static void ConnectRightVertex(Tesselator tess, ActiveRegion regUp, HalfEdge 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.
*/
{
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);
}
/* __gl_meshAddEdgeVertex( eOrg ) creates a new edge eNew such that
* eNew == eOrg.Lnext, and eNew.Dst is a newly created vertex.
* eOrg and eNew will have the same left face.
*/
private static HalfEdge meshAddEdgeVertex(HalfEdge eOrg)
{
HalfEdge eNewSym;
HalfEdge eNew = MakeEdge(eOrg);
eNewSym = eNew.otherHalfOfThisEdge;
/* Connect the new edge appropriately */
Splice(eNew, eOrg.nextEdgeCCWAroundLeftFace);
/* Set the vertex and face information */
eNew.originVertex = eOrg.directionVertex;
{
ContourVertex newVertex = new ContourVertex();
MakeVertex(newVertex, eNewSym, eNew.originVertex);
}
eNew.leftFace = eNewSym.leftFace = eOrg.leftFace;
return eNew;
}
/* MakeEdge creates a new pair of half-edges which form their own loop.
* No vertex or face structures are allocated, but these must be assigned
* before the current edge operation is completed.
*/
private static HalfEdge MakeEdge(HalfEdge eNext)
{
HalfEdge ePrev;
EdgePair pair = new EdgePair();
/* Make sure eNext points to the first edge of the edge pair */
if (eNext.otherHalfOfThisEdge.isFirstHalfEdge)
{
eNext = eNext.otherHalfOfThisEdge;
}
/* Insert in circular doubly-linked list before eNext.
* Note that the prev pointer is stored in Sym.next.
*/
ePrev = eNext.otherHalfOfThisEdge.nextHalfEdge;
pair.eSym.nextHalfEdge = ePrev;
ePrev.otherHalfOfThisEdge.nextHalfEdge = pair.e;
pair.e.nextHalfEdge = eNext;
eNext.otherHalfOfThisEdge.nextHalfEdge = pair.eSym;
pair.e.isFirstHalfEdge = true;
pair.e.otherHalfOfThisEdge = pair.eSym;
pair.e.nextEdgeCCWAroundOrigin = pair.e;
pair.e.nextEdgeCCWAroundLeftFace = pair.eSym;
pair.e.originVertex = null;
pair.e.leftFace = null;
pair.e.winding = 0;
pair.e.regionThisIsUpperEdgeOf = null;
pair.eSym.isFirstHalfEdge = false;
pair.eSym.otherHalfOfThisEdge = pair.e;
pair.eSym.nextEdgeCCWAroundOrigin = pair.eSym;
pair.eSym.nextEdgeCCWAroundLeftFace = pair.e;
pair.eSym.originVertex = null;
pair.eSym.leftFace = null;
pair.eSym.winding = 0;
pair.eSym.regionThisIsUpperEdgeOf = null;
return pair.e;
}
/* Splice( a, b ) is best described by the Guibas/Stolfi paper or the
* CS348a notes (see mesh.h). Basically it modifies the mesh so that
* a.Onext and b.Onext are exchanged. This can have various effects
* depending on whether a and b belong to different face or vertex rings.
* For more explanation see __gl_meshSplice() below.
*/
private static void Splice(HalfEdge a, HalfEdge b)
{
HalfEdge aOnext = a.nextEdgeCCWAroundOrigin;
HalfEdge bOnext = b.nextEdgeCCWAroundOrigin;
aOnext.otherHalfOfThisEdge.nextEdgeCCWAroundLeftFace = b;
bOnext.otherHalfOfThisEdge.nextEdgeCCWAroundLeftFace = a;
a.nextEdgeCCWAroundOrigin = bOnext;
b.nextEdgeCCWAroundOrigin = aOnext;
}
/* KillEdge( eDel ) destroys an edge (the half-edges eDel and eDel.Sym),
* and removes from the global edge list.
*/
private static void KillEdge(HalfEdge eDel)
{
HalfEdge ePrev, eNext;
/* Half-edges are allocated in pairs, see EdgePair above */
if (eDel.otherHalfOfThisEdge.isFirstHalfEdge)
{
eDel = eDel.otherHalfOfThisEdge;
}
/* delete from circular doubly-linked list */
eNext = eDel.nextHalfEdge;
ePrev = eDel.otherHalfOfThisEdge.nextHalfEdge;
eNext.otherHalfOfThisEdge.nextHalfEdge = ePrev;
ePrev.otherHalfOfThisEdge.nextHalfEdge = eNext;
}
/*
* 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.
*/
static ActiveRegion AddRegionBelow(Tesselator tess,
ActiveRegion regAbove,
HalfEdge eNewUp)
{
ActiveRegion 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;
}
private static void MakeFace(Face newFace, HalfEdge eOrig, Face fNext)
{
HalfEdge e;
Face fPrev;
Face fNew = newFace;
fNew.indexDebug = faceIndex++;
// insert in circular doubly-linked list before fNext
fPrev = fNext.prevFace;
fNew.prevFace = fPrev;
fPrev.nextFace = fNew;
fNew.nextFace = fNext;
fNext.prevFace = fNew;
fNew.halfEdgeThisIsLeftFaceOf = eOrig;
fNew.trail = null;
fNew.marked = false;
// The new face is marked "inside" if the old one was. This is a
// convenience for the common case where a face has been split in two.
fNew.isInterior = fNext.isInterior;
// fix other edges on this face loop
e = eOrig;
do
{
e.leftFace = fNew;
e = e.nextEdgeCCWAroundLeftFace;
} while (e != eOrig);
}
public void AddVertex(double[] coords3, int data)
{
int i;
double x;
double[] clamped = new double[3];
RequireState(ProcessingState.InContour);
if (emptyCache)
{
EmptyCache();
lastHalfEdge = null;
}
for (i = 0; i < 3; ++i)
{
x = coords3[i];
if (x < -MAX_COORD)
{
throw new Exception("Your coordinate exceeded -" + MAX_COORD.ToString() + ".");
}
if (x > MAX_COORD)
{
throw new Exception("Your coordinate exceeded " + MAX_COORD.ToString() + ".");
}
clamped[i] = x;
}
if (mesh == null)
{
if (cacheCount < MAX_CACHE_SIZE)
{
CacheVertex(clamped, data);
return;
}
EmptyCache();
}
AddVertex(clamped[0], clamped[1], data);
}
public void BeginContour()
{
RequireState(ProcessingState.InPolygon);
processingState = ProcessingState.InContour;
lastHalfEdge = null;
if (cacheCount > 0)
{
// Just set a flag so we don't get confused by empty contours
emptyCache = true;
}
}
public int size; /* number of triangles used */
#endregion Fields
#region Constructors
public FaceCount(int _size, HalfEdge _eStart, RenderDelegate _render)
{
size = _size;
eStart = _eStart;
render = _render;
}
// routine to render this primitive
public void CallRender(Tesselator tess, HalfEdge edge, int data)
{
render(tess, edge, data);
}
public FaceCount(int _size, HalfEdge _eStart, RenderDelegate _render)
{
size = _size;
eStart = _eStart;
render = _render;
}
/*
* 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.
*/
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);
}
/*
* 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.
*/
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);
}
}
static bool FixUpperEdge(ActiveRegion reg, HalfEdge newEdge)
/*
* Replace an upper edge which needs fixing (see ConnectRightVertex).
*/
{
if (!reg.fixUpperEdge)
{
throw new Exception();
}
Mesh.DeleteHalfEdge(reg.upperHalfEdge);
reg.fixUpperEdge = false;
reg.upperHalfEdge = newEdge;
newEdge.regionThisIsUpperEdgeOf = reg;
return true;
}
static void RenderFan(Tesselator tess, HalfEdge e, int size)
{
/* Render as many CCW triangles as possible in a fan starting from
* edge "e". The fan *should* contain exactly "size" triangles
* (otherwise we've goofed up somewhere).
*/
tess.CallBegin(Tesselator.TriangleListType.TriangleFan);
tess.CallVertex(e.originVertex.clientIndex);
tess.CallVertex(e.directionVertex.clientIndex);
while (!e.leftFace.Marked())
{
e.leftFace.marked = true;
--size;
e = e.nextEdgeCCWAroundOrigin;
tess.CallVertex(e.directionVertex.clientIndex);
}
if (size != 0)
{
throw new Exception();
}
tess.CallEnd();
}
static void AddRightEdges(Tesselator tess, ActiveRegion regUp,
HalfEdge eFirst, HalfEdge eLast, HalfEdge eTopLeft,
bool cleanUp)
/*
* 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.
*/
{
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);
}
}
static void RenderStrip(Tesselator tess, HalfEdge halfEdge, int size)
{
/* Render as many CCW triangles as possible in a strip starting from
* edge "e". The strip *should* contain exactly "size" triangles
* (otherwise we've goofed up somewhere).
*/
tess.CallBegin(Tesselator.TriangleListType.TriangleStrip);
tess.CallVertex(halfEdge.originVertex.clientIndex);
tess.CallVertex(halfEdge.directionVertex.clientIndex);
while (!halfEdge.leftFace.Marked())
{
halfEdge.leftFace.marked = true;
--size;
halfEdge = halfEdge.Dprev;
tess.CallVertex(halfEdge.originVertex.clientIndex);
if (halfEdge.leftFace.Marked()) break;
halfEdge.leftFace.marked = true;
--size;
halfEdge = halfEdge.nextEdgeCCWAroundOrigin;
tess.CallVertex(halfEdge.directionVertex.clientIndex);
}
if (size != 0)
{
throw new Exception();
}
tess.CallEnd();
}
/* face.TessellateMonoRegion() 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).
*/
internal bool TessellateMonoRegion()
{
/* 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.
*/
HalfEdge up = this.halfEdgeThisIsLeftFaceOf;
if (up.nextEdgeCCWAroundLeftFace == up || up.nextEdgeCCWAroundLeftFace.nextEdgeCCWAroundLeftFace == up)
{
throw new Exception();
}
for (; up.directionVertex.VertLeq(up.originVertex); up = up.Lprev)
{
;
}
for (; up.originVertex.VertLeq(up.directionVertex); up = up.nextEdgeCCWAroundLeftFace)
{
;
}
HalfEdge lo = up.Lprev;
while (up.nextEdgeCCWAroundLeftFace != lo)
{
if (up.directionVertex.VertLeq(lo.originVertex))
{
/* 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.nextEdgeCCWAroundLeftFace != up && (lo.nextEdgeCCWAroundLeftFace.EdgeGoesLeft() ||
ContourVertex.EdgeSign(lo.originVertex, lo.directionVertex, lo.nextEdgeCCWAroundLeftFace.directionVertex) <= 0))
{
HalfEdge tempHalfEdge = Mesh.meshConnect(lo.nextEdgeCCWAroundLeftFace, lo);
lo = tempHalfEdge.otherHalfOfThisEdge;
}
lo = lo.Lprev;
}
else
{
/* lo.Org is on the left. We can make CCW triangles from up.Dst. */
while (lo.nextEdgeCCWAroundLeftFace != up && (up.Lprev.EdgeGoesRight() ||
ContourVertex.EdgeSign(up.directionVertex, up.originVertex, up.Lprev.originVertex) >= 0))
{
HalfEdge tempHalfEdge = Mesh.meshConnect(up, up.Lprev);
up = tempHalfEdge.otherHalfOfThisEdge;
}
up = up.nextEdgeCCWAroundLeftFace;
}
}
// Now lo.Org == up.Dst == the leftmost vertex. The remaining region
// can be tessellated in a fan from this leftmost vertex.
if (lo.nextEdgeCCWAroundLeftFace == up)
{
throw new Exception();
}
while (lo.nextEdgeCCWAroundLeftFace.nextEdgeCCWAroundLeftFace != up)
{
HalfEdge tempHalfEdge = Mesh.meshConnect(lo.nextEdgeCCWAroundLeftFace, lo);
lo = tempHalfEdge.otherHalfOfThisEdge;
}
return(true);
}
bool AddVertex(double x, double y, int data)
{
HalfEdge e;
e = this.lastHalfEdge;
if (e == null)
{
/* Make a self-loop (one vertex, one edge). */
e = this.mesh.MakeEdge();
Mesh.meshSplice(e, e.otherHalfOfThisEdge);
}
else
{
/* Create a new vertex and edge which immediately follow e
* in the ordering around the left face.
*/
if (Mesh.meshSplitEdge(e) == null)
{
return false;
}
e = e.nextEdgeCCWAroundLeftFace;
}
/* The new vertex is now e.Org. */
e.originVertex.clientIndex = data;
e.originVertex.coords[0] = x;
e.originVertex.coords[1] = y;
/* The winding of an edge says how the winding number changes as we
* cross from the edge''s right face to its left face. We add the
* vertices in such an order that a CCW contour will add +1 to
* the winding number of the region inside the contour.
*/
e.winding = 1;
e.otherHalfOfThisEdge.winding = -1;
this.lastHalfEdge = e;
return true;
}
/* MakeVertex( newVertex, eOrig, vNext ) attaches a new vertex and makes it the
* origin of all edges in the vertex loop to which eOrig belongs. "vNext" gives
* a place to insert the new vertex in the global vertex list. We insert
* the new vertex *before* vNext so that algorithms which walk the vertex
* list will not see the newly created vertices.
*/
private static void MakeVertex(ContourVertex newVertex, HalfEdge eOrig, ContourVertex vNext)
{
HalfEdge e;
ContourVertex vPrev;
ContourVertex vNew = newVertex;
/* insert in circular doubly-linked list before vNext */
vPrev = vNext.prevVertex;
vNew.prevVertex = vPrev;
vPrev.nextVertex = vNew;
vNew.nextVertex = vNext;
vNext.prevVertex = vNew;
vNew.edgeThisIsOriginOf = eOrig;
vNew.clientIndex = 0;
/* leave coords, s, t undefined */
/* fix other edges on this vertex loop */
e = eOrig;
do
{
e.originVertex = vNew;
e = e.nextEdgeCCWAroundOrigin;
} while (e != eOrig);
}
FaceCount MaximumFan(HalfEdge eOrig)
{
/* eOrig.Lface is the face we want to render. We want to find the size
* of a maximal fan around eOrig.Org. To do this we just walk around
* the origin vertex as far as possible in both directions.
*/
FaceCount newFace = new FaceCount(0, null, new FaceCount.RenderDelegate(RenderFan));
Face trail = null;
HalfEdge e;
for (e = eOrig; !e.leftFace.Marked(); e = e.nextEdgeCCWAroundOrigin)
{
Face.AddToTrail(ref e.leftFace, ref trail);
++newFace.size;
}
for (e = eOrig; !e.rightFace.Marked(); e = e.Oprev)
{
Face f = e.rightFace;
Face.AddToTrail(ref f, ref trail);
e.rightFace = f;
++newFace.size;
}
newFace.eStart = e;
Face.FreeTrail(ref trail);
return newFace;
}
/* __gl_meshSplice( eOrg, eDst ) is the basic operation for changing the
* mesh connectivity and topology. It changes the mesh so that
* eOrg.Onext <- OLD( eDst.Onext )
* eDst.Onext <- OLD( eOrg.Onext )
* where OLD(...) means the value before the meshSplice operation.
*
* This can have two effects on the vertex structure:
* - if eOrg.Org != eDst.Org, the two vertices are merged together
* - if eOrg.Org == eDst.Org, the origin is split into two vertices
* In both cases, eDst.Org is changed and eOrg.Org is untouched.
*
* Similarly (and independently) for the face structure,
* - if eOrg.Lface == eDst.Lface, one loop is split into two
* - if eOrg.Lface != eDst.Lface, two distinct loops are joined into one
* In both cases, eDst.Lface is changed and eOrg.Lface is unaffected.
*
* Some special cases:
* If eDst == eOrg, the operation has no effect.
* If eDst == eOrg.Lnext, the new face will have a single edge.
* If eDst == eOrg.Lprev, the old face will have a single edge.
* If eDst == eOrg.Onext, the new vertex will have a single edge.
* If eDst == eOrg.Oprev, the old vertex will have a single edge.
*/
public static void meshSplice(HalfEdge eOrg, HalfEdge eDst)
{
bool joiningLoops = false;
bool joiningVertices = false;
if (eOrg == eDst) return;
if (eDst.originVertex != eOrg.originVertex)
{
/* We are merging two disjoint vertices -- destroy eDst.Org */
joiningVertices = true;
KillVertex(eDst.originVertex, eOrg.originVertex);
}
if (eDst.leftFace != eOrg.leftFace)
{
/* We are connecting two disjoint loops -- destroy eDst.Lface */
joiningLoops = true;
KillFace(eDst.leftFace, eOrg.leftFace);
}
/* Change the edge structure */
Splice(eDst, eOrg);
if (!joiningVertices)
{
ContourVertex newVertex = new ContourVertex();
/* We split one vertex into two -- the new vertex is eDst.Org.
* Make sure the old vertex points to a valid half-edge.
*/
MakeVertex(newVertex, eDst, eOrg.originVertex);
eOrg.originVertex.edgeThisIsOriginOf = eOrg;
}
if (!joiningLoops)
{
Face newFace = new Face();
/* We split one loop into two -- the new loop is eDst.Lface.
* Make sure the old face points to a valid half-edge.
*/
MakeFace(newFace, eDst, eOrg.leftFace);
eOrg.leftFace.halfEdgeThisIsLeftFaceOf = eOrg;
}
}
FaceCount MaximumStrip(HalfEdge eOrig)
{
/* Here we are looking for a maximal strip that contains the vertices
* eOrig.Org, eOrig.Dst, eOrig.Lnext.Dst (in that order or the
* reverse, such that all triangles are oriented CCW).
*
* Again we walk forward and backward as far as possible. However for
* strips there is a twist: to get CCW orientations, there must be
* an *even* number of triangles in the strip on one side of eOrig.
* We walk the strip starting on a side with an even number of triangles;
* if both side have an odd number, we are forced to shorten one side.
*/
FaceCount newFace = new FaceCount(0, null, RenderStrip);
int headSize = 0, tailSize = 0;
Face trail = null;
HalfEdge e, eTail, eHead;
for (e = eOrig; !e.leftFace.Marked(); ++tailSize, e = e.nextEdgeCCWAroundOrigin)
{
Face.AddToTrail(ref e.leftFace, ref trail);
++tailSize;
e = e.Dprev;
if (e.leftFace.Marked()) break;
Face.AddToTrail(ref e.leftFace, ref trail);
}
eTail = e;
for (e = eOrig; !e.rightFace.Marked(); ++headSize, e = e.Dnext)
{
Face f = e.rightFace;
Face.AddToTrail(ref f, ref trail);
e.rightFace = f;
++headSize;
e = e.Oprev;
if (e.rightFace.Marked()) break;
f = e.rightFace;
Face.AddToTrail(ref f, ref trail);
e.rightFace = f;
}
eHead = e;
newFace.size = tailSize + headSize;
if (IsEven(tailSize))
{
newFace.eStart = eTail.otherHalfOfThisEdge;
}
else if (IsEven(headSize))
{
newFace.eStart = eHead;
}
else
{
/* Both sides have odd length, we must shorten one of them. In fact,
* we must start from eHead to guarantee inclusion of eOrig.Lface.
*/
--newFace.size;
newFace.eStart = eHead.nextEdgeCCWAroundOrigin;
}
Face.FreeTrail(ref trail);
return newFace;
}
/* __gl_meshDelete( eDel ) removes the edge eDel. There are several cases:
* if (eDel.Lface != eDel.Rface), we join two loops into one; the loop
* eDel.Lface is deleted. Otherwise, we are splitting one loop into two;
* the newly created loop will contain eDel.Dst. If the deletion of eDel
* would create isolated vertices, those are deleted as well.
*
* This function could be implemented as two calls to __gl_meshSplice
* plus a few calls to free, but this would allocate and delete
* unnecessary vertices and faces.
*/
public static void DeleteHalfEdge(HalfEdge edgeToDelete)
{
HalfEdge otherHalfOfEdgeToDelete = edgeToDelete.otherHalfOfThisEdge;
bool joiningLoops = false;
// First step: disconnect the origin vertex eDel.Org. We make all
// changes to get a consistent mesh in this "intermediate" state.
if (edgeToDelete.leftFace != edgeToDelete.rightFace)
{
// We are joining two loops into one -- remove the left face
joiningLoops = true;
KillFace(edgeToDelete.leftFace, edgeToDelete.rightFace);
}
if (edgeToDelete.nextEdgeCCWAroundOrigin == edgeToDelete)
{
KillVertex(edgeToDelete.originVertex, null);
}
else
{
// Make sure that eDel.Org and eDel.Rface point to valid half-edges
edgeToDelete.rightFace.halfEdgeThisIsLeftFaceOf = edgeToDelete.Oprev;
edgeToDelete.originVertex.edgeThisIsOriginOf = edgeToDelete.nextEdgeCCWAroundOrigin;
Splice(edgeToDelete, edgeToDelete.Oprev);
if (!joiningLoops)
{
Face newFace = new Face();
// We are splitting one loop into two -- create a new loop for eDel.
MakeFace(newFace, edgeToDelete, edgeToDelete.leftFace);
}
}
// Claim: the mesh is now in a consistent state, except that eDel.Org
// may have been deleted. Now we disconnect eDel.Dst.
if (otherHalfOfEdgeToDelete.nextEdgeCCWAroundOrigin == otherHalfOfEdgeToDelete)
{
KillVertex(otherHalfOfEdgeToDelete.originVertex, null);
KillFace(otherHalfOfEdgeToDelete.leftFace, null);
}
else
{
// Make sure that eDel.Dst and eDel.Lface point to valid half-edges
edgeToDelete.leftFace.halfEdgeThisIsLeftFaceOf = otherHalfOfEdgeToDelete.Oprev;
otherHalfOfEdgeToDelete.originVertex.edgeThisIsOriginOf = otherHalfOfEdgeToDelete.nextEdgeCCWAroundOrigin;
Splice(otherHalfOfEdgeToDelete, otherHalfOfEdgeToDelete.Oprev);
}
// Any isolated vertices or faces have already been freed.
KillEdge(edgeToDelete);
}
void RenderTriangle(Tesselator tess, HalfEdge e, int size)
{
/* Just add the triangle to a triangle list, so we can render all
* the separate triangles at once.
*/
if (size != 1)
{
throw new Exception();
}
Face.AddToTrail(ref e.leftFace, ref this.lonelyTriList);
}
/* __gl_meshSplitEdge( eOrg ) splits eOrg into two edges eOrg and eNew,
* such that eNew == eOrg.Lnext. The new vertex is eOrg.Dst == eNew.Org.
* eOrg and eNew will have the same left face.
*/
public static HalfEdge meshSplitEdge(HalfEdge eOrg)
{
HalfEdge eNew;
HalfEdge tempHalfEdge = meshAddEdgeVertex(eOrg);
eNew = tempHalfEdge.otherHalfOfThisEdge;
/* Disconnect eOrg from eOrg.Dst and connect it to eNew.Org */
Splice(eOrg.otherHalfOfThisEdge, eOrg.otherHalfOfThisEdge.Oprev);
Splice(eOrg.otherHalfOfThisEdge, eNew);
/* Set the vertex and face information */
eOrg.directionVertex = eNew.originVertex;
eNew.directionVertex.edgeThisIsOriginOf = eNew.otherHalfOfThisEdge; /* may have pointed to eOrg.Sym */
eNew.rightFace = eOrg.rightFace;
eNew.winding = eOrg.winding; /* copy old winding information */
eNew.otherHalfOfThisEdge.winding = eOrg.otherHalfOfThisEdge.winding;
return eNew;
}
public FaceCount(int _size, HalfEdge _eStart, Action <Tesselator, HalfEdge, int> _render)
{
size = _size;
eStart = _eStart;
render = _render;
}
/* __gl_meshConnect( eOrg, eDst ) creates a new edge from eOrg.Dst
* to eDst.Org, and returns the corresponding half-edge eNew.
* If eOrg.Lface == eDst.Lface, this splits one loop into two,
* and the newly created loop is eNew.Lface. Otherwise, two disjoint
* loops are merged into one, and the loop eDst.Lface is destroyed.
*
* If (eOrg == eDst), the new face will have only two edges.
* If (eOrg.Lnext == eDst), the old face is reduced to a single edge.
* If (eOrg.Lnext.Lnext == eDst), the old face is reduced to two edges.
*/
public static HalfEdge meshConnect(HalfEdge eOrg, HalfEdge eDst)
{
HalfEdge eNewSym;
bool joiningLoops = false;
HalfEdge eNew = MakeEdge(eOrg);
eNewSym = eNew.otherHalfOfThisEdge;
if (eDst.leftFace != eOrg.leftFace)
{
/* We are connecting two disjoint loops -- destroy eDst.Lface */
joiningLoops = true;
KillFace(eDst.leftFace, eOrg.leftFace);
}
/* Connect the new edge appropriately */
Splice(eNew, eOrg.nextEdgeCCWAroundLeftFace);
Splice(eNewSym, eDst);
/* Set the vertex and face information */
eNew.originVertex = eOrg.directionVertex;
eNewSym.originVertex = eDst.originVertex;
eNew.leftFace = eNewSym.leftFace = eOrg.leftFace;
/* Make sure the old face points to a valid half-edge */
eOrg.leftFace.halfEdgeThisIsLeftFaceOf = eNewSym;
if (!joiningLoops)
{
Face newFace = new Face();
/* We split one loop into two -- the new loop is eNew.Lface */
MakeFace(newFace, eNew, eOrg.leftFace);
}
return eNew;
}
// routine to render this primitive
public void CallRender(Tesselator tess, HalfEdge edge, int data)
{
render(tess, edge, data);
}
/*
* Invariants for the Edge Dictionary.
* - each pair of adjacent edges e2=Succ(e1) satisfies EdgeLeq(e1,e2)
* at any valid location of the sweep event
* - if EdgeLeq(e2,e1) as well (at any valid sweep event), then e1 and e2
* share a common endpoint
* - for each e, e.Dst has been processed, but not e.Org
* - each edge e satisfies VertLeq(e.Dst,currentSweepVertex) && VertLeq(currentSweepVertex,e.Org)
* where "currentSweepVertex" is the current sweep line event.
* - no edge e has zero length
*
* Invariants for the Mesh (the processed portion).
* - the portion of the mesh left of the sweep line is a planar graph,
* ie. there is *some* way to embed it in the plane
* - no processed edge has zero length
* - no two processed vertices have identical coordinates
* - each "inside" region is monotone, ie. can be broken into two chains
* of monotonically increasing vertices according to VertLeq(v1,v2)
* - a non-invariant: these chains may intersect (very slightly)
*
* Invariants for the Sweep.
* - if none of the edges incident to the currentSweepVertex vertex have an activeRegion
* (ie. none of these edges are in the edge dictionary), then the vertex
* has only right-going edges.
* - if an edge is marked "fixUpperEdge" (it is a temporary edge introduced
* by ConnectRightVertex), then it is the only right-going edge from
* its associated vertex. (This says that these edges exist only
* when it is necessary.)
*/
//#undef MAX
//#undef MIN
//#define MAX(x,y) ((x) >= (y) ? (x) : (y))
//#define MIN(x,y) ((x) <= (y) ? (x) : (y))
/* When we merge two edges into one, we need to compute the combined
* winding of the new edge.
*/
static void AddWinding(HalfEdge eDst, HalfEdge eSrc)
{
eDst.winding += eSrc.winding;
eDst.otherHalfOfThisEdge.winding += eSrc.otherHalfOfThisEdge.winding;
}
private FaceCount MaximumStrip(HalfEdge eOrig)
{
/* Here we are looking for a maximal strip that contains the vertices
* eOrig.Org, eOrig.Dst, eOrig.Lnext.Dst (in that order or the
* reverse, such that all triangles are oriented CCW).
*
* Again we walk forward and backward as far as possible. However for
* strips there is a twist: to get CCW orientations, there must be
* an *even* number of triangles in the strip on one side of eOrig.
* We walk the strip starting on a side with an even number of triangles;
* if both side have an odd number, we are forced to shorten one side.
*/
FaceCount newFace = new FaceCount(0, null, RenderStrip);
int headSize = 0, tailSize = 0;
Face trail = null;
HalfEdge e, eTail, eHead;
for (e = eOrig; !e.leftFace.Marked(); ++tailSize, e = e.nextEdgeCCWAroundOrigin)
{
Face.AddToTrail(ref e.leftFace, ref trail);
++tailSize;
e = e.Dprev;
if (e.leftFace.Marked())
{
break;
}
Face.AddToTrail(ref e.leftFace, ref trail);
}
eTail = e;
for (e = eOrig; !e.rightFace.Marked(); ++headSize, e = e.Dnext)
{
Face f = e.rightFace;
Face.AddToTrail(ref f, ref trail);
e.rightFace = f;
++headSize;
e = e.Oprev;
if (e.rightFace.Marked())
{
break;
}
f = e.rightFace;
Face.AddToTrail(ref f, ref trail);
e.rightFace = f;
}
eHead = e;
newFace.size = tailSize + headSize;
if (IsEven(tailSize))
{
newFace.eStart = eTail.otherHalfOfThisEdge;
}
else if (IsEven(headSize))
{
newFace.eStart = eHead;
}
else
{
/* Both sides have odd length, we must shorten one of them. In fact,
* we must start from eHead to guarantee inclusion of eOrig.Lface.
*/
--newFace.size;
newFace.eStart = eHead.nextEdgeCCWAroundOrigin;
}
Face.FreeTrail(ref trail);
return(newFace);
}
static ActiveRegion AddRegionBelow(Tesselator tess,
ActiveRegion regAbove,
HalfEdge eNewUp)
/*
* 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.
*/
{
ActiveRegion 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;
}
/* __gl_meshCheckMesh( mesh ) checks a mesh for self-consistency.
*/
public void CheckMesh()
{
Face fHead = this.faceHead;
ContourVertex vHead = this.vertexHead;
HalfEdge eHead = this.halfEdgeHead;
Face f, fPrev;
ContourVertex v, vPrev;
HalfEdge e, ePrev;
fPrev = fHead;
for (fPrev = fHead; (f = fPrev.nextFace) != fHead; fPrev = f)
{
if (f.prevFace != fPrev)
{
throw new Exception();
}
e = f.halfEdgeThisIsLeftFaceOf;
do
{
if (e.otherHalfOfThisEdge == e)
{
throw new Exception();
}
if (e.otherHalfOfThisEdge.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundLeftFace.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge.nextEdgeCCWAroundLeftFace != e)
{
throw new Exception();
}
if (e.leftFace != f)
{
throw new Exception();
}
e = e.nextEdgeCCWAroundLeftFace;
} while (e != f.halfEdgeThisIsLeftFaceOf);
}
if (f.prevFace != fPrev || f.halfEdgeThisIsLeftFaceOf != null)
{
throw new Exception();
}
vPrev = vHead;
for (vPrev = vHead; (v = vPrev.nextVertex) != vHead; vPrev = v)
{
if (v.prevVertex != vPrev)
{
throw new Exception();
}
e = v.edgeThisIsOriginOf;
do
{
if (e.otherHalfOfThisEdge == e)
{
throw new Exception();
}
if (e.otherHalfOfThisEdge.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundLeftFace.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge.nextEdgeCCWAroundLeftFace != e)
{
throw new Exception();
}
if (e.originVertex != v)
{
throw new Exception();
}
e = e.nextEdgeCCWAroundOrigin;
} while (e != v.edgeThisIsOriginOf);
}
if (v.prevVertex != vPrev || v.edgeThisIsOriginOf != null || v.clientIndex != 0)
{
throw new Exception();
}
ePrev = eHead;
for (ePrev = eHead; (e = ePrev.nextHalfEdge) != eHead; ePrev = e)
{
if (e.otherHalfOfThisEdge.nextHalfEdge != ePrev.otherHalfOfThisEdge)
{
throw new Exception();
}
if (e.otherHalfOfThisEdge == e)
{
throw new Exception();
}
if (e.otherHalfOfThisEdge.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.originVertex == null)
{
throw new Exception();
}
if (e.directionVertex == null)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundLeftFace.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge != e)
{
throw new Exception();
}
if (e.nextEdgeCCWAroundOrigin.otherHalfOfThisEdge.nextEdgeCCWAroundLeftFace != e)
{
throw new Exception();
}
}
if (e.otherHalfOfThisEdge.nextHalfEdge != ePrev.otherHalfOfThisEdge ||
e.otherHalfOfThisEdge != this.otherHalfOfThisEdgeHead ||
e.otherHalfOfThisEdge.otherHalfOfThisEdge != e ||
e.originVertex != null || e.directionVertex != null ||
e.leftFace != null || e.rightFace != null)
{
throw new Exception();
}
}
static void SpliceMergeVertices(Tesselator tess, HalfEdge e1, HalfEdge e2)
/*
* Two vertices with idential coordinates are combined into one.
* e1.Org is kept, while e2.Org is discarded.
*/
{
int[] data4 = new int[4];
double[] weights4 = new double[] { 0.5f, 0.5f, 0, 0 };
data4[0] = e1.originVertex.clientIndex;
data4[1] = e2.originVertex.clientIndex;
CallCombine(tess, e1.originVertex, data4, weights4, false);
Mesh.meshSplice(e1, e2);
}
/*
* Two vertices with idential coordinates are combined into one.
* e1.Org is kept, while e2.Org is discarded.
*/
static void SpliceMergeVertices(Tesselator tess, HalfEdge e1, HalfEdge e2)
{
int[] data4 = new int[4];
double[] weights4 = new double[] { 0.5f, 0.5f, 0, 0 };
data4[0] = e1.originVertex.clientIndex;
data4[1] = e2.originVertex.clientIndex;
CallCombine(tess, e1.originVertex, data4, weights4, false);
Mesh.meshSplice(e1, e2);
}
