void Check4DeadEvent(ref Otri checktri, SweepEvent[] eventheap, ref int heapsize)
{
SweepEvent deadevent;
SweepEventVertex eventvertex;
int eventnum = -1;
eventvertex = checktri.Org() as SweepEventVertex;
if (eventvertex != null)
{
deadevent = eventvertex.evt;
eventnum = deadevent.heapposition;
HeapDelete(eventheap, heapsize, eventnum);
heapsize--;
checktri.SetOrg(null);
}
}
/// <summary>
/// Transform two triangles to two different triangles by flipping an edge
/// counterclockwise within a quadrilateral.
/// </summary>
/// <param name="flipedge">Handle to the edge that will be flipped.</param>
/// <remarks>Imagine the original triangles, abc and bad, oriented so that the
/// shared edge ab lies in a horizontal plane, with the vertex b on the left
/// and the vertex a on the right. The vertex c lies below the edge, and
/// the vertex d lies above the edge. The 'flipedge' handle holds the edge
/// ab of triangle abc, and is directed left, from vertex a to vertex b.
///
/// The triangles abc and bad are deleted and replaced by the triangles cdb
/// and dca. The triangles that represent abc and bad are NOT deallocated;
/// they are reused for dca and cdb, respectively. Hence, any handles that
/// may have held the original triangles are still valid, although not
/// directed as they were before.
///
/// Upon completion of this routine, the 'flipedge' handle holds the edge
/// dc of triangle dca, and is directed down, from vertex d to vertex c.
/// (Hence, the two triangles have rotated counterclockwise.)
///
/// WARNING: This transformation is geometrically valid only if the
/// quadrilateral adbc is convex. Furthermore, this transformation is
/// valid only if there is not a subsegment between the triangles abc and
/// bad. This routine does not check either of these preconditions, and
/// it is the responsibility of the calling routine to ensure that they are
/// met. If they are not, the streets shall be filled with wailing and
/// gnashing of teeth.
///
/// Terminology
///
/// A "local transformation" replaces a small set of triangles with another
/// set of triangles. This may or may not involve inserting or deleting a
/// vertex.
///
/// The term "casing" is used to describe the set of triangles that are
/// attached to the triangles being transformed, but are not transformed
/// themselves. Think of the casing as a fixed hollow structure inside
/// which all the action happens. A "casing" is only defined relative to
/// a single transformation; each occurrence of a transformation will
/// involve a different casing.
/// </remarks>
internal void Flip(ref Otri flipedge)
{
Otri botleft = default(Otri), botright = default(Otri);
Otri topleft = default(Otri), topright = default(Otri);
Otri top = default(Otri);
Otri botlcasing = default(Otri), botrcasing = default(Otri);
Otri toplcasing = default(Otri), toprcasing = default(Otri);
Osub botlsubseg = default(Osub), botrsubseg = default(Osub);
Osub toplsubseg = default(Osub), toprsubseg = default(Osub);
Vertex leftvertex, rightvertex, botvertex;
Vertex farvertex;
// Identify the vertices of the quadrilateral.
rightvertex = flipedge.Org();
leftvertex = flipedge.Dest();
botvertex = flipedge.Apex();
flipedge.Sym(ref top);
// SELF CHECK
//if (top.triangle == dummytri)
//{
// logger.Error("Attempt to flip on boundary.", "Mesh.Flip()");
// flipedge.LnextSelf();
// return;
//}
//if (checksegments)
//{
// flipedge.SegPivot(ref toplsubseg);
// if (toplsubseg.ss != dummysub)
// {
// logger.Error("Attempt to flip a segment.", "Mesh.Flip()");
// flipedge.LnextSelf();
// return;
// }
//}
farvertex = top.Apex();
// Identify the casing of the quadrilateral.
top.Lprev(ref topleft);
topleft.Sym(ref toplcasing);
top.Lnext(ref topright);
topright.Sym(ref toprcasing);
flipedge.Lnext(ref botleft);
botleft.Sym(ref botlcasing);
flipedge.Lprev(ref botright);
botright.Sym(ref botrcasing);
// Rotate the quadrilateral one-quarter turn counterclockwise.
topleft.Bond(ref botlcasing);
botleft.Bond(ref botrcasing);
botright.Bond(ref toprcasing);
topright.Bond(ref toplcasing);
if (checksegments)
{
// Check for subsegments and rebond them to the quadrilateral.
topleft.SegPivot(ref toplsubseg);
botleft.SegPivot(ref botlsubseg);
botright.SegPivot(ref botrsubseg);
topright.SegPivot(ref toprsubseg);
if (toplsubseg.seg == Mesh.dummysub)
{
topright.SegDissolve();
}
else
{
topright.SegBond(ref toplsubseg);
}
if (botlsubseg.seg == Mesh.dummysub)
{
topleft.SegDissolve();
}
else
{
topleft.SegBond(ref botlsubseg);
}
if (botrsubseg.seg == Mesh.dummysub)
{
botleft.SegDissolve();
}
else
{
botleft.SegBond(ref botrsubseg);
}
if (toprsubseg.seg == Mesh.dummysub)
{
botright.SegDissolve();
}
else
{
botright.SegBond(ref toprsubseg);
}
}
// New vertex assignments for the rotated quadrilateral.
flipedge.SetOrg(farvertex);
flipedge.SetDest(botvertex);
flipedge.SetApex(rightvertex);
top.SetOrg(botvertex);
top.SetDest(farvertex);
top.SetApex(leftvertex);
}
/// <summary>
/// Create a new subsegment and inserts it between two triangles. Its
/// vertices are properly initialized.
/// </summary>
/// <param name="tri">The new subsegment is inserted at the edge
/// described by this handle.</param>
/// <param name="subsegmark">The marker 'subsegmark' is applied to the
/// subsegment and, if appropriate, its vertices.</param>
internal void InsertSubseg(ref Otri tri, int subsegmark)
{
Otri oppotri = default(Otri);
Osub newsubseg = default(Osub);
Vertex triorg, tridest;
triorg = tri.Org();
tridest = tri.Dest();
// Mark vertices if possible.
if (triorg.mark == 0)
{
triorg.mark = subsegmark;
}
if (tridest.mark == 0)
{
tridest.mark = subsegmark;
}
// Check if there's already a subsegment here.
tri.SegPivot(ref newsubseg);
if (newsubseg.seg == dummysub)
{
// Make new subsegment and initialize its vertices.
MakeSegment(ref newsubseg);
newsubseg.SetOrg(tridest);
newsubseg.SetDest(triorg);
newsubseg.SetSegOrg(tridest);
newsubseg.SetSegDest(triorg);
// Bond new subsegment to the two triangles it is sandwiched between.
// Note that the facing triangle 'oppotri' might be equal to 'dummytri'
// (outer space), but the new subsegment is bonded to it all the same.
tri.SegBond(ref newsubseg);
tri.Sym(ref oppotri);
newsubseg.SymSelf();
oppotri.SegBond(ref newsubseg);
newsubseg.seg.boundary = subsegmark;
}
else
{
if (newsubseg.seg.boundary == 0)
{
newsubseg.seg.boundary = subsegmark;
}
}
}
/// <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;
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)
{
logger.Error("Attempt to find intersection of parallel segments.",
"Mesh.SegmentIntersection()");
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,
this.nextras);
newvertex.hash = this.hash_vtx++;
newvertex.id = newvertex.hash;
// Interpolate its attributes.
for (int i = 0; i < nextras; i++)
{
newvertex.attributes[i] = torg.attributes[i] + split * (tdest.attributes[i] - torg.attributes[i]);
}
vertices.Add(newvertex.hash, newvertex);
// Insert the intersection vertex. This should always succeed.
success = InsertVertex(newvertex, ref splittri, ref splitsubseg, false, false);
if (success != InsertVertexResult.Successful)
{
logger.Error("Failure to split a segment.", "Mesh.SegmentIntersection()");
throw new Exception("Failure to split a segment.");
}
// Record a triangle whose origin is the new vertex.
newvertex.tri = splittri;
if (steinerleft > 0)
{
steinerleft--;
}
// Divide the segment into two, and correct the segment endpoints.
splitsubseg.SymSelf();
splitsubseg.Pivot(ref opposubseg);
splitsubseg.Dissolve();
opposubseg.Dissolve();
do
{
splitsubseg.SetSegOrg(newvertex);
splitsubseg.NextSelf();
} while (splitsubseg.seg != Mesh.dummysub);
do
{
opposubseg.SetSegOrg(newvertex);
opposubseg.NextSelf();
} while (opposubseg.seg != Mesh.dummysub);
// 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.OnextSelf();
}
else if ((rightvertex.x != endpoint1.x) || (rightvertex.y != endpoint1.y))
{
logger.Error("Topological inconsistency after splitting a segment.", "Mesh.SegmentIntersection()");
throw new Exception("Topological inconsistency after splitting a segment.");
}
// 'splittri' should have destination endpoint1.
}
/// <summary>
/// Delete a vertex from a Delaunay triangulation, ensuring that the
/// triangulation remains Delaunay.
/// </summary>
/// <param name="deltri"></param>
/// <remarks>The origin of 'deltri' is deleted. The union of the triangles
/// adjacent to this vertex is a polygon, for which the Delaunay triangulation
/// is found. Two triangles are removed from the mesh.
///
/// Only interior vertices that do not lie on segments or boundaries
/// may be deleted.
/// </remarks>
internal void DeleteVertex(ref Otri deltri)
{
Otri countingtri = default(Otri);
Otri firstedge = default(Otri), lastedge = default(Otri);
Otri deltriright = default(Otri);
Otri lefttri = default(Otri), righttri = default(Otri);
Otri leftcasing = default(Otri), rightcasing = default(Otri);
Osub leftsubseg = default(Osub), rightsubseg = default(Osub);
Vertex delvertex;
Vertex neworg;
int edgecount;
delvertex = deltri.Org();
VertexDealloc(delvertex);
// Count the degree of the vertex being deleted.
deltri.Onext(ref countingtri);
edgecount = 1;
while (!deltri.Equal(countingtri))
{
edgecount++;
countingtri.OnextSelf();
}
if (edgecount > 3)
{
// Triangulate the polygon defined by the union of all triangles
// adjacent to the vertex being deleted. Check the quality of
// the resulting triangles.
deltri.Onext(ref firstedge);
deltri.Oprev(ref lastedge);
TriangulatePolygon(firstedge, lastedge, edgecount, false, behavior.NoBisect == 0);
}
// Splice out two triangles.
deltri.Lprev(ref deltriright);
deltri.Dnext(ref lefttri);
lefttri.Sym(ref leftcasing);
deltriright.Oprev(ref righttri);
righttri.Sym(ref rightcasing);
deltri.Bond(ref leftcasing);
deltriright.Bond(ref rightcasing);
lefttri.SegPivot(ref leftsubseg);
if (leftsubseg.seg != Mesh.dummysub)
{
deltri.SegBond(ref leftsubseg);
}
righttri.SegPivot(ref rightsubseg);
if (rightsubseg.seg != Mesh.dummysub)
{
deltriright.SegBond(ref rightsubseg);
}
// Set the new origin of 'deltri' and check its quality.
neworg = lefttri.Org();
deltri.SetOrg(neworg);
if (behavior.NoBisect == 0)
{
quality.TestTriangle(ref deltri);
}
// Delete the two spliced-out triangles.
TriangleDealloc(lefttri.triangle);
TriangleDealloc(righttri.triangle);
}
/// <summary>
/// Force a segment into a constrained Delaunay triangulation by deleting the
/// triangles it intersects, and triangulating the polygons that form on each
/// side of it.
/// </summary>
/// <param name="starttri"></param>
/// <param name="endpoint2"></param>
/// <param name="newmark"></param>
/// <remarks>
/// Generates a single subsegment connecting 'endpoint1' to 'endpoint2'.
/// The triangle 'starttri' has 'endpoint1' as its origin. 'newmark' is the
/// boundary marker of the segment.
///
/// To insert a segment, every triangle whose interior intersects the
/// segment is deleted. The union of these deleted triangles is a polygon
/// (which is not necessarily monotone, but is close enough), which is
/// divided into two polygons by the new segment. This routine's task is
/// to generate the Delaunay triangulation of these two polygons.
///
/// You might think of this routine's behavior as a two-step process. The
/// first step is to walk from endpoint1 to endpoint2, flipping each edge
/// encountered. This step creates a fan of edges connected to endpoint1,
/// including the desired edge to endpoint2. The second step enforces the
/// Delaunay condition on each side of the segment in an incremental manner:
/// proceeding along the polygon from endpoint1 to endpoint2 (this is done
/// independently on each side of the segment), each vertex is "enforced"
/// as if it had just been inserted, but affecting only the previous
/// vertices. The result is the same as if the vertices had been inserted
/// in the order they appear on the polygon, so the result is Delaunay.
///
/// In truth, ConstrainedEdge() interleaves these two steps. The procedure
/// walks from endpoint1 to endpoint2, and each time an edge is encountered
/// and flipped, the newly exposed vertex (at the far end of the flipped
/// edge) is "enforced" upon the previously flipped edges, usually affecting
/// only one side of the polygon (depending upon which side of the segment
/// the vertex falls on).
///
/// The algorithm is complicated by the need to handle polygons that are not
/// convex. Although the polygon is not necessarily monotone, it can be
/// triangulated in a manner similar to the stack-based algorithms for
/// monotone polygons. For each reflex vertex (local concavity) of the
/// polygon, there will be an inverted triangle formed by one of the edge
/// flips. (An inverted triangle is one with negative area - that is, its
/// vertices are arranged in clockwise order - and is best thought of as a
/// wrinkle in the fabric of the mesh.) Each inverted triangle can be
/// thought of as a reflex vertex pushed on the stack, waiting to be fixed
/// later.
///
/// A reflex vertex is popped from the stack when a vertex is inserted that
/// is visible to the reflex vertex. (However, if the vertex behind the
/// reflex vertex is not visible to the reflex vertex, a new inverted
/// triangle will take its place on the stack.) These details are handled
/// by the DelaunayFixup() routine above.
/// </remarks>
private void ConstrainedEdge(ref Otri starttri, Vertex endpoint2, int newmark)
{
Otri fixuptri = default(Otri), fixuptri2 = default(Otri);
Osub crosssubseg = default(Osub);
Vertex endpoint1;
Vertex farvertex;
double area;
bool collision;
bool done;
endpoint1 = starttri.Org();
starttri.Lnext(ref fixuptri);
Flip(ref fixuptri);
// 'collision' indicates whether we have found a vertex directly
// between endpoint1 and endpoint2.
collision = false;
done = false;
do
{
farvertex = fixuptri.Org();
// 'farvertex' is the extreme point of the polygon we are "digging"
// to get from endpoint1 to endpoint2.
if ((farvertex.x == endpoint2.x) && (farvertex.y == endpoint2.y))
{
fixuptri.Oprev(ref fixuptri2);
// Enforce the Delaunay condition around endpoint2.
DelaunayFixup(ref fixuptri, false);
DelaunayFixup(ref fixuptri2, true);
done = true;
}
else
{
// Check whether farvertex is to the left or right of the segment being
// inserted, to decide which edge of fixuptri to dig through next.
area = Primitives.CounterClockwise(endpoint1, endpoint2, farvertex);
if (area == 0.0)
{
// We've collided with a vertex between endpoint1 and endpoint2.
collision = true;
fixuptri.Oprev(ref fixuptri2);
// Enforce the Delaunay condition around farvertex.
DelaunayFixup(ref fixuptri, false);
DelaunayFixup(ref fixuptri2, true);
done = true;
}
else
{
if (area > 0.0)
{
// farvertex is to the left of the segment.
fixuptri.Oprev(ref fixuptri2);
// Enforce the Delaunay condition around farvertex, on the
// left side of the segment only.
DelaunayFixup(ref fixuptri2, true);
// Flip the edge that crosses the segment. After the edge is
// flipped, one of its endpoints is the fan vertex, and the
// destination of fixuptri is the fan vertex.
fixuptri.LprevSelf();
}
else
{
// farvertex is to the right of the segment.
DelaunayFixup(ref fixuptri, false);
// Flip the edge that crosses the segment. After the edge is
// flipped, one of its endpoints is the fan vertex, and the
// destination of fixuptri is the fan vertex.
fixuptri.OprevSelf();
}
// Check for two intersecting segments.
fixuptri.SegPivot(ref crosssubseg);
if (crosssubseg.seg == Mesh.dummysub)
{
Flip(ref fixuptri); // May create inverted triangle at left.
}
else
{
// We've collided with a segment between endpoint1 and endpoint2.
collision = true;
// Insert a vertex at the intersection.
SegmentIntersection(ref fixuptri, ref crosssubseg, endpoint2);
done = true;
}
}
}
} while (!done);
// Insert a subsegment to make the segment permanent.
InsertSubseg(ref fixuptri, newmark);
// If there was a collision with an interceding vertex, install another
// segment connecting that vertex with endpoint2.
if (collision)
{
// Insert the remainder of the segment.
if (!ScoutSegment(ref fixuptri, endpoint2, newmark))
{
ConstrainedEdge(ref fixuptri, endpoint2, newmark);
}
}
}
/// <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 = Primitives.CounterClockwise(searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
// Is 'searchpoint' to the right?
rightccw = Primitives.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.triangle == Mesh.dummytri)
{
leftflag = false;
}
else
{
rightflag = false;
}
}
while (leftflag)
{
// Turn left until satisfied.
searchtri.OnextSelf();
if (searchtri.triangle == Mesh.dummytri)
{
logger.Error("Unable to find a triangle on path.", "Mesh.FindDirection().1");
throw new Exception("Unable to find a triangle on path.");
}
leftvertex = searchtri.Apex();
rightccw = leftccw;
leftccw = Primitives.CounterClockwise(searchpoint, startvertex, leftvertex);
leftflag = leftccw > 0.0;
}
while (rightflag)
{
// Turn right until satisfied.
searchtri.OprevSelf();
if (searchtri.triangle == Mesh.dummytri)
{
logger.Error("Unable to find a triangle on path.", "Mesh.FindDirection().2");
throw new Exception("Unable to find a triangle on path.");
}
rightvertex = searchtri.Dest();
leftccw = rightccw;
rightccw = Primitives.CounterClockwise(startvertex, searchpoint, rightvertex);
rightflag = rightccw > 0.0;
}
if (leftccw == 0.0)
{
return FindDirectionResult.Leftcollinear;
}
else if (rightccw == 0.0)
{
return FindDirectionResult.Rightcollinear;
}
else
{
return FindDirectionResult.Within;
}
}
/// <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);
}
/// <summary>
/// Transform two triangles to two different triangles by flipping an edge
/// clockwise within a quadrilateral. Reverses the flip() operation so that
/// the data structures representing the triangles are back where they were
/// before the flip().
/// </summary>
/// <param name="flipedge"></param>
/// <remarks>
/// See above Flip() remarks for more information.
///
/// Upon completion of this routine, the 'flipedge' handle holds the edge
/// cd of triangle cdb, and is directed up, from vertex c to vertex d.
/// (Hence, the two triangles have rotated clockwise.)
/// </remarks>
internal void Unflip(ref Otri flipedge)
{
Otri botleft = default(Otri), botright = default(Otri);
Otri topleft = default(Otri), topright = default(Otri);
Otri top = default(Otri);
Otri botlcasing = default(Otri), botrcasing = default(Otri);
Otri toplcasing = default(Otri), toprcasing = default(Otri);
Osub botlsubseg = default(Osub), botrsubseg = default(Osub);
Osub toplsubseg = default(Osub), toprsubseg = default(Osub);
Vertex leftvertex, rightvertex, botvertex;
Vertex farvertex;
// Identify the vertices of the quadrilateral.
rightvertex = flipedge.Org();
leftvertex = flipedge.Dest();
botvertex = flipedge.Apex();
flipedge.Sym(ref top);
farvertex = top.Apex();
// Identify the casing of the quadrilateral.
top.Lprev(ref topleft);
topleft.Sym(ref toplcasing);
top.Lnext(ref topright);
topright.Sym(ref toprcasing);
flipedge.Lnext(ref botleft);
botleft.Sym(ref botlcasing);
flipedge.Lprev(ref botright);
botright.Sym(ref botrcasing);
// Rotate the quadrilateral one-quarter turn clockwise.
topleft.Bond(ref toprcasing);
botleft.Bond(ref toplcasing);
botright.Bond(ref botlcasing);
topright.Bond(ref botrcasing);
if (checksegments)
{
// Check for subsegments and rebond them to the quadrilateral.
topleft.SegPivot(ref toplsubseg);
botleft.SegPivot(ref botlsubseg);
botright.SegPivot(ref botrsubseg);
topright.SegPivot(ref toprsubseg);
if (toplsubseg.seg == Mesh.dummysub)
{
botleft.SegDissolve();
}
else
{
botleft.SegBond(ref toplsubseg);
}
if (botlsubseg.seg == Mesh.dummysub)
{
botright.SegDissolve();
}
else
{
botright.SegBond(ref botlsubseg);
}
if (botrsubseg.seg == Mesh.dummysub)
{
topright.SegDissolve();
}
else
{
topright.SegBond(ref botrsubseg);
}
if (toprsubseg.seg == Mesh.dummysub)
{
topleft.SegDissolve();
}
else
{
topleft.SegBond(ref toprsubseg);
}
}
// New vertex assignments for the rotated quadrilateral.
flipedge.SetOrg(botvertex);
flipedge.SetDest(farvertex);
flipedge.SetApex(leftvertex);
top.SetOrg(farvertex);
top.SetDest(botvertex);
top.SetApex(rightvertex);
}
/// <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>
/// Given the triangulation, and a vertex returns the minimum distance to the
/// vertices of the triangle where the given vertex located.
/// </summary>
/// <param name="newlocX"></param>
/// <param name="newlocY"></param>
/// <param name="searchtri"></param>
/// <returns></returns>
private double MinDistanceToNeighbor(double newlocX, double newlocY, ref Otri searchtri)
{
Otri horiz = default(Otri); // for search operation
LocateResult intersect = LocateResult.Outside;
Vertex v1, v2, v3, torg, tdest;
double d1, d2, d3, ahead;
//triangle ptr; // Temporary variable used by sym().
Point newvertex = new Point(newlocX, newlocY);
// printf("newvertex %f,%f\n", newvertex[0], newvertex[1]);
// Find the location of the vertex to be inserted. Check if a good
// starting triangle has already been provided by the caller.
// Find a boundary triangle.
//horiz.tri = m.dummytri;
//horiz.orient = 0;
//horiz.symself();
// Search for a triangle containing 'newvertex'.
// Start searching from the triangle provided by the caller.
// Where are we?
torg = searchtri.Org();
tdest = searchtri.Dest();
// Check the starting triangle's vertices.
if ((torg.x == newvertex.x) && (torg.y == newvertex.y))
{
intersect = LocateResult.OnVertex;
searchtri.Copy(ref horiz);
}
else if ((tdest.x == newvertex.x) && (tdest.y == newvertex.y))
{
searchtri.LnextSelf();
intersect = LocateResult.OnVertex;
searchtri.Copy(ref horiz);
}
else
{
// Orient 'searchtri' to fit the preconditions of calling preciselocate().
ahead = Primitives.CounterClockwise(torg, tdest, newvertex);
if (ahead < 0.0)
{
// Turn around so that 'searchpoint' is to the left of the
// edge specified by 'searchtri'.
searchtri.SymSelf();
searchtri.Copy(ref horiz);
intersect = mesh.locator.PreciseLocate(newvertex, ref horiz, false);
}
else if (ahead == 0.0)
{
// Check if 'searchpoint' is between 'torg' and 'tdest'.
if (((torg.x < newvertex.x) == (newvertex.x < tdest.x)) &&
((torg.y < newvertex.y) == (newvertex.y < tdest.y)))
{
intersect = LocateResult.OnEdge;
searchtri.Copy(ref horiz);
}
}
else
{
searchtri.Copy(ref horiz);
intersect = mesh.locator.PreciseLocate(newvertex, ref horiz, false);
}
}
if (intersect == LocateResult.OnVertex || intersect == LocateResult.Outside)
{
// set distance to 0
//m.VertexDealloc(newvertex);
return 0.0;
}
else
{ // intersect == ONEDGE || intersect == INTRIANGLE
// find the triangle vertices
v1 = horiz.Org();
v2 = horiz.Dest();
v3 = horiz.Apex();
d1 = (v1.x - newvertex.x) * (v1.x - newvertex.x) + (v1.y - newvertex.y) * (v1.y - newvertex.y);
d2 = (v2.x - newvertex.x) * (v2.x - newvertex.x) + (v2.y - newvertex.y) * (v2.y - newvertex.y);
d3 = (v3.x - newvertex.x) * (v3.x - newvertex.x) + (v3.y - newvertex.y) * (v3.y - newvertex.y);
//m.VertexDealloc(newvertex);
// find minimum of the distance
if (d1 <= d2 && d1 <= d3)
{
return d1;
}
else if (d2 <= d3)
{
return d2;
}
else
{
return d3;
}
}
}
/// <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>
/// Check if given triangle is blinded by given segment.
/// </summary>
/// <param name="tri">Triangle.</param>
/// <param name="seg">Segments</param>
/// <returns>Returns true, if the triangle is blinded.</returns>
private bool TriangleIsBlinded(ref Otri tri, ref Osub seg)
{
Point c, pt;
Vertex torg = tri.Org();
Vertex tdest = tri.Dest();
Vertex tapex = tri.Apex();
Vertex sorg = seg.Org();
Vertex sdest = seg.Dest();
c = this.points[tri.triangle.id];
if (SegmentsIntersect(sorg, sdest, c, torg, out pt, true))
{
return true;
}
if (SegmentsIntersect(sorg, sdest, c, tdest, out pt, true))
{
return true;
}
if (SegmentsIntersect(sorg, sdest, c, tapex, out pt, true))
{
return true;
}
return false;
}
/// <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;
double dxod, dyod, dxda, dyda, dxao, dyao;
double dxod2, dyod2, dxda2, dyda2, dxao2, dyao2;
double apexlen, orglen, destlen, minedge;
double angle;
double area;
double dist1, dist2;
double 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 = 0.5 * (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;
}
// Check whether the user thinks this triangle is too large.
if (behavior.Usertest && userTest != null)
{
if (userTest(torg, tdest, tapex, area))
{
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 * Math.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 * Math.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 * Math.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);
}
}