/* 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.
*/
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);
}
public static bool VertCCW(ContourVertex <T> u, ContourVertex <T> v, ContourVertex <T> w)
{
/* For almost-degenerate situations, the results are not reliable.
* Unless the floating-point arithmetic can be performed without
* rounding errors, *any* implementation will give incorrect results
* on some degenerate inputs, so the client must have some way to
* handle this situation.
*/
return((u.x.Multiply(v.y.Subtract(w.y)).Add(v.x.Multiply(w.y.Subtract(u.y))).Add(w.x.Multiply(u.y.Subtract(v.y)))).GreaterThanOrEqualTo(0));
}
public C5.IPriorityQueueHandle <ContourVertex <T> > priorityQueueHandle; /* to allow deletion from priority queue */
public int CompareTo(ContourVertex <T> otherVertex)
{
if (VertEq(otherVertex))
{
return(0);
}
if (this.VertLeq(otherVertex))
{
return(-1);
}
return(1);
}
// __gl_meshMakeEdge creates one edge, two vertices, and a loop (face).
// The loop consists of the two new half-edges.
public HalfEdge MakeEdge()
{
ContourVertex newVertex1 = new ContourVertex();
ContourVertex newVertex2 = new ContourVertex();
Face newFace = new Face();
HalfEdge e;
e = MakeEdge(this.halfEdgeHead);
MakeVertex(newVertex1, e, this.vertexHead);
MakeVertex(newVertex2, e.otherHalfOfThisEdge, this.vertexHead);
MakeFace(newFace, e, this.faceHead);
return(e);
}
private void ProjectPolygon()
{
ContourVertex v, vHead = this.mesh.vertexHead;
// Project the vertices onto the sweep plane
for (v = vHead.nextVertex; v != vHead; v = v.nextVertex)
{
v.x = v.coords[0];
v.y = -v.coords[1];
}
CheckOrientation();
}
/* __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;
}
}
/* __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.
*/
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);
}
/* KillVertex( vDel ) destroys a vertex and removes it from the global
* vertex list. It updates the vertex loop to point to a given new vertex.
*/
static void KillVertex(ContourVertex vDel, ContourVertex newOrg)
{
HalfEdge e, eStart = vDel.edgeThisIsOriginOf;
ContourVertex vPrev, vNext;
/* change the origin of all affected edges */
e = eStart;
do
{
e.originVertex = newOrg;
e = e.nextEdgeCCWAroundOrigin;
} while (e != eStart);
/* delete from circular doubly-linked list */
vPrev = vDel.prevVertex;
vNext = vDel.nextVertex;
vNext.prevVertex = vPrev;
vPrev.nextVertex = vNext;
}
/* __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 originalEdge)
{
HalfEdge newEdgeOtherHalf;
HalfEdge newEdge = MakeEdge(originalEdge);
newEdgeOtherHalf = newEdge.otherHalfOfThisEdge;
/* Connect the new edge appropriately */
Splice(newEdge, originalEdge.nextEdgeCCWAroundLeftFace);
/* Set the vertex and face information */
newEdge.originVertex = originalEdge.directionVertex;
{
ContourVertex newVertex = new ContourVertex();
MakeVertex(newVertex, newEdgeOtherHalf, newEdge.originVertex);
}
newEdge.leftFace = newEdgeOtherHalf.leftFace = originalEdge.leftFace;
return(newEdge);
}
public static T EdgeEval(ContourVertex <T> u, ContourVertex <T> v, ContourVertex <T> w)
{
/* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
* evaluates the t-coord of the edge uw at the s-coord of the vertex v.
* Returns v.t - (uw)(v.s), ie. the signed distance from uw to v.
* If uw is vertical (and thus passes thru v), the result is zero.
*
* The calculation is extremely accurate and stable, even when v
* is very close to u or w. In particular if we set v.t = 0 and
* let r be the negated result (this evaluates (uw)(v.s)), then
* r is guaranteed to satisfy MIN(u.t,w.t) <= r <= MAX(u.t,w.t).
*/
T gapL, gapR;
if (!((u.VertLeq(u) && v.VertLeq(v))))
{
throw new Exception();
}
gapL = v.x.Subtract(u.x);
gapR = w.x.Subtract(v.x);
if (gapL.Add(gapR).GreaterThan(0))
{
if (gapL.LessThan(gapR))
{
return(v.y.Subtract(u.y).Add(
u.y.Subtract(w.y).Multiply(
gapL.Divide(gapL.Add(gapR)))));
}
else
{
return(v.y.Subtract(w.y).Add(w.y.Subtract(u.y).Multiply(gapR.Divide(gapL.Add(gapR)))));
}
}
// vertical line
return(M.Zero <T>());
}
static public T EdgeSign(ContourVertex <T> u, ContourVertex <T> v, ContourVertex <T> w)
{
/* Returns a number whose sign matches EdgeEval(u,w) but which
* is cheaper to evaluate. Returns > 0, == 0 , or < 0
* as v is above, on, or below the edge uw.
*/
T gapL, gapR;
if (!u.VertLeq(v) || !v.VertLeq(w))
{
throw new System.Exception();
}
gapL = v.x.Subtract(u.x);
gapR = w.x.Subtract(v.x);
if (gapL.Add(gapR).GreaterThan(0))
{
return(v.y.Subtract(w.y).Multiply(gapL).Add(v.y.Subtract(u.y).Multiply(gapR)));
}
/* vertical line */
return(M.Zero <T>());
}
/* __gl_meshUnion( mesh1, mesh2 ) forms the union of all structures in
* both meshes, and returns the new mesh (the old meshes are destroyed).
*/
Mesh meshUnion(Mesh mesh1, Mesh mesh2)
{
Face f1 = mesh1.faceHead;
ContourVertex v1 = mesh1.vertexHead;
HalfEdge e1 = mesh1.halfEdgeHead;
Face f2 = mesh2.faceHead;
ContourVertex v2 = mesh2.vertexHead;
HalfEdge e2 = mesh2.halfEdgeHead;
/* Add the faces, vertices, and edges of mesh2 to those of mesh1 */
if (f2.nextFace != f2)
{
f1.prevFace.nextFace = f2.nextFace;
f2.nextFace.prevFace = f1.prevFace;
f2.prevFace.nextFace = f1;
f1.prevFace = f2.prevFace;
}
if (v2.nextVertex != v2)
{
v1.prevVertex.nextVertex = v2.nextVertex;
v2.nextVertex.prevVertex = v1.prevVertex;
v2.prevVertex.nextVertex = v1;
v1.prevVertex = v2.prevVertex;
}
if (e2.nextHalfEdge != e2)
{
e1.otherHalfOfThisEdge.nextHalfEdge.otherHalfOfThisEdge.nextHalfEdge = e2.nextHalfEdge;
e2.nextHalfEdge.otherHalfOfThisEdge.nextHalfEdge = e1.otherHalfOfThisEdge.nextHalfEdge;
e2.otherHalfOfThisEdge.nextHalfEdge.otherHalfOfThisEdge.nextHalfEdge = e1;
e1.otherHalfOfThisEdge.nextHalfEdge = e2.otherHalfOfThisEdge.nextHalfEdge;
}
mesh2 = null;
return(mesh1);
}
private void CheckOrientation()
{
double area;
Face curFace, faceHead = this.mesh.faceHead;
ContourVertex vHead = this.mesh.vertexHead;
HalfEdge curHalfEdge;
/* When we compute the normal automatically, we choose the orientation
* so that the sum of the signed areas of all contours is non-negative.
*/
area = 0;
for (curFace = faceHead.nextFace; curFace != faceHead; curFace = curFace.nextFace)
{
curHalfEdge = curFace.halfEdgeThisIsLeftFaceOf;
if (curHalfEdge.winding <= 0)
{
continue;
}
do
{
area += (curHalfEdge.originVertex.x - curHalfEdge.directionVertex.x)
* (curHalfEdge.originVertex.y + curHalfEdge.directionVertex.y);
curHalfEdge = curHalfEdge.nextEdgeCCWAroundLeftFace;
} while (curHalfEdge != curFace.halfEdgeThisIsLeftFaceOf);
}
if (area < 0)
{
/* Reverse the orientation by flipping all the t-coordinates */
for (ContourVertex curVertex = vHead.nextVertex; curVertex != vHead; curVertex = curVertex.nextVertex)
{
curVertex.y = -curVertex.y;
}
}
}
/* __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();
}
}
public bool TransLeq(ContourVertex <T> v)
{
return((this.y.LessThan(v.y)) || (this.y.Equals(v.y) && this.x.LessThanOrEqualTo(v.x)));
}
public bool VertLeq(ContourVertex <T> v)
{
return((this.x.LessThan(v.x)) || (this.x.Equals(v.x) && this.y.LessThan(v.y)));
}
public bool VertEq(ContourVertex <T> v)
{
return((this.x.Equals(v.x)) && this.y.Equals(v.y));
}
/* 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 <T> 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 <T> 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 <T> .EdgeSign(lo.originVertex, lo.directionVertex, lo.nextEdgeCCWAroundLeftFace.directionVertex).LessThanOrEqualTo(0)))
{
HalfEdge <T> tempHalfEdge = Mesh <T> .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 <T> .EdgeSign(up.directionVertex, up.originVertex, up.Lprev.originVertex).GreaterThanOrEqualTo(0)))
{
HalfEdge <T> tempHalfEdge = Mesh <T> .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 <T> tempHalfEdge = Mesh <T> .meshConnect(lo.nextEdgeCCWAroundLeftFace, lo);
lo = tempHalfEdge.otherHalfOfThisEdge;
}
return(true);
}
public bool Equal2D(ContourVertex <T> OtherVertex)
{
return(this.x.Equals(OtherVertex.x) && this.y.Equals(OtherVertex.y));
}