/// <summary>
/// Construct Voronoi region for given vertex.
/// </summary>
/// <param name="region"></param>
private void ConstructCell(VoronoiRegion region)
{
var vertex = region.Generator as Vertex;
var vpoints = new List <Point>();
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Otri f_prev = default(Otri);
Osub sub = default(Osub);
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
f_init.Copy(ref f);
f_init.Onext(ref f_next);
// Check if f_init lies on the boundary of the triangulation.
if (f_next.tri.id == Mesh.DUMMY)
{
f_init.Oprev(ref f_prev);
if (f_prev.tri.id != Mesh.DUMMY)
{
f_init.Copy(ref f_next);
// Move one triangle clockwise
f_init.Oprev();
f_init.Copy(ref f);
}
}
// Go counterclockwise until we reach the border or the initial triangle.
while (f_next.tri.id != Mesh.DUMMY)
{
// Add circumcenter of current triangle
vpoints.Add(points[f.tri.id]);
region.AddNeighbor(f.tri.id, regions[f.Apex().id]);
if (f_next.Equals(f_init))
{
// Voronoi cell is complete (bounded case).
region.Add(vpoints);
return;
}
f_next.Copy(ref f);
f_next.Onext();
}
// Voronoi cell is unbounded
region.Bounded = false;
Vertex torg, tdest, tapex;
Point intersection;
int sid, n = mesh.triangles.Count;
// Find the boundary segment id (we use this id to number the endpoints of infinit rays).
f.Lprev(ref f_next);
f_next.Pivot(ref sub);
sid = sub.seg.hash;
// Last valid f lies at the boundary. Add the circumcenter.
vpoints.Add(points[f.tri.id]);
region.AddNeighbor(f.tri.id, regions[f.Apex().id]);
// Check if the intersection with the bounding box has already been computed.
if (!rayPoints.TryGetValue(sid, out intersection))
{
torg = f.Org();
tapex = f.Apex();
intersection = IntersectionHelper.BoxRayIntersection(bounds, points[f.tri.id], torg.y - tapex.y, tapex.x - torg.x);
// Set the correct id for the vertex
intersection.id = n + rayIndex;
points[n + rayIndex] = intersection;
rayIndex++;
rayPoints.Add(sid, intersection);
}
vpoints.Add(intersection);
// Now walk from f_init clockwise till we reach the boundary.
vpoints.Reverse();
f_init.Copy(ref f);
f.Oprev(ref f_prev);
while (f_prev.tri.id != Mesh.DUMMY)
{
vpoints.Add(points[f_prev.tri.id]);
region.AddNeighbor(f_prev.tri.id, regions[f_prev.Apex().id]);
f_prev.Copy(ref f);
f_prev.Oprev();
}
// Find the boundary segment id.
f.Pivot(ref sub);
sid = sub.seg.hash;
if (!rayPoints.TryGetValue(sid, out intersection))
{
// Intersection has not been computed yet.
torg = f.Org();
tdest = f.Dest();
intersection = IntersectionHelper.BoxRayIntersection(bounds, points[f.tri.id], tdest.y - torg.y, torg.x - tdest.x);
// Set the correct id for the vertex
intersection.id = n + rayIndex;
rayPoints.Add(sid, intersection);
points[n + rayIndex] = intersection;
rayIndex++;
}
vpoints.Add(intersection);
region.AddNeighbor(intersection.id, regions[f.Dest().id]);
// Add the new points to the region (in counter-clockwise order)
vpoints.Reverse();
region.Add(vpoints);
}
private void ConstructCell(Vertex vertex)
{
VoronoiRegion region = new VoronoiRegion(vertex);
regions.Add(region);
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Osub sf = default(Osub);
Osub sfn = default(Osub);
Point cc_f, cc_f_next, p;
int n = _TriangleNetMesh.triangles.Count;
// Call P the polygon (cell) in construction
List <Point> vpoints = new List <Point>();
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
if (f_init.Org() != vertex)
{
throw new Exception("ConstructCell: inconsistent topology.");
}
// Let f be initialized to f_init
f_init.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_init.Onext(ref f_next);
// repeat ... until f = f_init
do
{
// Call Lffnext the line going through the circumcenters of f and f_next
cc_f = points[f.tri.id];
cc_f_next = points[f_next.tri.id];
// if f is tagged non-blind then
if (!f.tri.infected)
{
// Insert the circumcenter of f into P
vpoints.Add(cc_f);
if (f_next.tri.infected)
{
// Call S_fnext the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// Insert point Lf,f_next /\ Sf_next into P
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
else
{
// Call Sf the constrained edge blinding f
sf.seg = subsegMap[f.tri.hash];
// if f_next is tagged non-blind then
if (!f_next.tri.infected)
{
// Insert point Lf,f_next /\ Sf into P
if (SegmentsIntersect(sf.Org(), sf.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Call Sf_next the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// if Sf != Sf_next then
if (!sf.Equal(sfn))
{
// Insert Lf,fnext /\ Sf and Lf,fnext /\ Sfnext into P
if (SegmentsIntersect(sf.Org(), sf.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
}
// f <- f_next
f_next.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_next.Onext();
}while (!f.Equals(f_init));
// Output: Bounded Voronoi cell of x in counterclockwise order.
region.Add(vpoints);
}
private void ConstructBoundaryCell(Vertex vertex)
{
VoronoiRegion region = new VoronoiRegion(vertex);
regions.Add(region);
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Otri f_prev = default(Otri);
Osub sf = default(Osub);
Osub sfn = default(Osub);
Vertex torg, tdest, tapex, sorg, sdest;
Point cc_f, cc_f_next, p;
int n = _TriangleNetMesh.triangles.Count;
// Call P the polygon (cell) in construction
List <Point> vpoints = new List <Point>();
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
if (f_init.Org() != vertex)
{
throw new Exception("ConstructBoundaryCell: inconsistent topology.");
}
// Let f be initialized to f_init
f_init.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_init.Onext(ref f_next);
f_init.Oprev(ref f_prev);
// Is the border to the left?
if (f_prev.tri.id != TriangleNetMesh.DUMMY)
{
// Go clockwise until we reach the border (or the initial triangle)
while (f_prev.tri.id != TriangleNetMesh.DUMMY && !f_prev.Equals(f_init))
{
f_prev.Copy(ref f);
f_prev.Oprev();
}
f.Copy(ref f_init);
f.Onext(ref f_next);
}
if (f_prev.tri.id == TriangleNetMesh.DUMMY)
{
// For vertices on the domain boundaray, add the vertex. For
// internal boundaries don't add it.
p = new Point(vertex.x, vertex.y);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
// Add midpoint of start triangles' edge.
torg = f.Org();
tdest = f.Dest();
p = new Point((torg.x + tdest.x) / 2, (torg.y + tdest.y) / 2);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
// repeat ... until f = f_init
do
{
// Call Lffnext the line going through the circumcenters of f and f_next
cc_f = points[f.tri.id];
if (f_next.tri.id == TriangleNetMesh.DUMMY)
{
if (!f.tri.infected)
{
// Add last circumcenter
vpoints.Add(cc_f);
}
// Add midpoint of last triangles' edge (chances are it has already
// been added, so post process cell to remove duplicates???)
torg = f.Org();
tapex = f.Apex();
p = new Point((torg.x + tapex.x) / 2, (torg.y + tapex.y) / 2);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
break;
}
cc_f_next = points[f_next.tri.id];
// if f is tagged non-blind then
if (!f.tri.infected)
{
// Insert the circumcenter of f into P
vpoints.Add(cc_f);
if (f_next.tri.infected)
{
// Call S_fnext the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// Insert point Lf,f_next /\ Sf_next into P
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
else
{
// Call Sf the constrained edge blinding f
sf.seg = subsegMap[f.tri.hash];
sorg = sf.Org();
sdest = sf.Dest();
// if f_next is tagged non-blind then
if (!f_next.tri.infected)
{
tdest = f.Dest();
tapex = f.Apex();
// Both circumcenters lie on the blinded side, but we
// have to add the intersection with the segment.
// Center of f edge dest->apex
Point bisec = new Point((tdest.x + tapex.x) / 2, (tdest.y + tapex.y) / 2);
// Find intersection of seg with line through f's bisector and circumcenter
if (SegmentsIntersect(sorg, sdest, bisec, cc_f, out p, false))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
// Insert point Lf,f_next /\ Sf into P
if (SegmentsIntersect(sorg, sdest, cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Call Sf_next the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// if Sf != Sf_next then
if (!sf.Equal(sfn))
{
// Insert Lf,fnext /\ Sf and Lf,fnext /\ Sfnext into P
if (SegmentsIntersect(sorg, sdest, cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Both circumcenters lie on the blinded side, but we
// have to add the intersection with the segment.
// Center of f_next edge org->dest
Point bisec = new Point((torg.x + tdest.x) / 2, (torg.y + tdest.y) / 2);
// Find intersection of seg with line through f_next's bisector and circumcenter
if (SegmentsIntersect(sorg, sdest, bisec, cc_f_next, out p, false))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
}
// f <- f_next
f_next.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_next.Onext();
}while (!f.Equals(f_init));
// Output: Bounded Voronoi cell of x in counterclockwise order.
region.Add(vpoints);
}
internal void AddNeighbor(int id, VoronoiRegion neighbor)
{
neighbors.Add(id, neighbor);
}
/// <summary>
/// Construct Voronoi region for given vertex.
/// </summary>
/// <param name="region"></param>
private void ConstructCell(VoronoiRegion region)
{
var vertex = region.Generator as Vertex;
var vpoints = new List<Point>();
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Otri f_prev = default(Otri);
Osub sub = default(Osub);
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
f_init.Copy(ref f);
f_init.Onext(ref f_next);
// Check if f_init lies on the boundary of the triangulation.
if (f_next.tri.id == Mesh.DUMMY)
{
f_init.Oprev(ref f_prev);
if (f_prev.tri.id != Mesh.DUMMY)
{
f_init.Copy(ref f_next);
// Move one triangle clockwise
f_init.Oprev();
f_init.Copy(ref f);
}
}
// Go counterclockwise until we reach the border or the initial triangle.
while (f_next.tri.id != Mesh.DUMMY)
{
// Add circumcenter of current triangle
vpoints.Add(points[f.tri.id]);
region.AddNeighbor(f.tri.id, regions[f.Apex().id]);
if (f_next.Equals(f_init))
{
// Voronoi cell is complete (bounded case).
region.Add(vpoints);
return;
}
f_next.Copy(ref f);
f_next.Onext();
}
// Voronoi cell is unbounded
region.Bounded = false;
Vertex torg, tdest, tapex;
Point intersection;
int sid, n = mesh.triangles.Count;
// Find the boundary segment id (we use this id to number the endpoints of infinit rays).
f.Lprev(ref f_next);
f_next.Pivot(ref sub);
sid = sub.seg.hash;
// Last valid f lies at the boundary. Add the circumcenter.
vpoints.Add(points[f.tri.id]);
region.AddNeighbor(f.tri.id, regions[f.Apex().id]);
// Check if the intersection with the bounding box has already been computed.
if (!rayPoints.TryGetValue(sid, out intersection))
{
torg = f.Org();
tapex = f.Apex();
BoxRayIntersection(points[f.tri.id], torg.y - tapex.y, tapex.x - torg.x, out intersection);
// Set the correct id for the vertex
intersection.id = n + rayIndex;
points[n + rayIndex] = intersection;
rayIndex++;
rayPoints.Add(sid, intersection);
}
vpoints.Add(intersection);
// Now walk from f_init clockwise till we reach the boundary.
vpoints.Reverse();
f_init.Copy(ref f);
f.Oprev(ref f_prev);
while (f_prev.tri.id != Mesh.DUMMY)
{
vpoints.Add(points[f_prev.tri.id]);
region.AddNeighbor(f_prev.tri.id, regions[f_prev.Apex().id]);
f_prev.Copy(ref f);
f_prev.Oprev();
}
// Find the boundary segment id.
f.Pivot(ref sub);
sid = sub.seg.hash;
if (!rayPoints.TryGetValue(sid, out intersection))
{
// Intersection has not been computed yet.
torg = f.Org();
tdest = f.Dest();
BoxRayIntersection(points[f.tri.id], tdest.y - torg.y, torg.x - tdest.x, out intersection);
// Set the correct id for the vertex
intersection.id = n + rayIndex;
rayPoints.Add(sid, intersection);
points[n + rayIndex] = intersection;
rayIndex++;
}
vpoints.Add(intersection);
region.AddNeighbor(intersection.id, regions[f.Dest().id]);
// Add the new points to the region (in counter-clockwise order)
vpoints.Reverse();
region.Add(vpoints);
}
internal void AddNeighbor(int id, VoronoiRegion neighbor)
{
this.neighbors.Add(id, neighbor);
}
private void ConstructBoundaryCell(Vertex vertex)
{
VoronoiRegion region = new VoronoiRegion(vertex);
regions.Add(region);
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Otri f_prev = default(Otri);
Osub sf = default(Osub);
Osub sfn = default(Osub);
Vertex torg, tdest, tapex, sorg, sdest;
Point cc_f, cc_f_next, p;
int n = mesh.triangles.Count;
// Call P the polygon (cell) in construction
List<Point> vpoints = new List<Point>();
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
if (f_init.Org() != vertex)
{
throw new Exception("ConstructBoundaryCell: inconsistent topology.");
}
// Let f be initialized to f_init
f_init.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_init.Onext(ref f_next);
f_init.Oprev(ref f_prev);
// Is the border to the left?
if (f_prev.tri.id != Mesh.DUMMY)
{
// Go clockwise until we reach the border (or the initial triangle)
while (f_prev.tri.id != Mesh.DUMMY && !f_prev.Equals(f_init))
{
f_prev.Copy(ref f);
f_prev.Oprev();
}
f.Copy(ref f_init);
f.Onext(ref f_next);
}
if (f_prev.tri.id == Mesh.DUMMY)
{
// For vertices on the domain boundaray, add the vertex. For
// internal boundaries don't add it.
p = new Point(vertex.x, vertex.y);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
// Add midpoint of start triangles' edge.
torg = f.Org();
tdest = f.Dest();
p = new Point((torg.x + tdest.x) / 2, (torg.y + tdest.y) / 2);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
// repeat ... until f = f_init
do
{
// Call Lffnext the line going through the circumcenters of f and f_next
cc_f = this.points[f.tri.id];
if (f_next.tri.id == Mesh.DUMMY)
{
if (!f.tri.infected)
{
// Add last circumcenter
vpoints.Add(cc_f);
}
// Add midpoint of last triangles' edge (chances are it has already
// been added, so post process cell to remove duplicates???)
torg = f.Org();
tapex = f.Apex();
p = new Point((torg.x + tapex.x) / 2, (torg.y + tapex.y) / 2);
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
break;
}
cc_f_next = this.points[f_next.tri.id];
// if f is tagged non-blind then
if (!f.tri.infected)
{
// Insert the circumcenter of f into P
vpoints.Add(cc_f);
if (f_next.tri.infected)
{
// Call S_fnext the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// Insert point Lf,f_next /\ Sf_next into P
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
else
{
// Call Sf the constrained edge blinding f
sf.seg = subsegMap[f.tri.hash];
sorg = sf.Org();
sdest = sf.Dest();
// if f_next is tagged non-blind then
if (!f_next.tri.infected)
{
tdest = f.Dest();
tapex = f.Apex();
// Both circumcenters lie on the blinded side, but we
// have to add the intersection with the segment.
// Center of f edge dest->apex
Point bisec = new Point((tdest.x + tapex.x) / 2, (tdest.y + tapex.y) / 2);
// Find intersection of seg with line through f's bisector and circumcenter
if (SegmentsIntersect(sorg, sdest, bisec, cc_f, out p, false))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
// Insert point Lf,f_next /\ Sf into P
if (SegmentsIntersect(sorg, sdest, cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Call Sf_next the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// if Sf != Sf_next then
if (!sf.Equal(sfn))
{
// Insert Lf,fnext /\ Sf and Lf,fnext /\ Sfnext into P
if (SegmentsIntersect(sorg, sdest, cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Both circumcenters lie on the blinded side, but we
// have to add the intersection with the segment.
// Center of f_next edge org->dest
Point bisec = new Point((torg.x + tdest.x) / 2, (torg.y + tdest.y) / 2);
// Find intersection of seg with line through f_next's bisector and circumcenter
if (SegmentsIntersect(sorg, sdest, bisec, cc_f_next, out p, false))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
}
// f <- f_next
f_next.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_next.Onext();
}
while (!f.Equals(f_init));
// Output: Bounded Voronoi cell of x in counterclockwise order.
region.Add(vpoints);
}
private void ConstructCell(Vertex vertex)
{
VoronoiRegion region = new VoronoiRegion(vertex);
regions.Add(region);
Otri f = default(Otri);
Otri f_init = default(Otri);
Otri f_next = default(Otri);
Osub sf = default(Osub);
Osub sfn = default(Osub);
Point cc_f, cc_f_next, p;
int n = mesh.triangles.Count;
// Call P the polygon (cell) in construction
List<Point> vpoints = new List<Point>();
// Call f_init a triangle incident to x
vertex.tri.Copy(ref f_init);
if (f_init.Org() != vertex)
{
throw new Exception("ConstructCell: inconsistent topology.");
}
// Let f be initialized to f_init
f_init.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_init.Onext(ref f_next);
// repeat ... until f = f_init
do
{
// Call Lffnext the line going through the circumcenters of f and f_next
cc_f = this.points[f.tri.id];
cc_f_next = this.points[f_next.tri.id];
// if f is tagged non-blind then
if (!f.tri.infected)
{
// Insert the circumcenter of f into P
vpoints.Add(cc_f);
if (f_next.tri.infected)
{
// Call S_fnext the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// Insert point Lf,f_next /\ Sf_next into P
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
else
{
// Call Sf the constrained edge blinding f
sf.seg = subsegMap[f.tri.hash];
// if f_next is tagged non-blind then
if (!f_next.tri.infected)
{
// Insert point Lf,f_next /\ Sf into P
if (SegmentsIntersect(sf.Org(), sf.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
else
{
// Call Sf_next the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.tri.hash];
// if Sf != Sf_next then
if (!sf.Equal(sfn))
{
// Insert Lf,fnext /\ Sf and Lf,fnext /\ Sfnext into P
if (SegmentsIntersect(sf.Org(), sf.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
if (SegmentsIntersect(sfn.Org(), sfn.Dest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex++;
segPoints.Add(p);
vpoints.Add(p);
}
}
}
}
// f <- f_next
f_next.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_next.Onext();
}
while (!f.Equals(f_init));
// Output: Bounded Voronoi cell of x in counterclockwise order.
region.Add(vpoints);
}