/*
* 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.currentSweepVertex 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.
*/
private static bool CheckForRightSplice(Tesselator tess, ActiveRegion regUp)
{
ActiveRegion regLo = RegionBelow(regUp);
HalfEdge eUp = regUp.upperHalfEdge;
HalfEdge eLo = regLo.upperHalfEdge;
if (eUp.originVertex.VertLeq(eLo.originVertex))
{
if (ContourVertex.EdgeSign(eLo.directionVertex, eUp.originVertex, eLo.originVertex) > 0)
{
return false;
}
/* eUp.Org appears to be below eLo */
if (!eUp.originVertex.VertEq(eLo.originVertex))
{
/* Splice eUp.Org into eLo */
Mesh.meshSplitEdge(eLo.otherHalfOfThisEdge);
Mesh.meshSplice(eUp, eLo.Oprev);
regUp.dirty = regLo.dirty = true;
}
else if (eUp.originVertex != eLo.originVertex)
{
/* merge the two vertices, discarding eUp.Org */
tess.vertexPriorityQue.Delete(eUp.originVertex.priorityQueueHandle);
//pqDelete(tess.pq, eUp.Org.pqHandle); /* __gl_pqSortDelete */
SpliceMergeVertices(tess, eLo.Oprev, eUp);
}
}
else
{
if (ContourVertex.EdgeSign(eUp.directionVertex, eLo.originVertex, eUp.originVertex) < 0)
{
return false;
}
/* eLo.Org appears to be above eUp, so splice eLo.Org into eUp */
regUp.RegionAbove().dirty = regUp.dirty = true;
Mesh.meshSplitEdge(eUp.otherHalfOfThisEdge);
Mesh.meshSplice(eLo.Oprev, eUp);
}
return true;
}
private static void ComputeWinding(Tesselator tess, ActiveRegion reg)
{
reg.windingNumber = reg.RegionAbove().windingNumber + reg.upperHalfEdge.winding;
reg.inside = tess.IsWindingInside(reg.windingNumber);
}
/*
* 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.
*/
private static bool CheckForIntersect(Tesselator tess, ActiveRegion regUp)
{
ActiveRegion regLo = RegionBelow(regUp);
HalfEdge eUp = regUp.upperHalfEdge;
HalfEdge eLo = regLo.upperHalfEdge;
ContourVertex orgUp = eUp.originVertex;
ContourVertex orgLo = eLo.originVertex;
ContourVertex dstUp = eUp.directionVertex;
ContourVertex dstLo = eLo.directionVertex;
double tMinUp, tMaxLo;
var isect = new ContourVertex();
ContourVertex orgMin;
HalfEdge e;
if (dstLo.VertEq(dstUp))
{
throw new Exception();
}
if (ContourVertex.EdgeSign(dstUp, tess.currentSweepVertex, orgUp) > 0)
{
throw new Exception();
}
if (ContourVertex.EdgeSign(dstLo, tess.currentSweepVertex, orgLo) < 0)
{
throw new Exception();
}
if (orgUp == tess.currentSweepVertex || orgLo == tess.currentSweepVertex)
{
throw new Exception();
}
if (regUp.fixUpperEdge || regLo.fixUpperEdge)
{
throw new Exception();
}
if (orgUp == orgLo)
{
return false; /* right endpoints are the same */
}
tMinUp = Math.Min(orgUp.y, dstUp.y);
tMaxLo = Math.Max(orgLo.y, dstLo.y);
if (tMinUp > tMaxLo)
{
return false; /* t ranges do not overlap */
}
if (orgUp.VertLeq(orgLo))
{
if (ContourVertex.EdgeSign(dstLo, orgUp, orgLo) > 0)
{
return false;
}
}
else
{
if (ContourVertex.EdgeSign(dstUp, orgLo, orgUp) < 0)
{
return false;
}
}
EdgeIntersect(dstUp, orgUp, dstLo, orgLo, ref isect);
// The following properties are guaranteed:
if (!(Math.Min(orgUp.y, dstUp.y) <= isect.y))
{
throw new Exception();
}
if (!(isect.y <= Math.Max(orgLo.y, dstLo.y)))
{
throw new Exception();
}
if (!(Math.Min(dstLo.x, dstUp.x) <= isect.x))
{
throw new Exception();
}
if (!(isect.x <= Math.Max(orgLo.x, orgUp.x)))
{
throw new Exception();
}
if (isect.VertLeq(tess.currentSweepVertex))
{
/* 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.currentSweepVertex.
*/
isect.x = tess.currentSweepVertex.x;
isect.y = tess.currentSweepVertex.y;
}
/* 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 = orgUp.VertLeq(orgLo) ? orgUp : orgLo;
if (orgMin.VertLeq(isect))
{
isect.x = orgMin.x;
isect.y = orgMin.y;
}
if (isect.VertEq(orgUp) || isect.VertEq(orgLo))
{
/* Easy case -- intersection at one of the right endpoints */
CheckForRightSplice(tess, regUp);
return false;
}
if ((!dstUp.VertEq(tess.currentSweepVertex)
&& ContourVertex.EdgeSign(dstUp, tess.currentSweepVertex, isect) >= 0)
|| (!dstLo.VertEq(tess.currentSweepVertex)
&& ContourVertex.EdgeSign(dstLo, tess.currentSweepVertex, isect) <= 0))
{
/* Very unusual -- the new upper or lower edge would pass on the
* wrong side of the sweep currentSweepVertex, or through it. This can happen
* due to very small numerical errors in the intersection calculation.
*/
if (dstLo == tess.currentSweepVertex)
{
/* Splice dstLo into eUp, and process the new region(s) */
Mesh.meshSplitEdge(eUp.otherHalfOfThisEdge);
Mesh.meshSplice(eLo.otherHalfOfThisEdge, eUp);
regUp = TopLeftRegion(regUp);
eUp = RegionBelow(regUp).upperHalfEdge;
FinishLeftRegions(tess, RegionBelow(regUp), regLo);
AddRightEdges(tess, regUp, eUp.Oprev, eUp, eUp, true);
return true;
}
if (dstUp == tess.currentSweepVertex)
{
/* Splice dstUp into eLo, and process the new region(s) */
Mesh.meshSplitEdge(eLo.otherHalfOfThisEdge);
Mesh.meshSplice(eUp.nextEdgeCCWAroundLeftFace, eLo.Oprev);
regLo = regUp;
regUp = TopRightRegion(regUp);
e = RegionBelow(regUp).upperHalfEdge.Rprev;
regLo.upperHalfEdge = eLo.Oprev;
eLo = FinishLeftRegions(tess, regLo, null);
AddRightEdges(tess, regUp, eLo.nextEdgeCCWAroundOrigin, eUp.Rprev, e, true);
return true;
}
/* Special case: called from ConnectRightVertex. If either
* edge passes on the wrong side of tess.currentSweepVertex, split it
* (and wait for ConnectRightVertex to splice it appropriately).
*/
if (ContourVertex.EdgeSign(dstUp, tess.currentSweepVertex, isect) >= 0)
{
regUp.RegionAbove().dirty = regUp.dirty = true;
Mesh.meshSplitEdge(eUp.otherHalfOfThisEdge);
eUp.originVertex.x = tess.currentSweepVertex.x;
eUp.originVertex.y = tess.currentSweepVertex.y;
}
if (ContourVertex.EdgeSign(dstLo, tess.currentSweepVertex, isect) <= 0)
{
regUp.dirty = regLo.dirty = true;
Mesh.meshSplitEdge(eLo.otherHalfOfThisEdge);
eLo.originVertex.x = tess.currentSweepVertex.x;
eLo.originVertex.y = tess.currentSweepVertex.y;
}
/* 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).
*/
Mesh.meshSplitEdge(eUp.otherHalfOfThisEdge);
Mesh.meshSplitEdge(eLo.otherHalfOfThisEdge);
Mesh.meshSplice(eLo.Oprev, eUp);
eUp.originVertex.x = isect.x;
eUp.originVertex.y = isect.y;
tess.vertexPriorityQue.Add(ref eUp.originVertex.priorityQueueHandle, eUp.originVertex);
/* __gl_pqSortInsert */
GetIntersectData(tess, eUp.originVertex, orgUp, dstUp, orgLo, dstLo);
regUp.RegionAbove().dirty = regUp.dirty = regLo.dirty = true;
return false;
}
/*
* 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.
*/
private static bool CheckForLeftSplice(Tesselator tess, ActiveRegion regUp)
{
ActiveRegion regLo = RegionBelow(regUp);
HalfEdge eUp = regUp.upperHalfEdge;
HalfEdge eLo = regLo.upperHalfEdge;
HalfEdge e;
if (eUp.directionVertex.VertEq(eLo.directionVertex))
{
throw new Exception();
}
if (eUp.directionVertex.VertLeq(eLo.directionVertex))
{
if (ContourVertex.EdgeSign(eUp.directionVertex, eLo.directionVertex, eUp.originVertex) < 0)
{
return false;
}
/* eLo.Dst is above eUp, so splice eLo.Dst into eUp */
regUp.RegionAbove().dirty = regUp.dirty = true;
e = Mesh.meshSplitEdge(eUp);
Mesh.meshSplice(eLo.otherHalfOfThisEdge, e);
e.leftFace.isInterior = regUp.inside;
}
else
{
if (ContourVertex.EdgeSign(eLo.directionVertex, eUp.directionVertex, eLo.originVertex) > 0)
return false;
/* eUp.Dst is below eLo, so splice eUp.Dst into eLo */
regUp.dirty = regLo.dirty = true;
e = Mesh.meshSplitEdge(eLo);
Mesh.meshSplice(eUp.nextEdgeCCWAroundLeftFace, eLo.otherHalfOfThisEdge);
e.rightFace.isInterior = regUp.inside;
}
return true;
}
/*
* Delete a region from the sweep line. This happens when the upper
* and lower chains of a region meet (at a vertex on the sweep line).
* The "inside" flag is copied to the appropriate mesh face (we could
* not do this before -- since the structure of the mesh is always
* changing, this face may not have even existed until now).
*/
private static void FinishRegion(Tesselator tess, ActiveRegion reg)
{
HalfEdge e = reg.upperHalfEdge;
Face f = e.leftFace;
f.isInterior = reg.inside;
f.halfEdgeThisIsLeftFaceOf = e; // optimization for mesh.TessellateMonoRegion()
DeleteRegion(reg);
}
/*
* We add two sentinel edges above and below all other edges,
* to avoid special cases at the top and bottom.
*/
/* Make the sentinel coordinates big enough that they will never be
* merged with real input features. (Even with the largest possible
* input contour and the maximum tolerance of 1.0, no merging will be
* done with coordinates larger than 3 * GLU_TESS_MAX_COORD).
*/
private static void AddSentinel(Tesselator tess, double t)
{
HalfEdge halfEdge;
var activeRedion = new ActiveRegion();
halfEdge = tess.mesh.MakeEdge();
halfEdge.originVertex.x = SENTINEL_COORD;
halfEdge.originVertex.y = t;
halfEdge.directionVertex.x = -SENTINEL_COORD;
halfEdge.directionVertex.y = t;
tess.currentSweepVertex = halfEdge.directionVertex; /* initialize it */
activeRedion.upperHalfEdge = halfEdge;
activeRedion.windingNumber = 0;
activeRedion.inside = false;
activeRedion.fixUpperEdge = false;
activeRedion.sentinel = true;
activeRedion.dirty = false;
activeRedion.upperHalfEdgeDictNode = tess.edgeDictionary.Insert(activeRedion);
/* __gl_dictListInsertBefore */
}
/*
* Both edges must be directed from right to left (this is the canonical
* direction for the upper edge of each region).
*
* The strategy is to evaluate a "t" value for each edge at the
* current sweep line position, given by tess.currentSweepVertex. The calculations
* are designed to be very stable, but of course they are not perfect.
*
* Special case: if both edge destinations are at the sweep event,
* we sort the edges by slope (they would otherwise compare equally).
*/
public static bool EdgeLeq(Tesselator tess, ActiveRegion reg1, ActiveRegion reg2)
{
ContourVertex currentSweepVertex = tess.currentSweepVertex;
HalfEdge e1, e2;
double t1, t2;
e1 = reg1.upperHalfEdge;
e2 = reg2.upperHalfEdge;
if (e1.directionVertex == currentSweepVertex)
{
if (e2.directionVertex == currentSweepVertex)
{
/* Two edges right of the sweep line which meet at the sweep currentSweepVertex.
* Sort them by slope.
*/
if (e1.originVertex.VertLeq(e2.originVertex))
{
return ContourVertex.EdgeSign(e2.directionVertex, e1.originVertex, e2.originVertex) <= 0;
}
return ContourVertex.EdgeSign(e1.directionVertex, e2.originVertex, e1.originVertex) >= 0;
}
return ContourVertex.EdgeSign(e2.directionVertex, currentSweepVertex, e2.originVertex) <= 0;
}
if (e2.directionVertex == currentSweepVertex)
{
return ContourVertex.EdgeSign(e1.directionVertex, currentSweepVertex, e1.originVertex) >= 0;
}
/* General case - compute signed distance *from* e1, e2 to currentSweepVertex */
t1 = ContourVertex.EdgeEval(e1.directionVertex, currentSweepVertex, e1.originVertex);
t2 = ContourVertex.EdgeEval(e2.directionVertex, currentSweepVertex, e2.originVertex);
return (t1 >= t2);
}
/*
* 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.
*/
private static void ConnectRightVertex(Tesselator tess, ActiveRegion regUp, HalfEdge eBottomLeft)
{
HalfEdge eNew;
HalfEdge eTopLeft = eBottomLeft.nextEdgeCCWAroundOrigin;
ActiveRegion regLo = RegionBelow(regUp);
HalfEdge eUp = regUp.upperHalfEdge;
HalfEdge eLo = regLo.upperHalfEdge;
bool degenerate = false;
if (eUp.directionVertex != eLo.directionVertex)
{
CheckForIntersect(tess, regUp);
}
/* Possible new degeneracies: upper or lower edge of regUp may pass
* through vEvent, or may coincide with new intersection vertex
*/
if (eUp.originVertex.VertEq(tess.currentSweepVertex))
{
Mesh.meshSplice(eTopLeft.Oprev, eUp);
regUp = TopLeftRegion(regUp);
eTopLeft = RegionBelow(regUp).upperHalfEdge;
FinishLeftRegions(tess, RegionBelow(regUp), regLo);
degenerate = true;
}
if (eLo.originVertex.VertEq(tess.currentSweepVertex))
{
Mesh.meshSplice(eBottomLeft, eLo.Oprev);
eBottomLeft = FinishLeftRegions(tess, regLo, null);
degenerate = true;
}
if (degenerate)
{
AddRightEdges(tess, regUp, eBottomLeft.nextEdgeCCWAroundOrigin, eTopLeft, eTopLeft, true);
return;
}
/* Non-degenerate situation -- need to add a temporary, fixable edge.
* Connect to the closer of eLo.Org, eUp.Org.
*/
if (eLo.originVertex.VertLeq(eUp.originVertex))
{
eNew = eLo.Oprev;
}
else
{
eNew = eUp;
}
eNew = Mesh.meshConnect(eBottomLeft.Lprev, eNew);
/* 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.nextEdgeCCWAroundOrigin, eNew.nextEdgeCCWAroundOrigin, false);
eNew.otherHalfOfThisEdge.regionThisIsUpperEdgeOf.fixUpperEdge = true;
WalkDirtyRegions(tess, regUp);
}
private static ActiveRegion TopRightRegion(ActiveRegion reg)
{
ContourVertex dst = reg.upperHalfEdge.directionVertex;
/* Find the region above the uppermost edge with the same destination */
do
{
reg = reg.RegionAbove();
} while (reg.upperHalfEdge.directionVertex == dst);
return reg;
}
/*
* When the upper or lower edge of any region changes, the region is
* marked "dirty". This routine walks through all the dirty regions
* and makes sure that the dictionary invariants are satisfied
* (see the comments at the beginning of this file). Of course
* new dirty regions can be created as we make changes to restore
* the invariants.
*/
private static void WalkDirtyRegions(Tesselator tess, ActiveRegion regUp)
{
ActiveRegion regLo = RegionBelow(regUp);
HalfEdge eUp, eLo;
for (;;)
{
/* Find the lowest dirty region (we walk from the bottom up). */
while (regLo.dirty)
{
regUp = regLo;
regLo = RegionBelow(regLo);
}
if (!regUp.dirty)
{
regLo = regUp;
regUp = regUp.RegionAbove();
if (regUp == null || !regUp.dirty)
{
/* We've walked all the dirty regions */
return;
}
}
regUp.dirty = false;
eUp = regUp.upperHalfEdge;
eLo = regLo.upperHalfEdge;
if (eUp.directionVertex != eLo.directionVertex)
{
/* Check that the edge ordering is obeyed at the Dst vertices. */
if (CheckForLeftSplice(tess, regUp))
{
/* If the upper or lower edge was marked fixUpperEdge, then
* we no longer need it (since these edges are needed only for
* vertices which otherwise have no right-going edges).
*/
if (regLo.fixUpperEdge)
{
DeleteRegion(regLo);
Mesh.DeleteHalfEdge(eLo);
regLo = RegionBelow(regUp);
eLo = regLo.upperHalfEdge;
}
else if (regUp.fixUpperEdge)
{
DeleteRegion(regUp);
Mesh.DeleteHalfEdge(eUp);
regUp = regLo.RegionAbove();
eUp = regUp.upperHalfEdge;
}
}
}
if (eUp.originVertex != eLo.originVertex)
{
if (eUp.directionVertex != eLo.directionVertex
&& !regUp.fixUpperEdge && !regLo.fixUpperEdge
&&
(eUp.directionVertex == tess.currentSweepVertex ||
eLo.directionVertex == tess.currentSweepVertex))
{
/* When all else fails in CheckForIntersect(), it uses tess.currentSweepVertex
* as the intersection location. To make this possible, it requires
* that tess.currentSweepVertex lie between the upper and lower edges, and also
* that neither of these is marked fixUpperEdge (since in the worst
* case it might splice one of these edges into tess.currentSweepVertex, and
* violate the invariant that fixable edges are the only right-going
* edge from their associated vertex).
*/
if (CheckForIntersect(tess, regUp))
{
/* WalkDirtyRegions() was called recursively; we're done */
return;
}
}
else
{
/* Even though we can't use CheckForIntersect(), the Org vertices
* may violate the dictionary edge ordering. Check and correct this.
*/
CheckForRightSplice(tess, regUp);
}
}
if (eUp.originVertex == eLo.originVertex && eUp.directionVertex == eLo.directionVertex)
{
/* A degenerate loop consisting of only two edges -- delete it. */
AddWinding(eLo, eUp);
DeleteRegion(regUp);
Mesh.DeleteHalfEdge(eUp);
regUp = regLo.RegionAbove();
}
}
}
private static ActiveRegion TopLeftRegion(ActiveRegion reg)
{
ContourVertex org = reg.upperHalfEdge.originVertex;
HalfEdge e;
/* Find the region above the uppermost edge with the same origin */
do
{
reg = reg.RegionAbove();
} while (reg.upperHalfEdge.originVertex == org);
/* If the edge above was a temporary edge introduced by ConnectRightVertex,
* now is the time to fix it.
*/
if (reg.fixUpperEdge)
{
e = Mesh.meshConnect(RegionBelow(reg).upperHalfEdge.otherHalfOfThisEdge,
reg.upperHalfEdge.nextEdgeCCWAroundLeftFace);
if (e == null)
{
return null;
}
if (!FixUpperEdge(reg, e))
{
return null;
}
reg = reg.RegionAbove();
}
return reg;
}
private static ActiveRegion RegionBelow(ActiveRegion r)
{
return r.upperHalfEdgeDictNode.prev.Key;
}
/*
* Replace an upper edge which needs fixing (see ConnectRightVertex).
*/
private static bool FixUpperEdge(ActiveRegion reg, HalfEdge newEdge)
{
if (!reg.fixUpperEdge)
{
throw new Exception();
}
Mesh.DeleteHalfEdge(reg.upperHalfEdge);
reg.fixUpperEdge = false;
reg.upperHalfEdge = newEdge;
newEdge.regionThisIsUpperEdgeOf = reg;
return true;
}
/*
* The currentSweepVertex vertex lies exactly on an already-processed edge or vertex.
* Adding the new vertex involves splicing it into the already-processed
* part of the mesh.
*/
private static void ConnectLeftDegenerate(Tesselator tess, ActiveRegion regUp, ContourVertex vEvent)
{
HalfEdge e, eTopLeft, eTopRight, eLast;
ActiveRegion reg;
e = regUp.upperHalfEdge;
if (e.originVertex.VertEq(vEvent))
{
/* e.Org is an unprocessed vertex - just combine them, and wait
* for e.Org to be pulled from the queue
*/
SpliceMergeVertices(tess, e, vEvent.edgeThisIsOriginOf);
return;
}
if (!e.directionVertex.VertEq(vEvent))
{
/* General case -- splice vEvent into edge e which passes through it */
Mesh.meshSplitEdge(e.otherHalfOfThisEdge);
if (regUp.fixUpperEdge)
{
/* This edge was fixable -- delete unused portion of original edge */
Mesh.DeleteHalfEdge(e.nextEdgeCCWAroundOrigin);
regUp.fixUpperEdge = false;
}
Mesh.meshSplice(vEvent.edgeThisIsOriginOf, e);
SweepEvent(tess, vEvent); /* recurse */
return;
}
/* vEvent coincides with e.Dst, which has already been processed.
* Splice in the additional right-going edges.
*/
regUp = TopRightRegion(regUp);
reg = RegionBelow(regUp);
eTopRight = reg.upperHalfEdge.otherHalfOfThisEdge;
eTopLeft = eLast = eTopRight.nextEdgeCCWAroundOrigin;
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.
*/
if (eTopLeft == eTopRight)
{
throw new Exception(); /* there are some left edges too */
}
DeleteRegion(reg);
Mesh.DeleteHalfEdge(eTopRight);
eTopRight = eTopLeft.Oprev;
}
Mesh.meshSplice(vEvent.edgeThisIsOriginOf, eTopRight);
if (!eTopLeft.EdgeGoesLeft())
{
/* e.Dst had no left-going edges -- indicate this to AddRightEdges() */
eTopLeft = null;
}
AddRightEdges(tess, regUp, eTopRight.nextEdgeCCWAroundOrigin, eLast, eTopLeft, true);
}
/*
* Add a new active region to the sweep line, *somewhere* below "regAbove"
* (according to where the new edge belongs in the sweep-line dictionary).
* The upper edge of the new region will be "eNewUp".
* Winding number and "inside" flag are not updated.
*/
private static ActiveRegion AddRegionBelow(Tesselator tess,
ActiveRegion regAbove,
HalfEdge eNewUp)
{
var regNew = new ActiveRegion();
regNew.upperHalfEdge = eNewUp;
/* __gl_dictListInsertBefore */
regNew.upperHalfEdgeDictNode = tess.edgeDictionary.InsertBefore(regAbove.upperHalfEdgeDictNode, regNew);
regNew.fixUpperEdge = false;
regNew.sentinel = false;
regNew.dirty = false;
eNewUp.regionThisIsUpperEdgeOf = regNew;
return regNew;
}
/*
* 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 sub-cases 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
*/
private static void ConnectLeftVertex(Tesselator tess, ContourVertex vEvent)
{
ActiveRegion regUp, regLo, reg;
HalfEdge eUp, eLo, eNew;
var tmp = new ActiveRegion();
/* assert( vEvent.anEdge.Onext.Onext == vEvent.anEdge ); */
/* Get a pointer to the active region containing vEvent */
tmp.upperHalfEdge = vEvent.edgeThisIsOriginOf.otherHalfOfThisEdge;
/* __GL_DICTLISTKEY */
/* __gl_dictListSearch */
regUp = Dictionary.dictSearch(tess.edgeDictionary, tmp).Key;
regLo = RegionBelow(regUp);
eUp = regUp.upperHalfEdge;
eLo = regLo.upperHalfEdge;
/* Try merging with U or L first */
if (ContourVertex.EdgeSign(eUp.directionVertex, vEvent, eUp.originVertex) == 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 = eLo.directionVertex.VertLeq(eUp.directionVertex) ? regUp : regLo;
if (regUp.inside || reg.fixUpperEdge)
{
if (reg == regUp)
{
eNew = Mesh.meshConnect(vEvent.edgeThisIsOriginOf.otherHalfOfThisEdge, eUp.nextEdgeCCWAroundLeftFace);
}
else
{
HalfEdge tempHalfEdge = Mesh.meshConnect(eLo.Dnext, vEvent.edgeThisIsOriginOf);
eNew = tempHalfEdge.otherHalfOfThisEdge;
}
if (reg.fixUpperEdge)
{
FixUpperEdge(reg, eNew);
}
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.edgeThisIsOriginOf, vEvent.edgeThisIsOriginOf, null, true);
}
}
/*
* Purpose: insert right-going edges into the edge dictionary, and update
* winding numbers and mesh connectivity appropriately. All right-going
* edges share a common origin vOrg. Edges are inserted CCW starting at
* eFirst; the last edge inserted is eLast.Oprev. If vOrg has any
* left-going edges already processed, then eTopLeft must be the edge
* such that an imaginary upward vertical segment from vOrg would be
* contained between eTopLeft.Oprev and eTopLeft; otherwise eTopLeft
* should be null.
*/
private static void AddRightEdges(Tesselator tess, ActiveRegion regUp,
HalfEdge eFirst, HalfEdge eLast, HalfEdge eTopLeft,
bool cleanUp)
{
ActiveRegion reg, regPrev;
HalfEdge e, ePrev;
bool firstTime = true;
/* Insert the new right-going edges in the dictionary */
e = eFirst;
do
{
if (!e.originVertex.VertLeq(e.directionVertex))
{
throw new Exception();
}
AddRegionBelow(tess, regUp, e.otherHalfOfThisEdge);
e = e.nextEdgeCCWAroundOrigin;
} while (e != eLast);
/* Walk *all* right-going edges from e.Org, in the dictionary order,
* updating the winding numbers of each region, and re-linking the mesh
* edges to match the dictionary ordering (if necessary).
*/
if (eTopLeft == null)
{
eTopLeft = RegionBelow(regUp).upperHalfEdge.Rprev;
}
regPrev = regUp;
ePrev = eTopLeft;
for (;;)
{
reg = RegionBelow(regPrev);
e = reg.upperHalfEdge.otherHalfOfThisEdge;
if (e.originVertex != ePrev.originVertex) break;
if (e.nextEdgeCCWAroundOrigin != ePrev)
{
/* Unlink e from its current position, and relink below ePrev */
Mesh.meshSplice(e.Oprev, e);
Mesh.meshSplice(ePrev.Oprev, e);
}
/* Compute the winding number and "inside" flag for the new regions */
reg.windingNumber = regPrev.windingNumber - e.winding;
reg.inside = tess.IsWindingInside(reg.windingNumber);
/* Check for two outgoing edges with same slope -- process these
* before any intersection tests (see example in __gl_computeInterior).
*/
regPrev.dirty = true;
if (!firstTime && CheckForRightSplice(tess, regPrev))
{
AddWinding(e, ePrev);
DeleteRegion(regPrev);
Mesh.DeleteHalfEdge(ePrev);
}
firstTime = false;
regPrev = reg;
ePrev = e;
}
regPrev.dirty = true;
if (regPrev.windingNumber - e.winding != reg.windingNumber)
{
throw new Exception();
}
if (cleanUp)
{
/* Check for intersections between newly adjacent edges. */
WalkDirtyRegions(tess, regPrev);
}
}
private static void DeleteRegion(ActiveRegion reg)
{
if (reg.fixUpperEdge)
{
/* It was created with zero winding number, so it better be
* deleted with zero winding number (ie. it better not get merged
* with a real edge).
*/
if (reg.upperHalfEdge.winding != 0)
{
throw new Exception();
}
}
reg.upperHalfEdge.regionThisIsUpperEdgeOf = null;
reg.upperHalfEdgeDictNode.Delete();
reg = null;
}
/*
* 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.
*/
private static HalfEdge FinishLeftRegions(Tesselator tess,
ActiveRegion regFirst, ActiveRegion regLast)
{
ActiveRegion reg, regPrev;
HalfEdge e, ePrev;
regPrev = regFirst;
ePrev = regFirst.upperHalfEdge;
while (regPrev != regLast)
{
regPrev.fixUpperEdge = false; /* placement was OK */
reg = RegionBelow(regPrev);
e = reg.upperHalfEdge;
if (e.originVertex != ePrev.originVertex)
{
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 = Mesh.meshConnect(ePrev.Lprev, e.otherHalfOfThisEdge);
FixUpperEdge(reg, e);
}
/* Relink edges so that ePrev.Onext == e */
if (ePrev.nextEdgeCCWAroundOrigin != e)
{
Mesh.meshSplice(e.Oprev, e);
Mesh.meshSplice(ePrev, e);
}
FinishRegion(tess, regPrev); /* may change reg.eUp */
ePrev = reg.upperHalfEdge;
regPrev = reg;
}
return ePrev;
}