Edge *Subdivision::locate(const Vec2& x, Edge *start)
{
Edge *e = start;
double t = triArea(x, e->Dest(), e->Org());
if (t>0) { // x is to the right of edge e
t = -t;
e = e->Sym();
}
while (true)
{
Edge *eo = e->Onext();
Edge *ed = e->Dprev();
double to = triArea(x, eo->Dest(), eo->Org());
double td = triArea(x, ed->Dest(), ed->Org());
if (td>0) // x is below ed
if (to>0 || to==0 && t==0) {// x is interior, or origin endpoint
startingEdge = e;
return e;
}
else { // x is below ed, below eo
t = to;
e = eo;
}
else // x is on or above ed
if (to>0) // x is above eo
if (td==0 && t==0) { // x is destination endpoint
startingEdge = e;
return e;
}
else { // x is on or above ed and above eo
t = td;
e = ed;
}
else // x is on or below eo
if (t==0 && !leftOf(eo->Dest(), e))
// x on e but subdiv. is to right
e = e->Sym();
else if (rand()&1) { // x is on or above ed and
t = to; // on or below eo; step randomly
e = eo;
}
else {
t = td;
e = ed;
}
}
}
static inline void printFace(std::ostream &out, Face *f) {
out << "Face: " << f->getID() << std::endl;
FaceEdgeIterator eitr(f);
Edge *e = NULL;
int edge = 0;
while ((e = eitr.next())) {
out << "Edge " << edge << " with id: " << e->getID() << " from " <<
e->Org()->pos << " to " << e->Dest()->pos << std::endl;
++edge;
}
}
Edge *Cell::getOrbitOrg(Edge *edge, Vertex *org) {
assert(edge != 0);
assert(org != 0);
// traverse the Lnext orbit of _edge_ looking for an edge whose origin is
// _org_
Edge *scan = edge;
do {
if (scan->Org() == org) {
return scan;
}
scan = scan->Lnext();
} while (scan != edge);
return 0;
}
void Subdivision::InsertSite(const Point2d& x)
// Inserts a new point into a subdivision representing a Delaunay
// triangulation, and fixes the affected edges so that the result
// is still a Delaunay triangulation. This is based on the
// pseudocode from Guibas and Stolfi (1985) p.120, with slight
// modifications and a bug fix.
{
Edge* e = Locate(x);
if ((x == e->Org2d()) || (x == e->Dest2d())) // point is already in
return;
else if (OnEdge(x, e)) {
e = e->Oprev();
DeleteEdge(e->Onext());
}
// Connect the new point to the vertices of the containing
// triangle (or quadrilateral, if the new point fell on an
// existing edge.)
Edge* base = MakeEdge();
base->EndPoints(e->Org(), new Point2d(x));
Splice(base, e);
startingEdge = base;
do {
base = Connect(e, base->Sym());
e = base->Oprev();
} while (e->Lnext() != startingEdge);
// Examine suspect edges to ensure that the Delaunay condition
// is satisfied.
do {
Edge* t = e->Oprev();
if (RightOf(t->Dest2d(), e) &&
InCircle(e->Org2d(), t->Dest2d(), e->Dest2d(), x)) {
Swap(e);
e = e->Oprev();
}
else if (e->Onext() == startingEdge) // no more suspect edges
return;
else // pop a suspect edge
e = e->Onext()->Lprev();
} while (TRUE);
}
int main() {
using cgl::Point2d;
using cgl::Edge;
using cgl::make_edge;
// Point2d *a = new Point2d(0.0, 0.0); // 0
// Point2d *b = new Point2d(1.0, 0.0); // 1
// Point2d *c = new Point2d(1.0, 1.0); // 2
// Point2d *d = new Point2d(0.0, 1.0); // 3
Edge *ea = make_edge(0, 1);
Edge *eb = make_edge(ea->Dest(), 2);
Edge *ec = make_edge(eb->Dest(), 3);
Edge *ed = make_edge(ec->Dest(), 0);
Edge *ee = make_edge(eb->Dest(), ea->Org());
// Connect eb to ea->Dest()
splice(ea->Sym(), eb);
// Connect ec to eb->Dest()
splice(eb->Sym(), ec);
// Connect ed to ec->Sym() and ea
splice(ec->Sym(), ed);
splice(ed->Sym(), ea);
// Connect ee to ec and ea -- this is equivalent to Delaunay::connect
splice(ee, eb->Lnext());
splice(ee->Sym(), ea);
// Traverse the convex hull
if (ea->Dnext() != eb->Sym()) {
std::cerr << "Error: ea->Dnext() != eb->Sym()" << std::endl;
return 1;
}
if (eb->Dnext() != ec->Sym()) {
std::cerr << "Error: eb->Dnext() != ec->Sym()" << std::endl;
return 1;
}
if (ec->Dnext() != ed->Sym()) {
std::cerr << "Error: ec->Dnext() != ed->Sym()" << std::endl;
return 1;
}
if (ed->Dprev() != ee) {
std::cerr << "Error: ed->Dprev() != ee" << std::endl;
return 1;
}
// Cross linkage -- test algebra
// Rot / invRot
if (ee->Rot()->Org() != ed->invRot()->Org()) {
std::cerr << "Error: ee->Rot()->Org() != ed->invRot()->Org()" <<
std::endl;
return 1;
}
// Sym
if (ee->Sym()->Org() != 0) {
std::cerr << "Error: ee->Sym()->Org() != a" << std::endl;
return 1;
}
// Onext
if (ee->Onext() != eb->Sym()) {
std::cerr << "Error: ee->Onext() != eb->Sym()" << std::endl;
return 1;
}
// Oprev
if (ee->Oprev() != ec) {
std::cerr << "Error: ee->Oprev() != ec" << std::endl;
return 1;
}
// Dnext
if (ee->Dnext() != ed) {
std::cerr << "Error: ee->Dnext() != ed" << std::endl;
return 1;
}
// Dprev
if (ee->Dprev() != ea->Sym()) {
std::cerr << "Error: ee->Dprev() != ea->Sym()" << std::endl;
return 1;
}
// Lnext
if (ee->Lnext() != ea) {
std::cerr << "Error: ee->Lnext() != ea" << std::endl;
return 1;
}
// Lprev
if (ee->Lprev() != eb) {
std::cerr << "Error: ee->Lprev() != eb" << std::endl;
return 1;
}
// Rnext
if (ee->Rnext() != ec->Sym()) {
std::cerr << "Error: ee->Rnext() != ec->Sym()" << std::endl;
return 1;
}
// Rprev
if (ee->Rprev() != ed->Sym()) {
std::cerr << "Error: ee->Rprev() != ed->Sym()" << std::endl;
return 1;
}
// Org / Dest
if (ed->Org() != 3) {
std::cerr << "Error: ed->Org() != d" << std::endl;
return 1;
}
if (ed->Dest() != 0) {
std::cerr << "Error: ed->Dest() != a" << std::endl;
return 1;
}
if (ee->Org() != 2) {
std::cerr << "Error: ee->Org() != c" << std::endl;
return 1;
}
if (ee->Dest() != 0) {
std::cerr << "Error: ee->Dest() != a" << std::endl;
return 1;
}
// Let the system clean up the memory
return 0;
}
/*Type of Cut Strategy is defined as:
* (useAltCut, useVertical) = (true, true) => Alternating Cuts
* (useAltCut, useVertical) = (true, false) => Horizontal Cuts*
* (useAltCut, useVertical) = (false, true) => Vertical Cuts
* */
void delaunay(Vertex **ppVertices, long numVertices, Edge **ppLe, Edge **ppRe,
bool useAltCuts, bool useVertical) {
NOT_NULL(ppVertices);
if(numVertices == 2) {
Edge *pA = Edge::makeEdge();
if(*ppVertices[0] > *ppVertices[1]) {
ELEM_SWAP(ppVertices[0], ppVertices[1]);
}
pA->setOrg(ppVertices[0]);
pA->setDest(ppVertices[1]);
*ppLe = pA;
*ppRe = pA->Sym();
}
else if(numVertices == 3) {
Edge *pA = Edge::makeEdge(),
*pB = Edge::makeEdge(),
*pC = 0;
if(*ppVertices[0] > *ppVertices[1]) {
ELEM_SWAP(ppVertices[0], ppVertices[1]);
}
if(*ppVertices[1] > *ppVertices[2]) {
ELEM_SWAP(ppVertices[1], ppVertices[2]);
}
Edge::splice(pA->Sym(), pB);
pA->setOrg(ppVertices[0]);
pA->setDest(ppVertices[1]);
pB->setOrg(ppVertices[1]);
pB->setDest(ppVertices[2]);
REAL ccw = orient2d(ppVertices[0]->Pos(), ppVertices[1]->Pos(), ppVertices[2]->Pos());
if(ccw > 0) {
pC = Edge::connect(pB, pA);
*ppLe = pA;
*ppRe = pB->Sym();
}
else if(ccw < 0) {
pC = Edge::connect(pB, pA);
*ppLe = pC->Sym();
*ppRe = pC;
}
else {
*ppLe = pA;
*ppRe = pB->Sym();
}
}
else {
long middle = std::floor(numVertices/2);
Edge *pLdo = 0,
*pLdi = 0,
*pRdi = 0,
*pRdo = 0;
//These vertices are used for merging a horizontal cut
Vertex *pBotMax = 0, //highest vertex of bottom half
*pTopMin = 0, //lowest vertex of top half
*pMin = 0, //Lexicographically max vertex
*pMax = 0; //Lexicographically min vertex
//Find median partition by X or Y, depending on whether we're using a vertical cut
std::nth_element(ppVertices, ppVertices+middle, ppVertices+numVertices, useVertical ? Vertex::lessX : Vertex::lessY);
//Recursive calls
delaunay(ppVertices, middle, &pLdo, &pLdi, useAltCuts, useAltCuts ? !useVertical : useVertical);
delaunay(ppVertices+middle, numVertices - middle, &pRdi, &pRdo, useAltCuts, useAltCuts ? !useVertical : useVertical);
//Modify ldi be highest in bottom half and rdi to be lowest in top half
if(!useVertical) {
pBotMax = ppVertices[0];
pTopMin = ppVertices[middle];
pMin = (*ppVertices[0] < *ppVertices[middle]) ? ppVertices[0] : ppVertices[middle];
pMax = (*ppVertices[0] > *ppVertices[middle]) ? ppVertices[0] : ppVertices[middle];;
for(long i=1; i < middle; i++) {
if(*ppVertices[i] < *pMin) {
pMin = ppVertices[i];
}
else if(*ppVertices[i] > *pMax) {
pMax = ppVertices[i];
}
if(ppVertices[i]->gtY(*pBotMax)) {
pBotMax = ppVertices[i];
}
}
for(long i=middle+1; i < numVertices; i++) {
if(*ppVertices[i] < *pMin) {
pMin = ppVertices[i];
}
else if(*ppVertices[i] > *pMax) {
pMax = ppVertices[i];
}
if(ppVertices[i]->ltY(*pTopMin)) {
pTopMin = ppVertices[i];
}
}
pLdi = pBotMax->getCWHullEdge();
pRdi = pTopMin->getCCWHullEdge();
}
//Compute the lower common tangent of two sets of vertices
while (1) {
if(pLdi->leftOf(pRdi->Org())) {
pLdi = pLdi->Lnext();
}
else if(pRdi->rightOf(pLdi->Org())) {
pRdi = pRdi->Rprev();
}
else {
break;
}
}
// Create a first cross edge pBasel from pRdi.origin to pLdi.origin
Edge *pBasel = Edge::connect(pRdi->Sym(), pLdi);
if(pLdi->Org() == pLdo->Org()) {
pLdo = pBasel->Sym();
}
if(pRdi->Org() == pRdo->Org()) {
pRdo = pBasel;
}
//Merging two halves
while(1) {
//Locate the first Left point pLcand to be encou
Edge *pLcand = pBasel->Sym()->Onext();
bool leftFinished = !pLcand->valid(pBasel);
if(!leftFinished) {
while(incircle(pBasel->Dest()->Pos(),
pBasel->Org()->Pos(),
pLcand->Dest()->Pos(),
pLcand->Onext()->Dest()->Pos()) > 0) {
Edge *pT = pLcand->Onext();
Edge::deleteEdge(pLcand);
pLcand = pT;
}
}
//Symmetrically locate the first R point to be hit
Edge *pRcand = pBasel->Oprev();
bool rightFinished = !pRcand->valid(pBasel);
if(!rightFinished) {
while(incircle(pBasel->Dest()->Pos(),
pBasel->Org()->Pos(),
pRcand->Dest()->Pos(),
pRcand->Oprev()->Dest()->Pos()) > 0) {
Edge *pT = pRcand->Oprev();
Edge::deleteEdge(pRcand);
pRcand = pT;
}
}
//both are invalid, pBasel is upper common tangent
if(leftFinished && rightFinished) {
break;
}
//the next cross edge is to be connected to either pLcand.dest or pRcand.dest
if(leftFinished ||
(!rightFinished && incircle(pLcand->Dest()->Pos(),
pLcand->Org()->Pos(),
pRcand->Org()->Pos(),
pRcand->Dest()->Pos()) > 0)) {
pBasel = Edge::connect(pRcand, pBasel->Sym());
}
else {
pBasel = Edge::connect(pBasel->Sym(), pLcand->Sym());
}
}
//Modify pLdo and pRdo if we merging a horizontal cut
if(!useVertical) {
pLdo = pMin->getCCWHullEdge();
pRdo = pMax->getCWHullEdge();
}
*ppLe = pLdo;
*ppRe = pRdo;
}
return;
}