dad27e17b08ff79a4fe942e58a40364dce91656f
1 /*
2 * Digraph.h
3 * nlivarot
4 *
5 * Created by fred on Thu Jun 12 2003.
6 *
7 */
9 #ifndef my_shape
10 #define my_shape
12 #include <cmath>
13 #include <cstdio>
14 #include <cstdlib>
15 #include <inttypes.h>
16 #include <cstring>
17 #include <vector>
19 #include "libnr/nr-point.h"
20 #include "livarot/livarot-forward.h"
21 #include "livarot/LivarotDefs.h"
23 struct SweepTree;
24 struct SweepTreeList;
25 struct SweepEventQueue;
27 /*
28 * the Shape class (was the Digraph class, as the header says) stores digraphs (no kidding!) of which
29 * a very interesting kind are polygons.
30 * the main use of this class is the ConvertToShape() (or Booleen(), quite the same) function, which
31 * removes all problems a polygon can present: duplicate points or edges, self-intersection. you end up with a
32 * full-fledged polygon
33 */
35 // possible values for the "type" field in the Shape class:
36 enum
37 {
38 shape_graph = 0, // it's just a graph; a bunch of edges, maybe intersections
39 shape_polygon = 1, // a polygon: intersection-free, edges oriented so that the inside is on their left
40 shape_polypatch = 2 // a graph without intersection; each face is a polygon (not yet used)
41 };
43 class IntLigne;
44 class BitLigne;
45 class AlphaLigne;
47 class Shape
48 {
49 public:
51 struct back_data
52 {
53 int pathID, pieceID;
54 double tSt, tEn;
55 };
57 struct voronoi_point
58 { // info for points treated as points of a voronoi diagram (obtained by MakeShape())
59 double value; // distance to source
60 int winding; // winding relatively to source
61 };
63 struct voronoi_edge
64 { // info for edges, treated as approximation of edges of the voronoi diagram
65 int leF, riF; // left and right site
66 double leStX, leStY, riStX, riStY; // on the left side: (leStX,leStY) is the smallest vector from the source to st
67 // etc...
68 double leEnX, leEnY, riEnX, riEnY;
69 };
71 struct quick_raster_data
72 {
73 double x; // x-position on the sweepline
74 int bord; // index of the edge
75 int ind; // index of qrsData elem for edge (ie inverse of the bord)
76 int next,prev; // dbl linkage
77 };
79 enum sTreeChangeType
80 {
81 EDGE_INSERTED = 0,
82 EDGE_REMOVED = 1,
83 INTERSECTION = 2
84 };
86 struct sTreeChange
87 {
88 sTreeChangeType type; // type of modification to the sweepline:
89 int ptNo; // point at which the modification takes place
91 Shape *src; // left edge (or unique edge if not an intersection) involved in the event
92 int bord;
93 Shape *osrc; // right edge (if intersection)
94 int obord;
95 Shape *lSrc; // edge directly on the left in the sweepline at the moment of the event
96 int lBrd;
97 Shape *rSrc; // edge directly on the right
98 int rBrd;
99 };
101 struct incidenceData
102 {
103 int nextInc; // next incidence in the linked list
104 int pt; // point incident to the edge (there is one list per edge)
105 double theta; // coordinate of the incidence on the edge
106 };
108 Shape();
109 ~Shape();
111 void MakeBackData(bool nVal);
112 void MakeVoronoiData(bool nVal);
114 void Affiche();
116 // insertion/deletion/movement of elements in the graph
117 void Copy(Shape *a);
118 // -reset the graph, and ensure there's room for n points and m edges
119 void Reset(int n = 0, int m = 0);
120 // -points:
121 int AddPoint(const NR::Point x); // as the function name says
122 // returns the index at which the point has been added in the array
123 void SubPoint(int p); // removes the point at index p
124 // nota: this function relocates the last point to the index p
125 // so don't trust point indices if you use SubPoint
126 void SwapPoints(int a, int b); // swaps 2 points at indices a and b
127 void SwapPoints(int a, int b, int c); // swaps 3 points: c <- a <- b <- c
128 void SortPoints(); // sorts the points if needed (checks the need_points_sorting flag)
130 // -edges:
131 // add an edge between points of indices st and en
132 int AddEdge(int st, int en);
133 // return the edge index in the array
135 // add an edge between points of indices st and en
136 int AddEdge(int st, int en, int leF, int riF);
137 // return the edge index in the array
139 // version for the voronoi (with faces IDs)
140 void SubEdge(int e); // removes the edge at index e (same remarks as for SubPoint)
141 void SwapEdges(int a, int b); // swaps 2 edges
142 void SwapEdges(int a, int b, int c); // swaps 3 edges
143 void SortEdges(); // sort the edges if needed (checks the need_edges_sorting falg)
145 // primitives for topological manipulations
147 // endpoint of edge at index b that is different from the point p
148 inline int Other(int p, int b) const
149 {
150 if (getEdge(b).st == p) {
151 return getEdge(b).en;
152 }
153 return getEdge(b).st;
154 }
156 // next edge (after edge b) in the double-linked list at point p
157 inline int NextAt(int p, int b) const
158 {
159 if (p == getEdge(b).st) {
160 return getEdge(b).nextS;
161 }
162 else if (p == getEdge(b).en) {
163 return getEdge(b).nextE;
164 }
166 return -1;
167 }
169 // previous edge
170 inline int PrevAt(int p, int b) const
171 {
172 if (p == getEdge(b).st) {
173 return getEdge(b).prevS;
174 }
175 else if (p == getEdge(b).en) {
176 return getEdge(b).prevE;
177 }
179 return -1;
180 }
182 // same as NextAt, but the list is considered circular
183 inline int CycleNextAt(int p, int b) const
184 {
185 if (p == getEdge(b).st) {
186 if (getEdge(b).nextS < 0) {
187 return getPoint(p).incidentEdge[FIRST];
188 }
189 return getEdge(b).nextS;
190 } else if (p == getEdge(b).en) {
191 if (getEdge(b).nextE < 0) {
192 return getPoint(p).incidentEdge[FIRST];
193 }
195 return getEdge(b).nextE;
196 }
198 return -1;
199 }
201 // same as PrevAt, but the list is considered circular
202 inline int CyclePrevAt(int p, int b) const
203 {
204 if (p == getEdge(b).st) {
205 if (getEdge(b).prevS < 0) {
206 return getPoint(p).incidentEdge[LAST];
207 }
208 return getEdge(b).prevS;
209 } else if (p == getEdge(b).en) {
210 if (getEdge(b).prevE < 0) {
211 return getPoint(p).incidentEdge[LAST];
212 }
213 return getEdge(b).prevE;
214 }
216 return -1;
217 }
219 void ConnectStart(int p, int b); // set the point p as the start of edge b
220 void ConnectEnd(int p, int b); // set the point p as the end of edge b
221 void DisconnectStart(int b); // disconnect edge b from its start point
222 void DisconnectEnd(int b); // disconnect edge b from its end point
224 // reverses edge b (start <-> end)
225 void Inverse(int b);
226 // calc bounding box and sets leftX,rightX,topY and bottomY to their values
227 void CalcBBox(bool strict_degree = false);
229 // debug function: plots the graph (mac only)
230 void Plot(double ix, double iy, double ir, double mx, double my, bool doPoint,
231 bool edgesNo, bool pointNo, bool doDir, char *fileName);
233 // transforms a polygon in a "forme" structure, ie a set of contours, which can be holes (see ShapeUtils.h)
234 // return NULL in case it's not possible
235 void ConvertToForme(Path *dest);
237 // version to use when conversion was done with ConvertWithBackData(): will attempt to merge segment belonging to
238 // the same curve
239 // nota: apparently the function doesn't like very small segments of arc
240 void ConvertToForme(Path *dest, int nbP, Path **orig, bool splitWhenForced = false);
241 // version trying to recover the nesting of subpaths (ie: holes)
242 void ConvertToFormeNested(Path *dest, int nbP, Path **orig, int wildPath, int &nbNest,
243 int *&nesting, int *&contStart, bool splitWhenForced = false);
245 // sweeping a digraph to produce a intersection-free polygon
246 // return 0 if everything is ok and a return code otherwise (see LivarotDefs.h)
247 // the input is the Shape "a"
248 // directed=true <=> non-zero fill rule
249 int ConvertToShape(Shape *a, FillRule directed = fill_nonZero, bool invert = false);
250 // directed=false <=> even-odd fill rule
251 // invert=true: make as if you inverted all edges in the source
252 int Reoriente(Shape *a); // subcase of ConvertToShape: the input a is already intersection-free
253 // all that's missing are the correct directions of the edges
254 // Reoriented is equivalent to ConvertToShape(a,false,false) , but faster sicne
255 // it doesn't computes interections nor adjacencies
256 void ForceToPolygon(); // force the Shape to believe it's a polygon (eulerian+intersection-free+no
257 // duplicate edges+no duplicate points)
258 // be careful when using this function
260 // the coordinate rounding function
261 inline static double Round(double x)
262 {
263 return ldexp(rint(ldexp(x, 5)), -5);
264 }
266 // 2 miscannellous variations on it, to scale to and back the rounding grid
267 inline static double HalfRound(double x)
268 {
269 return ldexp(x, -5);
270 }
272 inline static double IHalfRound(double x)
273 {
274 return ldexp(x, 5);
275 }
277 // boolean operations on polygons (requests intersection-free poylygons)
278 // boolean operation types are defined in LivarotDefs.h
279 // same return code as ConvertToShape
280 int Booleen(Shape *a, Shape *b, BooleanOp mod, int cutPathID = -1);
282 // create a graph that is an offseted version of the graph "of"
283 // the offset is dec, with joins between edges of type "join" (see LivarotDefs.h)
284 // the result is NOT a polygon; you need a subsequent call to ConvertToShape to get a real polygon
285 int MakeOffset(Shape *of, double dec, JoinType join, double miter);
287 int PtWinding(const NR::Point px) const; // plus rapide
288 int Winding(const NR::Point px) const;
290 // rasterization
291 void BeginRaster(float &pos, int &curPt);
292 void EndRaster();
293 void BeginQuickRaster(float &pos, int &curPt);
294 void EndQuickRaster();
296 void Scan(float &pos, int &curP, float to, float step);
297 void QuickScan(float &pos, int &curP, float to, bool doSort, float step);
298 void DirectScan(float &pos, int &curP, float to, float step);
299 void DirectQuickScan(float &pos, int &curP, float to, bool doSort, float step);
301 void Scan(float &pos, int &curP, float to, FloatLigne *line, bool exact, float step);
302 void Scan(float &pos, int &curP, float to, FillRule directed, BitLigne *line, bool exact, float step);
303 void Scan(float &pos, int &curP, float to, AlphaLigne *line, bool exact, float step);
305 void QuickScan(float &pos, int &curP, float to, FloatLigne* line, float step);
306 void QuickScan(float &pos, int &curP, float to, FillRule directed, BitLigne* line, float step);
307 void QuickScan(float &pos, int &curP, float to, AlphaLigne* line, float step);
309 void Transform(NR::Matrix const &tr)
310 {for(std::vector<dg_point>::iterator it=_pts.begin();it!=_pts.end();it++) it->x*=tr;}
312 std::vector<back_data> ebData;
313 std::vector<voronoi_point> vorpData;
314 std::vector<voronoi_edge> voreData;
316 int nbQRas;
317 int firstQRas;
318 int lastQRas;
319 std::vector<quick_raster_data> qrsData;
321 std::vector<sTreeChange> chgts;
322 int nbInc;
323 int maxInc;
325 incidenceData *iData;
326 // these ones are allocated at the beginning of each sweep and freed at the end of the sweep
327 SweepTreeList *sTree;
328 SweepEventQueue *sEvts;
330 // bounding box stuff
331 double leftX, topY, rightX, bottomY;
333 // topological information: who links who?
334 struct dg_point
335 {
336 NR::Point x; // position
337 int dI, dO; // indegree and outdegree
338 int incidentEdge[2]; // first and last incident edge
339 int oldDegree;
341 int totalDegree() const { return dI + dO; }
342 };
344 struct dg_arete
345 {
346 NR::Point dx; // edge vector
347 int st, en; // start and end points of the edge
348 int nextS, prevS; // next and previous edge in the double-linked list at the start point
349 int nextE, prevE; // next and previous edge in the double-linked list at the end point
350 };
352 // lists of the nodes and edges
353 int maxPt; // [FIXME: remove this]
354 int maxAr; // [FIXME: remove this]
356 // flags
357 int type;
359 inline int numberOfPoints() const { return _pts.size(); }
360 inline bool hasPoints() const { return (_pts.empty() == false); }
361 inline int numberOfEdges() const { return _aretes.size(); }
362 inline bool hasEdges() const { return (_aretes.empty() == false); }
364 inline void needPointsSorting() { _need_points_sorting = true; }
365 inline void needEdgesSorting() { _need_edges_sorting = true; }
367 inline bool hasBackData() const { return _has_back_data; }
369 inline dg_point const &getPoint(int n) const { return _pts[n]; }
370 inline dg_arete const &getEdge(int n) const { return _aretes[n]; }
372 private:
374 friend class SweepTree;
375 friend class SweepEvent;
376 friend class SweepEventQueue;
378 // temporary data for the various algorithms
379 struct edge_data
380 {
381 int weight; // weight of the edge (to handle multiple edges)
382 NR::Point rdx; // rounded edge vector
383 double length, sqlength, ilength, isqlength; // length^2, length, 1/length^2, 1/length
384 double siEd, coEd; // siEd=abs(rdy/length) and coEd=rdx/length
385 edge_data() : weight(0), length(0.0), sqlength(0.0), ilength(0.0), isqlength(0.0), siEd(0.0), coEd(0.0) {}
386 // used to determine the "most horizontal" edge between 2 edges
387 };
389 struct sweep_src_data
390 {
391 void *misc; // pointer to the SweepTree* in the sweepline
392 int firstLinkedPoint; // not used
393 int stPt, enPt; // start- end end- points for this edge in the resulting polygon
394 int ind; // for the GetAdjacencies function: index in the sliceSegs array (for quick deletions)
395 int leftRnd, rightRnd; // leftmost and rightmost points (in the result polygon) that are incident to
396 // the edge, for the current sweep position
397 // not set if the edge doesn't start/end or intersect at the current sweep position
398 Shape *nextSh; // nextSh and nextBo identify the next edge in the list
399 int nextBo; // they are used to maintain a linked list of edge that start/end or intersect at
400 // the current sweep position
401 int curPoint, doneTo;
402 double curT;
403 };
405 struct sweep_dest_data
406 {
407 void *misc; // used to check if an edge has already been seen during the depth-first search
408 int suivParc, precParc; // previous and current next edge in the depth-first search
409 int leW, riW; // left and right winding numbers for this edge
410 int ind; // order of the edges during the depth-first search
411 };
413 struct raster_data
414 {
415 SweepTree *misc; // pointer to the associated SweepTree* in the sweepline
416 double lastX, lastY, curX, curY; // curX;curY is the current intersection of the edge with the sweepline
417 // lastX;lastY is the intersection with the previous sweepline
418 bool sens; // true if the edge goes down, false otherwise
419 double calcX; // horizontal position of the intersection of the edge with the
420 // previous sweepline
421 double dxdy, dydx; // horizontal change per unit vertical move of the intersection with the sweepline
422 int guess;
423 };
425 struct point_data
426 {
427 int oldInd, newInd; // back and forth indices used when sorting the points, to know where they have
428 // been relocated in the array
429 int pending; // number of intersection attached to this edge, and also used when sorting arrays
430 int edgeOnLeft; // not used (should help speeding up winding calculations)
431 int nextLinkedPoint; // not used
432 Shape *askForWindingS;
433 int askForWindingB;
434 NR::Point rx; // rounded coordinates of the point
435 };
438 struct edge_list
439 { // temporary array of edges for easier sorting
440 int no;
441 bool starting;
442 NR::Point x;
443 };
445 void initialisePointData();
446 void initialiseEdgeData();
447 void clearIncidenceData();
449 void _countUpDown(int P, int *numberUp, int *numberDown, int *upEdge, int *downEdge) const;
450 void _countUpDownTotalDegree2(int P, int *numberUp, int *numberDown, int *upEdge, int *downEdge) const;
451 void _updateIntersection(int e, int p);
453 // activation/deactivation of the temporary data arrays
454 void MakePointData(bool nVal);
455 void MakeEdgeData(bool nVal);
456 void MakeSweepSrcData(bool nVal);
457 void MakeSweepDestData(bool nVal);
458 void MakeRasterData(bool nVal);
459 void MakeQuickRasterData(bool nVal);
461 void SortPoints(int s, int e);
462 void SortPointsByOldInd(int s, int e);
464 // fonctions annexes pour ConvertToShape et Booleen
465 void ResetSweep(); // allocates sweep structures
466 void CleanupSweep(); // deallocates them
468 // edge sorting function
469 void SortEdgesList(edge_list *edges, int s, int e);
471 void TesteIntersection(SweepTree *t, Side s, bool onlyDiff); // test if there is an intersection
472 bool TesteIntersection(SweepTree *iL, SweepTree *iR, NR::Point &atx, double &atL, double &atR, bool onlyDiff);
473 bool TesteIntersection(Shape *iL, Shape *iR, int ilb, int irb,
474 NR::Point &atx, double &atL, double &atR,
475 bool onlyDiff);
476 bool TesteAdjacency(Shape *iL, int ilb, const NR::Point atx, int nPt,
477 bool push);
478 int PushIncidence(Shape *a, int cb, int pt, double theta);
479 int CreateIncidence(Shape *a, int cb, int pt);
480 void AssemblePoints(Shape *a);
481 int AssemblePoints(int st, int en);
482 void AssembleAretes(FillRule directed = fill_nonZero);
483 void AddChgt(int lastPointNo, int lastChgtPt, Shape *&shapeHead,
484 int &edgeHead, sTreeChangeType type, Shape *lS, int lB, Shape *rS,
485 int rB);
486 void CheckAdjacencies(int lastPointNo, int lastChgtPt, Shape *shapeHead, int edgeHead);
487 void CheckEdges(int lastPointNo, int lastChgtPt, Shape *a, Shape *b, BooleanOp mod);
488 void Avance(int lastPointNo, int lastChgtPt, Shape *iS, int iB, Shape *a, Shape *b, BooleanOp mod);
489 void DoEdgeTo(Shape *iS, int iB, int iTo, bool direct, bool sens);
490 void GetWindings(Shape *a, Shape *b = NULL, BooleanOp mod = bool_op_union, bool brutal = false);
492 void Validate();
494 int Winding(int nPt) const;
495 void SortPointsRounded();
496 void SortPointsRounded(int s, int e);
498 void CreateEdge(int no, float to, float step);
499 void AvanceEdge(int no, float to, bool exact, float step);
500 void DestroyEdge(int no, float to, FloatLigne *line);
501 void AvanceEdge(int no, float to, FloatLigne *line, bool exact, float step);
502 void DestroyEdge(int no, BitLigne *line);
503 void AvanceEdge(int no, float to, BitLigne *line, bool exact, float step);
504 void DestroyEdge(int no, AlphaLigne *line);
505 void AvanceEdge(int no, float to, AlphaLigne *line, bool exact, float step);
507 void AddContour(Path * dest, int nbP, Path **orig, int startBord,
508 int curBord, bool splitWhenForced);
509 int ReFormeLineTo(int bord, int curBord, Path *dest, Path *orig);
510 int ReFormeArcTo(int bord, int curBord, Path *dest, Path *orig);
511 int ReFormeCubicTo(int bord, int curBord, Path *dest, Path *orig);
512 int ReFormeBezierTo(int bord, int curBord, Path *dest, Path *orig);
513 void ReFormeBezierChunk(const NR::Point px, const NR::Point nx,
514 Path *dest, int inBezier, int nbInterm,
515 Path *from, int p, double ts, double te);
517 int QuickRasterChgEdge(int oBord, int nbord, double x);
518 int QuickRasterAddEdge(int bord, double x, int guess);
519 void QuickRasterSubEdge(int bord);
520 void QuickRasterSwapEdge(int a, int b);
521 void QuickRasterSort();
523 bool _need_points_sorting; ///< points have been added or removed: we need to sort the points again
524 bool _need_edges_sorting; ///< edges have been added: maybe they are not ordered clockwise
525 ///< nota: if you remove an edge, the clockwise order still holds
526 bool _has_points_data; ///< the pData array is allocated
527 bool _has_edges_data; ///< the eData array is allocated
528 bool _has_sweep_src_data; ///< the swsData array is allocated
529 bool _has_sweep_dest_data; ///< the swdData array is allocated
530 bool _has_raster_data; ///< the swrData array is allocated
531 bool _has_quick_raster_data;///< the swrData array is allocated
532 bool _has_back_data; //< the ebData array is allocated
533 bool _has_voronoi_data;
535 std::vector<dg_point> _pts;
536 std::vector<dg_arete> _aretes;
538 // the arrays of temporary data
539 // these ones are dynamically kept at a length of maxPt or maxAr
540 std::vector<edge_data> eData;
541 std::vector<sweep_src_data> swsData;
542 std::vector<sweep_dest_data> swdData;
543 std::vector<raster_data> swrData;
544 std::vector<point_data> pData;
546 static int CmpQRs(const quick_raster_data &p1, const quick_raster_data &p2) {
547 if ( fabs(p1.x - p2.x) < 0.00001 ) {
548 return 0;
549 }
551 return ( ( p1.x < p2.x ) ? -1 : 1 );
552 };
554 // edge direction comparison function
555 static int CmpToVert(const NR::Point ax, const NR::Point bx, bool as, bool bs);
556 };
558 bool directedEulerian(Shape const *s);
559 double distance(Shape const *s, NR::Point const &p);
560 bool distanceLessThanOrEqual(Shape const *s, NR::Point const &p, double const max_l2);
562 #endif