public virtual ValidationStatus Validate(double fDegenerateTol = MathUtil.ZeroTolerancef)
{
double dist_sqr_thresh = fDegenerateTol * fDegenerateTol;
int nStop = IsLoop ? Curve.VertexCount - 1 : Curve.VertexCount;
for (int k = 0; k < nStop; ++k)
{
Vector2d v0 = Curve[k];
Vector2d v1 = Curve[(k + 1) % Curve.VertexCount];
if (v0.DistanceSquared(v1) < dist_sqr_thresh)
{
return(ValidationStatus.NearDenegerateInputGeometry);
}
}
foreach (int eid in Mesh.EdgeIndices())
{
Index2i ev = Mesh.GetEdgeV(eid);
if (PointF(ev.a).DistanceSquared(PointF(ev.b)) < dist_sqr_thresh)
{
return(ValidationStatus.NearDegenerateMeshEdges);
}
}
return(ValidationStatus.Ok);
}
public Vector2d NearestPoint(Vector2d point)
{
Vector2d n1 = (Arc1IsSegment) ?
Segment1.NearestPoint(point) : Arc1.NearestPoint(point);
Vector2d n2 = (Arc2IsSegment) ?
Segment2.NearestPoint(point) : Arc2.NearestPoint(point);
return((n1.DistanceSquared(point) < n2.DistanceSquared(point)) ? n1 : n2);
}
// 2D curve utils?
public static double SampledDistance(IParametricCurve2d c, Vector2d point, int N = 100)
{
double tMax = c.ParamLength;
double min_dist = double.MaxValue;
for ( int i = 0; i <= N; ++i ) {
double fT = (double)i / (double)N;
fT *= tMax;
Vector2d p = c.SampleT(fT);
double d = p.DistanceSquared(point);
if ( d < min_dist )
min_dist = d;
}
return Math.Sqrt(min_dist);
}
public double DistanceSquared(Vector2d p)
{
double t = (p - Center).Dot(Direction);
if (t >= Extent)
{
return(P1.DistanceSquared(p));
}
else if (t <= -Extent)
{
return(P0.DistanceSquared(p));
}
Vector2d proj = Center + t * Direction;
return(proj.DistanceSquared(p));
}
public virtual bool Apply()
{
HashSet <int> OnCurveVerts = new HashSet <int>(); // original vertices that were epsilon-coincident w/ curve vertices
insert_corners(OnCurveVerts);
// [RMS] not using this?
//HashSet<int> corner_v = new HashSet<int>(CurveVertices);
// not sure we need to track all of these
HashSet <int> ZeroEdges = new HashSet <int>();
HashSet <int> ZeroVertices = new HashSet <int>();
OnCutEdges = new HashSet <int>();
HashSet <int> NewEdges = new HashSet <int>();
HashSet <int> NewCutVertices = new HashSet <int>();
sbyte[] signs = new sbyte[2 * Mesh.MaxVertexID + 2 * Curve.VertexCount];
HashSet <int> segTriangles = new HashSet <int>();
HashSet <int> segVertices = new HashSet <int>();
HashSet <int> segEdges = new HashSet <int>();
// loop over segments, insert each one in sequence
int N = (IsLoop) ? Curve.VertexCount : Curve.VertexCount - 1;
for (int si = 0; si < N; ++si)
{
int i0 = si;
int i1 = (si + 1) % Curve.VertexCount;
Segment2d seg = new Segment2d(Curve[i0], Curve[i1]);
int i0_vid = CurveVertices[i0];
int i1_vid = CurveVertices[i1];
// If these vertices are already connected by an edge, we can just continue.
int existing_edge = Mesh.FindEdge(i0_vid, i1_vid);
if (existing_edge != DMesh3.InvalidID)
{
add_cut_edge(existing_edge);
continue;
}
if (triSpatial != null)
{
segTriangles.Clear(); segVertices.Clear(); segEdges.Clear();
AxisAlignedBox2d segBounds = new AxisAlignedBox2d(seg.P0); segBounds.Contain(seg.P1);
segBounds.Expand(MathUtil.ZeroTolerancef * 10);
triSpatial.FindTrianglesInRange(segBounds, segTriangles);
IndexUtil.TrianglesToVertices(Mesh, segTriangles, segVertices);
IndexUtil.TrianglesToEdges(Mesh, segTriangles, segEdges);
}
int MaxVID = Mesh.MaxVertexID;
IEnumerable <int> vertices = Interval1i.Range(MaxVID);
if (triSpatial != null)
{
vertices = segVertices;
}
// compute edge-crossing signs
// [TODO] could walk along mesh from a to b, rather than computing for entire mesh?
if (signs.Length < MaxVID)
{
signs = new sbyte[2 * MaxVID];
}
gParallel.ForEach(vertices, (vid) => {
if (Mesh.IsVertex(vid))
{
if (vid == i0_vid || vid == i1_vid)
{
signs[vid] = 0;
}
else
{
Vector2d v2 = PointF(vid);
// tolerance defines band in which we will consider values to be zero
signs[vid] = (sbyte)seg.WhichSide(v2, SpatialEpsilon);
}
}
else
{
signs[vid] = sbyte.MaxValue;
}
});
// have to skip processing of new edges. If edge id
// is > max at start, is new. Otherwise if in NewEdges list, also new.
// (need both in case we re-use an old edge index)
int MaxEID = Mesh.MaxEdgeID;
NewEdges.Clear();
NewCutVertices.Clear();
NewCutVertices.Add(i0_vid);
NewCutVertices.Add(i1_vid);
// cut existing edges with segment
IEnumerable <int> edges = Interval1i.Range(MaxEID);
if (triSpatial != null)
{
edges = segEdges;
}
foreach (int eid in edges)
{
if (Mesh.IsEdge(eid) == false)
{
continue;
}
if (eid >= MaxEID || NewEdges.Contains(eid))
{
continue;
}
// cannot cut boundary edges?
if (Mesh.IsBoundaryEdge(eid))
{
continue;
}
Index2i ev = Mesh.GetEdgeV(eid);
int eva_sign = signs[ev.a];
int evb_sign = signs[ev.b];
// [RMS] should we be using larger epsilon here? If we don't track OnCurveVerts explicitly, we
// need to at least use same epsilon we passed to insert_corner_from_bary...do we still also
// need that to catch the edges we split in the poke?
bool eva_in_segment = false;
if (eva_sign == 0)
{
eva_in_segment = OnCurveVerts.Contains(ev.a) || Math.Abs(seg.Project(PointF(ev.a))) < (seg.Extent + SpatialEpsilon);
}
bool evb_in_segment = false;
if (evb_sign == 0)
{
evb_in_segment = OnCurveVerts.Contains(ev.b) || Math.Abs(seg.Project(PointF(ev.b))) < (seg.Extent + SpatialEpsilon);
}
// If one or both vertices are on-segment, we have special case.
// If just one vertex is on the segment, we can skip this edge.
// If both vertices are on segment, then we can just re-use this edge.
if (eva_in_segment || evb_in_segment)
{
if (eva_in_segment && evb_in_segment)
{
ZeroEdges.Add(eid);
add_cut_edge(eid);
NewCutVertices.Add(ev.a); NewCutVertices.Add(ev.b);
}
else
{
int zvid = eva_in_segment ? ev.a : ev.b;
ZeroVertices.Add(zvid);
NewCutVertices.Add(zvid);
}
continue;
}
// no crossing
if (eva_sign * evb_sign > 0)
{
continue;
}
// compute segment/segment intersection
Vector2d va = PointF(ev.a);
Vector2d vb = PointF(ev.b);
Segment2d edge_seg = new Segment2d(va, vb);
IntrSegment2Segment2 intr = new IntrSegment2Segment2(seg, edge_seg);
intr.Compute();
if (intr.Type == IntersectionType.Segment)
{
// [RMS] we should have already caught this above, so if it happens here it is probably spurious?
// we should have caught this case above, but numerics are different so it might occur again
ZeroEdges.Add(eid);
NewCutVertices.Add(ev.a); NewCutVertices.Add(ev.b);
add_cut_edge(eid);
continue;
}
else if (intr.Type != IntersectionType.Point)
{
continue; // no intersection
}
Vector2d x = intr.Point0;
double t = Math.Sqrt(x.DistanceSquared(va) / va.DistanceSquared(vb));
// this case happens if we aren't "on-segment" but after we do the test the intersection pt
// is within epsilon of one end of the edge. This is a spurious t-intersection and we
// can ignore it. Some other edge should exist that picks up this vertex as part of it.
// [TODO] what about if this edge is degenerate?
bool x_in_segment = Math.Abs(edge_seg.Project(x)) < (edge_seg.Extent - SpatialEpsilon);
if (!x_in_segment)
{
continue;
}
Index2i et = Mesh.GetEdgeT(eid);
spatial_remove_triangles(et.a, et.b);
// split edge at this segment
DMesh3.EdgeSplitInfo splitInfo;
MeshResult result = Mesh.SplitEdge(eid, out splitInfo, t);
if (result != MeshResult.Ok)
{
throw new Exception("MeshInsertUVSegment.Apply: SplitEdge failed - " + result.ToString());
//return false;
}
// move split point to intersection position
SetPointF(splitInfo.vNew, x);
NewCutVertices.Add(splitInfo.vNew);
NewEdges.Add(splitInfo.eNewBN);
NewEdges.Add(splitInfo.eNewCN);
spatial_add_triangles(et.a, et.b);
spatial_add_triangles(splitInfo.eNewT2, splitInfo.eNewT3);
// some splits - but not all - result in new 'other' edges that are on
// the polypath. We want to keep track of these edges so we can extract loop later.
Index2i ecn = Mesh.GetEdgeV(splitInfo.eNewCN);
if (NewCutVertices.Contains(ecn.a) && NewCutVertices.Contains(ecn.b))
{
add_cut_edge(splitInfo.eNewCN);
}
// since we don't handle bdry edges this should never be false, but maybe we will handle bdry later...
if (splitInfo.eNewDN != DMesh3.InvalidID)
{
NewEdges.Add(splitInfo.eNewDN);
Index2i edn = Mesh.GetEdgeV(splitInfo.eNewDN);
if (NewCutVertices.Contains(edn.a) && NewCutVertices.Contains(edn.b))
{
add_cut_edge(splitInfo.eNewDN);
}
}
}
}
// extract the cut paths
if (EnableCutSpansAndLoops)
{
find_cut_paths(OnCutEdges);
}
return(true);
} // Apply()
public void CollapseToMinEdgeLength(double fMinLen)
{
double sharp_threshold_deg = 140.0f;
double minLenSqr = fMinLen * fMinLen;
bool done = false;
int max_passes = 100;
int pass_count = 0;
while (done == false && pass_count++ < max_passes)
{
done = true;
// [RMS] do modulo-indexing here to avoid pathological cases where we do things like
// continually collapse a short edge adjacent to a long edge (which will result in crazy over-collapse)
int N = Graph.MaxEdgeID;
const int nPrime = 31337; // any prime will do...
int cur_eid = 0;
do
{
int eid = cur_eid;
cur_eid = (cur_eid + nPrime) % N;
if (!Graph.IsEdge(eid))
{
continue;
}
if (FixedEdgeFilterF(eid))
{
continue;
}
Index2i ev = Graph.GetEdgeV(eid);
Vector2d va = Graph.GetVertex(ev.a);
Vector2d vb = Graph.GetVertex(ev.b);
double distSqr = va.DistanceSquared(vb);
if (distSqr < minLenSqr)
{
int vtx_idx = -1; // collapse to this vertex
// check valences. want to preserve positions of non-valence-2
int na = Graph.GetVtxEdgeCount(ev.a);
int nb = Graph.GetVtxEdgeCount(ev.b);
if (na != 2 && nb != 2)
{
continue;
}
if (na != 2)
{
vtx_idx = 0;
}
else if (nb != 2)
{
vtx_idx = 1;
}
// check opening angles. want to preserve sharp(er) angles
if (vtx_idx == -1)
{
double opena = Math.Abs(Graph.OpeningAngle(ev.a));
double openb = Math.Abs(Graph.OpeningAngle(ev.b));
if (opena < sharp_threshold_deg && openb < sharp_threshold_deg)
{
continue;
}
else if (opena < sharp_threshold_deg)
{
vtx_idx = 0;
}
else if (openb < sharp_threshold_deg)
{
vtx_idx = 1;
}
}
Vector2d newPos = (vtx_idx == -1) ? 0.5 * (va + vb) : ((vtx_idx == 0) ? va : vb);
int keep = ev.a, remove = ev.b;
if (vtx_idx == 1)
{
remove = ev.a; keep = ev.b;
}
DGraph2.EdgeCollapseInfo collapseInfo;
if (Graph.CollapseEdge(keep, remove, out collapseInfo) == MeshResult.Ok)
{
Graph.SetVertex(collapseInfo.vKept, newPos);
done = false;
}
}
} while (cur_eid != 0);
}
}
/// <summary>
/// find closest vertex, within searchRadius
/// </summary>
protected int find_nearest_vertex(Vector2d pt, double searchRadius, int ignore_vid = -1)
{
KeyValuePair <int, double> found = (ignore_vid == -1) ?
PointHash.FindNearestInRadius(pt, searchRadius,
(b) => { return(pt.DistanceSquared(Graph.GetVertex(b))); })
:
PointHash.FindNearestInRadius(pt, searchRadius,
(b) => { return(pt.DistanceSquared(Graph.GetVertex(b))); },
(vid) => { return(vid == ignore_vid); });
if (found.Key == PointHash.InvalidValue)
{
return(-1);
}
return(found.Key);
}
public bool Contains(Vector2d p)
{
double d = Center.DistanceSquared(p);
return(d <= Radius * Radius);
}
Circle ExactCircle2(Vector2d P0, ref Vector2d P1)
{
return(new Circle(
0.5 * (P0 + P1), 0.25 * P1.DistanceSquared(P0)));
}
protected virtual void do_split(Line2d line, bool insert_edges, int insert_gid)
{
if (EdgeSigns.Length < Graph.MaxVertexID)
{
EdgeSigns.resize(Graph.MaxVertexID);
}
foreach (int vid in Graph.VertexIndices())
{
EdgeSigns[vid] = line.WhichSide(Graph.GetVertex(vid), OnVertexTol);
}
hits.Clear();
foreach (int eid in Graph.EdgeIndices())
{
Index2i ev = Graph.GetEdgeV(eid);
var signs = new Index2i(EdgeSigns[ev.a], EdgeSigns[ev.b]);
if (signs.a * signs.b > 0)
{
continue; // both positive or negative, ignore
}
var hit = new edge_hit()
{
hit_eid = eid, vtx_signs = signs, hit_vid = -1
};
Vector2d a = Graph.GetVertex(ev.a);
Vector2d b = Graph.GetVertex(ev.b);
// parallel-edge case (both are zero)
if (signs.a == signs.b)
{
if (a.DistanceSquared(b) > MathUtil.Epsilon)
{
// we need to somehow not insert a new segment for this span below.
// so, insert two hit points for the ray-interval, with same eid.
// This will result in this span being skipped by the same-eid test below
// *however*, if other edges self-intersect w/ this segment, this will *not work*
// and duplicate edges will be inserted
hit.hit_vid = ev.a;
hit.line_t = line.Project(a);
hits.Add(hit);
hit.hit_vid = ev.b;
hit.line_t = line.Project(b);
hits.Add(hit);
}
else
{
// degenerate edge - fall through to a == 0 case below
signs.b = 1;
}
}
if (signs.a == 0)
{
hit.hit_pos = a;
hit.hit_vid = ev.a;
hit.line_t = line.Project(a);
}
else if (signs.b == 0)
{
hit.hit_pos = b;
hit.hit_vid = ev.b;
hit.line_t = line.Project(b);
}
else
{
var intr = new IntrLine2Segment2(line, new Segment2d(a, b));
if (intr.Find() == false)
{
throw new Exception("GraphSplitter2d.Split: signs are different but ray did not it?");
}
if (intr.IsSimpleIntersection)
{
hit.hit_pos = intr.Point;
hit.line_t = intr.Parameter;
}
else
{
throw new Exception("GraphSplitter2d.Split: got parallel edge case!");
}
}
hits.Add(hit);
}
// sort by increasing ray-t
hits.Sort((hit0, hit1) => { return(hit0.line_t.CompareTo(hit1.line_t)); });
// insert segments between successive intersection points
int N = hits.Count;
for (int i = 0; i < N - 1; ++i)
{
int j = i + 1;
// note: skipping parallel segments depends on this eid == eid test (see above)
if (hits[i].line_t == hits[j].line_t || hits[i].hit_eid == hits[j].hit_eid)
{
continue;
}
int vi = hits[i].hit_vid;
int vj = hits[j].hit_vid;
if (vi == vj && vi >= 0)
{
continue;
}
if (vi >= 0 && vj >= 0)
{
int existing = Graph.FindEdge(vi, vj);
if (existing >= 0)
{
continue;
}
}
if (vi == -1)
{
DGraph2.EdgeSplitInfo split;
var result = Graph.SplitEdge(hits[i].hit_eid, out split);
if (result != MeshResult.Ok)
{
throw new Exception("GraphSplitter2d.Split: first edge split failed!");
}
vi = split.vNew;
Graph.SetVertex(vi, hits[i].hit_pos);
edge_hit tmp = hits[i]; tmp.hit_vid = vi; hits[i] = tmp;
}
if (vj == -1)
{
DGraph2.EdgeSplitInfo split;
var result = Graph.SplitEdge(hits[j].hit_eid, out split);
if (result != MeshResult.Ok)
{
throw new Exception("GraphSplitter2d.Split: second edge split failed!");
}
vj = split.vNew;
Graph.SetVertex(vj, hits[j].hit_pos);
edge_hit tmp = hits[j]; tmp.hit_vid = vj; hits[j] = tmp;
}
// check if we actually want to add this segment
if (InsideTestF != null)
{
Vector2d midpoint = 0.5 * (Graph.GetVertex(vi) + Graph.GetVertex(vj));
if (InsideTestF(midpoint) == false)
{
continue;
}
}
if (insert_edges)
{
Graph.AppendEdge(vi, vj, insert_gid);
}
}
}
