public static void WriteVoronoi(Mesh mesh, string filename)
{
Vertex vertex;
Vertex vertex1;
double x;
Otri otri = new Otri();
Otri otri1 = new Otri();
double num = 0;
double num1 = 0;
int num2 = 0;
otri.orient = 0;
using (StreamWriter streamWriter = new StreamWriter(new FileStream(filename, FileMode.Create)))
{
streamWriter.WriteLine("{0} 2 {1} 0", mesh.triangles.Count, mesh.nextras);
foreach (Triangle value in mesh.triangles.Values)
{
otri.triangle = value;
vertex = otri.Org();
vertex1 = otri.Dest();
Vertex vertex2 = otri.Apex();
Point point = Primitives.FindCircumcenter(vertex, vertex1, vertex2, ref num, ref num1);
object obj = num2;
x = point.X;
string str = x.ToString(FileWriter.nfi);
x = point.Y;
streamWriter.Write("{0} {1} {2}", obj, str, x.ToString(FileWriter.nfi));
for (int i = 0; i < mesh.nextras; i++)
{
streamWriter.Write(" 0");
}
streamWriter.WriteLine();
int num3 = num2;
num2 = num3 + 1;
otri.triangle.id = num3;
}
streamWriter.WriteLine("{0} 0", mesh.edges);
num2 = 0;
foreach (Triangle triangle in mesh.triangles.Values)
{
otri.triangle = triangle;
otri.orient = 0;
while (otri.orient < 3)
{
otri.Sym(ref otri1);
if (otri.triangle.id < otri1.triangle.id || otri1.triangle == Mesh.dummytri)
{
int num4 = otri.triangle.id;
if (otri1.triangle != Mesh.dummytri)
{
int num5 = otri1.triangle.id;
streamWriter.WriteLine("{0} {1} {2}", num2, num4, num5);
}
else
{
vertex = otri.Org();
vertex1 = otri.Dest();
object[] objArray = new object[] { num2, num4, null, null };
x = vertex1[1] - vertex[1];
objArray[2] = x.ToString(FileWriter.nfi);
x = vertex[0] - vertex1[0];
objArray[3] = x.ToString(FileWriter.nfi);
streamWriter.WriteLine("{0} {1} -1 {2} {3}", objArray);
}
num2++;
}
otri.orient = otri.orient + 1;
}
}
}
}
/// <summary>
/// Test a triangle for quality and size.
/// </summary>
/// <param name="testtri">Triangle to check.</param>
/// <remarks>
/// Tests a triangle to see if it satisfies the minimum angle condition and
/// the maximum area condition. Triangles that aren't up to spec are added
/// to the bad triangle queue.
/// </remarks>
public void TestTriangle(ref Otri testtri)
{
Otri tri1 = default(Otri), tri2 = default(Otri);
Osub testsub = default(Osub);
Vertex torg, tdest, tapex;
Vertex base1, base2;
Vertex org1, dest1, org2, dest2;
Vertex joinvertex;
float dxod, dyod, dxda, dyda, dxao, dyao;
float dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
float apexlen, orglen, destlen, minedge;
float angle;
float area;
float dist1, dist2;
float maxangle;
torg = testtri.Org();
tdest = testtri.Dest();
tapex = testtri.Apex();
dxod = torg.x - tdest.x;
dyod = torg.y - tdest.y;
dxda = tdest.x - tapex.x;
dyda = tdest.y - tapex.y;
dxao = tapex.x - torg.x;
dyao = tapex.y - torg.y;
dxod2 = dxod * dxod;
dyod2 = dyod * dyod;
dxda2 = dxda * dxda;
dyda2 = dyda * dyda;
dxao2 = dxao * dxao;
dyao2 = dyao * dyao;
// Find the lengths of the triangle's three edges.
apexlen = dxod2 + dyod2;
orglen = dxda2 + dyda2;
destlen = dxao2 + dyao2;
if ((apexlen < orglen) && (apexlen < destlen))
{
// The edge opposite the apex is shortest.
minedge = apexlen;
// Find the square of the cosine of the angle at the apex.
angle = dxda * dxao + dyda * dyao;
angle = angle * angle / (orglen * destlen);
base1 = torg;
base2 = tdest;
testtri.Copy(ref tri1);
}
else if (orglen < destlen)
{
// The edge opposite the origin is shortest.
minedge = orglen;
// Find the square of the cosine of the angle at the origin.
angle = dxod * dxao + dyod * dyao;
angle = angle * angle / (apexlen * destlen);
base1 = tdest;
base2 = tapex;
testtri.Lnext(ref tri1);
}
else
{
// The edge opposite the destination is shortest.
minedge = destlen;
// Find the square of the cosine of the angle at the destination.
angle = dxod * dxda + dyod * dyda;
angle = angle * angle / (apexlen * orglen);
base1 = tapex;
base2 = torg;
testtri.Lprev(ref tri1);
}
if (behavior.VarArea || behavior.fixedArea || behavior.Usertest)
{
// Check whether the area is larger than permitted.
area = 0.5f * (dxod * dyda - dyod * dxda);
if (behavior.fixedArea && (area > behavior.MaxArea))
{
// Add this triangle to the list of bad triangles.
queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
return;
}
// Nonpositive area constraints are treated as unconstrained.
if ((behavior.VarArea) && (area > testtri.triangle.area) && (testtri.triangle.area > 0.0))
{
// Add this triangle to the list of bad triangles.
queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
return;
}
}
// find the maximum edge and accordingly the pqr orientation
if ((apexlen > orglen) && (apexlen > destlen))
{
// The edge opposite the apex is longest.
// maxedge = apexlen;
// Find the cosine of the angle at the apex.
maxangle = (orglen + destlen - apexlen) / (2 * UnityEngine.Mathf.Sqrt(orglen * destlen));
}
else if (orglen > destlen)
{
// The edge opposite the origin is longest.
// maxedge = orglen;
// Find the cosine of the angle at the origin.
maxangle = (apexlen + destlen - orglen) / (2 * UnityEngine.Mathf.Sqrt(apexlen * destlen));
}
else
{
// The edge opposite the destination is longest.
// maxedge = destlen;
// Find the cosine of the angle at the destination.
maxangle = (apexlen + orglen - destlen) / (2 * UnityEngine.Mathf.Sqrt(apexlen * orglen));
}
// Check whether the angle is smaller than permitted.
if ((angle > behavior.goodAngle) || (maxangle < behavior.maxGoodAngle && behavior.MaxAngle != 0.0))
{
// Use the rules of Miller, Pav, and Walkington to decide that certain
// triangles should not be split, even if they have bad angles.
// A skinny triangle is not split if its shortest edge subtends a
// small input angle, and both endpoints of the edge lie on a
// concentric circular shell. For convenience, I make a small
// adjustment to that rule: I check if the endpoints of the edge
// both lie in segment interiors, equidistant from the apex where
// the two segments meet.
// First, check if both points lie in segment interiors.
if ((base1.type == VertexType.SegmentVertex) &&
(base2.type == VertexType.SegmentVertex))
{
// Check if both points lie in a common segment. If they do, the
// skinny triangle is enqueued to be split as usual.
tri1.SegPivot(ref testsub);
if (testsub.seg == Mesh.dummysub)
{
// No common segment. Find a subsegment that contains 'torg'.
tri1.Copy(ref tri2);
do
{
tri1.OprevSelf();
tri1.SegPivot(ref testsub);
} while (testsub.seg == Mesh.dummysub);
// Find the endpoints of the containing segment.
org1 = testsub.SegOrg();
dest1 = testsub.SegDest();
// Find a subsegment that contains 'tdest'.
do
{
tri2.DnextSelf();
tri2.SegPivot(ref testsub);
} while (testsub.seg == Mesh.dummysub);
// Find the endpoints of the containing segment.
org2 = testsub.SegOrg();
dest2 = testsub.SegDest();
// Check if the two containing segments have an endpoint in common.
joinvertex = null;
if ((dest1.x == org2.x) && (dest1.y == org2.y))
{
joinvertex = dest1;
}
else if ((org1.x == dest2.x) && (org1.y == dest2.y))
{
joinvertex = org1;
}
if (joinvertex != null)
{
// Compute the distance from the common endpoint (of the two
// segments) to each of the endpoints of the shortest edge.
dist1 = ((base1.x - joinvertex.x) * (base1.x - joinvertex.x) +
(base1.y - joinvertex.y) * (base1.y - joinvertex.y));
dist2 = ((base2.x - joinvertex.x) * (base2.x - joinvertex.x) +
(base2.y - joinvertex.y) * (base2.y - joinvertex.y));
// If the two distances are equal, don't split the triangle.
if ((dist1 < 1.001 * dist2) && (dist1 > 0.999 * dist2))
{
// Return now to avoid enqueueing the bad triangle.
return;
}
}
}
}
// Add this triangle to the list of bad triangles.
queue.Enqueue(ref testtri, minedge, tapex, torg, tdest);
}
}
/// <summary>
/// Split all the encroached subsegments.
/// </summary>
/// <param name="triflaws">A flag that specifies whether one should take
/// note of new bad triangles that result from inserting vertices to repair
/// encroached subsegments.</param>
/// <remarks>
/// Each encroached subsegment is repaired by splitting it - inserting a
/// vertex at or near its midpoint. Newly inserted vertices may encroach
/// upon other subsegments; these are also repaired.
/// </remarks>
private void SplitEncSegs(bool triflaws)
{
Otri enctri = default(Otri);
Otri testtri = default(Otri);
Osub testsh = default(Osub);
Osub currentenc = default(Osub);
BadSubseg seg;
Vertex eorg, edest, eapex;
Vertex newvertex;
InsertVertexResult success;
float segmentlength, nearestpoweroftwo;
float split;
float multiplier, divisor;
bool acuteorg, acuteorg2, acutedest, acutedest2;
// Note that steinerleft == -1 if an unlimited number
// of Steiner points is allowed.
while (badsubsegs.Count > 0)
{
if (mesh.steinerleft == 0)
{
break;
}
seg = badsubsegs.Dequeue();
currentenc = seg.encsubseg;
eorg = currentenc.Org();
edest = currentenc.Dest();
// Make sure that this segment is still the same segment it was
// when it was determined to be encroached. If the segment was
// enqueued multiple times (because several newly inserted
// vertices encroached it), it may have already been split.
if (!Osub.IsDead(currentenc.seg) && (eorg == seg.subsegorg) && (edest == seg.subsegdest))
{
// To decide where to split a segment, we need to know if the
// segment shares an endpoint with an adjacent segment.
// The concern is that, if we simply split every encroached
// segment in its center, two adjacent segments with a small
// angle between them might lead to an infinite loop; each
// vertex added to split one segment will encroach upon the
// other segment, which must then be split with a vertex that
// will encroach upon the first segment, and so on forever.
// To avoid this, imagine a set of concentric circles, whose
// radii are powers of two, about each segment endpoint.
// These concentric circles determine where the segment is
// split. (If both endpoints are shared with adjacent
// segments, split the segment in the middle, and apply the
// concentric circles for later splittings.)
// Is the origin shared with another segment?
currentenc.TriPivot(ref enctri);
enctri.Lnext(ref testtri);
testtri.SegPivot(ref testsh);
acuteorg = testsh.seg != Mesh.dummysub;
// Is the destination shared with another segment?
testtri.LnextSelf();
testtri.SegPivot(ref testsh);
acutedest = testsh.seg != Mesh.dummysub;
// If we're using Chew's algorithm (rather than Ruppert's)
// to define encroachment, delete free vertices from the
// subsegment's diametral circle.
if (!behavior.ConformingDelaunay && !acuteorg && !acutedest)
{
eapex = enctri.Apex();
while ((eapex.type == VertexType.FreeVertex) &&
((eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y) < 0.0))
{
mesh.DeleteVertex(ref testtri);
currentenc.TriPivot(ref enctri);
eapex = enctri.Apex();
enctri.Lprev(ref testtri);
}
}
// Now, check the other side of the segment, if there's a triangle there.
enctri.Sym(ref testtri);
if (testtri.triangle != Mesh.dummytri)
{
// Is the destination shared with another segment?
testtri.LnextSelf();
testtri.SegPivot(ref testsh);
acutedest2 = testsh.seg != Mesh.dummysub;
acutedest = acutedest || acutedest2;
// Is the origin shared with another segment?
testtri.LnextSelf();
testtri.SegPivot(ref testsh);
acuteorg2 = testsh.seg != Mesh.dummysub;
acuteorg = acuteorg || acuteorg2;
// Delete free vertices from the subsegment's diametral circle.
if (!behavior.ConformingDelaunay && !acuteorg2 && !acutedest2)
{
eapex = testtri.Org();
while ((eapex.type == VertexType.FreeVertex) &&
((eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y) < 0.0))
{
mesh.DeleteVertex(ref testtri);
enctri.Sym(ref testtri);
eapex = testtri.Apex();
testtri.LprevSelf();
}
}
}
// Use the concentric circles if exactly one endpoint is shared
// with another adjacent segment.
if (acuteorg || acutedest)
{
segmentlength = UnityEngine.Mathf.Sqrt((edest.x - eorg.x) * (edest.x - eorg.x) +
(edest.y - eorg.y) * (edest.y - eorg.y));
// Find the power of two that most evenly splits the segment.
// The worst case is a 2:1 ratio between subsegment lengths.
nearestpoweroftwo = 1.0f;
while (segmentlength > 3.0f * nearestpoweroftwo)
{
nearestpoweroftwo *= 2.0f;
}
while (segmentlength < 1.5f * nearestpoweroftwo)
{
nearestpoweroftwo *= 0.5f;
}
// Where do we split the segment?
split = nearestpoweroftwo / segmentlength;
if (acutedest)
{
split = 1.0f - split;
}
}
else
{
// If we're not worried about adjacent segments, split
// this segment in the middle.
split = 0.5f;
}
// Create the new vertex (interpolate coordinates).
newvertex = new Vertex(
eorg.x + split * (edest.x - eorg.x),
eorg.y + split * (edest.y - eorg.y),
currentenc.Mark(),
mesh.nextras);
newvertex.type = VertexType.SegmentVertex;
newvertex.hash = mesh.hash_vtx++;
newvertex.id = newvertex.hash;
mesh.vertices.Add(newvertex.hash, newvertex);
// Interpolate attributes.
for (int i = 0; i < mesh.nextras; i++)
{
newvertex.attributes[i] = eorg.attributes[i]
+ split * (edest.attributes[i] - eorg.attributes[i]);
}
if (!Behavior.NoExact)
{
// Roundoff in the above calculation may yield a 'newvertex'
// that is not precisely collinear with 'eorg' and 'edest'.
// Improve collinearity by one step of iterative refinement.
multiplier = Primitives.CounterClockwise(eorg, edest, newvertex);
divisor = ((eorg.x - edest.x) * (eorg.x - edest.x) +
(eorg.y - edest.y) * (eorg.y - edest.y));
if ((multiplier != 0.0) && (divisor != 0.0))
{
multiplier = multiplier / divisor;
// Watch out for NANs.
if (!float.IsNaN(multiplier))
{
newvertex.x += multiplier * (edest.y - eorg.y);
newvertex.y += multiplier * (eorg.x - edest.x);
}
}
}
// Check whether the new vertex lies on an endpoint.
if (((newvertex.x == eorg.x) && (newvertex.y == eorg.y)) ||
((newvertex.x == edest.x) && (newvertex.y == edest.y)))
{
logger.Error("Ran out of precision: I attempted to split a"
+ " segment to a smaller size than can be accommodated by"
+ " the finite precision of floating point arithmetic.",
"Quality.SplitEncSegs()");
throw new Exception("Ran out of precision");
}
// Insert the splitting vertex. This should always succeed.
success = mesh.InsertVertex(newvertex, ref enctri, ref currentenc, true, triflaws);
if ((success != InsertVertexResult.Successful) && (success != InsertVertexResult.Encroaching))
{
logger.Error("Failure to split a segment.", "Quality.SplitEncSegs()");
throw new Exception("Failure to split a segment.");
}
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
// Check the two new subsegments to see if they're encroached.
CheckSeg4Encroach(ref currentenc);
currentenc.NextSelf();
CheckSeg4Encroach(ref currentenc);
}
// Set subsegment's origin to NULL. This makes it possible to detect dead
// badsubsegs when traversing the list of all badsubsegs.
seg.subsegorg = null;
}
}
/// <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);
}
/// <summary>
/// Ensure that the mesh is (constrained) Delaunay.
/// </summary>
public bool CheckDelaunay()
{
Otri loop = default(Otri);
Otri oppotri = default(Otri);
Osub opposubseg = default(Osub);
Vertex triorg, tridest, triapex;
Vertex oppoapex;
bool shouldbedelaunay;
int horrors;
bool saveexact;
// Temporarily turn on exact arithmetic if it's off.
saveexact = Behavior.NoExact;
Behavior.NoExact = false;
horrors = 0;
// Run through the list of triangles, checking each one.
foreach (var tri in mesh.triangles.Values)
{
loop.triangle = tri;
// Check all three edges of the triangle.
for (loop.orient = 0; loop.orient < 3;
loop.orient++)
{
triorg = loop.Org();
tridest = loop.Dest();
triapex = loop.Apex();
loop.Sym(ref oppotri);
oppoapex = oppotri.Apex();
// Only test that the edge is locally Delaunay if there is an
// adjoining triangle whose pointer is larger (to ensure that
// each pair isn't tested twice).
shouldbedelaunay = (oppotri.triangle != Mesh.dummytri) &&
!Otri.IsDead(oppotri.triangle) && loop.triangle.id < oppotri.triangle.id &&
(triorg != mesh.infvertex1) && (triorg != mesh.infvertex2) &&
(triorg != mesh.infvertex3) &&
(tridest != mesh.infvertex1) && (tridest != mesh.infvertex2) &&
(tridest != mesh.infvertex3) &&
(triapex != mesh.infvertex1) && (triapex != mesh.infvertex2) &&
(triapex != mesh.infvertex3) &&
(oppoapex != mesh.infvertex1) && (oppoapex != mesh.infvertex2) &&
(oppoapex != mesh.infvertex3);
if (mesh.checksegments && shouldbedelaunay)
{
// If a subsegment separates the triangles, then the edge is
// constrained, so no local Delaunay test should be done.
loop.SegPivot(ref opposubseg);
if (opposubseg.seg != Mesh.dummysub)
{
shouldbedelaunay = false;
}
}
if (shouldbedelaunay)
{
if (Primitives.NonRegular(triorg, tridest, triapex, oppoapex) > 0.0)
{
logger.Warning(String.Format("Non-regular pair of triangles found (IDs {0}/{1}).",
loop.triangle.id, oppotri.triangle.id), "Quality.CheckDelaunay()");
horrors++;
}
}
}
}
if (horrors == 0) // && Behavior.Verbose
{
logger.Info("Mesh is Delaunay.");
}
// Restore the status of exact arithmetic.
Behavior.NoExact = saveexact;
return(horrors == 0);
}
/// <summary>
/// Reconstruct a triangulation from its raw data representation.
/// </summary>
/// <param name="mesh"></param>
/// <param name="input"></param>
/// <returns></returns>
/// <remarks>
/// Reads an .ele file and reconstructs the original mesh. If the -p switch
/// is used, this procedure will also read a .poly file and reconstruct the
/// subsegments of the original mesh. If the -a switch is used, this
/// procedure will also read an .area file and set a maximum area constraint
/// on each triangle.
///
/// Vertices that are not corners of triangles, such as nodes on edges of
/// subparametric elements, are discarded.
///
/// This routine finds the adjacencies between triangles (and subsegments)
/// by forming one stack of triangles for each vertex. Each triangle is on
/// three different stacks simultaneously. Each triangle's subsegment
/// pointers are used to link the items in each stack. This memory-saving
/// feature makes the code harder to read. The most important thing to keep
/// in mind is that each triangle is removed from a stack precisely when
/// the corresponding pointer is adjusted to refer to a subsegment rather
/// than the next triangle of the stack.
/// </remarks>
public static int Reconstruct(Mesh mesh, InputGeometry input, ITriangle[] triangles)
{
int hullsize = 0;
Otri tri = default(Otri);
Otri triangleleft = default(Otri);
Otri checktri = default(Otri);
Otri checkleft = default(Otri);
Otri checkneighbor = default(Otri);
Osub subseg = default(Osub);
List <Otri>[] vertexarray; // Triangle
Otri prevlink; // Triangle
Otri nexttri; // Triangle
Vertex tdest, tapex;
Vertex checkdest, checkapex;
Vertex shorg;
Vertex segmentorg, segmentdest;
int[] corner = new int[3];
int[] end = new int[2];
//bool segmentmarkers = false;
int boundmarker;
int aroundvertex;
bool notfound;
int i = 0;
int elements = triangles == null ? 0 : triangles.Length;
int numberofsegments = input.segments.Count;
mesh.inelements = elements;
mesh.regions.AddRange(input.regions);
// Create the triangles.
for (i = 0; i < mesh.inelements; i++)
{
mesh.MakeTriangle(ref tri);
// Mark the triangle as living.
//tri.triangle.neighbors[0].triangle = tri.triangle;
}
if (mesh.behavior.Poly)
{
mesh.insegments = numberofsegments;
// Create the subsegments.
for (i = 0; i < mesh.insegments; i++)
{
mesh.MakeSegment(ref subseg);
// Mark the subsegment as living.
//subseg.ss.subsegs[0].ss = subseg.ss;
}
}
// Allocate a temporary array that maps each vertex to some adjacent
// triangle. I took care to allocate all the permanent memory for
// triangles and subsegments first.
vertexarray = new List <Otri> [mesh.vertices.Count];
// Each vertex is initially unrepresented.
for (i = 0; i < mesh.vertices.Count; i++)
{
Otri tmp = default(Otri);
tmp.triangle = Mesh.dummytri;
vertexarray[i] = new List <Otri>(3);
vertexarray[i].Add(tmp);
}
i = 0;
// Read the triangles from the .ele file, and link
// together those that share an edge.
foreach (var item in mesh.triangles.Values)
{
tri.triangle = item;
corner[0] = triangles[i].P0;
corner[1] = triangles[i].P1;
corner[2] = triangles[i].P2;
// Copy the triangle's three corners.
for (int j = 0; j < 3; j++)
{
if ((corner[j] < 0) || (corner[j] >= mesh.invertices))
{
SimpleLog.Instance.Error("Triangle has an invalid vertex index.", "MeshReader.Reconstruct()");
throw new Exception("Triangle has an invalid vertex index.");
}
}
// Read the triangle's attributes.
tri.triangle.region = triangles[i].Region;
// TODO: VarArea
if (mesh.behavior.VarArea)
{
tri.triangle.area = triangles[i].Area;
}
// Set the triangle's vertices.
tri.orient = 0;
tri.SetOrg(mesh.vertices[corner[0]]);
tri.SetDest(mesh.vertices[corner[1]]);
tri.SetApex(mesh.vertices[corner[2]]);
// Try linking the triangle to others that share these vertices.
for (tri.orient = 0; tri.orient < 3; tri.orient++)
{
// Take the number for the origin of triangleloop.
aroundvertex = corner[tri.orient];
int index = vertexarray[aroundvertex].Count - 1;
// Look for other triangles having this vertex.
nexttri = vertexarray[aroundvertex][index];
// Link the current triangle to the next one in the stack.
//tri.triangle.neighbors[tri.orient] = nexttri;
// Push the current triangle onto the stack.
vertexarray[aroundvertex].Add(tri);
checktri = nexttri;
if (checktri.triangle != Mesh.dummytri)
{
tdest = tri.Dest();
tapex = tri.Apex();
// Look for other triangles that share an edge.
do
{
checkdest = checktri.Dest();
checkapex = checktri.Apex();
if (tapex == checkdest)
{
// The two triangles share an edge; bond them together.
tri.Lprev(ref triangleleft);
triangleleft.Bond(ref checktri);
}
if (tdest == checkapex)
{
// The two triangles share an edge; bond them together.
checktri.Lprev(ref checkleft);
tri.Bond(ref checkleft);
}
// Find the next triangle in the stack.
index--;
nexttri = vertexarray[aroundvertex][index];
checktri = nexttri;
} while (checktri.triangle != Mesh.dummytri);
}
}
i++;
}
// Prepare to count the boundary edges.
hullsize = 0;
if (mesh.behavior.Poly)
{
// Read the segments from the .poly file, and link them
// to their neighboring triangles.
boundmarker = 0;
i = 0;
foreach (var item in mesh.subsegs.Values)
{
subseg.seg = item;
end[0] = input.segments[i].P0;
end[1] = input.segments[i].P1;
boundmarker = input.segments[i].Boundary;
for (int j = 0; j < 2; j++)
{
if ((end[j] < 0) || (end[j] >= mesh.invertices))
{
SimpleLog.Instance.Error("Segment has an invalid vertex index.",
"MeshReader.Reconstruct()");
throw new Exception("Segment has an invalid vertex index.");
}
}
// set the subsegment's vertices.
subseg.orient = 0;
segmentorg = mesh.vertices[end[0]];
segmentdest = mesh.vertices[end[1]];
subseg.SetOrg(segmentorg);
subseg.SetDest(segmentdest);
subseg.SetSegOrg(segmentorg);
subseg.SetSegDest(segmentdest);
subseg.seg.boundary = boundmarker;
// Try linking the subsegment to triangles that share these vertices.
for (subseg.orient = 0; subseg.orient < 2; subseg.orient++)
{
// Take the number for the destination of subsegloop.
aroundvertex = end[1 - subseg.orient];
int index = vertexarray[aroundvertex].Count - 1;
// Look for triangles having this vertex.
prevlink = vertexarray[aroundvertex][index];
nexttri = vertexarray[aroundvertex][index];
checktri = nexttri;
shorg = subseg.Org();
notfound = true;
// Look for triangles having this edge. Note that I'm only
// comparing each triangle's destination with the subsegment;
// each triangle's apex is handled through a different vertex.
// Because each triangle appears on three vertices' lists, each
// occurrence of a triangle on a list can (and does) represent
// an edge. In this way, most edges are represented twice, and
// every triangle-subsegment bond is represented once.
while (notfound && (checktri.triangle != Mesh.dummytri))
{
checkdest = checktri.Dest();
if (shorg == checkdest)
{
// We have a match. Remove this triangle from the list.
//prevlink = vertexarray[aroundvertex][index];
vertexarray[aroundvertex].Remove(prevlink);
// Bond the subsegment to the triangle.
checktri.SegBond(ref subseg);
// Check if this is a boundary edge.
checktri.Sym(ref checkneighbor);
if (checkneighbor.triangle == Mesh.dummytri)
{
// The next line doesn't insert a subsegment (because there's
// already one there), but it sets the boundary markers of
// the existing subsegment and its vertices.
mesh.InsertSubseg(ref checktri, 1);
hullsize++;
}
notfound = false;
}
index--;
// Find the next triangle in the stack.
prevlink = vertexarray[aroundvertex][index];
nexttri = vertexarray[aroundvertex][index];
checktri = nexttri;
}
}
i++;
}
}
// Mark the remaining edges as not being attached to any subsegment.
// Also, count the (yet uncounted) boundary edges.
for (i = 0; i < mesh.vertices.Count; i++)
{
// Search the stack of triangles adjacent to a vertex.
int index = vertexarray[i].Count - 1;
nexttri = vertexarray[i][index];
checktri = nexttri;
while (checktri.triangle != Mesh.dummytri)
{
// Find the next triangle in the stack before this
// information gets overwritten.
index--;
nexttri = vertexarray[i][index];
// No adjacent subsegment. (This overwrites the stack info.)
checktri.SegDissolve();
checktri.Sym(ref checkneighbor);
if (checkneighbor.triangle == Mesh.dummytri)
{
mesh.InsertSubseg(ref checktri, 1);
hullsize++;
}
checktri = nexttri;
}
}
return(hullsize);
}
private void ConstructBoundaryBvdCell(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("ConstructBoundaryBvdCell: 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.triangle != Mesh.dummytri)
{
// Go clockwise until we reach the border (or the initial triangle)
while (f_prev.triangle != Mesh.dummytri && !f_prev.Equal(f_init))
{
f_prev.Copy(ref f);
f_prev.OprevSelf();
}
f.Copy(ref f_init);
f.Onext(ref f_next);
}
if (f_prev.triangle == Mesh.dummytri)
{
// 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;
points[n + segIndex] = p;
segIndex++;
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;
points[n + segIndex] = p;
segIndex++;
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.triangle.id];
if (f_next.triangle == Mesh.dummytri)
{
if (!f.triangle.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;
points[n + segIndex] = p;
segIndex++;
vpoints.Add(p);
break;
}
cc_f_next = this.points[f_next.triangle.id];
// if f is tagged non-blind then
if (!f.triangle.infected)
{
// Insert the circumcenter of f into P
vpoints.Add(cc_f);
if (f_next.triangle.infected)
{
// Call S_fnext the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.triangle.hash];
// Insert point Lf,f_next /\ Sf_next into P
if (SegmentsIntersect(sfn.SegOrg(), sfn.SegDest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex;
points[n + segIndex] = p;
segIndex++;
vpoints.Add(p);
}
}
}
else
{
// Call Sf the constrained edge blinding f
sf.seg = subsegMap[f.triangle.hash];
sorg = sf.SegOrg();
sdest = sf.SegDest();
// if f_next is tagged non-blind then
if (!f_next.triangle.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;
points[n + segIndex] = p;
segIndex++;
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;
points[n + segIndex] = p;
segIndex++;
vpoints.Add(p);
}
}
else
{
// Call Sf_next the constrained edge blinding f_next
sfn.seg = subsegMap[f_next.triangle.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;
points[n + segIndex] = p;
segIndex++;
vpoints.Add(p);
}
if (SegmentsIntersect(sfn.SegOrg(), sfn.SegDest(), cc_f, cc_f_next, out p, true))
{
p.id = n + segIndex;
points[n + segIndex] = p;
segIndex++;
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;
points[n + segIndex] = p;
segIndex++;
vpoints.Add(p);
}
}
}
}
// f <- f_next
f_next.Copy(ref f);
// Call f_next the next triangle counterclockwise around x
f_next.OnextSelf();
}while (!f.Equal(f_init));
// Output: Bounded Voronoi cell of x in counterclockwise order.
region.Add(vpoints);
}
/// <summary>
/// Find the first triangle on the path from one point to another.
/// </summary>
/// <param name="searchtri"></param>
/// <param name="searchpoint"></param>
/// <returns>
/// The return value notes whether the destination or apex of the found
/// triangle is collinear with the two points in question.
/// </returns>
/// <remarks>
/// Finds the triangle that intersects a line segment drawn from the
/// origin of 'searchtri' to the point 'searchpoint', and returns the result
/// in 'searchtri'. The origin of 'searchtri' does not change, even though
/// the triangle returned may differ from the one passed in. This routine
/// is used to find the direction to move in to get from one point to
/// another.
/// </remarks>
private FindDirectionResult FindDirection(ref Otri searchtri, Vertex searchpoint)
{
Otri checktri = default(Otri);
Vertex startvertex;
Vertex leftvertex, rightvertex;
double leftccw, rightccw;
bool leftflag, rightflag;
startvertex = searchtri.Org();
rightvertex = searchtri.Dest();
leftvertex = searchtri.Apex();
// Is 'searchpoint' to the left?
leftccw = RobustPredicates.CounterClockwise(searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
// Is 'searchpoint' to the right?
rightccw = RobustPredicates.CounterClockwise(startvertex, searchpoint, rightvertex);
rightflag = rightccw > 0.0;
if (leftflag && rightflag)
{
// 'searchtri' faces directly away from 'searchpoint'. We could go left
// or right. Ask whether it's a triangle or a boundary on the left.
searchtri.Onext(ref checktri);
if (checktri.tri.Id == Mesh.DUMMY)
{
leftflag = false;
}
else
{
rightflag = false;
}
}
while (leftflag)
{
// Turn left until satisfied.
searchtri.Onext();
if (searchtri.tri.Id == Mesh.DUMMY)
{
throw new Exception("Unable to find a triangle on path.");
}
leftvertex = searchtri.Apex();
rightccw = leftccw;
leftccw = RobustPredicates.CounterClockwise(searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
}
while (rightflag)
{
// Turn right until satisfied.
searchtri.Oprev();
if (searchtri.tri.Id == Mesh.DUMMY)
{
throw new Exception("Unable to find a triangle on path.");
}
rightvertex = searchtri.Dest();
leftccw = rightccw;
rightccw = RobustPredicates.CounterClockwise(startvertex, searchpoint, rightvertex);
rightflag = rightccw > 0.0;
}
if (leftccw == 0.0)
{
return(FindDirectionResult.Leftcollinear);
}
if (rightccw == 0.0)
{
return(FindDirectionResult.Rightcollinear);
}
return(FindDirectionResult.Within);
}
/// <summary>
/// Find the intersection of an existing segment and a segment that is being
/// inserted. Insert a vertex at the intersection, splitting an existing subsegment.
/// </summary>
/// <param name="splittri"></param>
/// <param name="splitsubseg"></param>
/// <param name="endpoint2"></param>
/// <remarks>
/// The segment being inserted connects the apex of splittri to endpoint2.
/// splitsubseg is the subsegment being split, and MUST adjoin splittri.
/// Hence, endpoints of the subsegment being split are the origin and
/// destination of splittri.
/// On completion, splittri is a handle having the newly inserted
/// intersection point as its origin, and endpoint1 as its destination.
/// </remarks>
private void SegmentIntersection(ref Otri splittri, ref Osub splitsubseg, Vertex endpoint2)
{
Osub opposubseg = default(Osub);
Vertex endpoint1;
Vertex torg, tdest;
Vertex leftvertex, rightvertex;
Vertex newvertex;
InsertVertexResult success;
var dummysub = mesh.dummysub;
double ex, ey;
double tx, ty;
double etx, ety;
double split, denom;
// Find the other three segment endpoints.
endpoint1 = splittri.Apex();
torg = splittri.Org();
tdest = splittri.Dest();
// Segment intersection formulae; see the Antonio reference.
tx = tdest.X - torg.X;
ty = tdest.Y - torg.Y;
ex = endpoint2.X - endpoint1.X;
ey = endpoint2.Y - endpoint1.Y;
etx = torg.X - endpoint2.X;
ety = torg.Y - endpoint2.Y;
denom = ty * ex - tx * ey;
if (denom == 0.0)
{
throw new Exception("Attempt to find intersection of parallel segments.");
}
split = (ey * etx - ex * ety) / denom;
// Create the new vertex.
newvertex = new Vertex(
torg.X + split * (tdest.X - torg.X),
torg.Y + split * (tdest.Y - torg.Y),
splitsubseg.seg.boundary);
newvertex.Id = mesh.hash_vtx++;
mesh.vertices.Add(newvertex.Id, newvertex);
// Insert the intersection vertex. This should always succeed.
success = mesh.InsertVertex(newvertex, ref splittri, ref splitsubseg, false, false);
if (success != InsertVertexResult.Successful)
{
throw new Exception("Failure to split a segment.");
}
// Record a triangle whose origin is the new vertex.
newvertex.tri = splittri;
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
// Divide the segment into two, and correct the segment endpoints.
splitsubseg.Sym();
splitsubseg.Pivot(ref opposubseg);
splitsubseg.Dissolve(dummysub);
opposubseg.Dissolve(dummysub);
do
{
splitsubseg.SetSegOrg(newvertex);
splitsubseg.Next();
} while (splitsubseg.seg.hash != Mesh.DUMMY);
do
{
opposubseg.SetSegOrg(newvertex);
opposubseg.Next();
} while (opposubseg.seg.hash != Mesh.DUMMY);
// Inserting the vertex may have caused edge flips. We wish to rediscover
// the edge connecting endpoint1 to the new intersection vertex.
FindDirection(ref splittri, endpoint1);
rightvertex = splittri.Dest();
leftvertex = splittri.Apex();
if ((leftvertex.X == endpoint1.X) && (leftvertex.Y == endpoint1.Y))
{
splittri.Onext();
}
else if ((rightvertex.X != endpoint1.X) || (rightvertex.Y != endpoint1.Y))
{
throw new Exception("Topological inconsistency after splitting a segment.");
}
// 'splittri' should have destination endpoint1.
}
public bool CheckMesh()
{
Otri otri = new Otri();
Otri otri1 = new Otri();
Otri otri2 = new Otri();
bool noExact = Behavior.NoExact;
Behavior.NoExact = false;
int num = 0;
foreach (Triangle value in this.mesh.triangles.Values)
{
otri.triangle = value;
otri.orient = 0;
while (otri.orient < 3)
{
Vertex vertex = otri.Org();
Vertex vertex1 = otri.Dest();
if (otri.orient == 0 && Primitives.CounterClockwise(vertex, vertex1, otri.Apex()) <= 0)
{
this.logger.Warning("Triangle is flat or inverted.", "Quality.CheckMesh()");
num++;
}
otri.Sym(ref otri1);
if (otri1.triangle != Mesh.dummytri)
{
otri1.Sym(ref otri2);
if (otri.triangle != otri2.triangle || otri.orient != otri2.orient)
{
if (otri.triangle == otri2.triangle)
{
this.logger.Warning("Asymmetric triangle-triangle bond: (Right triangle, wrong orientation)", "Quality.CheckMesh()");
}
num++;
}
Vertex vertex2 = otri1.Org();
if (vertex != otri1.Dest() || vertex1 != vertex2)
{
this.logger.Warning("Mismatched edge coordinates between two triangles.", "Quality.CheckMesh()");
num++;
}
}
otri.orient = otri.orient + 1;
}
}
this.mesh.MakeVertexMap();
foreach (Vertex value1 in this.mesh.vertices.Values)
{
if (value1.tri.triangle != null)
{
continue;
}
this.logger.Warning(string.Concat("Vertex (ID ", value1.id, ") not connected to mesh (duplicate input vertex?)"), "Quality.CheckMesh()");
}
if (num == 0)
{
this.logger.Info("Mesh topology appears to be consistent.");
}
Behavior.NoExact = noExact;
return(num == 0);
}
private void ConstructBoundaryBvdCell(Vertex vertex)
{
Vertex vertex1;
Point point;
VoronoiRegion voronoiRegion = new VoronoiRegion(vertex);
this.regions.Add(voronoiRegion);
Otri otri = new Otri();
Otri otri1 = new Otri();
Otri otri2 = new Otri();
Otri otri3 = new Otri();
Osub item = new Osub();
Osub osub = new Osub();
int count = this.mesh.triangles.Count;
List <Point> points = new List <Point>();
vertex.tri.Copy(ref otri1);
if (otri1.Org() != vertex)
{
throw new Exception("ConstructBoundaryBvdCell: inconsistent topology.");
}
otri1.Copy(ref otri);
otri1.Onext(ref otri2);
otri1.Oprev(ref otri3);
if (otri3.triangle != Mesh.dummytri)
{
while (otri3.triangle != Mesh.dummytri && !otri3.Equal(otri1))
{
otri3.Copy(ref otri);
otri3.OprevSelf();
}
otri.Copy(ref otri1);
otri.Onext(ref otri2);
}
if (otri3.triangle == Mesh.dummytri)
{
point = new Point(vertex.x, vertex.y)
{
id = count + this.segIndex
};
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
Vertex vertex2 = otri.Org();
Vertex vertex3 = otri.Dest();
point = new Point((vertex2.X + vertex3.X) / 2, (vertex2.Y + vertex3.Y) / 2)
{
id = count + this.segIndex
};
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
do
{
Point point1 = this.points[otri.triangle.id];
if (otri2.triangle != Mesh.dummytri)
{
Point point2 = this.points[otri2.triangle.id];
if (otri.triangle.infected)
{
item.seg = this.subsegMap[otri.triangle.hash];
Vertex vertex4 = item.SegOrg();
Vertex vertex5 = item.SegDest();
if (otri2.triangle.infected)
{
osub.seg = this.subsegMap[otri2.triangle.hash];
if (!item.Equal(osub))
{
if (this.SegmentsIntersect(vertex4, vertex5, point1, point2, out point, true))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
if (this.SegmentsIntersect(osub.SegOrg(), osub.SegDest(), point1, point2, out point, true))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
}
else if (this.SegmentsIntersect(vertex4, vertex5, new Point((vertex2.X + vertex3.X) / 2, (vertex2.Y + vertex3.Y) / 2), point2, out point, false))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
}
else
{
vertex3 = otri.Dest();
vertex1 = otri.Apex();
if (this.SegmentsIntersect(vertex4, vertex5, new Point((vertex3.X + vertex1.X) / 2, (vertex3.Y + vertex1.Y) / 2), point1, out point, false))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
if (this.SegmentsIntersect(vertex4, vertex5, point1, point2, out point, true))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
}
}
else
{
points.Add(point1);
if (otri2.triangle.infected)
{
osub.seg = this.subsegMap[otri2.triangle.hash];
if (this.SegmentsIntersect(osub.SegOrg(), osub.SegDest(), point1, point2, out point, true))
{
point.id = count + this.segIndex;
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
}
}
}
otri2.Copy(ref otri);
otri2.OnextSelf();
}
else
{
if (!otri.triangle.infected)
{
points.Add(point1);
}
vertex2 = otri.Org();
vertex1 = otri.Apex();
point = new Point((vertex2.X + vertex1.X) / 2, (vertex2.Y + vertex1.Y) / 2)
{
id = count + this.segIndex
};
this.points[count + this.segIndex] = point;
this.segIndex = this.segIndex + 1;
points.Add(point);
break;
}
}while (!otri.Equal(otri1));
voronoiRegion.Add(points);
}
public void TestTriangle(ref Otri testtri)
{
Vertex vertex;
Vertex vertex1;
double num;
double num1;
double num2;
Otri otri = new Otri();
Otri otri1 = new Otri();
Osub osub = new Osub();
Vertex vertex2 = testtri.Org();
Vertex vertex3 = testtri.Dest();
Vertex vertex4 = testtri.Apex();
double num3 = vertex2.x - vertex3.x;
double num4 = vertex2.y - vertex3.y;
double num5 = vertex3.x - vertex4.x;
double num6 = vertex3.y - vertex4.y;
double num7 = vertex4.x - vertex2.x;
double num8 = vertex4.y - vertex2.y;
double num9 = num3 * num3;
double num10 = num4 * num4;
double num11 = num5 * num5;
double num12 = num6 * num6;
double num13 = num8 * num8;
double num14 = num9 + num10;
double num15 = num11 + num12;
double num16 = num7 * num7 + num13;
if (num14 < num15 && num14 < num16)
{
num = num14;
num1 = num5 * num7 + num6 * num8;
num1 = num1 * num1 / (num15 * num16);
vertex = vertex2;
vertex1 = vertex3;
testtri.Copy(ref otri);
}
else if (num15 >= num16)
{
num = num16;
num1 = num3 * num5 + num4 * num6;
num1 = num1 * num1 / (num14 * num15);
vertex = vertex4;
vertex1 = vertex2;
testtri.Lprev(ref otri);
}
else
{
num = num15;
num1 = num3 * num7 + num4 * num8;
num1 = num1 * num1 / (num14 * num16);
vertex = vertex3;
vertex1 = vertex4;
testtri.Lnext(ref otri);
}
if (this.behavior.VarArea || this.behavior.fixedArea || this.behavior.Usertest)
{
double num17 = 0.5 * (num3 * num6 - num4 * num5);
if (this.behavior.fixedArea && num17 > this.behavior.MaxArea)
{
this.queue.Enqueue(ref testtri, num, vertex4, vertex2, vertex3);
return;
}
if (this.behavior.VarArea && num17 > testtri.triangle.area && testtri.triangle.area > 0)
{
this.queue.Enqueue(ref testtri, num, vertex4, vertex2, vertex3);
return;
}
if (this.behavior.Usertest && this.userTest != null && this.userTest(vertex2, vertex3, vertex4, num17))
{
this.queue.Enqueue(ref testtri, num, vertex4, vertex2, vertex3);
return;
}
}
if (num14 <= num15 || num14 <= num16)
{
num2 = (num15 <= num16 ? (num14 + num15 - num16) / (2 * Math.Sqrt(num14 * num15)) : (num14 + num16 - num15) / (2 * Math.Sqrt(num14 * num16)));
}
else
{
num2 = (num15 + num16 - num14) / (2 * Math.Sqrt(num15 * num16));
}
if (num1 > this.behavior.goodAngle || num2 < this.behavior.maxGoodAngle && this.behavior.MaxAngle != 0)
{
if (vertex.type == VertexType.SegmentVertex && vertex1.type == VertexType.SegmentVertex)
{
otri.SegPivot(ref osub);
if (osub.seg == Mesh.dummysub)
{
otri.Copy(ref otri1);
do
{
otri.OprevSelf();
otri.SegPivot(ref osub);
}while (osub.seg == Mesh.dummysub);
Vertex vertex5 = osub.SegOrg();
Vertex vertex6 = osub.SegDest();
do
{
otri1.DnextSelf();
otri1.SegPivot(ref osub);
}while (osub.seg == Mesh.dummysub);
Vertex vertex7 = osub.SegOrg();
Vertex vertex8 = osub.SegDest();
Vertex vertex9 = null;
if (vertex6.x == vertex7.x && vertex6.y == vertex7.y)
{
vertex9 = vertex6;
}
else if (vertex5.x == vertex8.x && vertex5.y == vertex8.y)
{
vertex9 = vertex5;
}
if (vertex9 != null)
{
double num18 = (vertex.x - vertex9.x) * (vertex.x - vertex9.x) + (vertex.y - vertex9.y) * (vertex.y - vertex9.y);
double num19 = (vertex1.x - vertex9.x) * (vertex1.x - vertex9.x) + (vertex1.y - vertex9.y) * (vertex1.y - vertex9.y);
if (num18 < 1.001 * num19 && num18 > 0.999 * num19)
{
return;
}
}
}
}
this.queue.Enqueue(ref testtri, num, vertex4, vertex2, vertex3);
}
}
private void SplitTriangle(BadTriangle badtri)
{
Point point;
Otri otri = new Otri();
double num = 0;
double num1 = 0;
otri = badtri.poortri;
Vertex vertex = otri.Org();
Vertex vertex1 = otri.Dest();
Vertex vertex2 = otri.Apex();
if (!Otri.IsDead(otri.triangle) && vertex == badtri.triangorg && vertex1 == badtri.triangdest && vertex2 == badtri.triangapex)
{
bool flag = false;
point = (this.behavior.fixedArea || this.behavior.VarArea ? Primitives.FindCircumcenter(vertex, vertex1, vertex2, ref num, ref num1, this.behavior.offconstant) : this.newLocation.FindLocation(vertex, vertex1, vertex2, ref num, ref num1, true, otri));
if ((point.x != vertex.x || point.y != vertex.y) && (point.x != vertex1.x || point.y != vertex1.y) && (point.x != vertex2.x || point.y != vertex2.y))
{
Vertex vertex3 = new Vertex(point.x, point.y, 0, this.mesh.nextras)
{
type = VertexType.FreeVertex
};
for (int i = 0; i < this.mesh.nextras; i++)
{
vertex3.attributes[i] = vertex.attributes[i] + num * (vertex1.attributes[i] - vertex.attributes[i]) + num1 * (vertex2.attributes[i] - vertex.attributes[i]);
}
if (num1 < num)
{
otri.LprevSelf();
}
Osub osub = new Osub();
InsertVertexResult insertVertexResult = this.mesh.InsertVertex(vertex3, ref otri, ref osub, true, true);
if (insertVertexResult == InsertVertexResult.Successful)
{
Mesh mesh = this.mesh;
int hashVtx = mesh.hash_vtx;
mesh.hash_vtx = hashVtx + 1;
vertex3.hash = hashVtx;
vertex3.id = vertex3.hash;
this.mesh.vertices.Add(vertex3.hash, vertex3);
if (this.mesh.steinerleft > 0)
{
Mesh mesh1 = this.mesh;
mesh1.steinerleft = mesh1.steinerleft - 1;
}
}
else if (insertVertexResult == InsertVertexResult.Encroaching)
{
this.mesh.UndoVertex();
}
else if (insertVertexResult != InsertVertexResult.Violating && Behavior.Verbose)
{
this.logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
flag = true;
}
}
else if (Behavior.Verbose)
{
this.logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
flag = true;
}
if (flag)
{
this.logger.Error("The new vertex is at the circumcenter of triangle: This probably means that I am trying to refine triangles to a smaller size than can be accommodated by the finite precision of floating point arithmetic.", "Quality.SplitTriangle()");
throw new Exception("The new vertex is at the circumcenter of triangle.");
}
}
}
private void SplitEncSegs(bool triflaws)
{
Vertex vertex;
double num;
Otri otri = new Otri();
Otri otri1 = new Otri();
Osub osub = new Osub();
Osub osub1 = new Osub();
while (this.badsubsegs.Count > 0 && this.mesh.steinerleft != 0)
{
BadSubseg badSubseg = this.badsubsegs.Dequeue();
osub1 = badSubseg.encsubseg;
Vertex vertex1 = osub1.Org();
Vertex vertex2 = osub1.Dest();
if (!Osub.IsDead(osub1.seg) && vertex1 == badSubseg.subsegorg && vertex2 == badSubseg.subsegdest)
{
osub1.TriPivot(ref otri);
otri.Lnext(ref otri1);
otri1.SegPivot(ref osub);
bool flag = osub.seg != Mesh.dummysub;
otri1.LnextSelf();
otri1.SegPivot(ref osub);
bool flag1 = osub.seg != Mesh.dummysub;
if (!this.behavior.ConformingDelaunay && !flag && !flag1)
{
vertex = otri.Apex();
while (vertex.type == VertexType.FreeVertex && (vertex1.x - vertex.x) * (vertex2.x - vertex.x) + (vertex1.y - vertex.y) * (vertex2.y - vertex.y) < 0)
{
this.mesh.DeleteVertex(ref otri1);
osub1.TriPivot(ref otri);
vertex = otri.Apex();
otri.Lprev(ref otri1);
}
}
otri.Sym(ref otri1);
if (otri1.triangle != Mesh.dummytri)
{
otri1.LnextSelf();
otri1.SegPivot(ref osub);
bool flag2 = osub.seg != Mesh.dummysub;
flag1 = flag1 | flag2;
otri1.LnextSelf();
otri1.SegPivot(ref osub);
bool flag3 = osub.seg != Mesh.dummysub;
flag = flag | flag3;
if (!this.behavior.ConformingDelaunay && !flag3 && !flag2)
{
vertex = otri1.Org();
while (vertex.type == VertexType.FreeVertex && (vertex1.x - vertex.x) * (vertex2.x - vertex.x) + (vertex1.y - vertex.y) * (vertex2.y - vertex.y) < 0)
{
this.mesh.DeleteVertex(ref otri1);
otri.Sym(ref otri1);
vertex = otri1.Apex();
otri1.LprevSelf();
}
}
}
if (!(flag | flag1))
{
num = 0.5;
}
else
{
double num1 = Math.Sqrt((vertex2.x - vertex1.x) * (vertex2.x - vertex1.x) + (vertex2.y - vertex1.y) * (vertex2.y - vertex1.y));
double num2 = 1;
while (num1 > 3 * num2)
{
num2 = num2 * 2;
}
while (num1 < 1.5 * num2)
{
num2 = num2 * 0.5;
}
num = num2 / num1;
if (flag1)
{
num = 1 - num;
}
}
Vertex vertex3 = new Vertex(vertex1.x + num * (vertex2.x - vertex1.x), vertex1.y + num * (vertex2.y - vertex1.y), osub1.Mark(), this.mesh.nextras)
{
type = VertexType.SegmentVertex
};
Mesh mesh = this.mesh;
int hashVtx = mesh.hash_vtx;
mesh.hash_vtx = hashVtx + 1;
vertex3.hash = hashVtx;
vertex3.id = vertex3.hash;
this.mesh.vertices.Add(vertex3.hash, vertex3);
for (int i = 0; i < this.mesh.nextras; i++)
{
vertex3.attributes[i] = vertex1.attributes[i] + num * (vertex2.attributes[i] - vertex1.attributes[i]);
}
if (!Behavior.NoExact)
{
double num3 = Primitives.CounterClockwise(vertex1, vertex2, vertex3);
double num4 = (vertex1.x - vertex2.x) * (vertex1.x - vertex2.x) + (vertex1.y - vertex2.y) * (vertex1.y - vertex2.y);
if (num3 != 0 && num4 != 0)
{
num3 = num3 / num4;
if (!double.IsNaN(num3))
{
Vertex vertex4 = vertex3;
vertex4.x = vertex4.x + num3 * (vertex2.y - vertex1.y);
Vertex vertex5 = vertex3;
vertex5.y = vertex5.y + num3 * (vertex1.x - vertex2.x);
}
}
}
if (vertex3.x == vertex1.x && vertex3.y == vertex1.y || vertex3.x == vertex2.x && vertex3.y == vertex2.y)
{
this.logger.Error("Ran out of precision: I attempted to split a segment to a smaller size than can be accommodated by the finite precision of floating point arithmetic.", "Quality.SplitEncSegs()");
throw new Exception("Ran out of precision");
}
InsertVertexResult insertVertexResult = this.mesh.InsertVertex(vertex3, ref otri, ref osub1, true, triflaws);
if (insertVertexResult != InsertVertexResult.Successful && insertVertexResult != InsertVertexResult.Encroaching)
{
this.logger.Error("Failure to split a segment.", "Quality.SplitEncSegs()");
throw new Exception("Failure to split a segment.");
}
if (this.mesh.steinerleft > 0)
{
Mesh mesh1 = this.mesh;
mesh1.steinerleft = mesh1.steinerleft - 1;
}
this.CheckSeg4Encroach(ref osub1);
osub1.NextSelf();
this.CheckSeg4Encroach(ref osub1);
}
badSubseg.subsegorg = null;
}
}
/// <summary>
/// Find a triangle or edge containing a given point.
/// </summary>
/// <param name="searchpoint">The point to locate.</param>
/// <param name="searchtri">The triangle to start the search at.</param>
/// <param name="stopatsubsegment"> If 'stopatsubsegment' is set, the search
/// will stop if it tries to walk through a subsegment, and will return OUTSIDE.</param>
/// <returns>Location information.</returns>
/// <remarks>
/// Begins its search from 'searchtri'. It is important that 'searchtri'
/// be a handle with the property that 'searchpoint' is strictly to the left
/// of the edge denoted by 'searchtri', or is collinear with that edge and
/// does not intersect that edge. (In particular, 'searchpoint' should not
/// be the origin or destination of that edge.)
///
/// These conditions are imposed because preciselocate() is normally used in
/// one of two situations:
///
/// (1) To try to find the location to insert a new point. Normally, we
/// know an edge that the point is strictly to the left of. In the
/// incremental Delaunay algorithm, that edge is a bounding box edge.
/// In Ruppert's Delaunay refinement algorithm for quality meshing,
/// that edge is the shortest edge of the triangle whose circumcenter
/// is being inserted.
///
/// (2) To try to find an existing point. In this case, any edge on the
/// convex hull is a good starting edge. You must screen out the
/// possibility that the vertex sought is an endpoint of the starting
/// edge before you call preciselocate().
///
/// On completion, 'searchtri' is a triangle that contains 'searchpoint'.
///
/// This implementation differs from that given by Guibas and Stolfi. It
/// walks from triangle to triangle, crossing an edge only if 'searchpoint'
/// is on the other side of the line containing that edge. After entering
/// a triangle, there are two edges by which one can leave that triangle.
/// If both edges are valid ('searchpoint' is on the other side of both
/// edges), one of the two is chosen by drawing a line perpendicular to
/// the entry edge (whose endpoints are 'forg' and 'fdest') passing through
/// 'fapex'. Depending on which side of this perpendicular 'searchpoint'
/// falls on, an exit edge is chosen.
///
/// This implementation is empirically faster than the Guibas and Stolfi
/// point location routine (which I originally used), which tends to spiral
/// in toward its target.
///
/// Returns ONVERTEX if the point lies on an existing vertex. 'searchtri'
/// is a handle whose origin is the existing vertex.
///
/// Returns ONEDGE if the point lies on a mesh edge. 'searchtri' is a
/// handle whose primary edge is the edge on which the point lies.
///
/// Returns INTRIANGLE if the point lies strictly within a triangle.
/// 'searchtri' is a handle on the triangle that contains the point.
///
/// Returns OUTSIDE if the point lies outside the mesh. 'searchtri' is a
/// handle whose primary edge the point is to the right of. This might
/// occur when the circumcenter of a triangle falls just slightly outside
/// the mesh due to floating-point roundoff error. It also occurs when
/// seeking a hole or region point that a foolish user has placed outside
/// the mesh.
///
/// WARNING: This routine is designed for convex triangulations, and will
/// not generally work after the holes and concavities have been carved.
/// However, it can still be used to find the circumcenter of a triangle, as
/// long as the search is begun from the triangle in question.</remarks>
public LocateResult PreciseLocate(Point searchpoint, ref Otri searchtri,
bool stopatsubsegment)
{
Otri backtracktri = default(Otri);
Osub checkedge = default(Osub);
Vertex forg, fdest, fapex;
double orgorient, destorient;
bool moveleft;
// Where are we?
forg = searchtri.Org();
fdest = searchtri.Dest();
fapex = searchtri.Apex();
while (true)
{
// Check whether the apex is the point we seek.
if ((fapex.x == searchpoint.X) && (fapex.y == searchpoint.Y))
{
searchtri.LprevSelf();
return(LocateResult.OnVertex);
}
// Does the point lie on the other side of the line defined by the
// triangle edge opposite the triangle's destination?
destorient = Primitives.CounterClockwise(forg, fapex, searchpoint);
// Does the point lie on the other side of the line defined by the
// triangle edge opposite the triangle's origin?
orgorient = Primitives.CounterClockwise(fapex, fdest, searchpoint);
if (destorient > 0.0)
{
if (orgorient > 0.0)
{
// Move left if the inner product of (fapex - searchpoint) and
// (fdest - forg) is positive. This is equivalent to drawing
// a line perpendicular to the line (forg, fdest) and passing
// through 'fapex', and determining which side of this line
// 'searchpoint' falls on.
moveleft = (fapex.x - searchpoint.X) * (fdest.x - forg.x) +
(fapex.y - searchpoint.Y) * (fdest.y - forg.y) > 0.0;
}
else
{
moveleft = true;
}
}
else
{
if (orgorient > 0.0)
{
moveleft = false;
}
else
{
// The point we seek must be on the boundary of or inside this
// triangle.
if (destorient == 0.0)
{
searchtri.LprevSelf();
return(LocateResult.OnEdge);
}
if (orgorient == 0.0)
{
searchtri.LnextSelf();
return(LocateResult.OnEdge);
}
return(LocateResult.InTriangle);
}
}
// Move to another triangle. Leave a trace 'backtracktri' in case
// floating-point roundoff or some such bogey causes us to walk
// off a boundary of the triangulation.
if (moveleft)
{
searchtri.Lprev(ref backtracktri);
fdest = fapex;
}
else
{
searchtri.Lnext(ref backtracktri);
forg = fapex;
}
backtracktri.Sym(ref searchtri);
if (mesh.checksegments && stopatsubsegment)
{
// Check for walking through a subsegment.
backtracktri.SegPivot(ref checkedge);
if (checkedge.seg != Mesh.dummysub)
{
// Go back to the last triangle.
backtracktri.Copy(ref searchtri);
return(LocateResult.Outside);
}
}
// Check for walking right out of the triangulation.
if (searchtri.triangle == Mesh.dummytri)
{
// Go back to the last triangle.
backtracktri.Copy(ref searchtri);
return(LocateResult.Outside);
}
fapex = searchtri.Apex();
}
}
/// <summary>
/// Enforce the Delaunay condition at an edge, fanning out recursively from
/// an existing vertex. Pay special attention to stacking inverted triangles.
/// </summary>
/// <param name="fixuptri"></param>
/// <param name="leftside">
/// Indicates whether or not fixuptri is to the left of
/// the segment being inserted. (Imagine that the segment is pointing up from
/// endpoint1 to endpoint2.)
/// </param>
/// <remarks>
/// This is a support routine for inserting segments into a constrained
/// Delaunay triangulation.
/// The origin of fixuptri is treated as if it has just been inserted, and
/// the local Delaunay condition needs to be enforced. It is only enforced
/// in one sector, however, that being the angular range defined by
/// fixuptri.
/// This routine also needs to make decisions regarding the "stacking" of
/// triangles. (Read the description of ConstrainedEdge() below before
/// reading on here, so you understand the algorithm.) If the position of
/// the new vertex (the origin of fixuptri) indicates that the vertex before
/// it on the polygon is a reflex vertex, then "stack" the triangle by
/// doing nothing. (fixuptri is an inverted triangle, which is how stacked
/// triangles are identified.)
/// Otherwise, check whether the vertex before that was a reflex vertex.
/// If so, perform an edge flip, thereby eliminating an inverted triangle
/// (popping it off the stack). The edge flip may result in the creation
/// of a new inverted triangle, depending on whether or not the new vertex
/// is visible to the vertex three edges behind on the polygon.
/// If neither of the two vertices behind the new vertex are reflex
/// vertices, fixuptri and fartri, the triangle opposite it, are not
/// inverted; hence, ensure that the edge between them is locally Delaunay.
/// </remarks>
private void DelaunayFixup(ref Otri fixuptri, bool leftside)
{
Otri neartri = default(Otri);
Otri fartri = default(Otri);
Osub faredge = default(Osub);
Vertex nearvertex, leftvertex, rightvertex, farvertex;
fixuptri.Lnext(ref neartri);
neartri.Sym(ref fartri);
// Check if the edge opposite the origin of fixuptri can be flipped.
if (fartri.tri.Id == Mesh.DUMMY)
{
return;
}
neartri.Pivot(ref faredge);
if (faredge.seg.hash != Mesh.DUMMY)
{
return;
}
// Find all the relevant vertices.
nearvertex = neartri.Apex();
leftvertex = neartri.Org();
rightvertex = neartri.Dest();
farvertex = fartri.Apex();
// Check whether the previous polygon vertex is a reflex vertex.
if (leftside)
{
if (RobustPredicates.CounterClockwise(nearvertex, leftvertex, farvertex) <= 0.0)
{
// leftvertex is a reflex vertex too. Nothing can
// be done until a convex section is found.
return;
}
}
else
{
if (RobustPredicates.CounterClockwise(farvertex, rightvertex, nearvertex) <= 0.0)
{
// rightvertex is a reflex vertex too. Nothing can
// be done until a convex section is found.
return;
}
}
if (RobustPredicates.CounterClockwise(rightvertex, leftvertex, farvertex) > 0.0)
{
// fartri is not an inverted triangle, and farvertex is not a reflex
// vertex. As there are no reflex vertices, fixuptri isn't an
// inverted triangle, either. Hence, test the edge between the
// triangles to ensure it is locally Delaunay.
if (RobustPredicates.InCircle(leftvertex, farvertex, rightvertex, nearvertex) <= 0.0)
{
return;
}
// Not locally Delaunay; go on to an edge flip.
}
// else fartri is inverted; remove it from the stack by flipping.
mesh.Flip(ref neartri);
fixuptri.Lprev(); // Restore the origin of fixuptri after the flip.
// Recursively process the two triangles that result from the flip.
DelaunayFixup(ref fixuptri, leftside);
DelaunayFixup(ref fartri, leftside);
}
/// <summary>
/// Write the Voronoi diagram to a .voro file.
/// </summary>
/// <param name="mesh"></param>
/// <param name="filename"></param>
/// <returns></returns>
/// <remarks>
/// The Voronoi diagram is the geometric dual of the Delaunay triangulation.
/// Hence, the Voronoi vertices are listed by traversing the Delaunay
/// triangles, and the Voronoi edges are listed by traversing the Delaunay
/// edges.
///
/// WARNING: In order to assign numbers to the Voronoi vertices, this
/// procedure messes up the subsegments or the extra nodes of every
/// element. Hence, you should call this procedure last.</remarks>
public static void WriteVoronoi(Mesh mesh, string filename)
{
Otri tri = default(Otri), trisym = default(Otri);
Vertex torg, tdest, tapex;
Point circumcenter;
double xi = 0, eta = 0;
int p1, p2, index = 0;
tri.orient = 0;
using (StreamWriter writer = new StreamWriter(filename))
{
// Number of triangles, two dimensions, number of vertex attributes, no markers.
writer.WriteLine("{0} 2 {1} 0", mesh.triangles.Count, mesh.nextras);
foreach (var item in mesh.triangles.Values)
{
tri.triangle = item;
torg = tri.Org();
tdest = tri.Dest();
tapex = tri.Apex();
circumcenter = Primitives.FindCircumcenter(torg, tdest, tapex, ref xi, ref eta);
// X and y coordinates.
writer.Write("{0} {1} {2}", index, circumcenter.X.ToString(nfi),
circumcenter.Y.ToString(nfi));
for (int i = 0; i < mesh.nextras; i++)
{
writer.Write(" 0");
// TODO
// Interpolate the vertex attributes at the circumcenter.
//writer.Write(" {0}", torg.attribs[i] + xi * (tdes.attribst[i] - torg.attribs[i]) +
// eta * (tapex.attribs[i] - torg.attribs[i]));
}
writer.WriteLine();
tri.triangle.id = index++;
}
// Number of edges, zero boundary markers.
writer.WriteLine("{0} 0", mesh.edges);
index = 0;
// To loop over the set of edges, loop over all triangles, and look at
// the three edges of each triangle. If there isn't another triangle
// adjacent to the edge, operate on the edge. If there is another
// adjacent triangle, operate on the edge only if the current triangle
// has a smaller pointer than its neighbor. This way, each edge is
// considered only once.
foreach (var item in mesh.triangles.Values)
{
tri.triangle = item;
for (tri.orient = 0; tri.orient < 3; tri.orient++)
{
tri.Sym(ref trisym);
if ((tri.triangle.id < trisym.triangle.id) || (trisym.triangle == Mesh.dummytri))
{
// Find the number of this triangle (and Voronoi vertex).
p1 = tri.triangle.id;
if (trisym.triangle == Mesh.dummytri)
{
torg = tri.Org();
tdest = tri.Dest();
// Write an infinite ray. Edge number, index of one endpoint,
// -1, and x and y coordinates of a vector representing the
// direction of the ray.
writer.WriteLine("{0} {1} -1 {2} {3}", index, p1,
(tdest[1] - torg[1]).ToString(nfi),
(torg[0] - tdest[0]).ToString(nfi));
}
else
{
// Find the number of the adjacent triangle (and Voronoi vertex).
p2 = trisym.triangle.id;
// Finite edge. Write indices of two endpoints.
writer.WriteLine("{0} {1} {2}", index, p1, p2);
}
index++;
}
}
}
}
}
private void ConstructVoronoiRegion(Vertex vertex)
{
Vertex vertex1;
Vertex vertex2;
VoronoiRegion voronoiRegion = new VoronoiRegion(vertex);
this.regions.Add(voronoiRegion);
List <Point> points = new List <Point>();
Otri otri = new Otri();
Otri otri1 = new Otri();
Otri otri2 = new Otri();
Otri otri3 = new Otri();
Osub osub = new Osub();
vertex.tri.Copy(ref otri1);
otri1.Copy(ref otri);
otri1.Onext(ref otri2);
if (otri2.triangle == Mesh.dummytri)
{
otri1.Oprev(ref otri3);
if (otri3.triangle != Mesh.dummytri)
{
otri1.Copy(ref otri2);
otri1.OprevSelf();
otri1.Copy(ref otri);
}
}
while (otri2.triangle != Mesh.dummytri)
{
points.Add(this.points[otri.triangle.id]);
if (otri2.Equal(otri1))
{
voronoiRegion.Add(points);
return;
}
otri2.Copy(ref otri);
otri2.OnextSelf();
}
voronoiRegion.Bounded = false;
int count = this.mesh.triangles.Count;
otri.Lprev(ref otri2);
otri2.SegPivot(ref osub);
int num = osub.seg.hash;
points.Add(this.points[otri.triangle.id]);
if (!this.rayPoints.ContainsKey(num))
{
vertex1 = otri.Org();
Vertex vertex3 = otri.Apex();
this.BoxRayIntersection(this.points[otri.triangle.id], vertex1.y - vertex3.y, vertex3.x - vertex1.x, out vertex2);
vertex2.id = count + this.rayIndex;
this.points[count + this.rayIndex] = vertex2;
this.rayIndex = this.rayIndex + 1;
points.Add(vertex2);
this.rayPoints.Add(num, vertex2);
}
else
{
points.Add(this.rayPoints[num]);
}
points.Reverse();
otri1.Copy(ref otri);
otri.Oprev(ref otri3);
while (otri3.triangle != Mesh.dummytri)
{
points.Add(this.points[otri3.triangle.id]);
otri3.Copy(ref otri);
otri3.OprevSelf();
}
otri.SegPivot(ref osub);
num = osub.seg.hash;
if (!this.rayPoints.ContainsKey(num))
{
vertex1 = otri.Org();
Vertex vertex4 = otri.Dest();
this.BoxRayIntersection(this.points[otri.triangle.id], vertex4.y - vertex1.y, vertex1.x - vertex4.x, out vertex2);
vertex2.id = count + this.rayIndex;
this.points[count + this.rayIndex] = vertex2;
this.rayIndex = this.rayIndex + 1;
points.Add(vertex2);
this.rayPoints.Add(num, vertex2);
}
else
{
points.Add(this.rayPoints[num]);
}
points.Reverse();
voronoiRegion.Add(points);
}
public int Triangulate(Mesh mesh)
{
SweepLine.SweepEvent[] sweepEventArray;
SweepLine.SweepEvent sweepEvent;
Vertex vertex;
Vertex vertex1;
Vertex vertex2;
Vertex vertex3;
this.mesh = mesh;
this.xminextreme = 10 * mesh.bounds.Xmin - 9 * mesh.bounds.Xmax;
Otri otri = new Otri();
Otri otri1 = new Otri();
Otri otri2 = new Otri();
Otri otri3 = new Otri();
Otri otri4 = new Otri();
Otri otri5 = new Otri();
Otri otri6 = new Otri();
bool i = false;
this.splaynodes = new List <SweepLine.SplayNode>();
SweepLine.SplayNode splayNode = null;
this.CreateHeap(out sweepEventArray);
int num = mesh.invertices;
mesh.MakeTriangle(ref otri2);
mesh.MakeTriangle(ref otri3);
otri2.Bond(ref otri3);
otri2.LnextSelf();
otri3.LprevSelf();
otri2.Bond(ref otri3);
otri2.LnextSelf();
otri3.LprevSelf();
otri2.Bond(ref otri3);
Vertex vertex4 = sweepEventArray[0].vertexEvent;
this.HeapDelete(sweepEventArray, num, 0);
num--;
do
{
if (num == 0)
{
SimpleLog.Instance.Error("Input vertices are all identical.", "SweepLine.SweepLineDelaunay()");
throw new Exception("Input vertices are all identical.");
}
vertex = sweepEventArray[0].vertexEvent;
this.HeapDelete(sweepEventArray, num, 0);
num--;
if (vertex4.x != vertex.x || vertex4.y != vertex.y)
{
continue;
}
if (Behavior.Verbose)
{
SimpleLog.Instance.Warning("A duplicate vertex appeared and was ignored.", "SweepLine.SweepLineDelaunay().1");
}
vertex.type = VertexType.UndeadVertex;
Mesh mesh1 = mesh;
mesh1.undeads = mesh1.undeads + 1;
}while (vertex4.x == vertex.x && vertex4.y == vertex.y);
otri2.SetOrg(vertex4);
otri2.SetDest(vertex);
otri3.SetOrg(vertex);
otri3.SetDest(vertex4);
otri2.Lprev(ref otri);
Vertex vertex5 = vertex;
while (num > 0)
{
SweepLine.SweepEvent sweepEvent1 = sweepEventArray[0];
this.HeapDelete(sweepEventArray, num, 0);
num--;
bool flag = true;
if (sweepEvent1.xkey >= mesh.bounds.Xmin)
{
Vertex vertex6 = sweepEvent1.vertexEvent;
if (vertex6.x != vertex5.x || vertex6.y != vertex5.y)
{
vertex5 = vertex6;
splayNode = this.FrontLocate(splayNode, otri, vertex6, ref otri1, ref i);
otri.Copy(ref otri1);
for (i = false; !i && this.RightOfHyperbola(ref otri1, vertex6); i = otri1.Equal(otri))
{
otri1.OnextSelf();
}
this.Check4DeadEvent(ref otri1, sweepEventArray, ref num);
otri1.Copy(ref otri5);
otri1.Sym(ref otri4);
mesh.MakeTriangle(ref otri2);
mesh.MakeTriangle(ref otri3);
Vertex vertex7 = otri5.Dest();
otri2.SetOrg(vertex7);
otri2.SetDest(vertex6);
otri3.SetOrg(vertex6);
otri3.SetDest(vertex7);
otri2.Bond(ref otri3);
otri2.LnextSelf();
otri3.LprevSelf();
otri2.Bond(ref otri3);
otri2.LnextSelf();
otri3.LprevSelf();
otri2.Bond(ref otri4);
otri3.Bond(ref otri5);
if (!i && otri5.Equal(otri))
{
otri2.Copy(ref otri);
}
if (this.randomnation(SweepLine.SAMPLERATE) == 0)
{
splayNode = this.SplayInsert(splayNode, otri2, vertex6);
}
else if (this.randomnation(SweepLine.SAMPLERATE) == 0)
{
otri3.Lnext(ref otri6);
splayNode = this.SplayInsert(splayNode, otri6, vertex6);
}
}
else
{
if (Behavior.Verbose)
{
SimpleLog.Instance.Warning("A duplicate vertex appeared and was ignored.", "SweepLine.SweepLineDelaunay().2");
}
vertex6.type = VertexType.UndeadVertex;
Mesh mesh2 = mesh;
mesh2.undeads = mesh2.undeads + 1;
flag = false;
}
}
else
{
Otri otri7 = sweepEvent1.otriEvent;
otri7.Oprev(ref otri4);
this.Check4DeadEvent(ref otri4, sweepEventArray, ref num);
otri7.Onext(ref otri5);
this.Check4DeadEvent(ref otri5, sweepEventArray, ref num);
if (otri4.Equal(otri))
{
otri7.Lprev(ref otri);
}
mesh.Flip(ref otri7);
otri7.SetApex(null);
otri7.Lprev(ref otri2);
otri7.Lnext(ref otri3);
otri2.Sym(ref otri4);
if (this.randomnation(SweepLine.SAMPLERATE) == 0)
{
otri7.SymSelf();
vertex1 = otri7.Dest();
vertex2 = otri7.Apex();
vertex3 = otri7.Org();
splayNode = this.CircleTopInsert(splayNode, otri2, vertex1, vertex2, vertex3, sweepEvent1.ykey);
}
}
if (!flag)
{
continue;
}
vertex1 = otri4.Apex();
vertex2 = otri2.Dest();
vertex3 = otri2.Apex();
double num1 = Primitives.CounterClockwise(vertex1, vertex2, vertex3);
if (num1 > 0)
{
sweepEvent = new SweepLine.SweepEvent()
{
xkey = this.xminextreme,
ykey = this.CircleTop(vertex1, vertex2, vertex3, num1),
otriEvent = otri2
};
this.HeapInsert(sweepEventArray, num, sweepEvent);
num++;
otri2.SetOrg(new SweepLine.SweepEventVertex(sweepEvent));
}
vertex1 = otri3.Apex();
vertex2 = otri3.Org();
vertex3 = otri5.Apex();
double num2 = Primitives.CounterClockwise(vertex1, vertex2, vertex3);
if (num2 <= 0)
{
continue;
}
sweepEvent = new SweepLine.SweepEvent()
{
xkey = this.xminextreme,
ykey = this.CircleTop(vertex1, vertex2, vertex3, num2),
otriEvent = otri5
};
this.HeapInsert(sweepEventArray, num, sweepEvent);
num++;
otri5.SetOrg(new SweepLine.SweepEventVertex(sweepEvent));
}
this.splaynodes.Clear();
otri.LprevSelf();
return(this.RemoveGhosts(ref otri));
}
private void GetAspectHistogram(Mesh mesh)
{
int[] aspecttable;
double[] ratiotable;
aspecttable = new int[16];
ratiotable = new double[] {
1.5, 2.0, 2.5, 3.0, 4.0, 6.0, 10.0, 15.0, 25.0, 50.0,
100.0, 300.0, 1000.0, 10000.0, 100000.0, 0.0
};
Otri tri = default(Otri);
Vertex[] p = new Vertex[3];
double[] dx = new double[3], dy = new double[3];
double[] edgelength = new double[3];
double triarea;
double trilongest2;
double triminaltitude2;
double triaspect2;
int aspectindex;
int i, j, k;
tri.orient = 0;
foreach (var t in mesh.triangles.Values)
{
tri.triangle = t;
p[0] = tri.Org();
p[1] = tri.Dest();
p[2] = tri.Apex();
trilongest2 = 0.0;
for (i = 0; i < 3; i++)
{
j = plus1Mod3[i];
k = minus1Mod3[i];
dx[i] = p[j].x - p[k].x;
dy[i] = p[j].y - p[k].y;
edgelength[i] = dx[i] * dx[i] + dy[i] * dy[i];
if (edgelength[i] > trilongest2)
{
trilongest2 = edgelength[i];
}
}
//triarea = Primitives.CounterClockwise(p[0], p[1], p[2]);
triarea = Math.Abs((p[2].x - p[0].x) * (p[1].y - p[0].y) -
(p[1].x - p[0].x) * (p[2].y - p[0].y)) / 2.0;
triminaltitude2 = triarea * triarea / trilongest2;
triaspect2 = trilongest2 / triminaltitude2;
aspectindex = 0;
while ((triaspect2 > ratiotable[aspectindex] * ratiotable[aspectindex]) && (aspectindex < 15))
{
aspectindex++;
}
aspecttable[aspectindex]++;
}
}
public IMesh Triangulate(IList <Vertex> points, Configuration config)
{
this.predicates = config.Predicates();
this.mesh = new Mesh(config);
this.mesh.TransferNodes(points);
// Nonexistent x value used as a flag to mark circle events in sweepline
// Delaunay algorithm.
xminextreme = 10 * mesh.bounds.Left - 9 * mesh.bounds.Right;
SweepEvent[] eventheap;
SweepEvent nextevent;
SweepEvent newevent;
SplayNode splayroot;
Otri bottommost = default(Otri);
Otri searchtri = default(Otri);
Otri fliptri;
Otri lefttri = default(Otri);
Otri righttri = default(Otri);
Otri farlefttri = default(Otri);
Otri farrighttri = default(Otri);
Otri inserttri = default(Otri);
Vertex firstvertex, secondvertex;
Vertex nextvertex, lastvertex;
Vertex connectvertex;
Vertex leftvertex, midvertex, rightvertex;
double lefttest, righttest;
int heapsize;
bool check4events, farrightflag = false;
splaynodes = new List <SplayNode>();
splayroot = null;
heapsize = points.Count;
CreateHeap(out eventheap, heapsize);//, out events, out freeevents);
mesh.MakeTriangle(ref lefttri);
mesh.MakeTriangle(ref righttri);
lefttri.Bond(ref righttri);
lefttri.Lnext();
righttri.Lprev();
lefttri.Bond(ref righttri);
lefttri.Lnext();
righttri.Lprev();
lefttri.Bond(ref righttri);
firstvertex = eventheap[0].vertexEvent;
HeapDelete(eventheap, heapsize, 0);
heapsize--;
do
{
if (heapsize == 0)
{
Log.Instance.Error("Input vertices are all identical.", "SweepLine.Triangulate()");
throw new Exception("Input vertices are all identical.");
}
secondvertex = eventheap[0].vertexEvent;
HeapDelete(eventheap, heapsize, 0);
heapsize--;
if ((firstvertex.x == secondvertex.x) &&
(firstvertex.y == secondvertex.y))
{
if (Log.Verbose)
{
Log.Instance.Warning("A duplicate vertex appeared and was ignored (ID " + secondvertex.id + ").",
"SweepLine.Triangulate().1");
}
secondvertex.type = VertexType.UndeadVertex;
mesh.undeads++;
}
} while ((firstvertex.x == secondvertex.x) &&
(firstvertex.y == secondvertex.y));
lefttri.SetOrg(firstvertex);
lefttri.SetDest(secondvertex);
righttri.SetOrg(secondvertex);
righttri.SetDest(firstvertex);
lefttri.Lprev(ref bottommost);
lastvertex = secondvertex;
while (heapsize > 0)
{
nextevent = eventheap[0];
HeapDelete(eventheap, heapsize, 0);
heapsize--;
check4events = true;
if (nextevent.xkey < mesh.bounds.Left)
{
fliptri = nextevent.otriEvent;
fliptri.Oprev(ref farlefttri);
Check4DeadEvent(ref farlefttri, eventheap, ref heapsize);
fliptri.Onext(ref farrighttri);
Check4DeadEvent(ref farrighttri, eventheap, ref heapsize);
if (farlefttri.Equals(bottommost))
{
fliptri.Lprev(ref bottommost);
}
mesh.Flip(ref fliptri);
fliptri.SetApex(null);
fliptri.Lprev(ref lefttri);
fliptri.Lnext(ref righttri);
lefttri.Sym(ref farlefttri);
if (randomnation(SAMPLERATE) == 0)
{
fliptri.Sym();
leftvertex = fliptri.Dest();
midvertex = fliptri.Apex();
rightvertex = fliptri.Org();
splayroot = CircleTopInsert(splayroot, lefttri, leftvertex, midvertex, rightvertex, nextevent.ykey);
}
}
else
{
nextvertex = nextevent.vertexEvent;
if ((nextvertex.x == lastvertex.x) &&
(nextvertex.y == lastvertex.y))
{
if (Log.Verbose)
{
Log.Instance.Warning("A duplicate vertex appeared and was ignored (ID " + nextvertex.id + ").",
"SweepLine.Triangulate().2");
}
nextvertex.type = VertexType.UndeadVertex;
mesh.undeads++;
check4events = false;
}
else
{
lastvertex = nextvertex;
splayroot = FrontLocate(splayroot, bottommost, nextvertex, ref searchtri, ref farrightflag);
//bottommost.Copy(ref searchtri);
//farrightflag = false;
//while (!farrightflag && RightOfHyperbola(ref searchtri, nextvertex))
//{
// searchtri.OnextSelf();
// farrightflag = searchtri.Equal(bottommost);
//}
Check4DeadEvent(ref searchtri, eventheap, ref heapsize);
searchtri.Copy(ref farrighttri);
searchtri.Sym(ref farlefttri);
mesh.MakeTriangle(ref lefttri);
mesh.MakeTriangle(ref righttri);
connectvertex = farrighttri.Dest();
lefttri.SetOrg(connectvertex);
lefttri.SetDest(nextvertex);
righttri.SetOrg(nextvertex);
righttri.SetDest(connectvertex);
lefttri.Bond(ref righttri);
lefttri.Lnext();
righttri.Lprev();
lefttri.Bond(ref righttri);
lefttri.Lnext();
righttri.Lprev();
lefttri.Bond(ref farlefttri);
righttri.Bond(ref farrighttri);
if (!farrightflag && farrighttri.Equals(bottommost))
{
lefttri.Copy(ref bottommost);
}
if (randomnation(SAMPLERATE) == 0)
{
splayroot = SplayInsert(splayroot, lefttri, nextvertex);
}
else if (randomnation(SAMPLERATE) == 0)
{
righttri.Lnext(ref inserttri);
splayroot = SplayInsert(splayroot, inserttri, nextvertex);
}
}
}
if (check4events)
{
leftvertex = farlefttri.Apex();
midvertex = lefttri.Dest();
rightvertex = lefttri.Apex();
lefttest = predicates.CounterClockwise(leftvertex, midvertex, rightvertex);
if (lefttest > 0.0)
{
newevent = new SweepEvent();
newevent.xkey = xminextreme;
newevent.ykey = CircleTop(leftvertex, midvertex, rightvertex, lefttest);
newevent.otriEvent = lefttri;
HeapInsert(eventheap, heapsize, newevent);
heapsize++;
lefttri.SetOrg(new SweepEventVertex(newevent));
}
leftvertex = righttri.Apex();
midvertex = righttri.Org();
rightvertex = farrighttri.Apex();
righttest = predicates.CounterClockwise(leftvertex, midvertex, rightvertex);
if (righttest > 0.0)
{
newevent = new SweepEvent();
newevent.xkey = xminextreme;
newevent.ykey = CircleTop(leftvertex, midvertex, rightvertex, righttest);
newevent.otriEvent = farrighttri;
HeapInsert(eventheap, heapsize, newevent);
heapsize++;
farrighttri.SetOrg(new SweepEventVertex(newevent));
}
}
}
splaynodes.Clear();
bottommost.Lprev();
this.mesh.hullsize = RemoveGhosts(ref bottommost);
return(this.mesh);
}
/// <summary>
/// Ensure that the mesh is (constrained) Delaunay.
/// </summary>
private static bool IsDelaunay(Mesh mesh, bool constrained)
{
Otri loop = default(Otri);
Otri oppotri = default(Otri);
Osub opposubseg = default(Osub);
Vertex org, dest, apex;
Vertex oppoapex;
bool shouldbedelaunay;
var logger = Log.Instance;
// Temporarily turn on exact arithmetic if it's off.
bool saveexact = Behavior.NoExact;
Behavior.NoExact = false;
int horrors = 0;
var inf1 = mesh.infvertex1;
var inf2 = mesh.infvertex2;
var inf3 = mesh.infvertex3;
// Run through the list of triangles, checking each one.
foreach (var tri in mesh.triangles)
{
loop.tri = tri;
// Check all three edges of the triangle.
for (loop.orient = 0; loop.orient < 3; loop.orient++)
{
org = loop.Org();
dest = loop.Dest();
apex = loop.Apex();
loop.Sym(ref oppotri);
oppoapex = oppotri.Apex();
// Only test that the edge is locally Delaunay if there is an
// adjoining triangle whose pointer is larger (to ensure that
// each pair isn't tested twice).
shouldbedelaunay = (loop.tri.id < oppotri.tri.id) &&
!Otri.IsDead(oppotri.tri) && (oppotri.tri.id != Mesh.DUMMY) &&
(org != inf1) && (org != inf2) && (org != inf3) &&
(dest != inf1) && (dest != inf2) && (dest != inf3) &&
(apex != inf1) && (apex != inf2) && (apex != inf3) &&
(oppoapex != inf1) && (oppoapex != inf2) && (oppoapex != inf3);
if (constrained && mesh.checksegments && shouldbedelaunay)
{
// If a subsegment separates the triangles, then the edge is
// constrained, so no local Delaunay test should be done.
loop.Pivot(ref opposubseg);
if (opposubseg.seg.hash != Mesh.DUMMY)
{
shouldbedelaunay = false;
}
}
if (shouldbedelaunay)
{
if (predicates.NonRegular(org, dest, apex, oppoapex) > 0.0)
{
if (Log.Verbose)
{
logger.Warning(String.Format("Non-regular pair of triangles found (IDs {0}/{1}).",
loop.tri.id, oppotri.tri.id), "MeshValidator.IsDelaunay()");
}
horrors++;
}
}
}
}
// Restore the status of exact arithmetic.
Behavior.NoExact = saveexact;
return(horrors == 0);
}
private void WriteMesh(TriangleNetMesh triangleNetMesh, bool skip)
{
// Mesh may have changed, but we choose to skip
if (triangles == triangleNetMesh.triangles.Count && skip)
{
return;
}
// Header line
stream.WriteLine("#!M{0}", iteration++);
Vertex p1, p2, p3;
if (VerticesChanged(triangleNetMesh))
{
HashVertices(triangleNetMesh);
// Number of vertices.
stream.WriteLine("{0}", triangleNetMesh.vertices.Count);
foreach (var v in triangleNetMesh.vertices.Values)
{
// Vertex number, x and y coordinates and marker.
stream.WriteLine("{0} {1} {2} {3}", v.id, v.x.ToString(nfi), v.y.ToString(nfi), v.label);
}
}
else
{
stream.WriteLine("0");
}
// Number of segments.
stream.WriteLine("{0}", triangleNetMesh.subsegs.Count);
Osub subseg = default(Osub);
subseg.orient = 0;
foreach (var item in triangleNetMesh.subsegs.Values)
{
if (item.hash <= 0)
{
continue;
}
subseg.seg = item;
p1 = subseg.Org();
p2 = subseg.Dest();
// Segment number, indices of its two endpoints, and marker.
stream.WriteLine("{0} {1} {2} {3}", subseg.seg.hash, p1.id, p2.id, subseg.seg.boundary);
}
Otri tri = default(Otri), trisym = default(Otri);
tri.orient = 0;
int n1, n2, n3, h1, h2, h3;
// Number of triangles.
stream.WriteLine("{0}", triangleNetMesh.triangles.Count);
foreach (var item in triangleNetMesh.triangles)
{
tri.tri = item;
p1 = tri.Org();
p2 = tri.Dest();
p3 = tri.Apex();
h1 = (p1 == null) ? -1 : p1.id;
h2 = (p2 == null) ? -1 : p2.id;
h3 = (p3 == null) ? -1 : p3.id;
// Triangle number, indices for three vertices.
stream.Write("{0} {1} {2} {3}", tri.tri.hash, h1, h2, h3);
tri.orient = 1;
tri.Sym(ref trisym);
n1 = trisym.tri.hash;
tri.orient = 2;
tri.Sym(ref trisym);
n2 = trisym.tri.hash;
tri.orient = 0;
tri.Sym(ref trisym);
n3 = trisym.tri.hash;
// Neighboring triangle numbers.
stream.WriteLine(" {0} {1} {2}", n1, n2, n3);
}
}
/// <summary>
/// Test the mesh for topological consistency.
/// </summary>
public static bool IsConsistent(Mesh mesh)
{
Otri tri = default(Otri);
Otri oppotri = default(Otri), oppooppotri = default(Otri);
Vertex org, dest, apex;
Vertex oppoorg, oppodest;
var logger = Log.Instance;
// Temporarily turn on exact arithmetic if it's off.
bool saveexact = Behavior.NoExact;
Behavior.NoExact = false;
int horrors = 0;
// Run through the list of triangles, checking each one.
foreach (var t in mesh.triangles)
{
tri.tri = t;
// Check all three edges of the triangle.
for (tri.orient = 0; tri.orient < 3; tri.orient++)
{
org = tri.Org();
dest = tri.Dest();
if (tri.orient == 0)
{
// Only test for inversion once.
// Test if the triangle is flat or inverted.
apex = tri.Apex();
if (predicates.CounterClockwise(org, dest, apex) <= 0.0)
{
if (Log.Verbose)
{
logger.Warning(String.Format("Triangle is flat or inverted (ID {0}).", t.id),
"MeshValidator.IsConsistent()");
}
horrors++;
}
}
// Find the neighboring triangle on this edge.
tri.Sym(ref oppotri);
if (oppotri.tri.id != Mesh.DUMMY)
{
// Check that the triangle's neighbor knows it's a neighbor.
oppotri.Sym(ref oppooppotri);
if ((tri.tri != oppooppotri.tri) || (tri.orient != oppooppotri.orient))
{
if (tri.tri == oppooppotri.tri && Log.Verbose)
{
logger.Warning("Asymmetric triangle-triangle bond: (Right triangle, wrong orientation)",
"MeshValidator.IsConsistent()");
}
horrors++;
}
// Check that both triangles agree on the identities
// of their shared vertices.
oppoorg = oppotri.Org();
oppodest = oppotri.Dest();
if ((org != oppodest) || (dest != oppoorg))
{
if (Log.Verbose)
{
logger.Warning("Mismatched edge coordinates between two triangles.",
"MeshValidator.IsConsistent()");
}
horrors++;
}
}
}
}
// Check for unconnected vertices
mesh.MakeVertexMap();
foreach (var v in mesh.vertices.Values)
{
if (v.tri.tri == null && Log.Verbose)
{
logger.Warning("Vertex (ID " + v.id + ") not connected to mesh (duplicate input vertex?)",
"MeshValidator.IsConsistent()");
}
}
// Restore the status of exact arithmetic.
Behavior.NoExact = saveexact;
return(horrors == 0);
}
/// <summary>
/// Check a subsegment to see if it is encroached; add it to the list if it is.
/// </summary>
/// <param name="testsubseg">The subsegment to check.</param>
/// <returns>Returns a nonzero value if the subsegment is encroached.</returns>
/// <remarks>
/// A subsegment is encroached if there is a vertex in its diametral lens.
/// For Ruppert's algorithm (-D switch), the "diametral lens" is the
/// diametral circle. For Chew's algorithm (default), the diametral lens is
/// just big enough to enclose two isosceles triangles whose bases are the
/// subsegment. Each of the two isosceles triangles has two angles equal
/// to 'b.minangle'.
///
/// Chew's algorithm does not require diametral lenses at all--but they save
/// time. Any vertex inside a subsegment's diametral lens implies that the
/// triangle adjoining the subsegment will be too skinny, so it's only a
/// matter of time before the encroaching vertex is deleted by Chew's
/// algorithm. It's faster to simply not insert the doomed vertex in the
/// first place, which is why I use diametral lenses with Chew's algorithm.
/// </remarks>
public int CheckSeg4Encroach(ref Osub testsubseg)
{
Otri neighbortri = default(Otri);
Osub testsym = default(Osub);
BadSubseg encroachedseg;
float dotproduct;
int encroached;
int sides;
Vertex eorg, edest, eapex;
encroached = 0;
sides = 0;
eorg = testsubseg.Org();
edest = testsubseg.Dest();
// Check one neighbor of the subsegment.
testsubseg.TriPivot(ref neighbortri);
// Does the neighbor exist, or is this a boundary edge?
if (neighbortri.triangle != Mesh.dummytri)
{
sides++;
// Find a vertex opposite this subsegment.
eapex = neighbortri.Apex();
// Check whether the apex is in the diametral lens of the subsegment
// (the diametral circle if 'conformdel' is set). A dot product
// of two sides of the triangle is used to check whether the angle
// at the apex is greater than (180 - 2 'minangle') degrees (for
// lenses; 90 degrees for diametral circles).
dotproduct = (eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y);
if (dotproduct < 0.0)
{
if (behavior.ConformingDelaunay ||
(dotproduct * dotproduct >=
(2.0 * behavior.goodAngle - 1.0) * (2.0 * behavior.goodAngle - 1.0) *
((eorg.x - eapex.x) * (eorg.x - eapex.x) +
(eorg.y - eapex.y) * (eorg.y - eapex.y)) *
((edest.x - eapex.x) * (edest.x - eapex.x) +
(edest.y - eapex.y) * (edest.y - eapex.y))))
{
encroached = 1;
}
}
}
// Check the other neighbor of the subsegment.
testsubseg.Sym(ref testsym);
testsym.TriPivot(ref neighbortri);
// Does the neighbor exist, or is this a boundary edge?
if (neighbortri.triangle != Mesh.dummytri)
{
sides++;
// Find the other vertex opposite this subsegment.
eapex = neighbortri.Apex();
// Check whether the apex is in the diametral lens of the subsegment
// (or the diametral circle, if 'conformdel' is set).
dotproduct = (eorg.x - eapex.x) * (edest.x - eapex.x) +
(eorg.y - eapex.y) * (edest.y - eapex.y);
if (dotproduct < 0.0)
{
if (behavior.ConformingDelaunay ||
(dotproduct * dotproduct >=
(2.0 * behavior.goodAngle - 1.0) * (2.0 * behavior.goodAngle - 1.0) *
((eorg.x - eapex.x) * (eorg.x - eapex.x) +
(eorg.y - eapex.y) * (eorg.y - eapex.y)) *
((edest.x - eapex.x) * (edest.x - eapex.x) +
(edest.y - eapex.y) * (edest.y - eapex.y))))
{
encroached += 2;
}
}
}
if (encroached > 0 && (behavior.NoBisect == 0 || ((behavior.NoBisect == 1) && (sides == 2))))
{
// Add the subsegment to the list of encroached subsegments.
// Be sure to get the orientation right.
encroachedseg = new BadSubseg();
if (encroached == 1)
{
encroachedseg.encsubseg = testsubseg;
encroachedseg.subsegorg = eorg;
encroachedseg.subsegdest = edest;
}
else
{
encroachedseg.encsubseg = testsym;
encroachedseg.subsegorg = edest;
encroachedseg.subsegdest = eorg;
}
badsubsegs.Enqueue(encroachedseg);
}
return(encroached);
}
private void WriteMesh(Mesh mesh, bool skip)
{
Vertex vertex;
Vertex vertex1;
if (this.triangles == mesh.triangles.Count & skip)
{
return;
}
StreamWriter streamWriter = this.stream;
int num = this.iteration;
this.iteration = num + 1;
streamWriter.WriteLine("#!M{0}", num);
if (!this.VerticesChanged(mesh))
{
this.stream.WriteLine("0");
}
else
{
this.HashVertices(mesh);
this.stream.WriteLine("{0}", mesh.vertices.Count);
foreach (Vertex value in mesh.vertices.Values)
{
this.stream.WriteLine("{0} {1} {2} {3}", new object[] { value.hash, value.x.ToString(DebugWriter.nfi), value.y.ToString(DebugWriter.nfi), value.mark });
}
}
this.stream.WriteLine("{0}", mesh.subsegs.Count);
Osub osub = new Osub()
{
orient = 0
};
foreach (Segment segment in mesh.subsegs.Values)
{
if (segment.hash <= 0)
{
continue;
}
osub.seg = segment;
vertex = osub.Org();
vertex1 = osub.Dest();
this.stream.WriteLine("{0} {1} {2} {3}", new object[] { osub.seg.hash, vertex.hash, vertex1.hash, osub.seg.boundary });
}
Otri otri = new Otri();
Otri otri1 = new Otri();
otri.orient = 0;
this.stream.WriteLine("{0}", mesh.triangles.Count);
foreach (Triangle triangle in mesh.triangles.Values)
{
otri.triangle = triangle;
vertex = otri.Org();
vertex1 = otri.Dest();
Vertex vertex2 = otri.Apex();
int num1 = (vertex == null ? -1 : vertex.hash);
int num2 = (vertex1 == null ? -1 : vertex1.hash);
int num3 = (vertex2 == null ? -1 : vertex2.hash);
this.stream.Write("{0} {1} {2} {3}", new object[] { otri.triangle.hash, num1, num2, num3 });
otri.orient = 1;
otri.Sym(ref otri1);
int num4 = otri1.triangle.hash;
otri.orient = 2;
otri.Sym(ref otri1);
int num5 = otri1.triangle.hash;
otri.orient = 0;
otri.Sym(ref otri1);
int num6 = otri1.triangle.hash;
this.stream.WriteLine(" {0} {1} {2}", num4, num5, num6);
}
}
/// <summary>
/// Test the mesh for topological consistency.
/// </summary>
public bool CheckMesh()
{
Otri tri = default(Otri);
Otri oppotri = default(Otri), oppooppotri = default(Otri);
Vertex triorg, tridest, triapex;
Vertex oppoorg, oppodest;
int horrors;
bool saveexact;
// Temporarily turn on exact arithmetic if it's off.
saveexact = Behavior.NoExact;
Behavior.NoExact = false;
horrors = 0;
// Run through the list of triangles, checking each one.
foreach (var t in mesh.triangles.Values)
{
tri.triangle = t;
// Check all three edges of the triangle.
for (tri.orient = 0; tri.orient < 3; tri.orient++)
{
triorg = tri.Org();
tridest = tri.Dest();
if (tri.orient == 0)
{ // Only test for inversion once.
// Test if the triangle is flat or inverted.
triapex = tri.Apex();
if (Primitives.CounterClockwise(triorg, tridest, triapex) <= 0.0)
{
logger.Warning("Triangle is flat or inverted.",
"Quality.CheckMesh()");
horrors++;
}
}
// Find the neighboring triangle on this edge.
tri.Sym(ref oppotri);
if (oppotri.triangle != Mesh.dummytri)
{
// Check that the triangle's neighbor knows it's a neighbor.
oppotri.Sym(ref oppooppotri);
if ((tri.triangle != oppooppotri.triangle) || (tri.orient != oppooppotri.orient))
{
if (tri.triangle == oppooppotri.triangle)
{
logger.Warning("Asymmetric triangle-triangle bond: (Right triangle, wrong orientation)",
"Quality.CheckMesh()");
}
horrors++;
}
// Check that both triangles agree on the identities
// of their shared vertices.
oppoorg = oppotri.Org();
oppodest = oppotri.Dest();
if ((triorg != oppodest) || (tridest != oppoorg))
{
logger.Warning("Mismatched edge coordinates between two triangles.",
"Quality.CheckMesh()");
horrors++;
}
}
}
}
// Check for unconnected vertices
mesh.MakeVertexMap();
foreach (var v in mesh.vertices.Values)
{
if (v.tri.triangle == null)
{
logger.Warning("Vertex (ID " + v.id + ") not connected to mesh (duplicate input vertex?)",
"Quality.CheckMesh()");
}
}
if (horrors == 0) // && Behavior.Verbose
{
logger.Info("Mesh topology appears to be consistent.");
}
// Restore the status of exact arithmetic.
Behavior.NoExact = saveexact;
return(horrors == 0);
}
/// <summary>
/// Merge two adjacent Delaunay triangulations into a single Delaunay triangulation.
/// </summary>
/// <param name="farleft">Bounding triangles of the left triangulation.</param>
/// <param name="innerleft">Bounding triangles of the left triangulation.</param>
/// <param name="innerright">Bounding triangles of the right triangulation.</param>
/// <param name="farright">Bounding triangles of the right triangulation.</param>
/// <param name="axis"></param>
/// <remarks>
/// This is similar to the algorithm given by Guibas and Stolfi, but uses
/// a triangle-based, rather than edge-based, data structure.
///
/// The algorithm walks up the gap between the two triangulations, knitting
/// them together. As they are merged, some of their bounding triangles
/// are converted into real triangles of the triangulation. The procedure
/// pulls each hull's bounding triangles apart, then knits them together
/// like the teeth of two gears. The Delaunay property determines, at each
/// step, whether the next "tooth" is a bounding triangle of the left hull
/// or the right. When a bounding triangle becomes real, its apex is
/// changed from NULL to a real vertex.
///
/// Only two new triangles need to be allocated. These become new bounding
/// triangles at the top and bottom of the seam. They are used to connect
/// the remaining bounding triangles (those that have not been converted
/// into real triangles) into a single fan.
///
/// On entry, 'farleft' and 'innerleft' are bounding triangles of the left
/// triangulation. The origin of 'farleft' is the leftmost vertex, and
/// the destination of 'innerleft' is the rightmost vertex of the
/// triangulation. Similarly, 'innerright' and 'farright' are bounding
/// triangles of the right triangulation. The origin of 'innerright' and
/// destination of 'farright' are the leftmost and rightmost vertices.
///
/// On completion, the origin of 'farleft' is the leftmost vertex of the
/// merged triangulation, and the destination of 'farright' is the rightmost
/// vertex.
/// </remarks>
void MergeHulls(ref Otri farleft, ref Otri innerleft, ref Otri innerright,
ref Otri farright, int axis)
{
Otri leftcand = default(Otri), rightcand = default(Otri);
Otri nextedge = default(Otri);
Otri sidecasing = default(Otri), topcasing = default(Otri), outercasing = default(Otri);
Otri checkedge = default(Otri);
Otri baseedge = default(Otri);
Vertex innerleftdest;
Vertex innerrightorg;
Vertex innerleftapex, innerrightapex;
Vertex farleftpt, farrightpt;
Vertex farleftapex, farrightapex;
Vertex lowerleft, lowerright;
Vertex upperleft, upperright;
Vertex nextapex;
Vertex checkvertex;
bool changemade;
bool badedge;
bool leftfinished, rightfinished;
innerleftdest = innerleft.Dest();
innerleftapex = innerleft.Apex();
innerrightorg = innerright.Org();
innerrightapex = innerright.Apex();
// Special treatment for horizontal cuts.
if (useDwyer && (axis == 1))
{
farleftpt = farleft.Org();
farleftapex = farleft.Apex();
farrightpt = farright.Dest();
farrightapex = farright.Apex();
// The pointers to the extremal vertices are shifted to point to the
// topmost and bottommost vertex of each hull, rather than the
// leftmost and rightmost vertices.
while (farleftapex.y < farleftpt.y)
{
farleft.LnextSelf();
farleft.SymSelf();
farleftpt = farleftapex;
farleftapex = farleft.Apex();
}
innerleft.Sym(ref checkedge);
checkvertex = checkedge.Apex();
while (checkvertex.y > innerleftdest.y)
{
checkedge.Lnext(ref innerleft);
innerleftapex = innerleftdest;
innerleftdest = checkvertex;
innerleft.Sym(ref checkedge);
checkvertex = checkedge.Apex();
}
while (innerrightapex.y < innerrightorg.y)
{
innerright.LnextSelf();
innerright.SymSelf();
innerrightorg = innerrightapex;
innerrightapex = innerright.Apex();
}
farright.Sym(ref checkedge);
checkvertex = checkedge.Apex();
while (checkvertex.y > farrightpt.y)
{
checkedge.Lnext(ref farright);
farrightapex = farrightpt;
farrightpt = checkvertex;
farright.Sym(ref checkedge);
checkvertex = checkedge.Apex();
}
}
// Find a line tangent to and below both hulls.
do
{
changemade = false;
// Make innerleftdest the "bottommost" vertex of the left hull.
if (Primitives.CounterClockwise(innerleftdest, innerleftapex, innerrightorg) > 0.0)
{
innerleft.LprevSelf();
innerleft.SymSelf();
innerleftdest = innerleftapex;
innerleftapex = innerleft.Apex();
changemade = true;
}
// Make innerrightorg the "bottommost" vertex of the right hull.
if (Primitives.CounterClockwise(innerrightapex, innerrightorg, innerleftdest) > 0.0)
{
innerright.LnextSelf();
innerright.SymSelf();
innerrightorg = innerrightapex;
innerrightapex = innerright.Apex();
changemade = true;
}
} while (changemade);
// Find the two candidates to be the next "gear tooth."
innerleft.Sym(ref leftcand);
innerright.Sym(ref rightcand);
// Create the bottom new bounding triangle.
mesh.MakeTriangle(ref baseedge);
// Connect it to the bounding boxes of the left and right triangulations.
baseedge.Bond(ref innerleft);
baseedge.LnextSelf();
baseedge.Bond(ref innerright);
baseedge.LnextSelf();
baseedge.SetOrg(innerrightorg);
baseedge.SetDest(innerleftdest);
// Apex is intentionally left NULL.
// Fix the extreme triangles if necessary.
farleftpt = farleft.Org();
if (innerleftdest == farleftpt)
{
baseedge.Lnext(ref farleft);
}
farrightpt = farright.Dest();
if (innerrightorg == farrightpt)
{
baseedge.Lprev(ref farright);
}
// The vertices of the current knitting edge.
lowerleft = innerleftdest;
lowerright = innerrightorg;
// The candidate vertices for knitting.
upperleft = leftcand.Apex();
upperright = rightcand.Apex();
// Walk up the gap between the two triangulations, knitting them together.
while (true)
{
// Have we reached the top? (This isn't quite the right question,
// because even though the left triangulation might seem finished now,
// moving up on the right triangulation might reveal a new vertex of
// the left triangulation. And vice-versa.)
leftfinished = Primitives.CounterClockwise(upperleft, lowerleft, lowerright) <= 0.0;
rightfinished = Primitives.CounterClockwise(upperright, lowerleft, lowerright) <= 0.0;
if (leftfinished && rightfinished)
{
// Create the top new bounding triangle.
mesh.MakeTriangle(ref nextedge);
nextedge.SetOrg(lowerleft);
nextedge.SetDest(lowerright);
// Apex is intentionally left NULL.
// Connect it to the bounding boxes of the two triangulations.
nextedge.Bond(ref baseedge);
nextedge.LnextSelf();
nextedge.Bond(ref rightcand);
nextedge.LnextSelf();
nextedge.Bond(ref leftcand);
// Special treatment for horizontal cuts.
if (useDwyer && (axis == 1))
{
farleftpt = farleft.Org();
farleftapex = farleft.Apex();
farrightpt = farright.Dest();
farrightapex = farright.Apex();
farleft.Sym(ref checkedge);
checkvertex = checkedge.Apex();
// The pointers to the extremal vertices are restored to the
// leftmost and rightmost vertices (rather than topmost and
// bottommost).
while (checkvertex.x < farleftpt.x)
{
checkedge.Lprev(ref farleft);
farleftapex = farleftpt;
farleftpt = checkvertex;
farleft.Sym(ref checkedge);
checkvertex = checkedge.Apex();
}
while (farrightapex.x > farrightpt.x)
{
farright.LprevSelf();
farright.SymSelf();
farrightpt = farrightapex;
farrightapex = farright.Apex();
}
}
return;
}
// Consider eliminating edges from the left triangulation.
if (!leftfinished)
{
// What vertex would be exposed if an edge were deleted?
leftcand.Lprev(ref nextedge);
nextedge.SymSelf();
nextapex = nextedge.Apex();
// If nextapex is NULL, then no vertex would be exposed; the
// triangulation would have been eaten right through.
if (nextapex != null)
{
// Check whether the edge is Delaunay.
badedge = Primitives.InCircle(lowerleft, lowerright, upperleft, nextapex) > 0.0;
while (badedge)
{
// Eliminate the edge with an edge flip. As a result, the
// left triangulation will have one more boundary triangle.
nextedge.LnextSelf();
nextedge.Sym(ref topcasing);
nextedge.LnextSelf();
nextedge.Sym(ref sidecasing);
nextedge.Bond(ref topcasing);
leftcand.Bond(ref sidecasing);
leftcand.LnextSelf();
leftcand.Sym(ref outercasing);
nextedge.LprevSelf();
nextedge.Bond(ref outercasing);
// Correct the vertices to reflect the edge flip.
leftcand.SetOrg(lowerleft);
leftcand.SetDest(null);
leftcand.SetApex(nextapex);
nextedge.SetOrg(null);
nextedge.SetDest(upperleft);
nextedge.SetApex(nextapex);
// Consider the newly exposed vertex.
upperleft = nextapex;
// What vertex would be exposed if another edge were deleted?
sidecasing.Copy(ref nextedge);
nextapex = nextedge.Apex();
if (nextapex != null)
{
// Check whether the edge is Delaunay.
badedge = Primitives.InCircle(lowerleft, lowerright, upperleft, nextapex) > 0.0;
}
else
{
// Avoid eating right through the triangulation.
badedge = false;
}
}
}
}
// Consider eliminating edges from the right triangulation.
if (!rightfinished)
{
// What vertex would be exposed if an edge were deleted?
rightcand.Lnext(ref nextedge);
nextedge.SymSelf();
nextapex = nextedge.Apex();
// If nextapex is NULL, then no vertex would be exposed; the
// triangulation would have been eaten right through.
if (nextapex != null)
{
// Check whether the edge is Delaunay.
badedge = Primitives.InCircle(lowerleft, lowerright, upperright, nextapex) > 0.0;
while (badedge)
{
// Eliminate the edge with an edge flip. As a result, the
// right triangulation will have one more boundary triangle.
nextedge.LprevSelf();
nextedge.Sym(ref topcasing);
nextedge.LprevSelf();
nextedge.Sym(ref sidecasing);
nextedge.Bond(ref topcasing);
rightcand.Bond(ref sidecasing);
rightcand.LprevSelf();
rightcand.Sym(ref outercasing);
nextedge.LnextSelf();
nextedge.Bond(ref outercasing);
// Correct the vertices to reflect the edge flip.
rightcand.SetOrg(null);
rightcand.SetDest(lowerright);
rightcand.SetApex(nextapex);
nextedge.SetOrg(upperright);
nextedge.SetDest(null);
nextedge.SetApex(nextapex);
// Consider the newly exposed vertex.
upperright = nextapex;
// What vertex would be exposed if another edge were deleted?
sidecasing.Copy(ref nextedge);
nextapex = nextedge.Apex();
if (nextapex != null)
{
// Check whether the edge is Delaunay.
badedge = Primitives.InCircle(lowerleft, lowerright, upperright, nextapex) > 0.0;
}
else
{
// Avoid eating right through the triangulation.
badedge = false;
}
}
}
}
if (leftfinished || (!rightfinished &&
(Primitives.InCircle(upperleft, lowerleft, lowerright, upperright) > 0.0)))
{
// Knit the triangulations, adding an edge from 'lowerleft'
// to 'upperright'.
baseedge.Bond(ref rightcand);
rightcand.Lprev(ref baseedge);
baseedge.SetDest(lowerleft);
lowerright = upperright;
baseedge.Sym(ref rightcand);
upperright = rightcand.Apex();
}
else
{
// Knit the triangulations, adding an edge from 'upperleft'
// to 'lowerright'.
baseedge.Bond(ref leftcand);
leftcand.Lnext(ref baseedge);
baseedge.SetOrg(lowerright);
lowerleft = upperleft;
baseedge.Sym(ref leftcand);
upperleft = leftcand.Apex();
}
}
}
/// <summary>
/// Inserts a vertex at the circumcenter of a triangle. Deletes
/// the newly inserted vertex if it encroaches upon a segment.
/// </summary>
/// <param name="badtri"></param>
private void SplitTriangle(BadTriangle badtri)
{
Otri badotri = default(Otri);
Vertex borg, bdest, bapex;
Point newloc; // Location of the new vertex
float xi = 0, eta = 0;
InsertVertexResult success;
bool errorflag;
badotri = badtri.poortri;
borg = badotri.Org();
bdest = badotri.Dest();
bapex = badotri.Apex();
// Make sure that this triangle is still the same triangle it was
// when it was tested and determined to be of bad quality.
// Subsequent transformations may have made it a different triangle.
if (!Otri.IsDead(badotri.triangle) && (borg == badtri.triangorg) &&
(bdest == badtri.triangdest) && (bapex == badtri.triangapex))
{
errorflag = false;
// Create a new vertex at the triangle's circumcenter.
// Using the original (simpler) Steiner point location method
// for mesh refinement.
// TODO: NewLocation doesn't work for refinement. Why? Maybe
// reset VertexType?
if (behavior.fixedArea || behavior.VarArea)
{
newloc = Primitives.FindCircumcenter(borg, bdest, bapex, ref xi, ref eta, behavior.offconstant);
}
else
{
newloc = newLocation.FindLocation(borg, bdest, bapex, ref xi, ref eta, true, badotri);
}
// Check whether the new vertex lies on a triangle vertex.
if (((newloc.x == borg.x) && (newloc.y == borg.y)) ||
((newloc.x == bdest.x) && (newloc.y == bdest.y)) ||
((newloc.x == bapex.x) && (newloc.y == bapex.y)))
{
if (Behavior.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
else
{
// The new vertex must be in the interior, and therefore is a
// free vertex with a marker of zero.
Vertex newvertex = new Vertex(newloc.x, newloc.y, 0, mesh.nextras);
newvertex.type = VertexType.FreeVertex;
for (int i = 0; i < mesh.nextras; i++)
{
// Interpolate the vertex attributes at the circumcenter.
newvertex.attributes[i] = borg.attributes[i]
+ xi * (bdest.attributes[i] - borg.attributes[i])
+ eta * (bapex.attributes[i] - borg.attributes[i]);
}
// Ensure that the handle 'badotri' does not represent the longest
// edge of the triangle. This ensures that the circumcenter must
// fall to the left of this edge, so point location will work.
// (If the angle org-apex-dest exceeds 90 degrees, then the
// circumcenter lies outside the org-dest edge, and eta is
// negative. Roundoff error might prevent eta from being
// negative when it should be, so I test eta against xi.)
if (eta < xi)
{
badotri.LprevSelf();
}
// Insert the circumcenter, searching from the edge of the triangle,
// and maintain the Delaunay property of the triangulation.
Osub tmp = default(Osub);
success = mesh.InsertVertex(newvertex, ref badotri, ref tmp, true, true);
if (success == InsertVertexResult.Successful)
{
newvertex.hash = mesh.hash_vtx++;
newvertex.id = newvertex.hash;
mesh.vertices.Add(newvertex.hash, newvertex);
if (mesh.steinerleft > 0)
{
mesh.steinerleft--;
}
}
else if (success == InsertVertexResult.Encroaching)
{
// If the newly inserted vertex encroaches upon a subsegment,
// delete the new vertex.
mesh.UndoVertex();
}
else if (success == InsertVertexResult.Violating)
{
// Failed to insert the new vertex, but some subsegment was
// marked as being encroached.
}
else
{ // success == DUPLICATEVERTEX
// Couldn't insert the new vertex because a vertex is already there.
if (Behavior.Verbose)
{
logger.Warning("New vertex falls on existing vertex.", "Quality.SplitTriangle()");
errorflag = true;
}
}
}
if (errorflag)
{
logger.Error("The new vertex is at the circumcenter of triangle: This probably "
+ "means that I am trying to refine triangles to a smaller size than can be "
+ "accommodated by the finite precision of floating point arithmetic.",
"Quality.SplitTriangle()");
throw new Exception("The new vertex is at the circumcenter of triangle.");
}
}
}
/// <summary>
/// Finds the adjacencies between triangles by forming a stack of triangles for
/// each vertex. Each triangle is on three different stacks simultaneously.
/// </summary>
private static List <Otri>[] SetNeighbors(Mesh mesh, ITriangle[] triangles)
{
Otri tri = default(Otri);
Otri triangleleft = default(Otri);
Otri checktri = default(Otri);
Otri checkleft = default(Otri);
Otri nexttri;
TVertex tdest, tapex;
TVertex checkdest, checkapex;
int[] corner = new int[3];
int aroundvertex;
int i;
// Allocate a temporary array that maps each vertex to some adjacent triangle.
var vertexarray = new List <Otri> [mesh.vertices.Count];
// Each vertex is initially unrepresented.
for (i = 0; i < mesh.vertices.Count; i++)
{
Otri tmp = default(Otri);
tmp.tri = mesh.dummytri;
vertexarray[i] = new List <Otri>(3);
vertexarray[i].Add(tmp);
}
i = 0;
// Read the triangles from the .ele file, and link
// together those that share an edge.
foreach (var item in mesh.triangles)
{
tri.tri = item;
// Copy the triangle's three corners.
for (int j = 0; j < 3; j++)
{
corner[j] = triangles[i].GetVertexID(j);
if ((corner[j] < 0) || (corner[j] >= mesh.invertices))
{
Log.Instance.Error("Triangle has an invalid vertex index.", "MeshReader.Reconstruct()");
throw new Exception("Triangle has an invalid vertex index.");
}
}
// Read the triangle's attributes.
tri.tri.label = triangles[i].Label;
// TODO: VarArea
if (mesh.behavior.VarArea)
{
tri.tri.area = triangles[i].Area;
}
// Set the triangle's vertices.
tri.orient = 0;
tri.SetOrg(mesh.vertices[corner[0]]);
tri.SetDest(mesh.vertices[corner[1]]);
tri.SetApex(mesh.vertices[corner[2]]);
// Try linking the triangle to others that share these vertices.
for (tri.orient = 0; tri.orient < 3; tri.orient++)
{
// Take the number for the origin of triangleloop.
aroundvertex = corner[tri.orient];
int index = vertexarray[aroundvertex].Count - 1;
// Look for other triangles having this vertex.
nexttri = vertexarray[aroundvertex][index];
// Push the current triangle onto the stack.
vertexarray[aroundvertex].Add(tri);
checktri = nexttri;
if (checktri.tri.id != Mesh.DUMMY)
{
tdest = tri.Dest();
tapex = tri.Apex();
// Look for other triangles that share an edge.
do
{
checkdest = checktri.Dest();
checkapex = checktri.Apex();
if (tapex == checkdest)
{
// The two triangles share an edge; bond them together.
tri.Lprev(ref triangleleft);
triangleleft.Bond(ref checktri);
}
if (tdest == checkapex)
{
// The two triangles share an edge; bond them together.
checktri.Lprev(ref checkleft);
tri.Bond(ref checkleft);
}
// Find the next triangle in the stack.
index--;
nexttri = vertexarray[aroundvertex][index];
checktri = nexttri;
}while (checktri.tri.id != Mesh.DUMMY);
}
}
i++;
}
return(vertexarray);
}