/// <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>
/// <returns>Location information.</returns>
/// <remarks>
/// Searching begins from one of: the input 'searchtri', a recently
/// encountered triangle 'recenttri', or from a triangle chosen from a
/// random sample. The choice is made by determining which triangle's
/// origin is closest to the point we are searching for. Normally,
/// 'searchtri' should be a handle on the convex hull of the triangulation.
///
/// Details on the random sampling method can be found in the Mucke, Saias,
/// and Zhu paper cited in the header of this code.
///
/// On completion, 'searchtri' is a triangle that contains 'searchpoint'.
///
/// 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.
/// </remarks>
public LocateResult Locate(Point searchpoint, ref Otri searchtri)
{
Otri sampletri = default(Otri);
Vertex torg, tdest;
float searchdist, dist;
float ahead;
// Record the distance from the suggested starting triangle to the
// point we seek.
torg = searchtri.Org();
searchdist = (searchpoint.X - torg.x) * (searchpoint.X - torg.x) +
(searchpoint.Y - torg.y) * (searchpoint.Y - torg.y);
// If a recently encountered triangle has been recorded and has not been
// deallocated, test it as a good starting point.
if (recenttri.triangle != null)
{
if (!Otri.IsDead(recenttri.triangle))
{
torg = recenttri.Org();
if ((torg.x == searchpoint.X) && (torg.y == searchpoint.Y))
{
recenttri.Copy(ref searchtri);
return(LocateResult.OnVertex);
}
dist = (searchpoint.X - torg.x) * (searchpoint.X - torg.x) +
(searchpoint.Y - torg.y) * (searchpoint.Y - torg.y);
if (dist < searchdist)
{
recenttri.Copy(ref searchtri);
searchdist = dist;
}
}
}
// TODO: Improve sampling.
sampler.Update(mesh);
int[] samples = sampler.GetSamples(mesh);
foreach (var key in samples)
{
sampletri.triangle = mesh.triangles[key];
if (!Otri.IsDead(sampletri.triangle))
{
torg = sampletri.Org();
dist = (searchpoint.X - torg.x) * (searchpoint.X - torg.x) +
(searchpoint.Y - torg.y) * (searchpoint.Y - torg.y);
if (dist < searchdist)
{
sampletri.Copy(ref searchtri);
searchdist = dist;
}
}
}
// Where are we?
torg = searchtri.Org();
tdest = searchtri.Dest();
// Check the starting triangle's vertices.
if ((torg.x == searchpoint.X) && (torg.y == searchpoint.Y))
{
return(LocateResult.OnVertex);
}
if ((tdest.x == searchpoint.X) && (tdest.y == searchpoint.Y))
{
searchtri.LnextSelf();
return(LocateResult.OnVertex);
}
// Orient 'searchtri' to fit the preconditions of calling preciselocate().
ahead = Primitives.CounterClockwise(torg, tdest, searchpoint);
if (ahead < 0.0)
{
// Turn around so that 'searchpoint' is to the left of the
// edge specified by 'searchtri'.
searchtri.SymSelf();
}
else if (ahead == 0.0)
{
// Check if 'searchpoint' is between 'torg' and 'tdest'.
if (((torg.x < searchpoint.X) == (searchpoint.X < tdest.x)) &&
((torg.y < searchpoint.Y) == (searchpoint.Y < tdest.y)))
{
return(LocateResult.OnEdge);
}
}
return(PreciseLocate(searchpoint, ref searchtri, false));
}
public void CarveHoles()
{
Otri otri = new Otri();
Triangle[] triangleArray = null;
if (!this.mesh.behavior.Convex)
{
this.InfectHull();
}
if (!this.mesh.behavior.NoHoles)
{
foreach (Point hole in this.mesh.holes)
{
if (!this.mesh.bounds.Contains(hole))
{
continue;
}
otri.triangle = Mesh.dummytri;
otri.orient = 0;
otri.SymSelf();
if (Primitives.CounterClockwise(otri.Org(), otri.Dest(), hole) <= 0 || this.mesh.locator.Locate(hole, ref otri) == LocateResult.Outside || otri.IsInfected())
{
continue;
}
otri.Infect();
this.viri.Add(otri.triangle);
}
}
if (this.mesh.regions.Count > 0)
{
int num = 0;
triangleArray = new Triangle[this.mesh.regions.Count];
foreach (RegionPointer region in this.mesh.regions)
{
triangleArray[num] = Mesh.dummytri;
if (this.mesh.bounds.Contains(region.point))
{
otri.triangle = Mesh.dummytri;
otri.orient = 0;
otri.SymSelf();
if (Primitives.CounterClockwise(otri.Org(), otri.Dest(), region.point) > 0 && this.mesh.locator.Locate(region.point, ref otri) != LocateResult.Outside && !otri.IsInfected())
{
triangleArray[num] = otri.triangle;
triangleArray[num].region = region.id;
}
}
num++;
}
}
if (this.viri.Count > 0)
{
this.Plague();
}
if (triangleArray != null)
{
RegionIterator regionIterator = new RegionIterator(this.mesh);
for (int i = 0; i < (int)triangleArray.Length; i++)
{
if (triangleArray[i] != Mesh.dummytri && !Otri.IsDead(triangleArray[i]))
{
regionIterator.Process(triangleArray[i]);
}
}
}
this.viri.Clear();
}
/// <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;
float 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>
/// 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>
/// 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>
/// 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>
/// 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);
}
