i++){
954 rChain.processNewVertex(dec_array[i], pStream);
956 /*process the bottom vertex*/
957 rChain.processNewVertex(botVertex, pStream);
960 else if(dec_current>= dec_chain->getNumElements()) /*no more vertices on dec_chain*/
962 inc_array = inc_chain->getArray();
963 inc_nVertices= inc_chain->getNumElements();
964 reflexChain rChain(20,1);
965 /*put the top vertex into the reflex chain*/
966 rChain.processNewVertex(topVertex, pStream);
967 /*process all the vertices on the inc_chain*/
968 for(i=inc_current; i<inc_nVertices; i++){
969 rChain.processNewVertex(inc_array[i], pStream);
971 /*process the bottom vertex*/
972 rChain.processNewVertex(botVertex, pStream);
974 else /*neither chain is empty*/
976 inc_array = inc_chain -> getArray();
977 dec_array = dec_chain -> getArray();
978 inc_nVertices= inc_chain->getNumElements();
979 dec_nVertices= dec_chain->getNumElements();
980 /*if top of inc_chain is 'lower' than top of dec_chain, process all the
981 *vertices on the dec_chain which are higher than top of inc_chain
983 if(compV2InY(inc_array[inc_current], dec_array[dec_current]) <= 0)
986 reflexChain rChain(20, 0);
987 rChain.processNewVertex(topVertex, pStream);
988 for(i=dec_current; i<dec_nVertices; i++)
990 if(compV2InY(inc_array[inc_current], dec_array[i]) <= 0)
991 rChain.processNewVertex(dec_array[i], pStream);
995 rChain.outputFan(inc_array[inc_current], pStream);
996 monoTriangulationRec(dec_array[i-1], botVertex,
997 inc_chain, inc_current,
1001 else /*compV2InY(inc_array[inc_current], dec_array[dec_current]) > 0*/
1004 reflexChain rChain(20, 1);
1005 rChain.processNewVertex(topVertex, pStream);
1006 for(i=inc_current; i<inc_nVertices; i++)
1008 if(compV2InY(inc_array[i], dec_array[dec_current]) >0)
1009 rChain.processNewVertex(inc_array[i], pStream);
1013 rChain.outputFan(dec_array[dec_current], pStream);
1014 monoTriangulationRec(inc_array[i-1], botVertex,
1016 dec_chain, dec_current,
1019 }/*end case neither is empty*/
1024 /* the name here assumes that the polygon is Y-monotone, but
1025 *this function also works for X-monotone polygons.
1026 * a monotne polygon consists of two extrem verteices: topVertex and botVertex, and
1027 *two monotone chains: inc_chain, and dec_chain. The edges of the increasing chain (inc_chain)
1028 *is ordered by following pointer: next, while the edges of the decreasing chain (dec_chain)
1029 *is ordered by following pointer: prev
1030 * inc_index index the vertex which is the toppest of the inc_chain which we are handling currently.
1031 * dec_index index the vertex which is the toppest of the dec_chain which we are handling currently.
1033 void monoTriangulationRec(directedLine* inc_chain, Int inc_index,
1034 directedLine* dec_chain, Int dec_index,
1035 directedLine* topVertex, Int top_index,
1036 directedLine* botVertex,
1037 primStream* pStream)
1040 directedLine *temp, *oldtemp = NULL;
1041 Int tempIndex, oldtempIndex = 0;
1043 assert(inc_chain != NULL && dec_chain != NULL);
1045 if(inc_chain == botVertex) {
1046 reflexChain rChain(20, 0);
1047 rChain.processNewVertex(topVertex->getVertex(top_index), pStream);
1048 for(i=dec_index; i< dec_chain->get_npoints(); i++){
1049 rChain.processNewVertex(dec_chain->getVertex(i), pStream);
1051 for(temp = dec_chain->getPrev(); temp != botVertex; temp = temp->getPrev())
1053 for(i=0; i<temp->get_npoints(); i++){
1054 rChain.processNewVertex(temp->getVertex(i), pStream);
1058 else if(dec_chain==botVertex) {
1059 reflexChain rChain(20, 1);
1060 rChain.processNewVertex(topVertex->getVertex(top_index), pStream);
1061 for(i=inc_index; i< inc_chain->get_npoints(); i++){
1062 rChain.processNewVertex(inc_chain->getVertex(i), pStream);
1064 for(temp = inc_chain->getPrev(); temp != botVertex; temp = temp->getNext())
1066 for(i=0; i<temp->get_npoints(); i++){
1067 rChain.processNewVertex(temp->getVertex(i), pStream);
1071 else /*neither reached the bottom*/{
1072 if(compV2InY(inc_chain->getVertex(inc_index), dec_chain->getVertex(dec_index)) <=0) {
1073 reflexChain rChain(20, 0);
1074 rChain.processNewVertex(topVertex -> getVertex(top_index), pStream);
1076 tempIndex = dec_index;
1077 while( compV2InY(inc_chain->getVertex(inc_index), temp->getVertex(tempIndex))<=0) {
1079 oldtempIndex = tempIndex;
1080 rChain.processNewVertex(temp->getVertex(tempIndex), pStream);
1082 if(tempIndex == temp->get_npoints()-1){
1084 temp = temp->getPrev();
1090 rChain.outputFan(inc_chain->getVertex(inc_index), pStream);
1091 monoTriangulationRec(inc_chain, inc_index, temp, tempIndex, oldtemp, oldtempIndex, botVertex, pStream);
1094 reflexChain rChain(20, 1);
1095 rChain.processNewVertex(topVertex -> getVertex(top_index), pStream);
1097 tempIndex = inc_index;
1098 while( compV2InY(temp->getVertex(tempIndex), dec_chain->getVertex(dec_index))>0){
1100 oldtempIndex = tempIndex;
1101 rChain.processNewVertex(temp->getVertex(tempIndex), pStream);
1103 if(tempIndex == temp->get_npoints()-1){
1105 temp = temp->getNext();
1111 rChain.outputFan(dec_chain->getVertex(dec_index), pStream);
1112 monoTriangulationRec(temp, tempIndex, dec_chain, dec_index, oldtemp, oldtempIndex, botVertex, pStream);
1114 } /*end case neither reached the bottom*/
1117 /***************************vertexArray begin here**********************************/
1118 vertexArray::vertexArray(Real2* vertices, Int nVertices)
1121 size = index = nVertices;
1122 array = (Real**) malloc(sizeof(Real*) * nVertices);
1124 for(i=0; i<nVertices; i++)
1126 array[i] = vertices[i];
1127 array[i] = vertices[i];
1131 vertexArray::vertexArray(Int s)
1134 array = (Real**) malloc(sizeof(Real*) * s);
1139 vertexArray::~vertexArray()
1144 void vertexArray::appendVertex(Real* ptr)
1148 Real** temp = (Real**) malloc(sizeof(Real*) * (2*size +1));
1150 for(i=0; i<index; i++)
1156 array[index++] = ptr;
1159 void vertexArray::print()
1161 printf("vertex Array:index=%i, size=%i\n", index, size);
1162 for(Int i=0; i<index; i++)
1164 printf("(%f,%f) ", array[i][0], array[i][1]);
1169 /*find the first i such that array[i][1] >= v
1170 * and array[i+1][1] <v
1171 * if index == 0 (the array is empty, return -1.
1172 * if v is above all, return -1.
1173 * if v is below all, return index-1.
1175 Int vertexArray::findIndexAbove(Real v)
1180 else if(array[0][1] < v)
1184 for(i=1; i<index; i++)
1193 /*find the first i<=endIndex such that array[i][1] <= v
1194 * and array[i-1][1] > v
1195 *if sartIndex>endIndex, then return endIndex+1.
1196 *otherwise, startIndex<=endIndex, it is assumed that
1197 * 0<=startIndex<=endIndex<index.
1198 * if v is below all, return endIndex+1
1199 * if v is above all, return startIndex.
1201 Int vertexArray::findIndexBelowGen(Real v, Int startIndex, Int endIndex)
1204 if(startIndex > endIndex)
1206 else if(array[endIndex][1] > v)
1208 else //now array[endIndex][1] <= v
1210 for(i=endIndex-1; i>=startIndex; i--)
1219 /*find the first i<=endIndex such that array[i-1][1] >= v
1220 * and array[i][1] < v
1221 *if sartIndex>endIndex, then return endIndex+1.
1222 *otherwise, startIndex<=endIndex, it is assumed that
1223 * 0<=startIndex<=endIndex<index.
1224 * if v is below or equal to all, return endIndex+1
1225 * if v is strictly above all, return startIndex.
1227 Int vertexArray::findIndexStrictBelowGen(Real v, Int startIndex, Int endIndex)
1230 if(startIndex > endIndex)
1232 else if(array[endIndex][1] >= v)
1234 else //now array[endIndex][1] < v
1236 for(i=endIndex-1; i>=startIndex; i--)
1238 if(array[i][1] >= v)
1245 /*find the first i>startIndex such that array[i-1][1] > v
1246 * and array[i][1] >=v
1247 *if sartIndex>endIndex, then return startIndex-1.
1248 *otherwise, startIndex<=endIndex, it is assumed that
1249 * 0<=startIndex<=endIndex<index.
1250 * if v is strictly above all, return startIndex-1
1251 * if v is strictly below all, return endIndex.
1253 Int vertexArray::findIndexFirstAboveEqualGen(Real v, Int startIndex, Int endIndex)
1257 if(startIndex > endIndex)
1258 return startIndex-1;
1259 else if(array[startIndex][1] < v)
1260 return startIndex-1;
1261 else //now array[startIndex][1] >= v
1264 for(i=startIndex; i<=endIndex; i++)
1266 if(array[i][1] <= v)
1269 if(i>endIndex) // v is strictly below all
1271 else if(array[i][1] == v)
1280 /*find the first i>=startIndex such that array[i][1] >= v
1281 * and array[i+1][1] <v
1282 *if sartIndex>endIndex, then return startIndex-1.
1283 *otherwise, startIndex<=endIndex, it is assumed that
1284 * 0<=startIndex<=endIndex<index.
1285 * if v is above all, return startIndex-1
1286 * if v is below all, return endIndex.
1288 Int vertexArray::findIndexAboveGen(Real v, Int startIndex, Int endIndex)
1291 if(startIndex > endIndex)
1292 return startIndex-1;
1293 else if(array[startIndex][1] < v)
1294 return startIndex-1;
1295 else //now array[startIndex][1] >= v
1297 for(i=startIndex+1; i<=endIndex; i++)
1306 Int vertexArray::findDecreaseChainFromEnd(Int begin, Int end)
1309 Real prevU = array[i][0];
1311 for(i=end-1; i>=begin; i--){
1312 thisU = array[i][0];
1321 //if(V(start) == v, return start, other wise return the
1322 //last i so that V(i)==v
1323 Int vertexArray::skipEqualityFromStart(Real v, Int start, Int end)
1326 if(array[start][1] != v)
1328 //now array[start][1] == v
1329 for(i=start+1; i<= end; i++)
1330 if(array[i][1] != v)
1336 /***************************vertexArray end****************************************/
1340 /***************************relfex chain stuff begin here*****************************/
1342 reflexChain::reflexChain(Int size, Int is_increasing)
1344 queue = (Real2*) malloc(sizeof(Real2) * size);
1348 isIncreasing = is_increasing;
1351 reflexChain::~reflexChain()
1356 /*put (u,v) at the end of the queue
1357 *pay attention to space
1359 void reflexChain::insert(Real u, Real v)
1362 if(index_queue >= size_queue) {
1363 Real2 *temp = (Real2*) malloc(sizeof(Real2) * (2*size_queue+1));
1367 for(i=0; i<index_queue; i++){
1368 temp[i][0] = queue[i][0];
1369 temp[i][1] = queue[i][1];
1374 size_queue = 2*size_queue + 1;
1377 queue[index_queue][0] = u;
1378 queue[index_queue][1] = v;
1382 void reflexChain::insert(Real v[2])
1388 static Real area(Real A[2], Real B[2], Real C[2])
1390 Real Bx, By, Cx, Cy;
1395 return Bx*Cy - Cx*By;
1399 /*the chain is reflex, and the vertex v is
1400 *on the other side of the chain, so that
1401 *we can outout the fan with v as the
1404 void reflexChain::outputFan(Real v[2], primStream* pStream)
1410 for(i=0; i<index_queue; i++)
1411 pStream->insert(queue[i]);
1414 for(i=index_queue-1; i>=0; i--)
1415 pStream->insert(queue[i]);
1417 pStream->end(PRIMITIVE_STREAM_FAN);
1420 void reflexChain::processNewVertex(Real v[2], primStream* pStream)
1424 /*if there are at most one vertex in the queue, then simply insert
1426 if(index_queue <=1){
1431 /*there are at least two vertices in the queue*/
1434 for(i=j; i>=1; i--) {
1436 isReflex = (area(queue[i-1], queue[i], v) <= 0.0);
1438 else /*decreasing*/{
1439 isReflex = (area(v, queue[i], queue[i-1]) <= 0.0);
1447 *if i<j then vertices: i+1--j are convex
1448 * output triangle fan:
1449 * v, and queue[i], i+1, ..., j
1457 pStream->insert(queue[k]);
1461 pStream->insert(queue[k]);
1464 pStream->end(PRIMITIVE_STREAM_FAN);
1467 /*delete vertices i+1--j from the queue*/
1469 /*finally insert v at the end of the queue*/
1474 void reflexChain::print()
1477 printf("reflex chain: isIncreasing=%i\n", isIncreasing);
1478 for(i=0; i<index_queue; i++) {
1479 printf("(%f,%f) ", queue[i][0], queue[i][1]);