/// <summary>
/// precompute constant coefficients of point winding number approximation
/// pointAreas must be provided, and pointSet must have vertex normals!
/// p: 'center' of expansion for points (area-weighted point avg)
/// r: max distance from p to points
/// order1: first-order vector coeff
/// order2: second-order matrix coeff
/// </summary>
public static void ComputeCoeffs(
IPointSet pointSet, IEnumerable <int> points, double[] pointAreas,
ref Vector3d p, ref double r,
ref Vector3d order1, ref Matrix3d order2)
{
if (pointSet.HasVertexNormals == false)
{
throw new Exception("FastPointWinding.ComputeCoeffs: point set does not have normals!");
}
p = Vector3d.Zero;
order1 = Vector3d.Zero;
order2 = Matrix3d.Zero;
r = 0;
// compute area-weighted centroid of points, we use this as the expansion point
double sum_area = 0;
foreach (int vid in points)
{
sum_area += pointAreas[vid];
p += pointAreas[vid] * pointSet.GetVertex(vid);
}
p /= sum_area;
// compute first and second-order coefficients of FWN taylor expansion, as well as
// 'radius' value r, which is max dist from any tri vertex to p
foreach (int vid in points)
{
Vector3d p_i = pointSet.GetVertex(vid);
Vector3d n_i = pointSet.GetVertexNormal(vid);
double a_i = pointAreas[vid];
order1 += a_i * n_i;
Vector3d dcp = p_i - p;
order2 += a_i * new Matrix3d(ref dcp, ref n_i);
// this is just for return value...
r = Math.Max(r, p_i.Distance(p));
}
}
public static void EdgeLengthStats(DMesh3 mesh, out double minEdgeLen, out double maxEdgeLen, out double avgEdgeLen, int samples = 0)
{
minEdgeLen = double.MaxValue;
maxEdgeLen = double.MinValue;
avgEdgeLen = 0;
int avg_count = 0;
int MaxID = mesh.MaxEdgeID;
// if we are only taking some samples, use a prime-modulo-loop instead of random
int nPrime = (samples == 0) ? 1 : nPrime = 31337;
int max_count = (samples == 0) ? MaxID : samples;
Vector3d a = Vector3d.Zero, b = Vector3d.Zero;
int eid = 0;
int count = 0;
do
{
if (mesh.IsEdge(eid))
{
mesh.GetEdgeV(eid, ref a, ref b);
double len = a.Distance(b);
if (len < minEdgeLen)
{
minEdgeLen = len;
}
if (len > maxEdgeLen)
{
maxEdgeLen = len;
}
avgEdgeLen += len;
avg_count++;
}
eid = (eid + nPrime) % MaxID;
} while (eid != 0 && count++ < max_count);
avgEdgeLen /= (double)avg_count;
}
protected bool check_for_cracks(DMesh3 mesh, out int boundary_edge_count, double crack_tol = MathUtil.ZeroTolerancef)
{
boundary_edge_count = 0;
var boundary_verts = new MeshVertexSelection(mesh);
foreach (int eid in mesh.BoundaryEdgeIndices())
{
Index2i ev = mesh.GetEdgeV(eid);
boundary_verts.Select(ev.a); boundary_verts.Select(ev.b);
boundary_edge_count++;
}
if (boundary_verts.Count == 0)
{
return(false);
}
AxisAlignedBox3d bounds = mesh.CachedBounds;
var borderV = new PointHashGrid3d <int>(bounds.MaxDim / 128, -1);
foreach (int vid in boundary_verts)
{
Vector3d v = mesh.GetVertex(vid);
var result = borderV.FindNearestInRadius(v, crack_tol, (existing_vid) =>
{
return(v.Distance(mesh.GetVertex(existing_vid)));
});
if (result.Key != -1)
{
return(true); // we found a crack vertex!
}
borderV.InsertPoint(vid, v);
}
// found no cracks
return(false);
}
public bool Fill()
{
compute_polygons();
// translate/scale fill loops to unit box. This will improve
// accuracy in the calcs below...
Vector2d shiftOrigin = Bounds.Center;
double scale = 1.0 / Bounds.MaxDim;
foreach (var floop in Loops)
{
floop.poly.Translate(-shiftOrigin);
floop.poly.Scale(scale * Vector2d.One, Vector2d.Zero);
}
Dictionary <PlanarComplex.Element, int> ElemToLoopMap = new Dictionary <PlanarComplex.Element, int>();
// [TODO] if we have multiple components in input mesh, we could do this per-component.
// This also helps avoid nested shells creating holes.
// *However*, we shouldn't *have* to because FindSolidRegions will do the right thing if
// the polygons have the same orientation
// add all loops to planar complex
PlanarComplex complex = new PlanarComplex();
for (int i = 0; i < Loops.Count; ++i)
{
var elem = complex.Add(Loops[i].poly);
ElemToLoopMap[elem] = i;
}
// sort into separate 2d solids
PlanarComplex.SolidRegionInfo solids =
complex.FindSolidRegions(PlanarComplex.FindSolidsOptions.SortPolygons);
// fill each 2d solid
List <Index2i> failed_inserts = new List <Index2i>();
List <Index2i> failed_merges = new List <Index2i>();
for (int fi = 0; fi < solids.Polygons.Count; ++fi)
{
var gpoly = solids.Polygons[fi];
PlanarComplex.GeneralSolid gsolid = solids.PolygonsSources[fi];
// [TODO] could do scale/translate here, per-polygon would be more precise
// generate planar mesh that we will insert polygons into
MeshGenerator meshgen;
float planeW = 1.5f;
int nDivisions = 0;
if (FillTargetEdgeLen < double.MaxValue && FillTargetEdgeLen > 0)
{
int n = (int)((planeW / (float)scale) / FillTargetEdgeLen) + 1;
nDivisions = (n <= 1) ? 0 : n;
}
if (nDivisions == 0)
{
meshgen = new TrivialRectGenerator()
{
IndicesMap = new Index2i(1, 2), Width = planeW, Height = planeW,
};
}
else
{
meshgen = new GriddedRectGenerator()
{
IndicesMap = new Index2i(1, 2), Width = planeW, Height = planeW,
EdgeVertices = nDivisions
};
}
DMesh3 FillMesh = meshgen.Generate().MakeDMesh();
FillMesh.ReverseOrientation(); // why?!?
// convenient list
List <Polygon2d> polys = new List <Polygon2d>()
{
gpoly.Outer
};
polys.AddRange(gpoly.Holes);
// for each poly, we track the set of vertices inserted into mesh
int[][] polyVertices = new int[polys.Count][];
// insert each poly
for (int pi = 0; pi < polys.Count; ++pi)
{
MeshInsertUVPolyCurve insert = new MeshInsertUVPolyCurve(FillMesh, polys[pi]);
ValidationStatus status = insert.Validate(MathUtil.ZeroTolerancef * scale);
bool failed = true;
if (status == ValidationStatus.Ok)
{
if (insert.Apply())
{
insert.Simplify();
polyVertices[pi] = insert.CurveVertices;
failed = (insert.Loops.Count != 1) ||
(insert.Loops[0].VertexCount != polys[pi].VertexCount);
}
}
if (failed)
{
failed_inserts.Add(new Index2i(fi, pi));
}
}
// remove any triangles not contained in gpoly
// [TODO] degenerate triangle handling? may be 'on' edge of gpoly...
List <int> removeT = new List <int>();
foreach (int tid in FillMesh.TriangleIndices())
{
Vector3d v = FillMesh.GetTriCentroid(tid);
if (gpoly.Contains(v.xy) == false)
{
removeT.Add(tid);
}
}
foreach (int tid in removeT)
{
FillMesh.RemoveTriangle(tid, true, false);
}
//Util.WriteDebugMesh(FillMesh, "c:\\scratch\\CLIPPED_MESH.obj");
// transform fill mesh back to 3d
MeshTransforms.PerVertexTransform(FillMesh, (v) => {
Vector2d v2 = v.xy;
v2 /= scale;
v2 += shiftOrigin;
return(to3D(v2));
});
//Util.WriteDebugMesh(FillMesh, "c:\\scratch\\PLANAR_MESH_WITH_LOOPS.obj");
//Util.WriteDebugMesh(MeshEditor.Combine(FillMesh, Mesh), "c:\\scratch\\FILLED_MESH.obj");
// figure out map between new mesh and original edge loops
// [TODO] if # of verts is different, we can still find correspondence, it is just harder
// [TODO] should check that edges (ie sequential verts) are boundary edges on fill mesh
// if not, can try to delete nbr tris to repair
IndexMap mergeMapV = new IndexMap(true);
if (MergeFillBoundary)
{
for (int pi = 0; pi < polys.Count; ++pi)
{
if (polyVertices[pi] == null)
{
continue;
}
int[] fillLoopVerts = polyVertices[pi];
int NV = fillLoopVerts.Length;
PlanarComplex.Element sourceElem = (pi == 0) ? gsolid.Outer : gsolid.Holes[pi - 1];
int loopi = ElemToLoopMap[sourceElem];
EdgeLoop sourceLoop = Loops[loopi].edgeLoop;
if (sourceLoop.VertexCount != NV)
{
failed_merges.Add(new Index2i(fi, pi));
continue;
}
for (int k = 0; k < NV; ++k)
{
Vector3d fillV = FillMesh.GetVertex(fillLoopVerts[k]);
Vector3d sourceV = Mesh.GetVertex(sourceLoop.Vertices[k]);
if (fillV.Distance(sourceV) < MathUtil.ZeroTolerancef)
{
mergeMapV[fillLoopVerts[k]] = sourceLoop.Vertices[k];
}
}
}
}
// append this fill to input mesh
MeshEditor editor = new MeshEditor(Mesh);
int[] mapV;
editor.AppendMesh(FillMesh, mergeMapV, out mapV, Mesh.AllocateTriangleGroup());
// [TODO] should verify that we actually merged the loops...
}
if (failed_inserts.Count > 0 || failed_merges.Count > 0)
{
return(false);
}
return(true);
}
public double Value(ref Vector3d pt)
{
return(pt.Distance(ref Origin) - Radius);
}
public double GetSquared()
{
if (DistanceSquared >= 0)
{
return(DistanceSquared);
}
if (cylinder.Height >= double.MaxValue)
{
return(get_squared_infinite());
}
// Convert the point to the cylinder coordinate system. In this system,
// the point believes (0,0,0) is the cylinder axis origin and (0,0,1) is
// the cylinder axis direction.
Vector3d basis0 = cylinder.Axis.Direction;
Vector3d basis1 = Vector3d.Zero, basis2 = Vector3d.Zero;
Vector3d.ComputeOrthogonalComplement(1, basis0, ref basis1, ref basis2);
double height = Cylinder.Height / 2.0;
Vector3d delta = point - cylinder.Axis.Origin;
var P = new Vector3d(basis1.Dot(delta), basis2.Dot(delta), basis0.Dot(delta));
double result_distance = 0; // signed!
Vector3d result_closest = Vector3d.Zero;
double sqrRadius = cylinder.Radius * cylinder.Radius;
double sqrDistance = P[0] * P[0] + P[1] * P[1];
// The point is outside the infinite cylinder, or on the cylinder wall.
double distance = Math.Sqrt(sqrDistance);
double inf_distance = distance - Cylinder.Radius;
double temp = Cylinder.Radius / distance;
var inf_closest = new Vector3d(temp * P.x, temp * P.y, P.z);
bool bOutside = (sqrDistance >= sqrRadius);
result_closest = inf_closest;
result_distance = inf_distance;
if (inf_closest.z >= height)
{
result_closest = (bOutside) ? inf_closest : P;
result_closest.z = height;
result_distance = result_closest.Distance(P); // TODO: only compute sqr here
bOutside = true;
}
else if (inf_closest.z <= -height)
{
result_closest = (bOutside) ? inf_closest : P;
result_closest.z = -height;
result_distance = result_closest.Distance(P); // TODO: only compute sqr here
bOutside = true;
}
else if (bOutside == false)
{
if (inf_closest.z > 0 && Math.Abs(inf_closest.z - height) < Math.Abs(inf_distance))
{
result_closest = P;
result_closest.z = height;
result_distance = result_closest.Distance(P); // TODO: only compute sqr here
}
else if (inf_closest.z < 0 && Math.Abs(inf_closest.z - -height) < Math.Abs(inf_distance))
{
result_closest = P;
result_closest.z = -height;
result_distance = result_closest.Distance(P); // TODO: only compute sqr here
}
}
SignedDistance = (bOutside) ? Math.Abs(result_distance) : -Math.Abs(result_distance);
// Convert the closest point from the cylinder coordinate system to the
// original coordinate system.
CylinderClosest = cylinder.Axis.Origin +
result_closest.x * basis1 +
result_closest.y * basis2 +
result_closest.z * basis0;
DistanceSquared = result_distance * result_distance;
return(DistanceSquared);
}
void generate_graph(DenseGrid3f supportGrid, DenseGridTrilinearImplicit distanceField)
{
int ni = supportGrid.ni, nj = supportGrid.nj, nk = supportGrid.nk;
float dx = (float)CellSize;
Vector3f origin = this.GridOrigin;
// parameters for initializing cost grid
float MODEL_SPACE = 0.01f; // needs small positive so that points on triangles count as inside (eg on ground plane)
//float MODEL_SPACE = 2.0f*(float)CellSize;
float CRAZY_DISTANCE = 99999.0f;
bool UNIFORM_DISTANCE = true;
float MAX_DIST = 10 * (float)CellSize;
// parameters for sorting seeds
Vector3i center_idx = new Vector3i(ni / 2, 0, nk / 2); // middle
//Vector3i center_idx = new Vector3i(0, 0, 0); // corner
bool reverse_per_layer = true;
DenseGrid3f costGrid = new DenseGrid3f(supportGrid);
foreach ( Vector3i ijk in costGrid.Indices() ) {
Vector3d cell_center = new Vector3f(ijk.x * dx, ijk.y * dx, ijk.z * dx) + origin;
float f = (float)distanceField.Value(ref cell_center);
if (f <= MODEL_SPACE)
f = CRAZY_DISTANCE;
else if (UNIFORM_DISTANCE)
f = 1.0f;
else if (f > MAX_DIST)
f = MAX_DIST;
costGrid[ijk] = f;
}
// Find seeds on each layer, sort, and add to accumulated bottom-up seeds list.
// This sorting has an *enormous* effect on the support generation.
List<Vector3i> seeds = new List<Vector3i>();
List<Vector3i> layer_seeds = new List<Vector3i>();
for (int j = 0; j < nj; ++j) {
layer_seeds.Clear();
for (int k = 0; k < nk; ++k) {
for (int i = 0; i < ni; ++i) {
if (supportGrid[i, j, k] == SUPPORT_TIP_BASE)
layer_seeds.Add(new Vector3i(i, j, k));
}
}
layer_seeds.Sort((a, b) => {
Vector3i pa = a; pa.y = 0;
Vector3i pb = b; pb.y = 0;
int sa = (pa-center_idx).LengthSquared, sb = (pb-center_idx).LengthSquared;
return sa.CompareTo(sb);
});
// reversing sort order is intresting?
if(reverse_per_layer)
layer_seeds.Reverse();
seeds.AddRange(layer_seeds);
}
HashSet<Vector3i> seed_indices = new HashSet<Vector3i>(seeds);
// gives very different results...
if (ProcessBottomUp == false)
seeds.Reverse();
// for linear index a, is this a node we allow in graph? (ie graph bounds)
Func<int, bool> node_filter_f = (a) => {
Vector3i ai = costGrid.to_index(a);
// why not y check??
return ai.x > 0 && ai.z > 0 && ai.x != ni - 1 && ai.y != nj - 1 && ai.z != nk - 1;
};
// distance from linear index a to linear index b
// this defines the cost field we want to find shortest path through
Func<int, int, float> node_dist_f = (a, b) => {
Vector3i ai = costGrid.to_index(a), bi = costGrid.to_index(b);
if (bi.y >= ai.y) // b.y should always be a.y-1
return float.MaxValue;
float sg = supportGrid[bi];
// don't connect to tips
//if (sg == SUPPORT_TIP_BASE || sg == SUPPORT_TIP_TOP)
// return float.MaxValue;
if (sg == SUPPORT_TIP_TOP)
return float.MaxValue;
if (sg < 0)
return -999999; // if b is already used, we will terminate there, so this is a good choice
// otherwise cost is sqr-grid-distance + costGrid value (which is basically distance to surface)
float c = costGrid[b];
float f = (float)(Math.Sqrt((bi - ai).LengthSquared) * CellSize);
//float f = 0;
return c + f;
};
// which linear-index nbrs to consider for linear index a
Func<int, IEnumerable<int>> neighbour_f = (a) => {
Vector3i ai = costGrid.to_index(a);
return down_neighbours(ai, costGrid);
};
// when do we terminate
Func<int, bool> terminate_f = (a) => {
Vector3i ai = costGrid.to_index(a);
// terminate if we hit existing support path
if (seed_indices.Contains(ai) == false && supportGrid[ai] < 0)
return true;
// terminate if we hit ground plane
if (ai.y == 0)
return true;
return false;
};
DijkstraGraphDistance dijkstra = new DijkstraGraphDistance(ni * nj * nk, false,
node_filter_f, node_dist_f, neighbour_f);
dijkstra.TrackOrder = true;
List<int> path = new List<int>();
Graph = new DGraph3();
Dictionary<Vector3i, int> CellToGraph = new Dictionary<Vector3i, int>();
TipVertices = new HashSet<int>();
TipBaseVertices = new HashSet<int>();
GroundVertices = new HashSet<int>();
// seeds are tip-base points
for (int k = 0; k < seeds.Count; ++k) {
// add seed point (which is a tip-base vertex) as seed for dijkstra prop
int seed = costGrid.to_linear(seeds[k]);
dijkstra.Reset();
dijkstra.AddSeed(seed, 0);
// compute to termination (ground, existing node, etc)
int base_node = dijkstra.ComputeToNode(terminate_f);
if (base_node < 0)
base_node = dijkstra.GetOrder().Last();
// extract the path
path.Clear();
dijkstra.GetPathToSeed(base_node, path);
int N = path.Count;
// first point on path is termination point.
// create vertex for it if we have not yet
Vector3i basept_idx = supportGrid.to_index(path[0]);
int basept_vid;
if ( CellToGraph.TryGetValue(basept_idx, out basept_vid) == false ) {
Vector3d curv = get_cell_center(basept_idx);
if (basept_idx.y == 0) {
curv.y = 0;
}
basept_vid = Graph.AppendVertex(curv);
if (basept_idx.y == 0) {
GroundVertices.Add(basept_vid);
}
CellToGraph[basept_idx] = basept_vid;
}
int cur_vid = basept_vid;
// now walk up path and create vertices as necessary
for (int i = 0; i < N; ++i) {
int idx = path[i];
if ( supportGrid[idx] >= 0 )
supportGrid[idx] = SUPPORT_GRID_USED;
if ( i > 0 ) {
Vector3i next_idx = supportGrid.to_index(path[i]);
int next_vid;
if (CellToGraph.TryGetValue(next_idx, out next_vid) == false) {
Vector3d nextv = get_cell_center(next_idx);
next_vid = Graph.AppendVertex(nextv);
CellToGraph[next_idx] = next_vid;
}
Graph.AppendEdge(cur_vid, next_vid);
cur_vid = next_vid;
}
}
// seed was tip-base so we should always get back there. Then we
// explicitly add tip-top and edge to it.
if ( supportGrid[path[N-1]] == SUPPORT_TIP_BASE ) {
Vector3i vec_idx = supportGrid.to_index(path[N-1]);
TipBaseVertices.Add(CellToGraph[vec_idx]);
Vector3i tip_idx = vec_idx + Vector3i.AxisY;
int tip_vid;
if (CellToGraph.TryGetValue(tip_idx, out tip_vid) == false) {
Vector3d tipv = get_cell_center(tip_idx);
tip_vid = Graph.AppendVertex(tipv);
CellToGraph[tip_idx] = tip_vid;
Graph.AppendEdge(cur_vid, tip_vid);
TipVertices.Add(tip_vid);
}
}
}
/*
* Snap tips to surface
*/
gParallel.ForEach(TipVertices, (tip_vid) => {
bool snapped = false;
Vector3d v = Graph.GetVertex(tip_vid);
Frame3f hitF;
// try shooting ray straight up. if that hits, and point is close, we use it
if (MeshQueries.RayHitPointFrame(Mesh, MeshSpatial, new Ray3d(v, Vector3d.AxisY), out hitF)) {
if (v.Distance(hitF.Origin) < 2 * CellSize) {
v = hitF.Origin;
snapped = true;
}
}
// if that failed, try straight down
if (!snapped) {
if (MeshQueries.RayHitPointFrame(Mesh, MeshSpatial, new Ray3d(v, -Vector3d.AxisY), out hitF)) {
if (v.Distance(hitF.Origin) < CellSize) {
v = hitF.Origin;
snapped = true;
}
}
}
// if it missed, or hit pt was too far, find nearest point and try that
if (!snapped) {
hitF = MeshQueries.NearestPointFrame(Mesh, MeshSpatial, v);
if (v.Distance(hitF.Origin) < 2 * CellSize) {
v = hitF.Origin;
snapped = true;
}
// can this ever fail? tips should always be within 2 cells...
}
if (snapped)
Graph.SetVertex(tip_vid, v);
});
}
void constrained_smooth(DGraph3 graph, double surfDist, double dotThresh, double alpha, int rounds)
{
int NV = graph.MaxVertexID;
Vector3d[] pos = new Vector3d[NV];
for (int ri = 0; ri < rounds; ++ri) {
gParallel.ForEach(graph.VertexIndices(), (vid) => {
Vector3d v = graph.GetVertex(vid);
if ( GroundVertices.Contains(vid) || TipVertices.Contains(vid) ) {
pos[vid] = v;
return;
}
// for tip base vertices, we could allow them to move down and away within angle cone...
if (TipBaseVertices.Contains(vid)) {
pos[vid] = v;
return;
}
// compute smoothed position of vtx
Vector3d centroid = Vector3d.Zero; int nbr_count = 0;
foreach (int nbr_vid in graph.VtxVerticesItr(vid)) {
centroid += graph.GetVertex(nbr_vid);
nbr_count++;
}
if (nbr_count == 1) {
pos[vid] = v;
return;
}
centroid /= nbr_count;
Vector3d vnew = (1 - alpha) * v + (alpha) * centroid;
// make sure we don't violate angle constraint to any nbrs
int attempt = 0;
try_again:
foreach ( int nbr_vid in graph.VtxVerticesItr(vid)) {
Vector3d dv = graph.GetVertex(nbr_vid) - vnew;
dv.Normalize();
double dot = dv.Dot(Vector3d.AxisY);
if ( Math.Abs(dot) < dotThresh ) {
if (attempt++ < 3) {
vnew = Vector3d.Lerp(v, vnew, 0.66);
goto try_again;
} else {
pos[vid] = v;
return;
}
}
}
// offset from nearest point on surface
Frame3f fNearest = MeshQueries.NearestPointFrame(Mesh, MeshSpatial, vnew, true);
Vector3d vNearest = fNearest.Origin;
double dist = vnew.Distance(vNearest);
bool inside = MeshSpatial.IsInside(vnew);
if (inside || dist < surfDist) {
Vector3d normal = fNearest.Z;
// don't push down?
if (normal.Dot(Vector3d.AxisY) < 0) {
normal.y = 0; normal.Normalize();
}
vnew = fNearest.Origin + surfDist * normal;
}
pos[vid] = vnew;
});
foreach (int vid in graph.VertexIndices())
graph.SetVertex(vid, pos[vid]);
}
}