private TriangulatedSet Triangulate(int _beginId, int _endId, int _depth)
{
// Number of points in this set
int size = _endId - _beginId + 1;
if (size == 2) // Segment
{
HalfEdge h = CreateHalfEdge(_beginId, _endId);
return(new TriangulatedSet(h.twin, h.twin));
}
else if (size == 3) // Triangle
{
HalfEdge hA = CreateHalfEdge(_beginId, _beginId + 1);
HalfEdge hB = CreateHalfEdge(_beginId + 1, _endId);
ConnectHalfedges(hA, hB);
// A,B,C are in CCW, which means A,B,C are inner halfedges
if (IsCcw(m_vertice[_beginId], m_vertice[_beginId + 1], m_vertice[_endId]))
{
// DONOT delete this line since it update other connection infomation
HalfEdge hC = BridgeHalfedges(hB, hA);
return(new TriangulatedSet(hA.twin, hB.twin));
}
// A,B,C are in CW, which means A,B,C are outer halfedges
else if (IsCcw(m_vertice[_beginId], m_vertice[_endId], m_vertice[_beginId + 1]))
{
HalfEdge hC = BridgeHalfedges(hB, hA);
return(new TriangulatedSet(hC, hC));
}
else
{
return(new TriangulatedSet(hA.twin, hB.twin));
}
}
else // size >= 4, Separate
{
// Recursively delaunay triangulate L and R halves
TriangulatedSet leftSet = Triangulate(_beginId, _beginId + (size / 2) - 1, _depth + 1);
TriangulatedSet rightSet = Triangulate(_beginId + (size / 2), _endId, _depth + 1);
HalfEdge LLh = leftSet.leftHalfedge;
HalfEdge LRh = leftSet.rightHalfedge;
HalfEdge RLh = rightSet.leftHalfedge;
HalfEdge RRh = rightSet.rightHalfedge;
// Compute the lowest common tangent of L and R
while (true)
{
if (IsLeftOf(RLh.DstId, LRh))
{
LRh = LRh.next;
}
else if (IsLeftOf(LRh.orgId, RLh))
{
RLh = RLh.Prev;
}
else
{
break;
}
}
HalfEdge baseH = BridgeHalfedges(RLh, LRh);
if (LRh.orgId == LLh.DstId)
{
LLh = baseH;
}
if (RLh.DstId == RRh.orgId)
{
RRh = baseH;
}
// Merge
while (true)
{
// Locate the first L point (Lcand.Org) to be encountered by the rising bubble
// and delete L edges that fail the circle test
HalfEdge Lcand = baseH.twin.Prev;
if (IsLeftOf(Lcand.orgId, baseH.twin))
{
while (IsInCircle(
baseH.DstId,
baseH.orgId,
Lcand.orgId,
Lcand.twin.Prev.orgId))
{
HalfEdge nextLcand = Lcand.twin.Prev;
DeleteHalfedge(Lcand);
Lcand = nextLcand;
}
}
HalfEdge Rcand = baseH.twin.next;
if (IsLeftOf(Rcand.DstId, baseH.twin))
{
while (IsInCircle(
baseH.DstId,
baseH.orgId,
Rcand.DstId,
Rcand.twin.next.DstId))
{
HalfEdge nextRcand = Rcand.twin.next;
DeleteHalfedge(Rcand);
Rcand = nextRcand;
}
}
// If both Lcand and Rcand are invalid, then baseH is the upper common tangent
if (IsLeftOf(Lcand.orgId, baseH.twin) == false && IsLeftOf(Rcand.DstId, baseH.twin) == false)
{
break;
}
// The next cross halfedge is to be connected to either Lcand.Org or rcand.Dst
// if both are valid, then choose the appropriate one using the inCircle test
if (IsLeftOf(Lcand.orgId, baseH.twin) && IsInCircle(Lcand.orgId, baseH.DstId, baseH.orgId, Rcand.DstId) == false)
{
baseH = BridgeHalfedges(baseH.twin, Lcand);
}
else
{
baseH = BridgeHalfedges(Rcand, baseH.twin);
}
}
return(new TriangulatedSet(LLh, RRh));
}
}
/// <summary>
/// Exclusive right
/// </summary>
/// <param name="_vId"></param>
/// <param name="_h"></param>
/// <returns></returns>
private bool IsRightOf(int _vId, HalfEdge _h)
{
return(!IsNotCw(m_vertice[_vId], m_vertice[_h.orgId], m_vertice[_h.DstId]));
}
/// <summary>
/// Exclusive left
/// </summary>
/// <param name="_vId"></param>
/// <param name="_h"></param>
/// <returns></returns>
private bool IsLeftOf(int _vId, HalfEdge _h)
{
return(IsCcw(m_vertice[_vId], m_vertice[_h.orgId], m_vertice[_h.DstId]));
}
/// <summary>
/// _hB should always be the isolated one to detach, _hA should be the base one.
/// _hB\ \
/// \ \
/// _hA ---- ---
/// </summary>
/// <param name="_hA"></param>
/// <param name="_hB"></param>
private void DisconnectHalfedges(HalfEdge _hA, HalfEdge _hB)
{
_hA.next = _hB.twin.next;
_hB.twin.next = _hB;
}
/// <summary>
/// Make halfedge A's head connect to halfedge B's rear
/// </summary>
/// <param name="_hA"></param>
/// <param name="_hB"></param>
private void ConnectHalfedges(HalfEdge _hA, HalfEdge _hB)
{
_hB.Prev.next = _hA.next;
_hA.next = _hB;
}
public TriangulatedSet(HalfEdge _lh, HalfEdge _rh)
{
leftHalfedge = _lh;
rightHalfedge = _rh;
}