/* __gl_meshTessellateMonoRegion( face ) 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 static bool __gl_meshTessellateMonoRegion(GLUface face)
{
GLUhalfEdge up, lo;
/* 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.
*/
up = face.anEdge;
//assert(up.Lnext != up && up.Lnext.Lnext != up);
for (; Geom.VertLeq(up.Sym.Org, up.Org); up = up.Onext.Sym)
{
;
}
for (; Geom.VertLeq(up.Org, up.Sym.Org); up = up.Lnext)
{
;
}
lo = up.Onext.Sym;
while (up.Lnext != lo)
{
if (Geom.VertLeq(up.Sym.Org, lo.Org))
{
/* up.Sym.Org 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.Lnext != up && (Geom.EdgeGoesLeft(lo.Lnext) || Geom.EdgeSign(lo.Org, lo.Sym.Org, lo.Lnext.Sym.Org) <= 0))
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(lo.Lnext, lo);
if (tempHalfEdge == null)
{
return(false);
}
lo = tempHalfEdge.Sym;
}
lo = lo.Onext.Sym;
}
else
{
/* lo.Org is on the left. We can make CCW triangles from up.Sym.Org. */
while (lo.Lnext != up && (Geom.EdgeGoesRight(up.Onext.Sym) || Geom.EdgeSign(up.Sym.Org, up.Org, up.Onext.Sym.Org) >= 0))
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(up, up.Onext.Sym);
if (tempHalfEdge == null)
{
return(false);
}
up = tempHalfEdge.Sym;
}
up = up.Lnext;
}
}
/* Now lo.Org == up.Sym.Org == the leftmost vertex. The remaining region
* can be tessellated in a fan from this leftmost vertex.
*/
//assert(lo.Lnext != up);
while (lo.Lnext.Lnext != up)
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(lo.Lnext, lo);
if (tempHalfEdge == null)
{
return(false);
}
lo = tempHalfEdge.Sym;
}
return(true);
}
/* __gl_meshTessellateMonoRegion( face ) 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 static bool __gl_meshTessellateMonoRegion(GLUface face)
{
GLUhalfEdge up, lo;
/* 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.
*/
up = face.anEdge;
//assert(up.Lnext != up && up.Lnext.Lnext != up);
for (; Geom.VertLeq(up.Sym.Org, up.Org); up = up.Onext.Sym)
;
for (; Geom.VertLeq(up.Org, up.Sym.Org); up = up.Lnext)
;
lo = up.Onext.Sym;
while (up.Lnext != lo)
{
if (Geom.VertLeq(up.Sym.Org, lo.Org))
{
/* up.Sym.Org 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.Lnext != up && (Geom.EdgeGoesLeft(lo.Lnext) || Geom.EdgeSign(lo.Org, lo.Sym.Org, lo.Lnext.Sym.Org) <= 0))
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(lo.Lnext, lo);
if (tempHalfEdge == null)
return false;
lo = tempHalfEdge.Sym;
}
lo = lo.Onext.Sym;
}
else
{
/* lo.Org is on the left. We can make CCW triangles from up.Sym.Org. */
while (lo.Lnext != up && (Geom.EdgeGoesRight(up.Onext.Sym) || Geom.EdgeSign(up.Sym.Org, up.Org, up.Onext.Sym.Org) >= 0))
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(up, up.Onext.Sym);
if (tempHalfEdge == null)
return false;
up = tempHalfEdge.Sym;
}
up = up.Lnext;
}
}
/* Now lo.Org == up.Sym.Org == the leftmost vertex. The remaining region
* can be tessellated in a fan from this leftmost vertex.
*/
//assert(lo.Lnext != up);
while (lo.Lnext.Lnext != up)
{
GLUhalfEdge tempHalfEdge = Mesh.__gl_meshConnect(lo.Lnext, lo);
if (tempHalfEdge == null)
return false;
lo = tempHalfEdge.Sym;
}
return true;
}
