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b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.2d.animation@5.0.4/Runtime/Triangle/Meshing/ConstraintMesher.cs new file mode 100644 index 0000000000000000000000000000000000000000..c0b8b2e43cbf41e5ac88e210997784457059e249 --- /dev/null +++ b/benchmark/NYU_CTF_Bench/test/2022/CSAW-Quals/rev/AnyaGacha/src/client/Library/PackageCache/com.unity.2d.animation@5.0.4/Runtime/Triangle/Meshing/ConstraintMesher.cs @@ -0,0 +1,1232 @@ +// ----------------------------------------------------------------------- +// +// Original Triangle code by Jonathan Richard Shewchuk, http://www.cs.cmu.edu/~quake/triangle.html +// Triangle.NET code by Christian Woltering, http://triangle.codeplex.com/ +// +// ----------------------------------------------------------------------- + +namespace UnityEngine.U2D.Animation.TriangleNet + .Meshing +{ + using System; + using System.Collections.Generic; + using Animation.TriangleNet.Geometry; + using Animation.TriangleNet.Logging; + using Animation.TriangleNet.Meshing.Iterators; + using Animation.TriangleNet.Topology; + + internal class ConstraintMesher + { + IPredicates predicates; + + Mesh mesh; + Behavior behavior; + TriangleLocator locator; + + List viri; + + ILog logger; + + public ConstraintMesher(Mesh mesh, Configuration config) + { + this.mesh = mesh; + this.predicates = config.Predicates(); + + this.behavior = mesh.behavior; + this.locator = mesh.locator; + + this.viri = new List(); + + logger = Log.Instance; + } + + /// + /// Insert segments into the mesh. + /// + /// The polygon. + /// Constraint options. + public void Apply(IPolygon input, ConstraintOptions options) + { + behavior.Poly = input.Segments.Count > 0; + + // Copy constraint options + if (options != null) + { + behavior.ConformingDelaunay = options.ConformingDelaunay; + behavior.Convex = options.Convex; + behavior.NoBisect = options.SegmentSplitting; + + if (behavior.ConformingDelaunay) + { + behavior.Quality = true; + } + } + + //if (input.EdgeMarkers != null) + //{ + // behavior.UseBoundaryMarkers = true; + //} + + behavior.useRegions = input.Regions.Count > 0; + + // Ensure that no vertex can be mistaken for a triangular bounding + // box vertex in insertvertex(). + mesh.infvertex1 = null; + mesh.infvertex2 = null; + mesh.infvertex3 = null; + + if (behavior.useSegments) + { + // Segments will be introduced next. + mesh.checksegments = true; + + // Insert PSLG segments and/or convex hull segments. + FormSkeleton(input); + } + + if (behavior.Poly && (mesh.triangles.Count > 0)) + { + // Copy holes and regions + mesh.holes.AddRange(input.Holes); + mesh.regions.AddRange(input.Regions); + + // Carve out holes and concavities. + CarveHoles(); + } + } + + /// + /// Find the holes and infect them. Find the area constraints and infect + /// them. Infect the convex hull. Spread the infection and kill triangles. + /// Spread the area constraints. + /// + private void CarveHoles() + { + Otri searchtri = default(Otri); + Vertex searchorg, searchdest; + LocateResult intersect; + + Triangle[] regionTris = null; + + var dummytri = mesh.dummytri; + + if (!mesh.behavior.Convex) + { + // Mark as infected any unprotected triangles on the boundary. + // This is one way by which concavities are created. + InfectHull(); + } + + if (!mesh.behavior.NoHoles) + { + // Infect each triangle in which a hole lies. + foreach (var hole in mesh.holes) + { + // Ignore holes that aren't within the bounds of the mesh. + if (mesh.bounds.Contains(hole)) + { + // Start searching from some triangle on the outer boundary. + searchtri.tri = dummytri; + searchtri.orient = 0; + searchtri.Sym(); + // Ensure that the hole is to the left of this boundary edge; + // otherwise, locate() will falsely report that the hole + // falls within the starting triangle. + searchorg = searchtri.Org(); + searchdest = searchtri.Dest(); + if (predicates.CounterClockwise(searchorg, searchdest, hole) > 0.0) + { + // Find a triangle that contains the hole. + intersect = mesh.locator.Locate(hole, ref searchtri); + if ((intersect != LocateResult.Outside) && (!searchtri.IsInfected())) + { + // Infect the triangle. This is done by marking the triangle + // as infected and including the triangle in the virus pool. + searchtri.Infect(); + viri.Add(searchtri.tri); + } + } + } + } + } + + // Now, we have to find all the regions BEFORE we carve the holes, because locate() won't + // work when the triangulation is no longer convex. (Incidentally, this is the reason why + // regional attributes and area constraints can't be used when refining a preexisting mesh, + // which might not be convex; they can only be used with a freshly triangulated PSLG.) + if (mesh.regions.Count > 0) + { + int i = 0; + + regionTris = new Triangle[mesh.regions.Count]; + + // Find the starting triangle for each region. + foreach (var region in mesh.regions) + { + regionTris[i] = dummytri; + // Ignore region points that aren't within the bounds of the mesh. + if (mesh.bounds.Contains(region.point)) + { + // Start searching from some triangle on the outer boundary. + searchtri.tri = dummytri; + searchtri.orient = 0; + searchtri.Sym(); + // Ensure that the region point is to the left of this boundary + // edge; otherwise, locate() will falsely report that the + // region point falls within the starting triangle. + searchorg = searchtri.Org(); + searchdest = searchtri.Dest(); + if (predicates.CounterClockwise(searchorg, searchdest, region.point) > 0.0) + { + // Find a triangle that contains the region point. + intersect = mesh.locator.Locate(region.point, ref searchtri); + if ((intersect != LocateResult.Outside) && (!searchtri.IsInfected())) + { + // Record the triangle for processing after the + // holes have been carved. + regionTris[i] = searchtri.tri; + regionTris[i].label = region.id; + regionTris[i].area = region.area; + } + } + } + + i++; + } + } + + if (viri.Count > 0) + { + // Carve the holes and concavities. + Plague(); + } + + if (regionTris != null) + { + var iterator = new RegionIterator(mesh); + + for (int i = 0; i < regionTris.Length; i++) + { + if (regionTris[i].id != Mesh.DUMMY) + { + // Make sure the triangle under consideration still exists. + // It may have been eaten by the virus. + if (!Otri.IsDead(regionTris[i])) + { + // Apply one region's attribute and/or area constraint. + iterator.Process(regionTris[i]); + } + } + } + } + + // Free up memory (virus pool should be empty anyway). + viri.Clear(); + } + + /// + /// Create the segments of a triangulation, including PSLG segments and edges + /// on the convex hull. + /// + private void FormSkeleton(IPolygon input) + { + // The segment endpoints. + Vertex p, q; + + mesh.insegments = 0; + + if (behavior.Poly) + { + // If the input vertices are collinear, there is no triangulation, + // so don't try to insert segments. + if (mesh.triangles.Count == 0) + { + return; + } + + // If segments are to be inserted, compute a mapping + // from vertices to triangles. + if (input.Segments.Count > 0) + { + mesh.MakeVertexMap(); + } + + // Read and insert the segments. + foreach (var seg in input.Segments) + { + mesh.insegments++; + + p = seg.GetVertex(0); + q = seg.GetVertex(1); + + if ((p.x == q.x) && (p.y == q.y)) + { + if (Log.Verbose) + { + logger.Warning("Endpoints of segment (IDs " + p.id + "/" + q.id + ") are coincident.", + "Mesh.FormSkeleton()"); + } + } + else + { + InsertSegment(p, q, seg.Label); + } + } + } + + if (behavior.Convex || !behavior.Poly) + { + // Enclose the convex hull with subsegments. + MarkHull(); + } + } + + #region Carving holes + + /// + /// Virally infect all of the triangles of the convex hull that are not + /// protected by subsegments. Where there are subsegments, set boundary + /// markers as appropriate. + /// + private void InfectHull() + { + Otri hulltri = default(Otri); + Otri nexttri = default(Otri); + Otri starttri = default(Otri); + Osub hullsubseg = default(Osub); + Vertex horg, hdest; + + var dummytri = mesh.dummytri; + + // Find a triangle handle on the hull. + hulltri.tri = dummytri; + hulltri.orient = 0; + hulltri.Sym(); + + // Remember where we started so we know when to stop. + hulltri.Copy(ref starttri); + // Go once counterclockwise around the convex hull. + do + { + // Ignore triangles that are already infected. + if (!hulltri.IsInfected()) + { + // Is the triangle protected by a subsegment? + hulltri.Pivot(ref hullsubseg); + if (hullsubseg.seg.hash == Mesh.DUMMY) + { + // The triangle is not protected; infect it. + if (!hulltri.IsInfected()) + { + hulltri.Infect(); + viri.Add(hulltri.tri); + } + } + else + { + // The triangle is protected; set boundary markers if appropriate. + if (hullsubseg.seg.boundary == 0) + { + hullsubseg.seg.boundary = 1; + horg = hulltri.Org(); + hdest = hulltri.Dest(); + if (horg.label == 0) + { + horg.label = 1; + } + if (hdest.label == 0) + { + hdest.label = 1; + } + } + } + } + // To find the next hull edge, go clockwise around the next vertex. + hulltri.Lnext(); + hulltri.Oprev(ref nexttri); + while (nexttri.tri.id != Mesh.DUMMY) + { + nexttri.Copy(ref hulltri); + hulltri.Oprev(ref nexttri); + } + } + while (!hulltri.Equals(starttri)); + } + + /// + /// Spread the virus from all infected triangles to any neighbors not + /// protected by subsegments. Delete all infected triangles. + /// + /// + /// This is the procedure that actually creates holes and concavities. + /// + /// This procedure operates in two phases. The first phase identifies all + /// the triangles that will die, and marks them as infected. They are + /// marked to ensure that each triangle is added to the virus pool only + /// once, so the procedure will terminate. + /// + /// The second phase actually eliminates the infected triangles. It also + /// eliminates orphaned vertices. + /// + void Plague() + { + Otri testtri = default(Otri); + Otri neighbor = default(Otri); + Osub neighborsubseg = default(Osub); + Vertex testvertex; + Vertex norg, ndest; + + var dummysub = mesh.dummysub; + var dummytri = mesh.dummytri; + + bool killorg; + + // Loop through all the infected triangles, spreading the virus to + // their neighbors, then to their neighbors' neighbors. + for (int i = 0; i < viri.Count; i++) + { + // WARNING: Don't use foreach, mesh.viri list may get modified. + + testtri.tri = viri[i]; + // A triangle is marked as infected by messing with one of its pointers + // to subsegments, setting it to an illegal value. Hence, we have to + // temporarily uninfect this triangle so that we can examine its + // adjacent subsegments. + // TODO: Not true in the C# version (so we could skip this). + testtri.Uninfect(); + + // Check each of the triangle's three neighbors. + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) + { + // Find the neighbor. + testtri.Sym(ref neighbor); + // Check for a subsegment between the triangle and its neighbor. + testtri.Pivot(ref neighborsubseg); + // Check if the neighbor is nonexistent or already infected. + if ((neighbor.tri.id == Mesh.DUMMY) || neighbor.IsInfected()) + { + if (neighborsubseg.seg.hash != Mesh.DUMMY) + { + // There is a subsegment separating the triangle from its + // neighbor, but both triangles are dying, so the subsegment + // dies too. + mesh.SubsegDealloc(neighborsubseg.seg); + if (neighbor.tri.id != Mesh.DUMMY) + { + // Make sure the subsegment doesn't get deallocated again + // later when the infected neighbor is visited. + neighbor.Uninfect(); + neighbor.SegDissolve(dummysub); + neighbor.Infect(); + } + } + } + else + { // The neighbor exists and is not infected. + if (neighborsubseg.seg.hash == Mesh.DUMMY) + { + // There is no subsegment protecting the neighbor, so + // the neighbor becomes infected. + neighbor.Infect(); + // Ensure that the neighbor's neighbors will be infected. + viri.Add(neighbor.tri); + } + else + { + // The neighbor is protected by a subsegment. + // Remove this triangle from the subsegment. + neighborsubseg.TriDissolve(dummytri); + // The subsegment becomes a boundary. Set markers accordingly. + if (neighborsubseg.seg.boundary == 0) + { + neighborsubseg.seg.boundary = 1; + } + norg = neighbor.Org(); + ndest = neighbor.Dest(); + if (norg.label == 0) + { + norg.label = 1; + } + if (ndest.label == 0) + { + ndest.label = 1; + } + } + } + } + // Remark the triangle as infected, so it doesn't get added to the + // virus pool again. + testtri.Infect(); + } + + foreach (var virus in viri) + { + testtri.tri = virus; + + // Check each of the three corners of the triangle for elimination. + // This is done by walking around each vertex, checking if it is + // still connected to at least one live triangle. + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) + { + testvertex = testtri.Org(); + // Check if the vertex has already been tested. + if (testvertex != null) + { + killorg = true; + // Mark the corner of the triangle as having been tested. + testtri.SetOrg(null); + // Walk counterclockwise about the vertex. + testtri.Onext(ref neighbor); + // Stop upon reaching a boundary or the starting triangle. + while ((neighbor.tri.id != Mesh.DUMMY) && + (!neighbor.Equals(testtri))) + { + if (neighbor.IsInfected()) + { + // Mark the corner of this triangle as having been tested. + neighbor.SetOrg(null); + } + else + { + // A live triangle. The vertex survives. + killorg = false; + } + // Walk counterclockwise about the vertex. + neighbor.Onext(); + } + // If we reached a boundary, we must walk clockwise as well. + if (neighbor.tri.id == Mesh.DUMMY) + { + // Walk clockwise about the vertex. + testtri.Oprev(ref neighbor); + // Stop upon reaching a boundary. + while (neighbor.tri.id != Mesh.DUMMY) + { + if (neighbor.IsInfected()) + { + // Mark the corner of this triangle as having been tested. + neighbor.SetOrg(null); + } + else + { + // A live triangle. The vertex survives. + killorg = false; + } + // Walk clockwise about the vertex. + neighbor.Oprev(); + } + } + if (killorg) + { + // Deleting vertex + testvertex.type = VertexType.UndeadVertex; + mesh.undeads++; + } + } + } + + // Record changes in the number of boundary edges, and disconnect + // dead triangles from their neighbors. + for (testtri.orient = 0; testtri.orient < 3; testtri.orient++) + { + testtri.Sym(ref neighbor); + if (neighbor.tri.id == Mesh.DUMMY) + { + // There is no neighboring triangle on this edge, so this edge + // is a boundary edge. This triangle is being deleted, so this + // boundary edge is deleted. + mesh.hullsize--; + } + else + { + // Disconnect the triangle from its neighbor. + neighbor.Dissolve(dummytri); + // There is a neighboring triangle on this edge, so this edge + // becomes a boundary edge when this triangle is deleted. + mesh.hullsize++; + } + } + // Return the dead triangle to the pool of triangles. + mesh.TriangleDealloc(testtri.tri); + } + + // Empty the virus pool. + viri.Clear(); + } + + #endregion + + #region Segment insertion + + /// + /// Find the first triangle on the path from one point to another. + /// + /// + /// + /// + /// The return value notes whether the destination or apex of the found + /// triangle is collinear with the two points in question. + /// + /// 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. + /// + 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 = predicates.CounterClockwise(searchpoint, startvertex, leftvertex); + leftflag = leftccw > 0.0; + // Is 'searchpoint' to the right? + rightccw = predicates.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) + { + 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 = predicates.CounterClockwise(searchpoint, startvertex, leftvertex); + leftflag = leftccw > 0.0; + } + while (rightflag) + { + // Turn right until satisfied. + searchtri.Oprev(); + if (searchtri.tri.id == Mesh.DUMMY) + { + 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 = predicates.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; + } + } + + /// + /// Find the intersection of an existing segment and a segment that is being + /// inserted. Insert a vertex at the intersection, splitting an existing subsegment. + /// + /// + /// + /// + /// + /// 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. + /// + 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) + { + 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 +#if USE_ATTRIBS + , mesh.nextras +#endif + ); + + newvertex.hash = mesh.hash_vtx++; + newvertex.id = newvertex.hash; + +#if USE_ATTRIBS + // Interpolate its attributes. + for (int i = 0; i < mesh.nextras; i++) + { + newvertex.attributes[i] = torg.attributes[i] + split * (tdest.attributes[i] - torg.attributes[i]); + } +#endif +#if USE_Z + newvertex.z = torg.z + split * (tdest.z - torg.z); +#endif + + mesh.vertices.Add(newvertex.hash, newvertex); + + // Insert the intersection vertex. This should always succeed. + success = mesh.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 (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)) + { + logger.Error("Topological inconsistency after splitting a segment.", "Mesh.SegmentIntersection()"); + throw new Exception("Topological inconsistency after splitting a segment."); + } + // 'splittri' should have destination endpoint1. + } + + /// + /// Scout the first triangle on the path from one endpoint to another, and check + /// for completion (reaching the second endpoint), a collinear vertex, or the + /// intersection of two segments. + /// + /// + /// + /// + /// Returns true if the entire segment is successfully inserted, and false + /// if the job must be finished by ConstrainedEdge(). + /// + /// If the first triangle on the path has the second endpoint as its + /// destination or apex, a subsegment is inserted and the job is done. + /// + /// If the first triangle on the path has a destination or apex that lies on + /// the segment, a subsegment is inserted connecting the first endpoint to + /// the collinear vertex, and the search is continued from the collinear + /// vertex. + /// + /// If the first triangle on the path has a subsegment opposite its origin, + /// then there is a segment that intersects the segment being inserted. + /// Their intersection vertex is inserted, splitting the subsegment. + /// + private bool ScoutSegment(ref Otri searchtri, Vertex endpoint2, int newmark) + { + Otri crosstri = default(Otri); + Osub crosssubseg = default(Osub); + Vertex leftvertex, rightvertex; + FindDirectionResult collinear; + + collinear = FindDirection(ref searchtri, endpoint2); + rightvertex = searchtri.Dest(); + leftvertex = searchtri.Apex(); + if (((leftvertex.x == endpoint2.x) && (leftvertex.y == endpoint2.y)) || + ((rightvertex.x == endpoint2.x) && (rightvertex.y == endpoint2.y))) + { + // The segment is already an edge in the mesh. + if ((leftvertex.x == endpoint2.x) && (leftvertex.y == endpoint2.y)) + { + searchtri.Lprev(); + } + // Insert a subsegment, if there isn't already one there. + mesh.InsertSubseg(ref searchtri, newmark); + return true; + } + else if (collinear == FindDirectionResult.Leftcollinear) + { + // We've collided with a vertex between the segment's endpoints. + // Make the collinear vertex be the triangle's origin. + searchtri.Lprev(); + mesh.InsertSubseg(ref searchtri, newmark); + // Insert the remainder of the segment. + return ScoutSegment(ref searchtri, endpoint2, newmark); + } + else if (collinear == FindDirectionResult.Rightcollinear) + { + // We've collided with a vertex between the segment's endpoints. + mesh.InsertSubseg(ref searchtri, newmark); + // Make the collinear vertex be the triangle's origin. + searchtri.Lnext(); + // Insert the remainder of the segment. + return ScoutSegment(ref searchtri, endpoint2, newmark); + } + else + { + searchtri.Lnext(ref crosstri); + crosstri.Pivot(ref crosssubseg); + // Check for a crossing segment. + if (crosssubseg.seg.hash == Mesh.DUMMY) + { + return false; + } + else + { + // Insert a vertex at the intersection. + SegmentIntersection(ref crosstri, ref crosssubseg, endpoint2); + crosstri.Copy(ref searchtri); + mesh.InsertSubseg(ref searchtri, newmark); + // Insert the remainder of the segment. + return ScoutSegment(ref searchtri, endpoint2, newmark); + } + } + } + + /// + /// Enforce the Delaunay condition at an edge, fanning out recursively from + /// an existing vertex. Pay special attention to stacking inverted triangles. + /// + /// + /// 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.) + /// + /// 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. + /// + 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 (predicates.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 (predicates.CounterClockwise(farvertex, rightvertex, nearvertex) <= 0.0) + { + // rightvertex is a reflex vertex too. Nothing can + // be done until a convex section is found. + return; + } + } + if (predicates.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 (predicates.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); + } + + /// + /// 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. + /// + /// + /// + /// + /// + /// 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. + /// + 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); + mesh.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 = predicates.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.Lprev(); + } + 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.Oprev(); + } + // Check for two intersecting segments. + fixuptri.Pivot(ref crosssubseg); + if (crosssubseg.seg.hash == Mesh.DUMMY) + { + mesh.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. + mesh.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); + } + } + } + + /// + /// Insert a PSLG segment into a triangulation. + /// + /// + /// + /// + private void InsertSegment(Vertex endpoint1, Vertex endpoint2, int newmark) + { + Otri searchtri1 = default(Otri), searchtri2 = default(Otri); + Vertex checkvertex = null; + + var dummytri = mesh.dummytri; + + // Find a triangle whose origin is the segment's first endpoint. + searchtri1 = endpoint1.tri; + if (searchtri1.tri != null) + { + checkvertex = searchtri1.Org(); + } + + if (checkvertex != endpoint1) + { + // Find a boundary triangle to search from. + searchtri1.tri = dummytri; + searchtri1.orient = 0; + searchtri1.Sym(); + // Search for the segment's first endpoint by point location. + if (locator.Locate(endpoint1, ref searchtri1) != LocateResult.OnVertex) + { + logger.Error("Unable to locate PSLG vertex in triangulation.", "Mesh.InsertSegment().1"); + throw new Exception("Unable to locate PSLG vertex in triangulation."); + } + } + // Remember this triangle to improve subsequent point location. + locator.Update(ref searchtri1); + + // Scout the beginnings of a path from the first endpoint + // toward the second. + if (ScoutSegment(ref searchtri1, endpoint2, newmark)) + { + // The segment was easily inserted. + return; + } + // The first endpoint may have changed if a collision with an intervening + // vertex on the segment occurred. + endpoint1 = searchtri1.Org(); + + // Find a triangle whose origin is the segment's second endpoint. + checkvertex = null; + searchtri2 = endpoint2.tri; + if (searchtri2.tri != null) + { + checkvertex = searchtri2.Org(); + } + if (checkvertex != endpoint2) + { + // Find a boundary triangle to search from. + searchtri2.tri = dummytri; + searchtri2.orient = 0; + searchtri2.Sym(); + // Search for the segment's second endpoint by point location. + if (locator.Locate(endpoint2, ref searchtri2) != LocateResult.OnVertex) + { + logger.Error("Unable to locate PSLG vertex in triangulation.", "Mesh.InsertSegment().2"); + throw new Exception("Unable to locate PSLG vertex in triangulation."); + } + } + // Remember this triangle to improve subsequent point location. + locator.Update(ref searchtri2); + // Scout the beginnings of a path from the second endpoint + // toward the first. + if (ScoutSegment(ref searchtri2, endpoint1, newmark)) + { + // The segment was easily inserted. + return; + } + // The second endpoint may have changed if a collision with an intervening + // vertex on the segment occurred. + endpoint2 = searchtri2.Org(); + + // Insert the segment directly into the triangulation. + ConstrainedEdge(ref searchtri1, endpoint2, newmark); + } + + /// + /// Cover the convex hull of a triangulation with subsegments. + /// + private void MarkHull() + { + Otri hulltri = default(Otri); + Otri nexttri = default(Otri); + Otri starttri = default(Otri); + + // Find a triangle handle on the hull. + hulltri.tri = mesh.dummytri; + hulltri.orient = 0; + hulltri.Sym(); + // Remember where we started so we know when to 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