/// <summary>
/// TessellateMonoRegion( 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).
/// </summary>
private void TessellateMonoRegion(MeshUtils.Face face)
{
// 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.
var up = face._anEdge;
Debug.Assert(up._Lnext != up && up._Lnext._Lnext != up);
for (; Geom.VertLeq(up.Dst, up._Org); up = up.Lprev)
{
}
for (; Geom.VertLeq(up._Org, up.Dst); up = up._Lnext)
{
}
var lo = up.Lprev;
while (up._Lnext != lo)
{
if (Geom.VertLeq(up.Dst, lo._Org))
{
// 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._Lnext != up && (Geom.EdgeGoesLeft(lo._Lnext) ||
Geom.EdgeSign(lo._Org, lo.Dst, lo._Lnext.Dst) <= 0.0f))
{
lo = _mesh.Connect(lo._Lnext, lo)._Sym;
}
lo = lo.Lprev;
}
else
{
// lo.Org is on the left. We can make CCW triangles from up.Dst.
while (lo._Lnext != up && (Geom.EdgeGoesRight(up.Lprev) ||
Geom.EdgeSign(up.Dst, up._Org, up.Lprev._Org) >= 0.0f))
{
up = _mesh.Connect(up, up.Lprev)._Sym;
}
up = up._Lnext;
}
}
// Now lo.Org == up.Dst == the leftmost vertex. The remaining region
// can be tessellated in a fan from this leftmost vertex.
Debug.Assert(lo._Lnext != up);
while (lo._Lnext._Lnext != up)
{
lo = _mesh.Connect(lo._Lnext, lo)._Sym;
}
}
/// <summary>
/// Destroys a face and removes it from the global face list. All edges of
/// fZap will have a NULL pointer as their left face. Any edges which
/// also have a NULL pointer as their right face are deleted entirely
/// (along with any isolated vertices this produces).
/// An entire mesh can be deleted by zapping its faces, one at a time,
/// in any order. Zapped faces cannot be used in further mesh operations!
/// </summary>
public void ZapFace(MeshUtils.Face fZap)
{
var eStart = fZap._anEdge;
// walk around face, deleting edges whose right face is also NULL
var eNext = eStart._Lnext;
MeshUtils.Edge e, eSym;
do
{
e = eNext;
eNext = e._Lnext;
e._Lface = null;
if (e.Rface == null)
{
// delete the edge -- see TESSmeshDelete above
if (e._Onext == e)
{
MeshUtils.KillVertex(e._Org, null);
}
else
{
// Make sure that e._Org points to a valid half-edge
e._Org._anEdge = e._Onext;
MeshUtils.Splice(e, e.Oprev);
}
eSym = e._Sym;
if (eSym._Onext == eSym)
{
MeshUtils.KillVertex(eSym._Org, null);
}
else
{
// Make sure that eSym._Org points to a valid half-edge
eSym._Org._anEdge = eSym._Onext;
MeshUtils.Splice(eSym, eSym.Oprev);
}
MeshUtils.KillEdge(e);
}
} while (e != eStart);
/* delete from circular doubly-linked list */
var fPrev = fZap._prev;
var fNext = fZap._next;
fNext._prev = fPrev;
fPrev._next = fNext;
}
// ReSharper restore InconsistentNaming
public Mesh()
{
var v = _vHead = new MeshUtils.Vertex();
var f = _fHead = new MeshUtils.Face();
var pair = MeshUtils.EdgePair.Create();
var e = _eHead = pair._e;
var eSym = _eHeadSym = pair._eSym;
v._next = v._prev = v;
v._anEdge = null;
f._next = f._prev = f;
f._anEdge = null;
f._trail = null;
f._marked = false;
f._inside = false;
e._next = e;
e._Sym = eSym;
e._Onext = null;
e._Lnext = null;
e._Org = null;
e._Lface = null;
e._winding = 0;
e._activeRegion = null;
eSym._next = eSym;
eSym._Sym = e;
eSym._Onext = null;
eSym._Lnext = null;
eSym._Org = null;
eSym._Lface = null;
eSym._winding = 0;
eSym._activeRegion = null;
}
