int tessComputeInterior( TESStesselator *tess )
/*
* tessComputeInterior( tess ) computes the planar arrangement specified
* by the given contours, and further subdivides this arrangement
* into regions. Each region is marked "inside" if it belongs
* to the polygon, according to the rule given by tess->windingRule.
* Each interior region is guaranteed be monotone.
*/
{
TESSvertex *v, *vNext;
/* Each vertex defines an event for our sweep line. Start by inserting
* all the vertices in a priority queue. Events are processed in
* lexicographic order, ie.
*
* e1 < e2 iff e1.x < e2.x || (e1.x == e2.x && e1.y < e2.y)
*/
RemoveDegenerateEdges( tess );
if ( !InitPriorityQ( tess ) ) return 0; /* if error */
InitEdgeDict( tess );
while( (v = (TESSvertex *)pqExtractMin( tess->pq )) != NULL ) {
for( ;; ) {
vNext = (TESSvertex *)pqMinimum( tess->pq );
if( vNext == NULL || ! VertEq( vNext, v )) break;
/* Merge together all vertices at exactly the same location.
* This is more efficient than processing them one at a time,
* simplifies the code (see ConnectLeftDegenerate), and is also
* important for correct handling of certain degenerate cases.
* For example, suppose there are two identical edges A and B
* that belong to different contours (so without this code they would
* be processed by separate sweep events). Suppose another edge C
* crosses A and B from above. When A is processed, we split it
* at its intersection point with C. However this also splits C,
* so when we insert B we may compute a slightly different
* intersection point. This might leave two edges with a small
* gap between them. This kind of error is especially obvious
* when using boundary extraction (TESS_BOUNDARY_ONLY).
*/
vNext = (TESSvertex *)pqExtractMin( tess->pq );
SpliceMergeVertices( tess, v->anEdge, vNext->anEdge );
}
SweepEvent( tess, v );
}
/* Set tess->event for debugging purposes */
tess->event = ((ActiveRegion *) dictKey( dictMin( tess->dict )))->eUp->Org;
DebugEvent( tess );
DoneEdgeDict( tess );
DonePriorityQ( tess );
if ( !RemoveDegenerateFaces( tess, tess->mesh ) ) return 0;
tessMeshCheckMesh( tess->mesh );
return 1;
}
static void DoneEdgeDict( TESStesselator *tess )
{
ActiveRegion *reg;
while( (reg = (ActiveRegion *)dictKey( dictMin( tess->dict ))) != NULL ) {
/*
* At the end of all processing, the dictionary should contain
* only the two sentinel edges, plus at most one "fixable" edge
* created by ConnectRightVertex().
*/
if( ! reg->sentinel ) {
assert( reg->fixUpperEdge );
//assert( ++fixedEdges == 1 );
}
assert( reg->windingNumber == 0 );
DeleteRegion( tess, reg );
/* tessMeshDelete( reg->eUp );*/
}
dictDeleteDict( &tess->alloc, tess->dict );
}
static void DoneEdgeDict( GLUtesselator *tess )
{
ActiveRegion *reg;
int fixedEdges = 0;
/* __GL_DICTLISTKEY */ /* __GL_DICTLISTMIN */
while( (reg = (ActiveRegion *)dictKey( dictMin( tess->dict ))) != NULL ) {
/*
* At the end of all processing, the dictionary should contain
* only the two sentinel edges, plus at most one "fixable" edge
* created by ConnectRightVertex().
*/
if( ! reg->sentinel ) {
assert( reg->fixUpperEdge );
assert( ++fixedEdges == 1 );
}
assert( reg->windingNumber == 0 );
DeleteRegion( tess, reg );
/* __gl_meshDelete( reg->eUp );*/
}
dictDeleteDict( tess->dict ); /* __gl_dictListDeleteDict */
}
// Parameter phase only for tracing
SimplexResult Tableau::primalSimplex(int phase) {
const int width = getWidth();
const int constraintCount = getConstraintCount();
for(int r = 1; r <= constraintCount; r++) {
const TableauRow &row = m_table[r];
const int bv = row.m_basisVariable;
const Real &a = row.m_a[bv];
if(a == 0) {
continue;
}
Real factor = getObjectFactor(bv) / a;
if(factor == 0) {
trace(TRACE_WARNINGS,_T("Warning:Cost factor[%s] = 0."), getVariableName(bv).cstr());
continue;
}
for(int col = 0; col <= width; col++) {
objectFactor(col) -= row.m_a[col] * factor;
}
objectFactor(bv) = 0;
}
bool looping = false;
for(int iteration = 1;; iteration++) {
if(isTracing(TRACE_ITERATIONS)) {
trace(_T("Phase %d. Iteration %d"), phase, iteration);
traceTableau();
// traceBasis(_T("Current basis:"));
}
int pivotColumn;
Real minCost = 1;
if(looping) {
for(int col = 1; col <= width; col++) { // Apply Bland's anti-cycling rule step 1.
const Real &cc = objectFactor(col);
if(cc < -EPS) {
minCost = cc;
pivotColumn = col;
break;
}
}
} else { // else find pivot column the old way
for(int col = 1; col <= width; col++) {
const Real &cc = objectFactor(col);
if(cc < minCost) {
minCost = cc;
pivotColumn = col;
}
}
}
if(minCost >= -EPS) {
return SIMPLEX_SOLUTION_OK; // Optimal value found
}
int pivotRow = -1;
Real minRatio = 0;
if(looping) { // apply Bland's anti-cycling rule step 2.
for(int r = 1; r <= constraintCount; r++) {
const Real &ar = m_table[r].m_a[pivotColumn];
if(ar > 10*EPS) {
const Real &br = getRightSide(r);
const Real ratio = br / ar;
if((pivotRow == -1) || (ratio < minRatio)) {
minRatio = ratio;
pivotRow = r;
}
}
}
if(pivotRow >= 0) {
int minIndex = -1;
for(int r = 1; r <= constraintCount; r++) {
const Real &ar = m_table[r].m_a[pivotColumn];
if(ar > 10*EPS) {
const Real &br = getRightSide(r);
const Real ratio = br / ar;
if(ratio == minRatio) {
const int index = m_table[r].m_basisVariable;
if(minIndex == -1 || index < minIndex) {
minIndex = index;
pivotRow = r;
}
}
}
}
}
} else { // else find pivot row the old way
for(int r = 1; r <= constraintCount; r++) {
const Real &ar = m_table[r].m_a[pivotColumn];
if(ar > EPS) {
const Real &br = getRightSide(r);
const Real ratio = br / ar;
if(pivotRow == -1 || ratio < minRatio) {
minRatio = ratio;
pivotRow = r;
}
}
}
}
if(pivotRow == -1) {
return SIMPLEX_SOLUTION_UNLIMITED;
}
// Check for degeneracy
traceDegeneracy(pivotRow, pivotColumn, minRatio);
DictionaryKey dictKey(this);
if(m_dictionarySet.contains(dictKey)) {
looping = true;
trace(TRACE_WARNINGS, _T("Looping. Applying Blands anti cycling rule."));
} else {
m_dictionarySet.add(dictKey);
}
pivot(pivotRow,pivotColumn,true);
}
}
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 );
}
}
