static int CheckForRightSplice( TESStesselator *tess, ActiveRegion *regUp ) /* * Check the upper and lower edge of "regUp", to make sure that the * eUp->Org is above eLo, or eLo->Org is below eUp (depending on which * origin is leftmost). * * The main purpose is to splice right-going edges with the same * dest vertex and nearly identical slopes (ie. we can't distinguish * the slopes numerically). However the splicing can also help us * to recover from numerical errors. For example, suppose at one * point we checked eUp and eLo, and decided that eUp->Org is barely * above eLo. Then later, we split eLo into two edges (eg. from * a splice operation like this one). This can change the result of * our test so that now eUp->Org is incident to eLo, or barely below it. * We must correct this condition to maintain the dictionary invariants. * * One possibility is to check these edges for intersection again * (ie. CheckForIntersect). This is what we do if possible. However * CheckForIntersect requires that tess->event lies between eUp and eLo, * so that it has something to fall back on when the intersection * calculation gives us an unusable answer. So, for those cases where * we can't check for intersection, this routine fixes the problem * by just splicing the offending vertex into the other edge. * This is a guaranteed solution, no matter how degenerate things get. * Basically this is a combinatorial solution to a numerical problem. */ { ActiveRegion *regLo = RegionBelow(regUp); TESShalfEdge *eUp = regUp->eUp; TESShalfEdge *eLo = regLo->eUp; if( VertLeq( eUp->Org, eLo->Org )) { if( EdgeSign( eLo->Dst, eUp->Org, eLo->Org ) > 0 ) return FALSE; /* eUp->Org appears to be below eLo */ if( ! VertEq( eUp->Org, eLo->Org )) { /* Splice eUp->Org into eLo */ if ( tessMeshSplitEdge( tess->mesh, eLo->Sym ) == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eUp, eLo->Oprev ) ) longjmp(tess->env,1); regUp->dirty = regLo->dirty = TRUE; } else if( eUp->Org != eLo->Org ) { /* merge the two vertices, discarding eUp->Org */ pqDelete( tess->pq, eUp->Org->pqHandle ); SpliceMergeVertices( tess, eLo->Oprev, eUp ); } } else { if( EdgeSign( eUp->Dst, eLo->Org, eUp->Org ) < 0 ) return FALSE; /* eLo->Org appears to be above eUp, so splice eLo->Org into eUp */ RegionAbove(regUp)->dirty = regUp->dirty = TRUE; if (tessMeshSplitEdge( tess->mesh, eUp->Sym ) == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eLo->Oprev, eUp ) ) longjmp(tess->env,1); } return TRUE; }
static int CheckForLeftSplice( TESStesselator *tess, ActiveRegion *regUp ) /* * Check the upper and lower edge of "regUp", to make sure that the * eUp->Dst is above eLo, or eLo->Dst is below eUp (depending on which * destination is rightmost). * * Theoretically, this should always be true. However, splitting an edge * into two pieces can change the results of previous tests. For example, * suppose at one point we checked eUp and eLo, and decided that eUp->Dst * is barely above eLo. Then later, we split eLo into two edges (eg. from * a splice operation like this one). This can change the result of * the test so that now eUp->Dst is incident to eLo, or barely below it. * We must correct this condition to maintain the dictionary invariants * (otherwise new edges might get inserted in the wrong place in the * dictionary, and bad stuff will happen). * * We fix the problem by just splicing the offending vertex into the * other edge. */ { ActiveRegion *regLo = RegionBelow(regUp); TESShalfEdge *eUp = regUp->eUp; TESShalfEdge *eLo = regLo->eUp; TESShalfEdge *e; assert( ! VertEq( eUp->Dst, eLo->Dst )); if( VertLeq( eUp->Dst, eLo->Dst )) { if( EdgeSign( eUp->Dst, eLo->Dst, eUp->Org ) < 0 ) return FALSE; /* eLo->Dst is above eUp, so splice eLo->Dst into eUp */ RegionAbove(regUp)->dirty = regUp->dirty = TRUE; e = tessMeshSplitEdge( tess->mesh, eUp ); if (e == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eLo->Sym, e ) ) longjmp(tess->env,1); e->Lface->inside = regUp->inside; } else { if( EdgeSign( eLo->Dst, eUp->Dst, eLo->Org ) > 0 ) return FALSE; /* eUp->Dst is below eLo, so splice eUp->Dst into eLo */ regUp->dirty = regLo->dirty = TRUE; e = tessMeshSplitEdge( tess->mesh, eLo ); if (e == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eUp->Lnext, eLo->Sym ) ) longjmp(tess->env,1); e->Rface->inside = regUp->inside; } return TRUE; }
static void ConnectLeftDegenerate( TESStesselator *tess, ActiveRegion *regUp, TESSvertex *vEvent ) /* * The event vertex lies exacty on an already-processed edge or vertex. * Adding the new vertex involves splicing it into the already-processed * part of the mesh. */ { TESShalfEdge *e, *eTopLeft, *eTopRight, *eLast; ActiveRegion *reg; e = regUp->eUp; if( VertEq( e->Org, vEvent )) { /* e->Org is an unprocessed vertex - just combine them, and wait * for e->Org to be pulled from the queue */ assert( TOLERANCE_NONZERO ); SpliceMergeVertices( tess, e, vEvent->anEdge ); return; } if( ! VertEq( e->Dst, vEvent )) { /* General case -- splice vEvent into edge e which passes through it */ if (tessMeshSplitEdge( tess->mesh, e->Sym ) == NULL) longjmp(tess->env,1); if( regUp->fixUpperEdge ) { /* This edge was fixable -- delete unused portion of original edge */ if ( !tessMeshDelete( tess->mesh, e->Onext ) ) longjmp(tess->env,1); regUp->fixUpperEdge = FALSE; } if ( !tessMeshSplice( tess->mesh, vEvent->anEdge, e ) ) longjmp(tess->env,1); SweepEvent( tess, vEvent ); /* recurse */ return; } /* vEvent coincides with e->Dst, which has already been processed. * Splice in the additional right-going edges. */ assert( TOLERANCE_NONZERO ); regUp = TopRightRegion( regUp ); reg = RegionBelow( regUp ); eTopRight = reg->eUp->Sym; eTopLeft = eLast = eTopRight->Onext; if( reg->fixUpperEdge ) { /* Here e->Dst has only a single fixable edge going right. * We can delete it since now we have some real right-going edges. */ assert( eTopLeft != eTopRight ); /* there are some left edges too */ DeleteRegion( tess, reg ); if ( !tessMeshDelete( tess->mesh, eTopRight ) ) longjmp(tess->env,1); eTopRight = eTopLeft->Oprev; } if ( !tessMeshSplice( tess->mesh, vEvent->anEdge, eTopRight ) ) longjmp(tess->env,1); if( ! EdgeGoesLeft( eTopLeft )) { /* e->Dst had no left-going edges -- indicate this to AddRightEdges() */ eTopLeft = NULL; } AddRightEdges( tess, regUp, eTopRight->Onext, eLast, eTopLeft, TRUE ); }
void tessAddContour( TESStesselator *tess, int size, const void* vertices, int stride, int numVertices ) { const unsigned char *src = (const unsigned char*)vertices; TESShalfEdge *e; int i; if ( tess->mesh == NULL ) tess->mesh = tessMeshNewMesh( &tess->alloc ); if ( tess->mesh == NULL ) { tess->outOfMemory = 1; return; } if ( size < 2 ) size = 2; if ( size > 3 ) size = 3; e = NULL; for( i = 0; i < numVertices; ++i ) { const TESSreal* coords = (const TESSreal*)src; src += stride; if( e == NULL ) { /* Make a self-loop (one vertex, one edge). */ e = tessMeshMakeEdge( tess->mesh ); if ( e == NULL ) { tess->outOfMemory = 1; return; } if ( !tessMeshSplice( tess->mesh, e, e->Sym ) ) { tess->outOfMemory = 1; return; } } else { /* Create a new vertex and edge which immediately follow e * in the ordering around the left face. */ if ( tessMeshSplitEdge( tess->mesh, e ) == NULL ) { tess->outOfMemory = 1; return; } e = e->Lnext; } /* The new vertex is now e->Org. */ e->Org->coords[0] = coords[0]; e->Org->coords[1] = coords[1]; if ( size > 2 ) e->Org->coords[2] = coords[2]; else e->Org->coords[2] = 0; /* Store the insertion number so that the vertex can be later recognized. */ e->Org->idx = tess->vertexIndexCounter++; /* The winding of an edge says how the winding number changes as we * cross from the edge''s right face to its left face. We add the * vertices in such an order that a CCW contour will add +1 to * the winding number of the region inside the contour. */ e->winding = 1; e->Sym->winding = -1; } }
static int CheckForIntersect( TESStesselator *tess, ActiveRegion *regUp ) /* * Check the upper and lower edges of the given region to see if * they intersect. If so, create the intersection and add it * to the data structures. * * Returns TRUE if adding the new intersection resulted in a recursive * call to AddRightEdges(); in this case all "dirty" regions have been * checked for intersections, and possibly regUp has been deleted. */ { ActiveRegion *regLo = RegionBelow(regUp); TESShalfEdge *eUp = regUp->eUp; TESShalfEdge *eLo = regLo->eUp; TESSvertex *orgUp = eUp->Org; TESSvertex *orgLo = eLo->Org; TESSvertex *dstUp = eUp->Dst; TESSvertex *dstLo = eLo->Dst; TESSreal tMinUp, tMaxLo; TESSvertex isect, *orgMin; TESShalfEdge *e; assert( ! VertEq( dstLo, dstUp )); assert( EdgeSign( dstUp, tess->event, orgUp ) <= 0 ); assert( EdgeSign( dstLo, tess->event, orgLo ) >= 0 ); assert( orgUp != tess->event && orgLo != tess->event ); assert( ! regUp->fixUpperEdge && ! regLo->fixUpperEdge ); if( orgUp == orgLo ) return FALSE; /* right endpoints are the same */ tMinUp = MIN( orgUp->t, dstUp->t ); tMaxLo = MAX( orgLo->t, dstLo->t ); if( tMinUp > tMaxLo ) return FALSE; /* t ranges do not overlap */ if( VertLeq( orgUp, orgLo )) { if( EdgeSign( dstLo, orgUp, orgLo ) > 0 ) return FALSE; } else { if( EdgeSign( dstUp, orgLo, orgUp ) < 0 ) return FALSE; } /* At this point the edges intersect, at least marginally */ DebugEvent( tess ); tesedgeIntersect( dstUp, orgUp, dstLo, orgLo, &isect ); /* The following properties are guaranteed: */ assert( MIN( orgUp->t, dstUp->t ) <= isect.t ); assert( isect.t <= MAX( orgLo->t, dstLo->t )); assert( MIN( dstLo->s, dstUp->s ) <= isect.s ); assert( isect.s <= MAX( orgLo->s, orgUp->s )); if( VertLeq( &isect, tess->event )) { /* The intersection point lies slightly to the left of the sweep line, * so move it until it''s slightly to the right of the sweep line. * (If we had perfect numerical precision, this would never happen * in the first place). The easiest and safest thing to do is * replace the intersection by tess->event. */ isect.s = tess->event->s; isect.t = tess->event->t; } /* Similarly, if the computed intersection lies to the right of the * rightmost origin (which should rarely happen), it can cause * unbelievable inefficiency on sufficiently degenerate inputs. * (If you have the test program, try running test54.d with the * "X zoom" option turned on). */ orgMin = VertLeq( orgUp, orgLo ) ? orgUp : orgLo; if( VertLeq( orgMin, &isect )) { isect.s = orgMin->s; isect.t = orgMin->t; } if( VertEq( &isect, orgUp ) || VertEq( &isect, orgLo )) { /* Easy case -- intersection at one of the right endpoints */ (void) CheckForRightSplice( tess, regUp ); return FALSE; } if( (! VertEq( dstUp, tess->event ) && EdgeSign( dstUp, tess->event, &isect ) >= 0) || (! VertEq( dstLo, tess->event ) && EdgeSign( dstLo, tess->event, &isect ) <= 0 )) { /* Very unusual -- the new upper or lower edge would pass on the * wrong side of the sweep event, or through it. This can happen * due to very small numerical errors in the intersection calculation. */ if( dstLo == tess->event ) { /* Splice dstLo into eUp, and process the new region(s) */ if (tessMeshSplitEdge( tess->mesh, eUp->Sym ) == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eLo->Sym, eUp ) ) longjmp(tess->env,1); regUp = TopLeftRegion( tess, regUp ); if (regUp == NULL) longjmp(tess->env,1); eUp = RegionBelow(regUp)->eUp; FinishLeftRegions( tess, RegionBelow(regUp), regLo ); AddRightEdges( tess, regUp, eUp->Oprev, eUp, eUp, TRUE ); return TRUE; } if( dstUp == tess->event ) { /* Splice dstUp into eLo, and process the new region(s) */ if (tessMeshSplitEdge( tess->mesh, eLo->Sym ) == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eUp->Lnext, eLo->Oprev ) ) longjmp(tess->env,1); regLo = regUp; regUp = TopRightRegion( regUp ); e = RegionBelow(regUp)->eUp->Rprev; regLo->eUp = eLo->Oprev; eLo = FinishLeftRegions( tess, regLo, NULL ); AddRightEdges( tess, regUp, eLo->Onext, eUp->Rprev, e, TRUE ); return TRUE; } /* Special case: called from ConnectRightVertex. If either * edge passes on the wrong side of tess->event, split it * (and wait for ConnectRightVertex to splice it appropriately). */ if( EdgeSign( dstUp, tess->event, &isect ) >= 0 ) { RegionAbove(regUp)->dirty = regUp->dirty = TRUE; if (tessMeshSplitEdge( tess->mesh, eUp->Sym ) == NULL) longjmp(tess->env,1); eUp->Org->s = tess->event->s; eUp->Org->t = tess->event->t; } if( EdgeSign( dstLo, tess->event, &isect ) <= 0 ) { regUp->dirty = regLo->dirty = TRUE; if (tessMeshSplitEdge( tess->mesh, eLo->Sym ) == NULL) longjmp(tess->env,1); eLo->Org->s = tess->event->s; eLo->Org->t = tess->event->t; } /* leave the rest for ConnectRightVertex */ return FALSE; } /* General case -- split both edges, splice into new vertex. * When we do the splice operation, the order of the arguments is * arbitrary as far as correctness goes. However, when the operation * creates a new face, the work done is proportional to the size of * the new face. We expect the faces in the processed part of * the mesh (ie. eUp->Lface) to be smaller than the faces in the * unprocessed original contours (which will be eLo->Oprev->Lface). */ if (tessMeshSplitEdge( tess->mesh, eUp->Sym ) == NULL) longjmp(tess->env,1); if (tessMeshSplitEdge( tess->mesh, eLo->Sym ) == NULL) longjmp(tess->env,1); if ( !tessMeshSplice( tess->mesh, eLo->Oprev, eUp ) ) longjmp(tess->env,1); eUp->Org->s = isect.s; eUp->Org->t = isect.t; eUp->Org->pqHandle = pqInsert( &tess->alloc, tess->pq, eUp->Org ); if (eUp->Org->pqHandle == INV_HANDLE) { pqDeletePriorityQ( &tess->alloc, tess->pq ); tess->pq = NULL; longjmp(tess->env,1); } GetIntersectData( tess, eUp->Org, orgUp, dstUp, orgLo, dstLo ); RegionAbove(regUp)->dirty = regUp->dirty = regLo->dirty = TRUE; return FALSE; }