public static void smooth_pass(DGraph2 graph, float alpha, Vector2d[] newPos)
{
foreach (int vid in graph.VertexIndices())
{
Vector2d v = graph.GetVertex(vid);
bool isvalid;
Vector2d l = DGraph2Util.VertexLaplacian(graph, vid, out isvalid);
v += alpha * l;
newPos[vid] = v;
}
foreach (int vid in graph.VertexIndices())
{
graph.SetVertex(vid, newPos[vid]);
}
}
public static DGraph2 perturb_fill_2(DGraph2 graphIn, GeneralPolygon2d bounds, double waveWidth, double stepSize)
{
DGraph2Util.Curves curves = DGraph2Util.ExtractCurves(graphIn);
Polygon2d poly = curves.Loops[0];
GeneralPolygon2dBoxTree gpTree = new GeneralPolygon2dBoxTree(bounds);
Polygon2dBoxTree outerTree = new Polygon2dBoxTree(bounds.Outer);
Polygon2dBoxTree innerTree = new Polygon2dBoxTree(bounds.Holes[0]);
DGraph2 graph = new DGraph2();
graph.EnableVertexColors(Vector3f.Zero);
graph.AppendPolygon(poly);
DGraph2Resampler resampler = new DGraph2Resampler(graph);
resampler.CollapseToMinEdgeLength(waveWidth);
if (graph.VertexCount % 2 != 0)
{
// TODO smallest edge
Index2i ev = graph.GetEdgeV(graph.EdgeIndices().First());
DGraph2.EdgeCollapseInfo cinfo;
graph.CollapseEdge(ev.a, ev.b, out cinfo);
}
// move to borders
int startv = graph.VertexIndices().First();
int eid = graph.VtxEdgesItr(startv).First();
int curv = startv;
bool outer = true;
do
{
Polygon2dBoxTree use_tree = (outer) ? outerTree : innerTree;
outer = !outer;
graph.SetVertex(curv, use_tree.NearestPoint(graph.GetVertex(curv)));
Index2i next = DGraph2Util.NextEdgeAndVtx(eid, curv, graph);
eid = next.a;
curv = next.b;
} while (curv != startv);
return(graph);
}
public static DGraph2 perturb_fill(DGraph2 graphIn, GeneralPolygon2d bounds, double waveWidth, double stepSize)
{
DGraph2Util.Curves curves = DGraph2Util.ExtractCurves(graphIn);
Polygon2d poly = curves.Loops[0];
GeneralPolygon2dBoxTree gpTree = new GeneralPolygon2dBoxTree(bounds);
Polygon2dBoxTree outerTree = new Polygon2dBoxTree(bounds.Outer);
Polygon2dBoxTree innerTree = new Polygon2dBoxTree(bounds.Holes[0]);
DGraph2 graph = new DGraph2();
graph.EnableVertexColors(Vector3f.Zero);
double len = poly.Perimeter;
int waves = (int)(len / waveWidth);
double lenScale = len / (MathUtil.TwoPI * waves);
double accum_len = 0;
int prev_vid = -1, start_vid = -1;
int N = poly.VertexCount;
for (int k = 0; k < N; ++k)
{
double t = accum_len / lenScale;
t = Math.Cos(t);
//Vector2d normal = poly.GetNormal(k);
Vector2d normal = poly[k].Normalized;
int vid = graph.AppendVertex(poly[k], new Vector3f(t, normal.x, normal.y));
if (prev_vid != -1)
{
graph.AppendEdge(prev_vid, vid);
accum_len += graph.GetVertex(prev_vid).Distance(graph.GetVertex(vid));
}
else
{
start_vid = vid;
}
prev_vid = vid;
}
graph.AppendEdge(prev_vid, start_vid);
Vector2d[] newPos = new Vector2d[graph.MaxVertexID];
for (int k = 0; k < 10; ++k)
{
smooth_pass(graph, 0.5f, newPos);
}
for (int k = 0; k < 20; ++k)
{
foreach (int vid in graph.VertexIndices())
{
Vector2d v = graph.GetVertex(vid);
Vector3f c = graph.GetVertexColor(vid);
float t = c.x;
Vector2d n = new Vector2d(c.y, c.z);
if (k == 0 || Math.Abs(t) > 0.9)
{
v += t * stepSize * n;
if (!bounds.Contains(v))
{
v = gpTree.NearestPoint(v);
}
}
newPos[vid] = v;
}
foreach (int vid in graph.VertexIndices())
{
graph.SetVertex(vid, newPos[vid]);
}
for (int j = 0; j < 5; ++j)
{
smooth_pass(graph, 0.1f, newPos);
}
}
return(graph);
}
protected DGraph2 compute_result(GeneralPolygon2d poly, double fOffset, double fTargetSpacing)
{
double dt = fTargetSpacing / 2;
int nSteps = (int)(Math.Abs(fOffset) / dt);
if (nSteps < 10)
{
nSteps = 10;
}
// [TODO] we could cache this over multiple runs...
DGraph2 graph = new DGraph2();
graph.AppendPolygon(poly.Outer);
foreach (var h in poly.Holes)
{
graph.AppendPolygon(h);
}
// resample to nbrhood of target spacing
SplitToMaxEdgeLength(graph, fTargetSpacing * 1.33);
// build bvtree for polygon
if (poly_tree == null || poly_tree.Polygon != poly)
{
poly_tree = new GeneralPolygon2dBoxTree(poly);
}
// allocate and resize caches as necessary
if (offset_cache == null)
{
offset_cache = new DVector <Vector2d>();
}
if (offset_cache.size < graph.VertexCount)
{
offset_cache.resize(graph.VertexCount * 2);
}
if (position_cache == null)
{
position_cache = new DVector <Vector2d>();
}
if (position_cache.size < graph.VertexCount)
{
position_cache.resize(graph.VertexCount * 2);
}
if (collapse_cache == null)
{
collapse_cache = new DVector <Vector2d>();
}
if (collapse_cache.size < graph.VertexCount)
{
collapse_cache.resize(graph.VertexCount * 2);
}
if (last_step_size == null)
{
last_step_size = new DVector <double>();
}
if (last_step_size.size < graph.VertexCount)
{
last_step_size.resize(graph.VertexCount * 2);
}
// insert all points into a hashgrid. We will dynamically update this grid as we proceed
// [TODO] is this a good bounds-size?
graph_cache = new PointHashGrid2d <int>(poly.Bounds.MaxDim / 64, -1);
foreach (int vid in graph.VertexIndices())
{
graph_cache.InsertPoint(vid, graph.GetVertex(vid));
}
LocalProfiler p = (_enable_profiling) ? new LocalProfiler() : null;
if (_enable_profiling)
{
p.Start("All");
}
// run a bunch of steps. The last few are tuning steps where we use half-steps,
// which seems to help?
int TUNE_STEPS = nSteps / 2;
nSteps *= 2;
for (int i = 0; i < nSteps; ++i)
{
if (_enable_profiling)
{
p.Start("offset");
}
double step_dt = dt;
if (i > nSteps - TUNE_STEPS)
{
step_dt = dt / 2;
}
if (last_step_size.size < graph.VertexCount)
{
last_step_size.resize(graph.VertexCount + 256);
}
// Each vertex steps forward. In fact we compute two steps and average them,
// this helps w/ convergence. To produce more accurate convergence, we track
// the size of the actual step we took at the last round, and use that the next
// time. (The assumption is that the steps will get smaller at the target distance).
gParallel.ForEach(graph.VertexIndices(), (vid) =>
{
// use tracked step size if we have it
double use_dt = step_dt;
if (last_step_size[vid] > 0)
{
use_dt = Math.Min(last_step_size[vid], dt);
}
Vector2d cur_pos = graph.GetVertex(vid);
double err, err_2;
// take two sequential steps and average them. this vastly improves convergence.
Vector2d new_pos = compute_offset_step(cur_pos, poly, fOffset, use_dt, out err);
Vector2d new_pos_2 = compute_offset_step(new_pos, poly, fOffset, use_dt, out err_2);
// weighted blend of points - prefer one w/ smaller error
//double w = 1.0 / Math.Max(err, MathUtil.ZeroTolerancef);
//double w_2 = 1.0 / Math.Max(err_2, MathUtil.ZeroTolerancef);
//new_pos = w * new_pos + w_2 * new_pos_2;
//new_pos /= (w + w_2);
// [RMS] weighted blend doesn't seem to matter if we are tracking per-vertex step size.
new_pos = Vector2d.Lerp(new_pos, new_pos_2, 0.5);
// keep track of actual step we are taking and use that next iteration
double actual_step_dist = cur_pos.Distance(new_pos);
if (last_step_size[vid] == 0)
{
last_step_size[vid] = actual_step_dist;
}
else
{
last_step_size[vid] = (0.75) * last_step_size[vid] + (0.25) * actual_step_dist;
}
// update point in hashtable and graph
graph_cache.UpdatePoint(vid, cur_pos, new_pos);
graph.SetVertex(vid, new_pos);
});
if (_enable_profiling)
{
p.StopAndAccumulate("offset"); p.Start("smooth");
}
// Do a smoothing pass, but for the last few steps, reduce smoothing
// (otherwise it pulls away from target solution)
int smooth_steps = 5; double smooth_alpha = 0.75;
if (i > nSteps - TUNE_STEPS)
{
smooth_steps = 2; smooth_alpha = 0.25;
}
smooth_pass(graph, smooth_steps, smooth_alpha, fTargetSpacing / 2);
if (_enable_profiling)
{
p.StopAndAccumulate("smooth"); p.Start("join");
}
// if a vertex is within targetSpacing from another vertex, and they are
// not geodesically connected in the graph, them we merge/weld them together.
int joined = 0;
do
{
//joined = JoinInTolerance(graph, fMergeThresh);
//joined = JoinInTolerance_Parallel(graph, fMergeThresh);
joined = JoinInTolerance_Parallel_Cache(graph, fTargetSpacing);
} while (joined > 0);
if (_enable_profiling)
{
p.StopAndAccumulate("join"); p.Start("refine");
}
// now do a pass of graph refinement, to collapse short edges and split long ones
CollapseToMinEdgeLength(graph, fTargetSpacing * 0.66f);
SplitToMaxEdgeLength(graph, fTargetSpacing * 1.33);
if (_enable_profiling)
{
p.StopAndAccumulate("refine");
}
}
if (_enable_profiling)
{
p.Stop("All");
System.Console.WriteLine("All: " + p.Elapsed("All"));
System.Console.WriteLine(p.AllAccumulatedTimes());
}
// get rid of junction vertices, if requested
if (DisconnectGraphJunctions)
{
DGraph2Util.DisconnectJunctions(graph);
}
return(graph);
}
// collapse edges shorter than fMinLen
// NOTE: basically the same as DGraph2Resampler.CollapseToMinEdgeLength, but updates
// our internal caches. Could we merge somehow?
protected void CollapseToMinEdgeLength(DGraph2 graph, 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;
}
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;
}
Vector2d remove_pos = graph.GetVertex(remove);
Vector2d keep_pos = graph.GetVertex(keep);
DGraph2.EdgeCollapseInfo collapseInfo;
if (graph.CollapseEdge(keep, remove, out collapseInfo) == MeshResult.Ok)
{
graph_cache.RemovePointUnsafe(collapseInfo.vRemoved, remove_pos);
last_step_size[collapseInfo.vRemoved] = 0;
graph_cache.UpdatePointUnsafe(collapseInfo.vKept, keep_pos, newPos);
graph.SetVertex(collapseInfo.vKept, newPos);
done = false;
}
}
} while (cur_eid != 0);
}
}
// 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]);
}
}
}
public static void test_splitter()
{
Polygon2d poly = Polygon2d.MakeCircle(1000, 16);
Polygon2d hole = Polygon2d.MakeCircle(500, 32); hole.Reverse();
GeneralPolygon2d gpoly = new GeneralPolygon2d(poly);
gpoly.AddHole(hole);
//Polygon2d poly = Polygon2d.MakeRectangle(Vector2d.Zero, 1000, 1000);
DGraph2 graph = new DGraph2();
graph.AppendPolygon(gpoly);
System.Console.WriteLine("Stats before: verts {0} edges {1} ", graph.VertexCount, graph.EdgeCount);
GraphSplitter2d splitter = new GraphSplitter2d(graph);
splitter.InsideTestF = gpoly.Contains;
for (int k = 0; k < poly.VertexCount; ++k)
{
Line2d line = new Line2d(poly[k], Vector2d.AxisY);
splitter.InsertLine(line);
}
System.Console.WriteLine("Stats after 1: verts {0} edges {1} ", graph.VertexCount, graph.EdgeCount);
for (int k = 0; k < poly.VertexCount; ++k)
{
Line2d line = new Line2d(poly[k], Vector2d.AxisX);
splitter.InsertLine(line);
}
for (int k = 0; k < poly.VertexCount; ++k)
{
Line2d line = new Line2d(poly[k], Vector2d.One.Normalized);
splitter.InsertLine(line);
}
for (int k = 0; k < poly.VertexCount; ++k)
{
Line2d line = new Line2d(poly[k], new Vector2d(1, -1).Normalized);
splitter.InsertLine(line);
}
System.Console.WriteLine("Stats after: verts {0} edges {1} ", graph.VertexCount, graph.EdgeCount);
Random r = new Random(31337);
foreach (int vid in graph.VertexIndices())
{
Vector2d v = graph.GetVertex(vid);
v += TestUtil.RandomPoints2(1, r, v, 25)[0];
graph.SetVertex(vid, v);
}
SVGWriter svg = new SVGWriter();
svg.AddGraph(graph);
var vtx_style = SVGWriter.Style.Outline("red", 1.0f);
foreach (int vid in graph.VertexIndices())
{
Vector2d v = graph.GetVertex(vid);
svg.AddCircle(new Circle2d(v, 10), vtx_style);
}
svg.Write(TestUtil.GetTestOutputPath("split_graph.svg"));
}
