private void FilterSelfOverlaps(double overlapRadius, bool bResample = true)
{
// [RMS] this tolerance business is not workign properly right now. The problem is
// that decimator loses corners!
// To simplify the computation we are going to resample the curve so that no adjacent
// are within a given distance. Then we can use distance-to-segments, with the two adjacent
// segments filtered out, to measure self-distance
double dist_thresh = overlapRadius;
double sharp_thresh_deg = 45;
//Profiler.Start("InitialResample");
// resample graph. the degenerate-edge thing is necessary to
// filter out tiny segments that are functionally sharp corners,
// but geometrically are made of multiple angles < threshold
// (maybe there is a better way to do this?)
DGraph2Resampler r = new DGraph2Resampler(Graph);
r.CollapseDegenerateEdges(overlapRadius / 10);
if (bResample)
{
r.SplitToMaxEdgeLength(overlapRadius / 2);
r.CollapseToMinEdgeLength(overlapRadius / 3);
}
r.CollapseDegenerateEdges(overlapRadius / 10);
//Profiler.StopAndAccumulate("InitialResample");
//Profiler.Start("SharpCorners");
// find sharp corners
List <int> sharp_corners = new List <int>();
foreach (int vid in Graph.VertexIndices())
{
if (is_fixed_v(vid))
{
continue;
}
double open_angle = Graph.OpeningAngle(vid);
if (open_angle < sharp_thresh_deg)
{
sharp_corners.Add(vid);
}
}
// disconnect at sharp corners
foreach (int vid in sharp_corners)
{
if (Graph.IsVertex(vid) == false)
{
continue;
}
int e0 = Graph.GetVtxEdges(vid)[0];
Index2i ev = Graph.GetEdgeV(e0);
int otherv = (ev.a == vid) ? ev.b : ev.a;
Vector2d newpos = Graph.GetVertex(vid); //0.5 * (Graph.GetVertex(vid) + Graph.GetVertex(otherv));
Graph.RemoveEdge(e0, false);
int newvid = Graph.AppendVertex(newpos);
Graph.AppendEdge(newvid, otherv);
}
//Profiler.StopAndAccumulate("SharpCorners");
//Profiler.Start("HashTable");
// build edge hash table (cell size is just a ballpark guess here...)
edge_hash = new SegmentHashGrid2d <int>(3 * overlapRadius, -1);
foreach (int eid in Graph.EdgeIndices())
{
Segment2d seg = Graph.GetEdgeSegment(eid);
edge_hash.InsertSegment(eid, seg.Center, seg.Extent);
}
if (CollisionGraph.EdgeCount > 0)
{
collision_edge_hash = new SegmentHashGrid2d <int>(3 * CollisionRadius, -1);
foreach (int eid in CollisionGraph.EdgeIndices())
{
Segment2d seg = CollisionGraph.GetEdgeSegment(eid);
collision_edge_hash.InsertSegment(eid, seg.Center, seg.Extent);
}
}
//Profiler.StopAndAccumulate("HashTable");
//Profiler.Start("Erode1");
// Step 1: erode from boundary vertices
List <int> boundaries = new List <int>();
foreach (int vid in Graph.VertexIndices())
{
if (Graph.GetVtxEdgeCount(vid) == 1)
{
boundaries.Add(vid);
}
}
foreach (int vid in boundaries)
{
if (Graph.IsVertex(vid) == false)
{
continue;
}
double dist = MinSelfSegDistance(vid, 2 * dist_thresh);
double collision_dist = MinCollisionConstraintDistance(vid, CollisionRadius);
if (dist < dist_thresh || collision_dist < CollisionRadius)
{
int eid = Graph.GetVtxEdges(vid)[0];
decimate_forward(vid, eid, dist_thresh);
}
}
//Profiler.StopAndAccumulate("Erode1");
//Profiler.Start("OpenAngleSort");
//
// Step 2: find any other possible self-overlaps and erode them.
//
// sort all vertices by opening angle. For any overlap, we can erode
// on either side. Prefer to erode on side with higher curvature.
List <Vector2d> remaining_v = new List <Vector2d>(Graph.MaxVertexID);
foreach (int vid in Graph.VertexIndices())
{
if (is_fixed_v(vid))
{
continue;
}
double open_angle = Graph.OpeningAngle(vid);
if (open_angle == double.MaxValue)
{
continue;
}
remaining_v.Add(new Vector2d(vid, open_angle));
}
remaining_v.Sort((a, b) => { return((a.y < b.y) ? -1 : (a.y > b.y ? 1 : 0)); });
//Profiler.StopAndAccumulate("OpenAngleSort");
//Profiler.Start("Erode2");
// look for overlap vertices. When we find one, erode on both sides.
foreach (Vector2d vinfo in remaining_v)
{
int vid = (int)vinfo.x;
if (Graph.IsVertex(vid) == false)
{
continue;
}
double dist = MinSelfSegDistance(vid, 2 * dist_thresh);
if (dist < dist_thresh)
{
List <int> nbrs = new List <int>(Graph.GetVtxEdges(vid));
foreach (int eid in nbrs)
{
if (Graph.IsEdge(eid)) // may have been decimated!
{
decimate_forward(vid, eid, dist_thresh);
}
}
}
}
//Profiler.StopAndAccumulate("Erode2");
//Profiler.Start("FlatCollapse");
// get rid of extra vertices
r.CollapseFlatVertices(FinalFlatCollapseAngleThreshDeg);
//Profiler.StopAndAccumulate("FlatCollapse");
}
private static DGraph2 CreateMinGraph(DGraph2 input, int NV, out Dictionary <int, List <int> > minEdgePaths, out DVector <double> edgeWeights)
{
/*
* OK, as input we have a graph of our original polygon and a bunch of inserted
* segments ("spans"). Orig polygon segments have gid < 0, and span segments >= 0.
* However between polygon/span junctions, we have an arbitrary # of polygon edges.
* So first step is to simplify these to single-edge "connectors", in new graph MinGraph.
* the [connector-edge, path] mappings (if pathlen > 1) are stored in MinEdgePaths
* We also store a weight for each connector edge in EdgeWeights (just distance for now)
*/
var minGraph = new DGraph2();
minEdgePaths = new Dictionary <int, List <int> >();
edgeWeights = new DVector <double>();
edgeWeights.resize(NV);
BitArray done_edge = new BitArray(input.MaxEdgeID); // we should see each edge twice, this avoids repetition
// vertex map from input graph to MinGraph
int[] MapV = new int[NV];
for (int i = 0; i < NV; ++i)
{
MapV[i] = -1;
}
for (int a = 0; a < NV; ++a)
{
if (input.IsVertex(a) == false || input.IsJunctionVertex(a) == false)
{
continue;
}
if (MapV[a] == -1)
{
MapV[a] = minGraph.AppendVertex(input.GetVertex(a));
}
foreach (int eid in input.VtxEdgesItr(a))
{
if (done_edge[eid])
{
continue;
}
Index2i ev = input.GetEdgeV(eid);
int b = (ev.a == a) ? ev.b : ev.a;
if (input.IsJunctionVertex(b))
{
// if we have junction/juntion connection, we can just copy this edge to MinGraph
if (MapV[b] == -1)
{
MapV[b] = minGraph.AppendVertex(input.GetVertex(b));
}
int gid = input.GetEdgeGroup(eid);
int existing = minGraph.FindEdge(MapV[a], MapV[b]);
if (existing == DMesh3.InvalidID)
{
int new_eid = minGraph.AppendEdge(MapV[a], MapV[b], gid);
double path_len = input.GetEdgeSegment(eid).Length;
edgeWeights.insertAt(path_len, new_eid);
}
else
{
// we may have inserted this edge already in the simplify branch, this happens eg at the
// edge of a circle where the minimal path is between the same vertices as the segment.
// But if this is also a fill edge, we want to treat it that way (determind via positive gid)
if (gid >= 0)
{
minGraph.SetEdgeGroup(existing, gid);
}
}
}
else
{
// not a junction - walk until we find other vtx, and add single edge to MinGraph
List <int> path = DGraph2Util.WalkToNextNonRegularVtx(input, a, eid);
if (path == null || path.Count < 2)
{
throw new Exception("build_min_graph: invalid walk!");
}
int c = path[path.Count - 1];
// it is somehow possible to get loops...
if (c == a)
{
goto skip_this_edge;
}
if (MapV[c] == -1)
{
MapV[c] = minGraph.AppendVertex(input.GetVertex(c));
}
if (minGraph.FindEdge(MapV[a], MapV[c]) == DMesh3.InvalidID)
{
int new_eid = minGraph.AppendEdge(MapV[a], MapV[c], -2);
path.Add(MapV[a]); path.Add(MapV[c]);
minEdgePaths[new_eid] = path;
double path_len = DGraph2Util.PathLength(input, path);
edgeWeights.insertAt(path_len, new_eid);
}
}
skip_this_edge:
done_edge[eid] = true;
}
}
return(minGraph);
}
/// <summary>
/// Assumption is that input graph is a polygon with inserted ray-spans. We want to
/// find a set of paths (ie no junctions) that cover all the spans, and travel between
/// adjacent spans along edges of the input polygon.
/// </summary>
protected DGraph2 BuildPathGraph(DGraph2 input)
{
int NV = input.MaxVertexID;
/*
* OK, as input we have a graph of our original polygon and a bunch of inserted
* segments ("spans"). Orig polygon segments have gid < 0, and span segments >= 0.
* However between polygon/span junctions, we have an arbitrary # of polygon edges.
* So first step is to simplify these to single-edge "connectors", in new graph MinGraph.
* the [connector-edge, path] mappings (if pathlen > 1) are stored in MinEdgePaths
* We also store a weight for each connector edge in EdgeWeights (just distance for now)
*/
DGraph2 MinGraph = new DGraph2();
Dictionary <int, List <int> > MinEdgePaths = new Dictionary <int, List <int> >();
DVector <double> EdgeWeights = new DVector <double>(); EdgeWeights.resize(NV);
BitArray done_edge = new BitArray(input.MaxEdgeID); // we should see each edge twice, this avoids repetition
// vertex map from input graph to MinGraph
int[] MapV = new int[NV];
for (int i = 0; i < NV; ++i)
{
MapV[i] = -1;
}
for (int a = 0; a < NV; ++a)
{
if (input.IsVertex(a) == false || input.IsJunctionVertex(a) == false)
{
continue;
}
if (MapV[a] == -1)
{
MapV[a] = MinGraph.AppendVertex(input.GetVertex(a));
}
foreach (int eid in input.VtxEdgesItr(a))
{
if (done_edge[eid])
{
continue;
}
Index2i ev = input.GetEdgeV(eid);
int b = (ev.a == a) ? ev.b : ev.a;
if (input.IsJunctionVertex(b))
{
// if we have junction/juntion connection, we can just copy this edge to MinGraph
if (MapV[b] == -1)
{
MapV[b] = MinGraph.AppendVertex(input.GetVertex(b));
}
int gid = input.GetEdgeGroup(eid);
int existing = MinGraph.FindEdge(MapV[a], MapV[b]);
if (existing == DMesh3.InvalidID)
{
int new_eid = MinGraph.AppendEdge(MapV[a], MapV[b], gid);
double path_len = input.GetEdgeSegment(eid).Length;
EdgeWeights.insertAt(path_len, new_eid);
}
else
{
// we may have inserted this edge already in the simplify branch, this happens eg at the
// edge of a circle where the minimal path is between the same vertices as the segment.
// But if this is also a fill edge, we want to treat it that way (determind via positive gid)
if (gid >= 0)
{
MinGraph.SetEdgeGroup(existing, gid);
}
}
}
else
{
// not a junction - walk until we find other vtx, and add single edge to MinGraph
List <int> path = DGraph2Util.WalkToNextNonRegularVtx(input, a, eid);
if (path == null || path.Count < 2)
{
throw new Exception("build_min_graph: invalid walk!");
}
int c = path[path.Count - 1];
// it is somehow possible to get loops...
if (c == a)
{
goto skip_this_edge;
}
if (MapV[c] == -1)
{
MapV[c] = MinGraph.AppendVertex(input.GetVertex(c));
}
if (MinGraph.FindEdge(MapV[a], MapV[c]) == DMesh3.InvalidID)
{
int new_eid = MinGraph.AppendEdge(MapV[a], MapV[c], -2);
path.Add(MapV[a]); path.Add(MapV[c]);
MinEdgePaths[new_eid] = path;
double path_len = DGraph2Util.PathLength(input, path);
EdgeWeights.insertAt(path_len, new_eid);
}
}
skip_this_edge:
done_edge[eid] = true;
}
}
// [TODO] filter MinGraph to remove invalid connectors
// - can a connector between two connectors happen? that would be bad.
/// - connector that is too close to paths should be ignored (ie avoid collisions)
/*
* Now that we have MinGraph, we can easily walk between the spans because
* they are connected by at most one edge. To find a sequence of spans, we
* pick one to start, then walk along connectors, discarding as we go,
* so that we don't pass through these vertices again. Repeat until
* there are no remaining spans.
*/
// [TODO]
// do we actually have to delete from MinGraph? this prevents us from doing
// certain things, like trying different options. Maybe could use a hash for
// remaining vertices and edges instead?
DGraph2 PathGraph = new DGraph2();
Vector2d sortAxis = Vector2d.FromAngleDeg(AngleDeg).Perp;
while (true)
{
// find most extreme edge to start at
// [TODO] could use segment gid here as we set them based on insertion span!
// [TODO] could use a smarter metric? like, closest to previous last endpoint? Using
// extrema like this tends to produce longest spans, though...
double min_dot = double.MaxValue;
int start_eid = -1;
foreach (int eid in MinGraph.EdgeIndices())
{
Index3i evg = MinGraph.GetEdge(eid);
if (evg.c >= 0)
{
double dot = MinGraph.GetVertex(evg.a).Dot(sortAxis);
if (dot < min_dot)
{
min_dot = dot;
start_eid = eid;
}
}
}
if (start_eid == -1)
{
break; // if we could not find a start edge, we must be done!
}
// ok now walk forward through connectors and spans. We do this in
// connector/span pairs - we are always at an end-of-span point, and
// we pick a next-connector and then a next-span.
// We need to keep track of vertices in both the pathgraph and mingraph,
// these are the "new" and "old" vertices
Index3i start_evg = MinGraph.GetEdge(start_eid);
int new_start = PathGraph.AppendVertex(MinGraph.GetVertex(start_evg.a));
int new_prev = PathGraph.AppendVertex(MinGraph.GetVertex(start_evg.b));
int old_prev = start_evg.b;
PathGraph.AppendEdge(new_start, new_prev, start_evg.c);
MinGraph.RemoveVertex(start_evg.a, true);
while (true)
{
// choose next connector edge, outgoing from current vtx
int connector_e = -1;
foreach (int eid in MinGraph.VtxEdgesItr(old_prev))
{
Index3i evg = MinGraph.GetEdge(eid);
if (evg.c >= 0)
{
continue; // what??
}
if (connector_e == -1 || EdgeWeights[connector_e] > EdgeWeights[eid])
{
connector_e = eid;
}
}
if (connector_e == -1)
{
break;
}
// find the vertex at end of connector
Index3i conn_evg = MinGraph.GetEdge(connector_e);
int old_conn_v = (conn_evg.a == old_prev) ? conn_evg.b : conn_evg.a;
// can never look at prev vertex again, or any edges connected to it
// [TODO] are we sure none of these edges are unused spans?!?
MinGraph.RemoveVertex(old_prev, true);
// now find outgoing span edge
int span_e = -1;
foreach (int eid in MinGraph.VtxEdgesItr(old_conn_v))
{
Index3i evg = MinGraph.GetEdge(eid);
if (evg.c >= 0)
{
span_e = eid;
break;
}
}
if (span_e == -1)
{
break; // disaster!
}
// find vertex at far end of span
Index3i span_evg = MinGraph.GetEdge(span_e);
int old_span_v = (span_evg.a == old_conn_v) ? span_evg.b : span_evg.a;
// ok we want to insert the connectr to the path graph, however the
// connector might actually have come from a more complex path in the input graph.
int new_conn_next = -1;
if (MinEdgePaths.ContainsKey(connector_e))
{
// complex path case. Note that the order [old_prev, old_conn_v] may be the opposite
// of the order in the pathv. But above, we appended the [a,b] edge order to the pathv.
// So we can check if we need to flip, but this means we need to be a bit clever w/ indices...
List <int> pathv = MinEdgePaths[connector_e];
int N = pathv.Count;
int path_prev = new_prev;
int k = 1;
if (pathv[N - 2] != old_prev) // case where order flipped
{
pathv.Reverse();
k = 3;
}
else
{
N = N - 2;
}
while (k < N)
{
int path_next = PathGraph.AppendVertex(input.GetVertex(pathv[k]));
PathGraph.AppendEdge(path_prev, path_next);
path_prev = path_next;
k++;
}
new_conn_next = path_prev;
}
else
{
new_conn_next = PathGraph.AppendVertex(MinGraph.GetVertex(old_conn_v));
PathGraph.AppendEdge(new_prev, new_conn_next, conn_evg.c);
}
// add span to path
int new_fill_next = PathGraph.AppendVertex(MinGraph.GetVertex(old_span_v));
PathGraph.AppendEdge(new_conn_next, new_fill_next, span_evg.c);
// remove the connector vertex
MinGraph.RemoveVertex(old_conn_v, true);
// next iter starts at far end of span
new_prev = new_fill_next;
old_prev = old_span_v;
}
sortAxis = -sortAxis;
}
// for testing/debugging
//SVGWriter writer = new SVGWriter();
////writer.AddGraph(input, SVGWriter.Style.Outline("blue", 0.1f));
//writer.AddGraph(MinGraph, SVGWriter.Style.Outline("red", 0.1f));
////foreach ( int eid in MinGraph.EdgeIndices() ) {
//// if ( MinGraph.GetEdgeGroup(eid) >= 0 ) writer.AddLine(MinGraph.GetEdgeSegment(eid), SVGWriter.Style.Outline("green", 0.07f));
////}
////writer.AddGraph(MinGraph, SVGWriter.Style.Outline("black", 0.03f));
//writer.AddGraph(PathGraph, SVGWriter.Style.Outline("black", 0.03f));
//foreach (int vid in PathGraph.VertexIndices()) {
// if (PathGraph.IsBoundaryVertex(vid))
// writer.AddCircle(new Circle2d(PathGraph.GetVertex(vid), 0.5f), SVGWriter.Style.Outline("blue", 0.03f));
//}
////writer.AddGraph(IntervalGraph, SVGWriter.Style.Outline("black", 0.03f));
//writer.Write("c:\\scratch\\MIN_GRAPH.svg");
return(PathGraph);
}
// join disconnected vertices within distance threshold. Use point-hashtable to make this faster.
protected int JoinInTolerance_Parallel_Cache(DGraph2 graph, double fMergeDist)
{
double mergeSqr = fMergeDist * fMergeDist;
int NV = graph.MaxVertexID;
if (collapse_cache.size < NV)
{
collapse_cache.resize(NV);
}
gParallel.ForEach(Interval1i.Range(NV), (a) =>
{
collapse_cache[a] = new Vector2d(-1, double.MaxValue);
if (!graph.IsVertex(a))
{
return;
}
Vector2d va = graph.GetVertex(a);
KeyValuePair <int, double> found =
graph_cache.FindNearestInRadius(va, mergeSqr,
(b) => { return(va.DistanceSquared(graph.GetVertex(b))); },
(b) => { return(b <= a || (graph.FindEdge(a, b) != DGraph2.InvalidID)); });
if (found.Key != -1)
{
collapse_cache[a] = new Vector2d(found.Key, found.Value);
}
});
// [TODO] sort
int merged = 0;
for (int a = 0; a < NV; ++a)
{
if (collapse_cache[a].x == -1)
{
continue;
}
int bNearest = (int)collapse_cache[a].x;
if (!graph.IsVertex(bNearest))
{
continue;
}
Vector2d pos_a = graph.GetVertex(a);
Vector2d pos_bNearest = graph.GetVertex(bNearest);
/*int eid = */
graph.AppendEdge(a, bNearest);
DGraph2.EdgeCollapseInfo collapseInfo;
graph.CollapseEdge(bNearest, a, out collapseInfo);
graph_cache.RemovePointUnsafe(a, pos_a);
last_step_size[a] = 0;
graph_cache.UpdatePointUnsafe(bNearest, pos_bNearest, graph.GetVertex(bNearest));
collapse_cache[bNearest] = new Vector2d(-1, double.MaxValue);
merged++;
}
return(merged);
}
// join disconnected vertices within distance threshold
protected int JoinInTolerance_Parallel(DGraph2 graph, double fMergeDist)
{
double mergeSqr = fMergeDist * fMergeDist;
int NV = graph.MaxVertexID;
if (collapse_cache.size < NV)
{
collapse_cache.resize(NV);
}
gParallel.ForEach(Interval1i.Range(NV), (a) =>
{
collapse_cache[a] = new Vector2d(-1, double.MaxValue);
if (!graph.IsVertex(a))
{
return;
}
Vector2d va = graph.GetVertex(a);
int bNearest = -1;
double nearDistSqr = double.MaxValue;
for (int b = a + 1; b < NV; ++b)
{
if (b == a || graph.IsVertex(b) == false)
{
continue;
}
double distsqr = va.DistanceSquared(graph.GetVertex(b));
if (distsqr < mergeSqr && distsqr < nearDistSqr)
{
if (graph.FindEdge(a, b) == DGraph2.InvalidID)
{
nearDistSqr = distsqr;
bNearest = b;
}
}
}
if (bNearest != -1)
{
collapse_cache[a] = new Vector2d(bNearest, nearDistSqr);
}
});
// [TODO] sort
int merged = 0;
for (int a = 0; a < NV; ++a)
{
if (collapse_cache[a].x == -1)
{
continue;
}
int bNearest = (int)collapse_cache[a].x;
Vector2d pos_a = graph.GetVertex(a);
Vector2d pos_bNearest = graph.GetVertex(bNearest);
/*int eid = */
graph.AppendEdge(a, bNearest);
DGraph2.EdgeCollapseInfo collapseInfo;
graph.CollapseEdge(bNearest, a, out collapseInfo);
graph_cache.RemovePointUnsafe(a, pos_a);
last_step_size[a] = 0;
graph_cache.UpdatePointUnsafe(bNearest, pos_bNearest, graph.GetVertex(bNearest));
merged++;
}
return(merged);
}
// smooth vertices, but don't move further than max_move
protected void smooth_pass(DGraph2 graph, int passes, double smooth_alpha, double max_move)
{
double max_move_sqr = max_move * max_move;
int NV = graph.MaxVertexID;
DVector <Vector2d> smoothedV = offset_cache;
if (smoothedV.size < NV)
{
smoothedV.resize(NV);
}
if (position_cache.size < NV)
{
position_cache.resize(NV);
}
for (int pi = 0; pi < passes; ++pi)
{
gParallel.ForEach(Interval1i.Range(NV), (vid) =>
{
if (!graph.IsVertex(vid))
{
return;
}
Vector2d v = graph.GetVertex(vid);
Vector2d c = Vector2d.Zero;
int n = 0;
foreach (int vnbr in graph.VtxVerticesItr(vid))
{
c += graph.GetVertex(vnbr);
n++;
}
if (n >= 2)
{
c /= n;
Vector2d dv = (smooth_alpha) * (c - v);
if (dv.LengthSquared > max_move_sqr)
{
/*double d = */
dv.Normalize();
dv *= max_move;
}
v += dv;
}
smoothedV[vid] = v;
});
if (pi == 0)
{
for (int vid = 0; vid < NV; ++vid)
{
if (graph.IsVertex(vid))
{
position_cache[vid] = graph.GetVertex(vid);
graph.SetVertex(vid, smoothedV[vid]);
}
}
}
else
{
for (int vid = 0; vid < NV; ++vid)
{
if (graph.IsVertex(vid))
{
graph.SetVertex(vid, smoothedV[vid]);
}
}
}
}
for (int vid = 0; vid < NV; ++vid)
{
if (graph.IsVertex(vid))
{
graph_cache.UpdatePointUnsafe(vid, position_cache[vid], smoothedV[vid]);
}
}
}