/// <summary>
/// Delete a vertex from a Delaunay triangulation, ensuring that the
/// triangulation remains Delaunay.
/// </summary>
/// <param name="deltri"></param>
/// <remarks>The origin of 'deltri' is deleted. The union of the triangles
/// adjacent to this vertex is a polygon, for which the Delaunay triangulation
/// is found. Two triangles are removed from the mesh.
///
/// Only interior vertices that do not lie on segments or boundaries
/// may be deleted.
/// </remarks>
internal void DeleteVertex(ref Otri deltri)
{
Otri countingtri = default(Otri);
Otri firstedge = default(Otri), lastedge = default(Otri);
Otri deltriright = default(Otri);
Otri lefttri = default(Otri), righttri = default(Otri);
Otri leftcasing = default(Otri), rightcasing = default(Otri);
Osub leftsubseg = default(Osub), rightsubseg = default(Osub);
Vertex delvertex;
Vertex neworg;
int edgecount;
delvertex = deltri.Org();
VertexDealloc(delvertex);
// Count the degree of the vertex being deleted.
deltri.Onext(ref countingtri);
edgecount = 1;
while (!deltri.Equal(countingtri))
{
edgecount++;
countingtri.OnextSelf();
}
if (edgecount > 3)
{
// Triangulate the polygon defined by the union of all triangles
// adjacent to the vertex being deleted. Check the quality of
// the resulting triangles.
deltri.Onext(ref firstedge);
deltri.Oprev(ref lastedge);
TriangulatePolygon(firstedge, lastedge, edgecount, false, behavior.NoBisect == 0);
}
// Splice out two triangles.
deltri.Lprev(ref deltriright);
deltri.Dnext(ref lefttri);
lefttri.Sym(ref leftcasing);
deltriright.Oprev(ref righttri);
righttri.Sym(ref rightcasing);
deltri.Bond(ref leftcasing);
deltriright.Bond(ref rightcasing);
lefttri.SegPivot(ref leftsubseg);
if (leftsubseg.seg != Mesh.dummysub)
{
deltri.SegBond(ref leftsubseg);
}
righttri.SegPivot(ref rightsubseg);
if (rightsubseg.seg != Mesh.dummysub)
{
deltriright.SegBond(ref rightsubseg);
}
// Set the new origin of 'deltri' and check its quality.
neworg = lefttri.Org();
deltri.SetOrg(neworg);
if (behavior.NoBisect == 0)
{
quality.TestTriangle(ref deltri);
}
// Delete the two spliced-out triangles.
TriangleDealloc(lefttri.triangle);
TriangleDealloc(righttri.triangle);
}
/// <summary>
/// Recursively form a Delaunay triangulation by the divide-and-conquer method.
/// </summary>
/// <param name="left"></param>
/// <param name="right"></param>
/// <param name="axis"></param>
/// <param name="farleft"></param>
/// <param name="farright"></param>
/// <remarks>
/// Recursively breaks down the problem into smaller pieces, which are
/// knitted together by mergehulls(). The base cases (problems of two or
/// three vertices) are handled specially here.
///
/// On completion, 'farleft' and 'farright' are bounding triangles such that
/// the origin of 'farleft' is the leftmost vertex (breaking ties by
/// choosing the highest leftmost vertex), and the destination of
/// 'farright' is the rightmost vertex (breaking ties by choosing the
/// lowest rightmost vertex).
/// </remarks>
void DivconqRecurse(int left, int right, int axis,
ref Otri farleft, ref Otri farright)
{
Otri midtri = default(Otri);
Otri tri1 = default(Otri);
Otri tri2 = default(Otri);
Otri tri3 = default(Otri);
Otri innerleft = default(Otri), innerright = default(Otri);
double area;
int vertices = right - left + 1;
int divider;
if (vertices == 2)
{
// The triangulation of two vertices is an edge. An edge is
// represented by two bounding triangles.
mesh.MakeTriangle(ref farleft);
farleft.SetOrg(sortarray[left]);
farleft.SetDest(sortarray[left + 1]);
// The apex is intentionally left NULL.
mesh.MakeTriangle(ref farright);
farright.SetOrg(sortarray[left + 1]);
farright.SetDest(sortarray[left]);
// The apex is intentionally left NULL.
farleft.Bond(ref farright);
farleft.LprevSelf();
farright.LnextSelf();
farleft.Bond(ref farright);
farleft.LprevSelf();
farright.LnextSelf();
farleft.Bond(ref farright);
// Ensure that the origin of 'farleft' is sortarray[0].
farright.Lprev(ref farleft);
return;
}
else if (vertices == 3)
{
// The triangulation of three vertices is either a triangle (with
// three bounding triangles) or two edges (with four bounding
// triangles). In either case, four triangles are created.
mesh.MakeTriangle(ref midtri);
mesh.MakeTriangle(ref tri1);
mesh.MakeTriangle(ref tri2);
mesh.MakeTriangle(ref tri3);
area = Primitives.CounterClockwise(sortarray[left], sortarray[left + 1], sortarray[left + 2]);
if (area == 0.0)
{
// Three collinear vertices; the triangulation is two edges.
midtri.SetOrg(sortarray[left]);
midtri.SetDest(sortarray[left + 1]);
tri1.SetOrg(sortarray[left + 1]);
tri1.SetDest(sortarray[left]);
tri2.SetOrg(sortarray[left + 2]);
tri2.SetDest(sortarray[left + 1]);
tri3.SetOrg(sortarray[left + 1]);
tri3.SetDest(sortarray[left + 2]);
// All apices are intentionally left NULL.
midtri.Bond(ref tri1);
tri2.Bond(ref tri3);
midtri.LnextSelf();
tri1.LprevSelf();
tri2.LnextSelf();
tri3.LprevSelf();
midtri.Bond(ref tri3);
tri1.Bond(ref tri2);
midtri.LnextSelf();
tri1.LprevSelf();
tri2.LnextSelf();
tri3.LprevSelf();
midtri.Bond(ref tri1);
tri2.Bond(ref tri3);
// Ensure that the origin of 'farleft' is sortarray[0].
tri1.Copy(ref farleft);
// Ensure that the destination of 'farright' is sortarray[2].
tri2.Copy(ref farright);
}
else
{
// The three vertices are not collinear; the triangulation is one
// triangle, namely 'midtri'.
midtri.SetOrg(sortarray[left]);
tri1.SetDest(sortarray[left]);
tri3.SetOrg(sortarray[left]);
// Apices of tri1, tri2, and tri3 are left NULL.
if (area > 0.0)
{
// The vertices are in counterclockwise order.
midtri.SetDest(sortarray[left + 1]);
tri1.SetOrg(sortarray[left + 1]);
tri2.SetDest(sortarray[left + 1]);
midtri.SetApex(sortarray[left + 2]);
tri2.SetOrg(sortarray[left + 2]);
tri3.SetDest(sortarray[left + 2]);
}
else
{
// The vertices are in clockwise order.
midtri.SetDest(sortarray[left + 2]);
tri1.SetOrg(sortarray[left + 2]);
tri2.SetDest(sortarray[left + 2]);
midtri.SetApex(sortarray[left + 1]);
tri2.SetOrg(sortarray[left + 1]);
tri3.SetDest(sortarray[left + 1]);
}
// The topology does not depend on how the vertices are ordered.
midtri.Bond(ref tri1);
midtri.LnextSelf();
midtri.Bond(ref tri2);
midtri.LnextSelf();
midtri.Bond(ref tri3);
tri1.LprevSelf();
tri2.LnextSelf();
tri1.Bond(ref tri2);
tri1.LprevSelf();
tri3.LprevSelf();
tri1.Bond(ref tri3);
tri2.LnextSelf();
tri3.LprevSelf();
tri2.Bond(ref tri3);
// Ensure that the origin of 'farleft' is sortarray[0].
tri1.Copy(ref farleft);
// Ensure that the destination of 'farright' is sortarray[2].
if (area > 0.0)
{
tri2.Copy(ref farright);
}
else
{
farleft.Lnext(ref farright);
}
}
return;
}
else
{
// Split the vertices in half.
divider = vertices >> 1;
// Recursively triangulate each half.
DivconqRecurse(left, left + divider - 1, 1 - axis, ref farleft, ref innerleft);
//DebugWriter.Session.Write(mesh, true);
DivconqRecurse(left + divider, right, 1 - axis, ref innerright, ref farright);
//DebugWriter.Session.Write(mesh, true);
// Merge the two triangulations into one.
MergeHulls(ref farleft, ref innerleft, ref innerright, ref farright, axis);
//DebugWriter.Session.Write(mesh, true);
}
}