} // end make_level_set_3
void make_level_set3_parallel(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f distances, int exact_band)
{
distances.resize(ni, nj, nk);
distances.assign((float)((ni + nj + nk) * dx)); // upper bound on distance
// closest triangle id for each grid cell
DenseGrid3i closest_tri = new DenseGrid3i(ni, nj, nk, -1);
// intersection_count(i,j,k) is # of tri intersections in (i-1,i]x{j}x{k}
DenseGrid3i intersection_count = new DenseGrid3i(ni, nj, nk, 0);
if (DebugPrint)
{
System.Console.WriteLine("start");
}
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
double invdx = 1.0 / dx;
// Compute narrow-band distances. For each triangle, we find its grid-coord-bbox,
// and compute exact distances within that box.
// To compute in parallel, we need to safely update grid cells. Current strategy is
// to use a spinlock to control access to grid. Partitioning the grid into a few regions,
// each w/ a separate spinlock, improves performance somewhat. Have also tried having a
// separate spinlock per-row, this resulted in a few-percent performance improvement.
// Also tried pre-sorting triangles into disjoint regions, this did not help much except
// on "perfect" cases like a sphere.
int wi = ni / 2, wj = nj / 2, wk = nk / 2;
SpinLock[] grid_locks = new SpinLock[8];
bool abort = false;
gParallel.ForEach(Mesh.TriangleIndices(), (tid) => {
if (tid % 100 == 0)
{
abort = CancelF();
}
if (abort)
{
return;
}
Vector3d xp = Vector3d.Zero, xq = Vector3d.Zero, xr = Vector3d.Zero;
Mesh.GetTriVertices(tid, ref xp, ref xq, ref xr);
// real ijk coordinates of xp/xq/xr
double fip = (xp[0] - ox) * invdx, fjp = (xp[1] - oy) * invdx, fkp = (xp[2] - oz) * invdx;
double fiq = (xq[0] - ox) * invdx, fjq = (xq[1] - oy) * invdx, fkq = (xq[2] - oz) * invdx;
double fir = (xr[0] - ox) * invdx, fjr = (xr[1] - oy) * invdx, fkr = (xr[2] - oz) * invdx;
// clamped integer bounding box of triangle plus exact-band
int i0 = MathUtil.Clamp(((int)MathUtil.Min(fip, fiq, fir)) - exact_band, 0, ni - 1);
int i1 = MathUtil.Clamp(((int)MathUtil.Max(fip, fiq, fir)) + exact_band + 1, 0, ni - 1);
int j0 = MathUtil.Clamp(((int)MathUtil.Min(fjp, fjq, fjr)) - exact_band, 0, nj - 1);
int j1 = MathUtil.Clamp(((int)MathUtil.Max(fjp, fjq, fjr)) + exact_band + 1, 0, nj - 1);
int k0 = MathUtil.Clamp(((int)MathUtil.Min(fkp, fkq, fkr)) - exact_band, 0, nk - 1);
int k1 = MathUtil.Clamp(((int)MathUtil.Max(fkp, fkq, fkr)) + exact_band + 1, 0, nk - 1);
// compute distance for each tri inside this bounding box
// note: this can be very conservative if the triangle is large and on diagonal to grid axes
for (int k = k0; k <= k1; ++k)
{
for (int j = j0; j <= j1; ++j)
{
int base_idx = ((j < wj) ? 0 : 1) | ((k < wk) ? 0 : 2); // construct index into spinlocks array
for (int i = i0; i <= i1; ++i)
{
Vector3d gx = new Vector3d((float)i * dx + origin[0], (float)j * dx + origin[1], (float)k * dx + origin[2]);
float d = (float)point_triangle_distance(ref gx, ref xp, ref xq, ref xr);
if (d < distances[i, j, k])
{
int lock_idx = base_idx | ((i < wi) ? 0 : 4);
bool taken = false;
grid_locks[lock_idx].Enter(ref taken);
if (d < distances[i, j, k]) // have to check again in case grid changed in another thread...
{
distances[i, j, k] = d;
closest_tri[i, j, k] = tid;
}
grid_locks[lock_idx].Exit();
}
}
}
}
});
if (CancelF())
{
return;
}
if (ComputeSigns == true)
{
if (DebugPrint)
{
System.Console.WriteLine("done narrow-band");
}
compute_intersections(origin, dx, ni, nj, nk, intersection_count);
if (CancelF())
{
return;
}
if (DebugPrint)
{
System.Console.WriteLine("done intersections");
}
if (ComputeMode == ComputeModes.FullGrid)
{
// and now we fill in the rest of the distances with fast sweeping
for (int pass = 0; pass < 2; ++pass)
{
sweep_pass(origin, dx, distances, closest_tri);
if (CancelF())
{
return;
}
}
if (DebugPrint)
{
System.Console.WriteLine("done sweeping");
}
}
else
{
// nothing!
if (DebugPrint)
{
System.Console.WriteLine("skipped sweeping");
}
}
if (DebugPrint)
{
System.Console.WriteLine("done sweeping");
}
// then figure out signs (inside/outside) from intersection counts
compute_signs(ni, nj, nk, distances, intersection_count);
if (CancelF())
{
return;
}
if (WantIntersectionsGrid)
{
intersections_grid = intersection_count;
}
if (DebugPrint)
{
System.Console.WriteLine("done signs");
}
}
if (WantClosestTriGrid)
{
closest_tri_grid = closest_tri;
}
} // end make_level_set_3
void make_level_set3(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f distances, int exact_band)
{
distances.resize(ni, nj, nk);
distances.assign((ni + nj + nk) * dx); // upper bound on distance
// closest triangle id for each grid cell
DenseGrid3i closest_tri = new DenseGrid3i(ni, nj, nk, -1);
// intersection_count(i,j,k) is # of tri intersections in (i-1,i]x{j}x{k}
DenseGrid3i intersection_count = new DenseGrid3i(ni, nj, nk, 0);
if (DebugPrint)
{
System.Console.WriteLine("start");
}
// Compute narrow-band distances. For each triangle, we find its grid-coord-bbox,
// and compute exact distances within that box. The intersection_count grid
// is also filled in this computation
double ddx = (double)dx;
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
Vector3d xp = Vector3d.Zero, xq = Vector3d.Zero, xr = Vector3d.Zero;
foreach (int tid in Mesh.TriangleIndices())
{
if (tid % 100 == 0 && CancelF())
{
break;
}
Mesh.GetTriVertices(tid, ref xp, ref xq, ref xr);
// real ijk coordinates of xp/xq/xr
double fip = (xp[0] - ox) / ddx, fjp = (xp[1] - oy) / ddx, fkp = (xp[2] - oz) / ddx;
double fiq = (xq[0] - ox) / ddx, fjq = (xq[1] - oy) / ddx, fkq = (xq[2] - oz) / ddx;
double fir = (xr[0] - ox) / ddx, fjr = (xr[1] - oy) / ddx, fkr = (xr[2] - oz) / ddx;
// clamped integer bounding box of triangle plus exact-band
int i0 = MathUtil.Clamp(((int)MathUtil.Min(fip, fiq, fir)) - exact_band, 0, ni - 1);
int i1 = MathUtil.Clamp(((int)MathUtil.Max(fip, fiq, fir)) + exact_band + 1, 0, ni - 1);
int j0 = MathUtil.Clamp(((int)MathUtil.Min(fjp, fjq, fjr)) - exact_band, 0, nj - 1);
int j1 = MathUtil.Clamp(((int)MathUtil.Max(fjp, fjq, fjr)) + exact_band + 1, 0, nj - 1);
int k0 = MathUtil.Clamp(((int)MathUtil.Min(fkp, fkq, fkr)) - exact_band, 0, nk - 1);
int k1 = MathUtil.Clamp(((int)MathUtil.Max(fkp, fkq, fkr)) + exact_band + 1, 0, nk - 1);
// compute distance for each tri inside this bounding box
// note: this can be very conservative if the triangle is large and on diagonal to grid axes
for (int k = k0; k <= k1; ++k)
{
for (int j = j0; j <= j1; ++j)
{
for (int i = i0; i <= i1; ++i)
{
Vector3d gx = new Vector3d((float)i * dx + origin[0], (float)j * dx + origin[1], (float)k * dx + origin[2]);
float d = (float)point_triangle_distance(ref gx, ref xp, ref xq, ref xr);
if (d < distances[i, j, k])
{
distances[i, j, k] = d;
closest_tri[i, j, k] = tid;
}
}
}
}
}
if (CancelF())
{
return;
}
if (ComputeSigns == true)
{
if (DebugPrint)
{
System.Console.WriteLine("done narrow-band");
}
compute_intersections(origin, dx, ni, nj, nk, intersection_count);
if (CancelF())
{
return;
}
if (DebugPrint)
{
System.Console.WriteLine("done intersections");
}
if (ComputeMode == ComputeModes.FullGrid)
{
// and now we fill in the rest of the distances with fast sweeping
for (int pass = 0; pass < 2; ++pass)
{
sweep_pass(origin, dx, distances, closest_tri);
if (CancelF())
{
return;
}
}
if (DebugPrint)
{
System.Console.WriteLine("done sweeping");
}
}
else
{
// nothing!
if (DebugPrint)
{
System.Console.WriteLine("skipped sweeping");
}
}
// then figure out signs (inside/outside) from intersection counts
compute_signs(ni, nj, nk, distances, intersection_count);
if (CancelF())
{
return;
}
if (DebugPrint)
{
System.Console.WriteLine("done signs");
}
if (WantIntersectionsGrid)
{
intersections_grid = intersection_count;
}
}
if (WantClosestTriGrid)
{
closest_tri_grid = closest_tri;
}
} // end make_level_set_3
public void Clear(float f)
{
BackgroundValue = f;
Grid.assign(BackgroundValue);
}
void make_level_set3(DMesh3 mesh, /*const std::vector<Vec3ui> &tri, const std::vector<Vec3f> &x*/
Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f phi, int exact_band)
{
phi.resize(ni, nj, nk);
phi.assign((ni + nj + nk) * dx); // upper bound on distance
DenseGrid3i closest_tri = new DenseGrid3i(ni, nj, nk, -1);
DenseGrid3i intersection_count = new DenseGrid3i(ni, nj, nk, 0); // intersection_count(i,j,k) is # of tri intersections in (i-1,i]x{j}x{k}
// we begin by initializing distances near the mesh, and figuring out intersection counts
System.Console.WriteLine("start");
//Vector3f ijkmin, ijkmax; // [RMS] unused in original code
double ddx = (double)dx;
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
foreach (int t in mesh.TriangleIndices())
{
Index3i triangle = mesh.GetTriangle(t);
int p = triangle.a, q = triangle.b, r = triangle.c;
Vector3d xp = mesh.GetVertex(p);
Vector3d xq = mesh.GetVertex(q);
Vector3d xr = mesh.GetVertex(r);
// coordinates in grid to high precision
double fip = (xp[0] - ox) / ddx, fjp = (xp[1] - oy) / ddx, fkp = (xp[2] - oz) / ddx;
double fiq = (xq[0] - ox) / ddx, fjq = (xq[1] - oy) / ddx, fkq = (xq[2] - oz) / ddx;
double fir = (xr[0] - ox) / ddx, fjr = (xr[1] - oy) / ddx, fkr = (xr[2] - oz) / ddx;
// do distances nearby
int i0 = MathUtil.Clamp(((int)MathUtil.Min(fip, fiq, fir)) - exact_band, 0, ni - 1);
int i1 = MathUtil.Clamp(((int)MathUtil.Max(fip, fiq, fir)) + exact_band + 1, 0, ni - 1);
int j0 = MathUtil.Clamp(((int)MathUtil.Min(fjp, fjq, fjr)) - exact_band, 0, nj - 1);
int j1 = MathUtil.Clamp(((int)MathUtil.Max(fjp, fjq, fjr)) + exact_band + 1, 0, nj - 1);
int k0 = MathUtil.Clamp(((int)MathUtil.Min(fkp, fkq, fkr)) - exact_band, 0, nk - 1);
int k1 = MathUtil.Clamp(((int)MathUtil.Max(fkp, fkq, fkr)) + exact_band + 1, 0, nk - 1);
for (int k = k0; k <= k1; ++k)
{
for (int j = j0; j <= j1; ++j)
{
for (int i = i0; i <= i1; ++i)
{
Vector3f gx = new Vector3f((float)i * dx + origin[0], (float)j * dx + origin[1], (float)k * dx + origin[2]);
float d = point_triangle_distance(gx, (Vector3f)xp, (Vector3f)xq, (Vector3f)xr);
if (d < phi[i, j, k])
{
phi[i, j, k] = d;
closest_tri[i, j, k] = t;
}
}
}
}
// and do intersection counts
j0 = MathUtil.Clamp((int)Math.Ceiling(MathUtil.Min(fjp, fjq, fjr)), 0, nj - 1);
j1 = MathUtil.Clamp((int)Math.Floor(MathUtil.Max(fjp, fjq, fjr)), 0, nj - 1);
k0 = MathUtil.Clamp((int)Math.Ceiling(MathUtil.Min(fkp, fkq, fkr)), 0, nk - 1);
k1 = MathUtil.Clamp((int)Math.Floor(MathUtil.Max(fkp, fkq, fkr)), 0, nk - 1);
for (int k = k0; k <= k1; ++k)
{
for (int j = j0; j <= j1; ++j)
{
double a, b, c;
if (point_in_triangle_2d(j, k, fjp, fkp, fjq, fkq, fjr, fkr, out a, out b, out c))
{
double fi = a * fip + b * fiq + c * fir; // intersection i coordinate
int i_interval = (int)(Math.Ceiling(fi)); // intersection is in (i_interval-1,i_interval]
if (i_interval < 0)
{
intersection_count.increment(0, j, k); // we enlarge the first interval to include everything to the -x direction
}
else if (i_interval < ni)
{
intersection_count.increment(i_interval, j, k);
}
// we ignore intersections that are beyond the +x side of the grid
}
}
}
}
System.Console.WriteLine("done narrow-band");
// and now we fill in the rest of the distances with fast sweeping
for (int pass = 0; pass < 2; ++pass)
{
sweep(mesh, phi, closest_tri, origin, dx, +1, +1, +1);
sweep(mesh, phi, closest_tri, origin, dx, -1, -1, -1);
sweep(mesh, phi, closest_tri, origin, dx, +1, +1, -1);
sweep(mesh, phi, closest_tri, origin, dx, -1, -1, +1);
sweep(mesh, phi, closest_tri, origin, dx, +1, -1, +1);
sweep(mesh, phi, closest_tri, origin, dx, -1, +1, -1);
sweep(mesh, phi, closest_tri, origin, dx, +1, -1, -1);
sweep(mesh, phi, closest_tri, origin, dx, -1, +1, +1);
}
System.Console.WriteLine("done sweeping");
// then figure out signs (inside/outside) from intersection counts
for (int k = 0; k < nk; ++k)
{
for (int j = 0; j < nj; ++j)
{
int total_count = 0;
for (int i = 0; i < ni; ++i)
{
total_count += intersection_count[i, j, k];
if (total_count % 2 == 1) // if parity of intersections so far is odd,
{
phi[i, j, k] = -phi[i, j, k]; // we are inside the mesh
}
}
}
}
System.Console.WriteLine("done signs");
} // end make_level_set_3
void generate_support(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f supportGrid)
{
supportGrid.resize(ni, nj, nk);
supportGrid.assign(1); // sentinel
if (DebugPrint) System.Console.WriteLine("start");
bool CHECKERBOARD = false;
System.Console.WriteLine("Computing SDF");
// compute unsigned SDF
MeshSignedDistanceGrid sdf = new MeshSignedDistanceGrid(Mesh, CellSize) {
ComputeSigns = true, ExactBandWidth = 3,
/*,ComputeMode = MeshSignedDistanceGrid.ComputeModes.FullGrid*/ };
sdf.CancelF = Cancelled;
sdf.Compute();
if (Cancelled())
return;
var distanceField = new DenseGridTrilinearImplicit(sdf.Grid, sdf.GridOrigin, sdf.CellSize);
double angle = MathUtil.Clamp(OverhangAngleDeg, 0.01, 89.99);
double cos_thresh = Math.Cos(angle * MathUtil.Deg2Rad);
System.Console.WriteLine("Marking overhangs");
// Compute narrow-band distances. For each triangle, we find its grid-coord-bbox,
// and compute exact distances within that box. The intersection_count grid
// is also filled in this computation
double ddx = (double)dx;
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
Vector3d va = Vector3d.Zero, vb = Vector3d.Zero, vc = Vector3d.Zero;
foreach (int tid in Mesh.TriangleIndices()) {
if (tid % 100 == 0 && Cancelled())
break;
Mesh.GetTriVertices(tid, ref va, ref vb, ref vc);
Vector3d normal = MathUtil.Normal(ref va, ref vb, ref vc);
if (normal.Dot(-Vector3d.AxisY) < cos_thresh)
continue;
// real ijk coordinates of va/vb/vc
double fip = (va[0] - ox) / ddx, fjp = (va[1] - oy) / ddx, fkp = (va[2] - oz) / ddx;
double fiq = (vb[0] - ox) / ddx, fjq = (vb[1] - oy) / ddx, fkq = (vb[2] - oz) / ddx;
double fir = (vc[0] - ox) / ddx, fjr = (vc[1] - oy) / ddx, fkr = (vc[2] - oz) / ddx;
// clamped integer bounding box of triangle plus exact-band
int exact_band = 0;
int i0 = MathUtil.Clamp(((int)MathUtil.Min(fip, fiq, fir)) - exact_band, 0, ni - 1);
int i1 = MathUtil.Clamp(((int)MathUtil.Max(fip, fiq, fir)) + exact_band + 1, 0, ni - 1);
int j0 = MathUtil.Clamp(((int)MathUtil.Min(fjp, fjq, fjr)) - exact_band, 0, nj - 1);
int j1 = MathUtil.Clamp(((int)MathUtil.Max(fjp, fjq, fjr)) + exact_band + 1, 0, nj - 1);
int k0 = MathUtil.Clamp(((int)MathUtil.Min(fkp, fkq, fkr)) - exact_band, 0, nk - 1);
int k1 = MathUtil.Clamp(((int)MathUtil.Max(fkp, fkq, fkr)) + exact_band + 1, 0, nk - 1);
// don't put into y=0 plane
if (j0 == 0)
j0 = 1;
// compute distance for each tri inside this bounding box
// note: this can be very conservative if the triangle is large and on diagonal to grid axes
for (int k = k0; k <= k1; ++k) {
for (int j = j0; j <= j1; ++j) {
for (int i = i0; i <= i1; ++i) {
Vector3d gx = new Vector3d((float)i * dx + origin[0], (float)j * dx + origin[1], (float)k * dx + origin[2]);
float d = (float)MeshSignedDistanceGrid.point_triangle_distance(ref gx, ref va, ref vb, ref vc);
// vertical checkerboard pattern (eg 'tips')
if (CHECKERBOARD) {
int zz = (k % 2 == 0) ? 1 : 0;
if (i % 2 == zz)
continue;
}
if (d < dx / 2) {
if (j > 1) {
supportGrid[i, j, k] = SUPPORT_TIP_TOP;
supportGrid[i, j - 1, k] = SUPPORT_TIP_BASE;
} else {
supportGrid[i, j, k] = SUPPORT_TIP_BASE;
}
}
}
}
}
}
if (Cancelled())
return;
//process_version1(supportGrid, distanceField);
//process_version2(supportGrid, distanceField);
generate_graph(supportGrid, distanceField);
//Util.WriteDebugMesh(MakeDebugGraphMesh(), "c:\\scratch\\__LAST_GRAPH_INIT.obj");
postprocess_graph();
//Util.WriteDebugMesh(MakeDebugGraphMesh(), "c:\\scratch\\__LAST_GRAPH_OPT.obj");
}
void generate_support(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f supportGrid)
{
supportGrid.resize(ni, nj, nk);
supportGrid.assign(1); // sentinel
bool CHECKERBOARD = false;
// compute unsigned SDF
int exact_band = 1;
if (SubtractMesh && SubtractMeshOffset > 0)
{
int offset_band = (int)(SubtractMeshOffset / CellSize) + 1;
exact_band = Math.Max(exact_band, offset_band);
}
sdf = new MeshSignedDistanceGrid(Mesh, CellSize)
{
ComputeSigns = true, ExactBandWidth = exact_band
};
sdf.CancelF = this.CancelF;
sdf.Compute();
if (CancelF())
{
return;
}
var distanceField = new DenseGridTrilinearImplicit(sdf.Grid, sdf.GridOrigin, sdf.CellSize);
double angle = MathUtil.Clamp(OverhangAngleDeg, 0.01, 89.99);
double cos_thresh = Math.Cos(angle * MathUtil.Deg2Rad);
// Compute narrow-band distances. For each triangle, we find its grid-coord-bbox,
// and compute exact distances within that box. The intersection_count grid
// is also filled in this computation
double ddx = (double)dx;
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
Vector3d va = Vector3d.Zero, vb = Vector3d.Zero, vc = Vector3d.Zero;
foreach (int tid in Mesh.TriangleIndices())
{
if (tid % 100 == 0 && CancelF())
{
break;
}
Mesh.GetTriVertices(tid, ref va, ref vb, ref vc);
Vector3d normal = MathUtil.Normal(ref va, ref vb, ref vc);
if (normal.Dot(-Vector3d.AxisY) < cos_thresh)
{
continue;
}
// real ijk coordinates of va/vb/vc
double fip = (va[0] - ox) / ddx, fjp = (va[1] - oy) / ddx, fkp = (va[2] - oz) / ddx;
double fiq = (vb[0] - ox) / ddx, fjq = (vb[1] - oy) / ddx, fkq = (vb[2] - oz) / ddx;
double fir = (vc[0] - ox) / ddx, fjr = (vc[1] - oy) / ddx, fkr = (vc[2] - oz) / ddx;
// clamped integer bounding box of triangle plus exact-band
int extra_band = 0;
int i0 = MathUtil.Clamp(((int)MathUtil.Min(fip, fiq, fir)) - extra_band, 0, ni - 1);
int i1 = MathUtil.Clamp(((int)MathUtil.Max(fip, fiq, fir)) + extra_band + 1, 0, ni - 1);
int j0 = MathUtil.Clamp(((int)MathUtil.Min(fjp, fjq, fjr)) - extra_band, 0, nj - 1);
int j1 = MathUtil.Clamp(((int)MathUtil.Max(fjp, fjq, fjr)) + extra_band + 1, 0, nj - 1);
int k0 = MathUtil.Clamp(((int)MathUtil.Min(fkp, fkq, fkr)) - extra_band, 0, nk - 1);
int k1 = MathUtil.Clamp(((int)MathUtil.Max(fkp, fkq, fkr)) + extra_band + 1, 0, nk - 1);
// don't put into y=0 plane
//if (j0 == 0)
// j0 = 1;
// compute distance for each tri inside this bounding box
// note: this can be very conservative if the triangle is large and on diagonal to grid axes
for (int k = k0; k <= k1; ++k)
{
for (int j = j0; j <= j1; ++j)
{
for (int i = i0; i <= i1; ++i)
{
Vector3d gx = new Vector3d((float)i * dx + origin[0], (float)j * dx + origin[1], (float)k * dx + origin[2]);
float d = (float)MeshSignedDistanceGrid.point_triangle_distance(ref gx, ref va, ref vb, ref vc);
// vertical checkerboard pattern (eg 'tips')
if (CHECKERBOARD)
{
int zz = (k % 2 == 0) ? 1 : 0;
if (i % 2 == zz)
{
continue;
}
}
if (d < dx / 2)
{
supportGrid[i, j, k] = SUPPORT_TIP_TOP;
}
}
}
}
}
if (CancelF())
{
return;
}
fill_vertical_spans(supportGrid, distanceField);
generate_mesh(supportGrid, distanceField);
}