void optimize_mesh(DMesh3 mesh)
{
Reducer reducer = new Reducer(mesh);
MeshConstraints constraints = new MeshConstraints();
MeshConstraintUtil.FixAllBoundaryEdges(constraints, mesh);
reducer.SetExternalConstraints(constraints);
reducer.ReduceToTriangleCount(1);
Vector3d a, b, c, d;
a = b = c = d = Vector3d.Zero;
bool done = false;
while (!done)
{
done = true;
for (int eid = 0; eid < mesh.MaxEdgeID; ++eid)
{
if (mesh.IsEdge(eid) == false)
{
continue;
}
Index4i evt = mesh.GetEdge(eid);
if (evt.d == DMesh3.InvalidID)
{
continue;
}
a = mesh.GetVertex(evt.a); b = mesh.GetVertex(evt.b);
Index2i ov = mesh.GetEdgeOpposingV(eid);
c = mesh.GetVertex(ov.a); d = mesh.GetVertex(ov.b);
if (c.DistanceSquared(d) > a.DistanceSquared(b))
{
continue;
}
if (MeshUtil.CheckIfEdgeFlipCreatesFlip(mesh, eid))
{
continue;
}
DMesh3.EdgeFlipInfo flipInfo;
if (mesh.FlipEdge(eid, out flipInfo) == MeshResult.Ok)
{
done = false;
}
}
}
}
public bool Apply()
{
// do a simple fill
SimpleHoleFiller simplefill = new SimpleHoleFiller(Mesh, FillLoop);
int fill_gid = Mesh.AllocateTriangleGroup();
bool bOK = simplefill.Fill(fill_gid);
if (bOK == false)
{
return(false);
}
if (FillLoop.Vertices.Length <= 3)
{
FillTriangles = simplefill.NewTriangles;
FillVertices = new int[0];
return(true);
}
// extract the simple fill mesh as a submesh, via RegionOperator, so we can backsub later
HashSet <int> intial_fill_tris = new HashSet <int>(simplefill.NewTriangles);
regionop = new RegionOperator(Mesh, simplefill.NewTriangles,
(submesh) => { submesh.ComputeTriMaps = true; });
fillmesh = regionop.Region.SubMesh;
// for each boundary vertex, compute the exterior angle sum
// we will use this to compute gaussian curvature later
boundaryv = new HashSet <int>(MeshIterators.BoundaryEdgeVertices(fillmesh));
exterior_angle_sums = new Dictionary <int, double>();
if (IgnoreBoundaryTriangles == false)
{
foreach (int sub_vid in boundaryv)
{
double angle_sum = 0;
int base_vid = regionop.Region.MapVertexToBaseMesh(sub_vid);
foreach (int tid in regionop.BaseMesh.VtxTrianglesItr(base_vid))
{
if (intial_fill_tris.Contains(tid) == false)
{
Index3i et = regionop.BaseMesh.GetTriangle(tid);
int idx = IndexUtil.find_tri_index(base_vid, ref et);
angle_sum += regionop.BaseMesh.GetTriInternalAngleR(tid, idx);
}
}
exterior_angle_sums[sub_vid] = angle_sum;
}
}
// try to guess a reasonable edge length that will give us enough geometry to work with in simplify pass
double loop_mine, loop_maxe, loop_avge, fill_mine, fill_maxe, fill_avge;
MeshQueries.EdgeLengthStatsFromEdges(Mesh, FillLoop.Edges, out loop_mine, out loop_maxe, out loop_avge);
MeshQueries.EdgeLengthStats(fillmesh, out fill_mine, out fill_maxe, out fill_avge);
double remesh_target_len = loop_avge;
if (fill_maxe / remesh_target_len > 10)
{
remesh_target_len = fill_maxe / 10;
}
//double remesh_target_len = Math.Min(loop_avge, fill_avge / 4);
// remesh up to target edge length, ideally gives us some triangles to work with
RemesherPro remesh1 = new RemesherPro(fillmesh);
remesh1.SmoothSpeedT = 1.0;
MeshConstraintUtil.FixAllBoundaryEdges(remesh1);
//remesh1.SetTargetEdgeLength(remesh_target_len / 2); // would this speed things up? on large regions?
//remesh1.FastestRemesh();
remesh1.SetTargetEdgeLength(remesh_target_len);
remesh1.FastestRemesh();
/*
* first round: collapse to minimal mesh, while flipping to try to
* get to ballpark minimal mesh. We stop these passes as soon as
* we have done two rounds where we couldn't do another collapse
*
* This is the most unstable part of the algorithm because there
* are strong ordering effects. maybe we could sort the edges somehow??
*/
int zero_collapse_passes = 0;
int collapse_passes = 0;
while (collapse_passes++ < 20 && zero_collapse_passes < 2)
{
// collapse pass
int NE = fillmesh.MaxEdgeID;
int collapses = 0;
for (int ei = 0; ei < NE; ++ei)
{
if (fillmesh.IsEdge(ei) == false || fillmesh.IsBoundaryEdge(ei))
{
continue;
}
Index2i ev = fillmesh.GetEdgeV(ei);
bool a_bdry = boundaryv.Contains(ev.a), b_bdry = boundaryv.Contains(ev.b);
if (a_bdry && b_bdry)
{
continue;
}
int keepv = (a_bdry) ? ev.a : ev.b;
int otherv = (keepv == ev.a) ? ev.b : ev.a;
Vector3d newv = fillmesh.GetVertex(keepv);
if (MeshUtil.CheckIfCollapseCreatesFlip(fillmesh, ei, newv))
{
continue;
}
DMesh3.EdgeCollapseInfo info;
MeshResult result = fillmesh.CollapseEdge(keepv, otherv, out info);
if (result == MeshResult.Ok)
{
collapses++;
}
}
if (collapses == 0)
{
zero_collapse_passes++;
}
else
{
zero_collapse_passes = 0;
}
// flip pass. we flip in these cases:
// 1) if angle between current triangles is too small (slightly more than 90 degrees, currently)
// 2) if angle between flipped triangles is smaller than between current triangles
// 3) if flipped edge length is shorter *and* such a flip won't flip the normal
NE = fillmesh.MaxEdgeID;
Vector3d n1, n2, on1, on2;
for (int ei = 0; ei < NE; ++ei)
{
if (fillmesh.IsEdge(ei) == false || fillmesh.IsBoundaryEdge(ei))
{
continue;
}
bool do_flip = false;
Index2i ev = fillmesh.GetEdgeV(ei);
MeshUtil.GetEdgeFlipNormals(fillmesh, ei, out n1, out n2, out on1, out on2);
double dot_cur = n1.Dot(n2);
double dot_flip = on1.Dot(on2);
if (n1.Dot(n2) < 0.1 || dot_flip > dot_cur + MathUtil.Epsilonf)
{
do_flip = true;
}
if (do_flip == false)
{
Index2i otherv = fillmesh.GetEdgeOpposingV(ei);
double len_e = fillmesh.GetVertex(ev.a).Distance(fillmesh.GetVertex(ev.b));
double len_flip = fillmesh.GetVertex(otherv.a).Distance(fillmesh.GetVertex(otherv.b));
if (len_flip < len_e)
{
if (MeshUtil.CheckIfEdgeFlipCreatesFlip(fillmesh, ei) == false)
{
do_flip = true;
}
}
}
if (do_flip)
{
DMesh3.EdgeFlipInfo info;
MeshResult result = fillmesh.FlipEdge(ei, out info);
}
}
}
// Sometimes, for some reason, we have a remaining interior vertex (have only ever seen one?)
// Try to force removal of such vertices, even if it makes ugly mesh
remove_remaining_interior_verts();
// enable/disable passes.
bool DO_FLATTER_PASS = true;
bool DO_CURVATURE_PASS = OptimizeDevelopability && true;
bool DO_AREA_PASS = OptimizeDevelopability && OptimizeTriangles && true;
/*
* In this pass we repeat the flipping iterations from the previous pass.
*
* Note that because of the always-flip-if-dot-is-small case (commented),
* this pass will frequently not converge, as some number of edges will
* be able to flip back and forth (because neither has large enough dot).
* This is not ideal, but also, if we remove this behavior, then we
* generally get worse fills. This case basically introduces a sort of
* randomization factor that lets us escape local minima...
*
*/
HashSet <int> remaining_edges = new HashSet <int>(fillmesh.EdgeIndices());
HashSet <int> updated_edges = new HashSet <int>();
int flatter_passes = 0;
int zero_flips_passes = 0;
while (flatter_passes++ < 40 && zero_flips_passes < 2 && remaining_edges.Count() > 0 && DO_FLATTER_PASS)
{
zero_flips_passes++;
foreach (int ei in remaining_edges)
{
if (fillmesh.IsBoundaryEdge(ei))
{
continue;
}
bool do_flip = false;
Index2i ev = fillmesh.GetEdgeV(ei);
Vector3d n1, n2, on1, on2;
MeshUtil.GetEdgeFlipNormals(fillmesh, ei, out n1, out n2, out on1, out on2);
double dot_cur = n1.Dot(n2);
double dot_flip = on1.Dot(on2);
if (flatter_passes < 20 && dot_cur < 0.1) // this check causes oscillatory behavior
{
do_flip = true;
}
if (dot_flip > dot_cur + MathUtil.Epsilonf)
{
do_flip = true;
}
if (do_flip)
{
DMesh3.EdgeFlipInfo info;
MeshResult result = fillmesh.FlipEdge(ei, out info);
if (result == MeshResult.Ok)
{
zero_flips_passes = 0;
add_all_edges(ei, updated_edges);
}
}
}
var tmp = remaining_edges;
remaining_edges = updated_edges;
updated_edges = tmp; updated_edges.Clear();
}
int curvature_passes = 0;
if (DO_CURVATURE_PASS)
{
curvatures = new double[fillmesh.MaxVertexID];
foreach (int vid in fillmesh.VertexIndices())
{
update_curvature(vid);
}
remaining_edges = new HashSet <int>(fillmesh.EdgeIndices());
updated_edges = new HashSet <int>();
/*
* In this pass we try to minimize gaussian curvature at all the vertices.
* This will recover sharp edges, etc, and do lots of good stuff.
* However, this pass will not make much progress if we are not already
* relatively close to a minimal mesh, so it really relies on the previous
* passes getting us in the ballpark.
*/
while (curvature_passes++ < 40 && remaining_edges.Count() > 0 && DO_CURVATURE_PASS)
{
foreach (int ei in remaining_edges)
{
if (fillmesh.IsBoundaryEdge(ei))
{
continue;
}
Index2i ev = fillmesh.GetEdgeV(ei);
Index2i ov = fillmesh.GetEdgeOpposingV(ei);
int find_other = fillmesh.FindEdge(ov.a, ov.b);
if (find_other != DMesh3.InvalidID)
{
continue;
}
double total_curv_cur = curvature_metric_cached(ev.a, ev.b, ov.a, ov.b);
if (total_curv_cur < MathUtil.ZeroTolerancef)
{
continue;
}
DMesh3.EdgeFlipInfo info;
MeshResult result = fillmesh.FlipEdge(ei, out info);
if (result != MeshResult.Ok)
{
continue;
}
double total_curv_flip = curvature_metric_eval(ev.a, ev.b, ov.a, ov.b);
bool keep_flip = total_curv_flip < total_curv_cur - MathUtil.ZeroTolerancef;
if (keep_flip == false)
{
result = fillmesh.FlipEdge(ei, out info);
}
else
{
update_curvature(ev.a); update_curvature(ev.b);
update_curvature(ov.a); update_curvature(ov.b);
add_all_edges(ei, updated_edges);
}
}
var tmp = remaining_edges;
remaining_edges = updated_edges;
updated_edges = tmp; updated_edges.Clear();
}
}
//System.Console.WriteLine("collapse {0} flatter {1} curvature {2}", collapse_passes, flatter_passes, curvature_passes);
/*
* In this final pass, we try to improve triangle quality. We flip if
* the flipped triangles have better total aspect ratio, and the
* curvature doesn't change **too** much. The .DevelopabilityTolerance
* parameter determines what is "too much" curvature change.
*/
if (DO_AREA_PASS)
{
remaining_edges = new HashSet <int>(fillmesh.EdgeIndices());
updated_edges = new HashSet <int>();
int area_passes = 0;
while (remaining_edges.Count() > 0 && area_passes < 20)
{
area_passes++;
foreach (int ei in remaining_edges)
{
if (fillmesh.IsBoundaryEdge(ei))
{
continue;
}
Index2i ev = fillmesh.GetEdgeV(ei);
Index2i ov = fillmesh.GetEdgeOpposingV(ei);
int find_other = fillmesh.FindEdge(ov.a, ov.b);
if (find_other != DMesh3.InvalidID)
{
continue;
}
double total_curv_cur = curvature_metric_cached(ev.a, ev.b, ov.a, ov.b);
double a = aspect_metric(ei);
if (a > 1)
{
continue;
}
DMesh3.EdgeFlipInfo info;
MeshResult result = fillmesh.FlipEdge(ei, out info);
if (result != MeshResult.Ok)
{
continue;
}
double total_curv_flip = curvature_metric_eval(ev.a, ev.b, ov.a, ov.b);
bool keep_flip = Math.Abs(total_curv_cur - total_curv_flip) < DevelopabilityTolerance;
if (keep_flip == false)
{
result = fillmesh.FlipEdge(ei, out info);
}
else
{
update_curvature(ev.a); update_curvature(ev.b);
update_curvature(ov.a); update_curvature(ov.b);
add_all_edges(ei, updated_edges);
}
}
var tmp = remaining_edges;
remaining_edges = updated_edges;
updated_edges = tmp; updated_edges.Clear();
}
}
regionop.BackPropropagate();
FillTriangles = regionop.CurrentBaseTriangles;
FillVertices = regionop.CurrentBaseInteriorVertices().ToArray();
return(true);
}