/* tessMeshTessellateMonoRegion( face ) tessellates a monotone region
* (what else would it do??) The region must consist of a single
* loop of half-edges (see mesh.h) oriented CCW. "Monotone" in this
* case means that any vertical line intersects the interior of the
* region in a single interval.
*
* Tessellation consists of adding interior edges (actually pairs of
* half-edges), to split the region into non-overlapping triangles.
*
* The basic idea is explained in Preparata and Shamos (which I don''t
* have handy right now), although their implementation is more
* complicated than this one. The are two edge chains, an upper chain
* and a lower chain. We process all vertices from both chains in order,
* from right to left.
*
* The algorithm ensures that the following invariant holds after each
* vertex is processed: the untessellated region consists of two
* chains, where one chain (say the upper) is a single edge, and
* the other chain is concave. The left vertex of the single edge
* is always to the left of all vertices in the concave chain.
*
* Each step consists of adding the rightmost unprocessed vertex to one
* of the two chains, and forming a fan of triangles from the rightmost
* of two chain endpoints. Determining whether we can add each triangle
* to the fan is a simple orientation test. By making the fan as large
* as possible, we restore the invariant (check it yourself).
*/
int tessMeshTessellateMonoRegion( TESSmesh *mesh, TESSface *face )
{
TESShalfEdge *up, *lo;
/* All edges are oriented CCW around the boundary of the region.
* First, find the half-edge whose origin vertex is rightmost.
* Since the sweep goes from left to right, face->anEdge should
* be close to the edge we want.
*/
up = face->anEdge;
if(!( up->Lnext != up && up->Lnext->Lnext != up )) return 1;
for( ; VertLeq( up->Dst, up->Org ); up = up->Lprev )
;
for( ; VertLeq( up->Org, up->Dst ); up = up->Lnext )
;
lo = up->Lprev;
while( up->Lnext != lo ) {
if( VertLeq( up->Dst, lo->Org )) {
/* up->Dst is on the left. It is safe to form triangles from lo->Org.
* The EdgeGoesLeft test guarantees progress even when some triangles
* are CW, given that the upper and lower chains are truly monotone.
*/
while( lo->Lnext != up && (EdgeGoesLeft( lo->Lnext )
|| EdgeSign( lo->Org, lo->Dst, lo->Lnext->Dst ) <= 0 )) {
TESShalfEdge *tempHalfEdge= tessMeshConnect( mesh, lo->Lnext, lo );
if (tempHalfEdge == NULL) return 0;
lo = tempHalfEdge->Sym;
}
lo = lo->Lprev;
} else {
/* lo->Org is on the left. We can make CCW triangles from up->Dst. */
while( lo->Lnext != up && (EdgeGoesRight( up->Lprev )
|| EdgeSign( up->Dst, up->Org, up->Lprev->Org ) >= 0 )) {
TESShalfEdge *tempHalfEdge= tessMeshConnect( mesh, up, up->Lprev );
if (tempHalfEdge == NULL) return 0;
up = tempHalfEdge->Sym;
}
up = up->Lnext;
}
}
/* Now lo->Org == up->Dst == the leftmost vertex. The remaining region
* can be tessellated in a fan from this leftmost vertex.
*/
if( lo->Lnext == up ) return 1;
while( lo->Lnext->Lnext != up ) {
TESShalfEdge *tempHalfEdge= tessMeshConnect( mesh, lo->Lnext, lo );
if (tempHalfEdge == NULL) return 0;
lo = tempHalfEdge->Sym;
}
return 1;
}
static TESShalfEdge *FinishLeftRegions( TESStesselator *tess,
ActiveRegion *regFirst, ActiveRegion *regLast )
/*
* We are given a vertex with one or more left-going edges. All affected
* edges should be in the edge dictionary. Starting at regFirst->eUp,
* we walk down deleting all regions where both edges have the same
* origin vOrg. At the same time we copy the "inside" flag from the
* active region to the face, since at this point each face will belong
* to at most one region (this was not necessarily true until this point
* in the sweep). The walk stops at the region above regLast; if regLast
* is NULL we walk as far as possible. At the same time we relink the
* mesh if necessary, so that the ordering of edges around vOrg is the
* same as in the dictionary.
*/
{
ActiveRegion *reg, *regPrev;
TESShalfEdge *e, *ePrev;
regPrev = regFirst;
ePrev = regFirst->eUp;
while( regPrev != regLast ) {
regPrev->fixUpperEdge = FALSE; /* placement was OK */
reg = RegionBelow( regPrev );
e = reg->eUp;
if( e->Org != ePrev->Org ) {
if( ! reg->fixUpperEdge ) {
/* Remove the last left-going edge. Even though there are no further
* edges in the dictionary with this origin, there may be further
* such edges in the mesh (if we are adding left edges to a vertex
* that has already been processed). Thus it is important to call
* FinishRegion rather than just DeleteRegion.
*/
FinishRegion( tess, regPrev );
break;
}
/* If the edge below was a temporary edge introduced by
* ConnectRightVertex, now is the time to fix it.
*/
e = tessMeshConnect( tess->mesh, ePrev->Lprev, e->Sym );
if (e == NULL) longjmp(tess->env,1);
if ( !FixUpperEdge( tess, reg, e ) ) longjmp(tess->env,1);
}
/* Relink edges so that ePrev->Onext == e */
if( ePrev->Onext != e ) {
if ( !tessMeshSplice( tess->mesh, e->Oprev, e ) ) longjmp(tess->env,1);
if ( !tessMeshSplice( tess->mesh, ePrev, e ) ) longjmp(tess->env,1);
}
FinishRegion( tess, regPrev ); /* may change reg->eUp */
ePrev = reg->eUp;
regPrev = reg;
}
return ePrev;
}
static ActiveRegion *TopLeftRegion( TESStesselator *tess, ActiveRegion *reg )
{
TESSvertex *org = reg->eUp->Org;
TESShalfEdge *e;
/* Find the region above the uppermost edge with the same origin */
do {
reg = RegionAbove( reg );
} while( reg->eUp->Org == org );
/* If the edge above was a temporary edge introduced by ConnectRightVertex,
* now is the time to fix it.
*/
if( reg->fixUpperEdge ) {
e = tessMeshConnect( tess->mesh, RegionBelow(reg)->eUp->Sym, reg->eUp->Lnext );
if (e == NULL) return NULL;
if ( !FixUpperEdge( tess, reg, e ) ) return NULL;
reg = RegionAbove( reg );
}
return reg;
}
static void ConnectLeftVertex( TESStesselator *tess, TESSvertex *vEvent )
/*
* Purpose: connect a "left" vertex (one where both edges go right)
* to the processed portion of the mesh. Let R be the active region
* containing vEvent, and let U and L be the upper and lower edge
* chains of R. There are two possibilities:
*
* - the normal case: split R into two regions, by connecting vEvent to
* the rightmost vertex of U or L lying to the left of the sweep line
*
* - the degenerate case: if vEvent is close enough to U or L, we
* merge vEvent into that edge chain. The subcases are:
* - merging with the rightmost vertex of U or L
* - merging with the active edge of U or L
* - merging with an already-processed portion of U or L
*/
{
ActiveRegion *regUp, *regLo, *reg;
TESShalfEdge *eUp, *eLo, *eNew;
ActiveRegion tmp;
/* assert( vEvent->anEdge->Onext->Onext == vEvent->anEdge ); */
/* Get a pointer to the active region containing vEvent */
tmp.eUp = vEvent->anEdge->Sym;
/* __GL_DICTLISTKEY */ /* tessDictListSearch */
regUp = (ActiveRegion *)dictKey( dictSearch( tess->dict, &tmp ));
regLo = RegionBelow( regUp );
if( !regLo ) {
// This may happen if the input polygon is coplanar.
return;
}
eUp = regUp->eUp;
eLo = regLo->eUp;
/* Try merging with U or L first */
if( EdgeSign( eUp->Dst, vEvent, eUp->Org ) == 0 ) {
ConnectLeftDegenerate( tess, regUp, vEvent );
return;
}
/* Connect vEvent to rightmost processed vertex of either chain.
* e->Dst is the vertex that we will connect to vEvent.
*/
reg = VertLeq( eLo->Dst, eUp->Dst ) ? regUp : regLo;
if( regUp->inside || reg->fixUpperEdge) {
if( reg == regUp ) {
eNew = tessMeshConnect( tess->mesh, vEvent->anEdge->Sym, eUp->Lnext );
if (eNew == NULL) longjmp(tess->env,1);
} else {
TESShalfEdge *tempHalfEdge= tessMeshConnect( tess->mesh, eLo->Dnext, vEvent->anEdge);
if (tempHalfEdge == NULL) longjmp(tess->env,1);
eNew = tempHalfEdge->Sym;
}
if( reg->fixUpperEdge ) {
if ( !FixUpperEdge( tess, reg, eNew ) ) longjmp(tess->env,1);
} else {
ComputeWinding( tess, AddRegionBelow( tess, regUp, eNew ));
}
SweepEvent( tess, vEvent );
} else {
/* The new vertex is in a region which does not belong to the polygon.
* We don''t need to connect this vertex to the rest of the mesh.
*/
AddRightEdges( tess, regUp, vEvent->anEdge, vEvent->anEdge, NULL, TRUE );
}
}
static void ConnectRightVertex( TESStesselator *tess, ActiveRegion *regUp,
TESShalfEdge *eBottomLeft )
/*
* Purpose: connect a "right" vertex vEvent (one where all edges go left)
* to the unprocessed portion of the mesh. Since there are no right-going
* edges, two regions (one above vEvent and one below) are being merged
* into one. "regUp" is the upper of these two regions.
*
* There are two reasons for doing this (adding a right-going edge):
* - if the two regions being merged are "inside", we must add an edge
* to keep them separated (the combined region would not be monotone).
* - in any case, we must leave some record of vEvent in the dictionary,
* so that we can merge vEvent with features that we have not seen yet.
* For example, maybe there is a vertical edge which passes just to
* the right of vEvent; we would like to splice vEvent into this edge.
*
* However, we don't want to connect vEvent to just any vertex. We don''t
* want the new edge to cross any other edges; otherwise we will create
* intersection vertices even when the input data had no self-intersections.
* (This is a bad thing; if the user's input data has no intersections,
* we don't want to generate any false intersections ourselves.)
*
* Our eventual goal is to connect vEvent to the leftmost unprocessed
* vertex of the combined region (the union of regUp and regLo).
* But because of unseen vertices with all right-going edges, and also
* new vertices which may be created by edge intersections, we don''t
* know where that leftmost unprocessed vertex is. In the meantime, we
* connect vEvent to the closest vertex of either chain, and mark the region
* as "fixUpperEdge". This flag says to delete and reconnect this edge
* to the next processed vertex on the boundary of the combined region.
* Quite possibly the vertex we connected to will turn out to be the
* closest one, in which case we won''t need to make any changes.
*/
{
TESShalfEdge *eNew;
TESShalfEdge *eTopLeft = eBottomLeft->Onext;
ActiveRegion *regLo = RegionBelow(regUp);
TESShalfEdge *eUp = regUp->eUp;
TESShalfEdge *eLo = regLo->eUp;
int degenerate = FALSE;
if( eUp->Dst != eLo->Dst ) {
(void) CheckForIntersect( tess, regUp );
}
/* Possible new degeneracies: upper or lower edge of regUp may pass
* through vEvent, or may coincide with new intersection vertex
*/
if( VertEq( eUp->Org, tess->event )) {
if ( !tessMeshSplice( tess->mesh, eTopLeft->Oprev, eUp ) ) longjmp(tess->env,1);
regUp = TopLeftRegion( tess, regUp );
if (regUp == NULL) longjmp(tess->env,1);
eTopLeft = RegionBelow( regUp )->eUp;
FinishLeftRegions( tess, RegionBelow(regUp), regLo );
degenerate = TRUE;
}
if( VertEq( eLo->Org, tess->event )) {
if ( !tessMeshSplice( tess->mesh, eBottomLeft, eLo->Oprev ) ) longjmp(tess->env,1);
eBottomLeft = FinishLeftRegions( tess, regLo, NULL );
degenerate = TRUE;
}
if( degenerate ) {
AddRightEdges( tess, regUp, eBottomLeft->Onext, eTopLeft, eTopLeft, TRUE );
return;
}
/* Non-degenerate situation -- need to add a temporary, fixable edge.
* Connect to the closer of eLo->Org, eUp->Org.
*/
if( VertLeq( eLo->Org, eUp->Org )) {
eNew = eLo->Oprev;
} else {
eNew = eUp;
}
eNew = tessMeshConnect( tess->mesh, eBottomLeft->Lprev, eNew );
if (eNew == NULL) longjmp(tess->env,1);
/* Prevent cleanup, otherwise eNew might disappear before we've even
* had a chance to mark it as a temporary edge.
*/
AddRightEdges( tess, regUp, eNew, eNew->Onext, eNew->Onext, FALSE );
eNew->Sym->activeRegion->fixUpperEdge = TRUE;
WalkDirtyRegions( tess, regUp );
}
