static void skeletonize_layer(DenseGrid3i grid, int j, int dilation_rounds = 1)
{
DenseGrid2i layer = grid.get_slice(j, 1);
DenseGrid2i tmp = new DenseGrid2i(layer.ni, layer.nj, 0);
for (int k = 0; k < dilation_rounds; ++k) {
tmp.assign(0);
dilate(layer, tmp);
}
bool done = false;
while (!done) {
int sum_before = layer.sum();
tmp.assign(0);
skeletonize_pass(layer, tmp, 0);
tmp.assign(0);
skeletonize_pass(layer, tmp, 1);
int sum_after = layer.sum();
if (sum_before == sum_after)
break;
}
for (int i = 0; i < grid.ni; ++i)
for (int k = 0; k < grid.nk; ++k)
grid[i, j, k] = layer[i, k];
}
static DenseGrid3i binarize(DenseGrid3f grid, float thresh = 0)
{
DenseGrid3i result = new DenseGrid3i();
result.resize(grid.ni, grid.nj, grid.nk);
int size = result.size;
for (int k = 0; k < size; ++k)
result[k] = (grid[k] < thresh) ? 1 : 0;
return result;
}
// iterate through each x-row of grid and set unsigned distances to be negative
// inside the mesh, based on the intersection_counts
void compute_signs(int ni, int nj, int nk, DenseGrid3f distances, DenseGrid3i intersection_counts)
{
Func <int, bool> isInsideF = (count) => { return(count % 2 == 1); };
if (InsideMode == InsideModes.ParityCount)
{
isInsideF = (count) => { return(count > 0); }
}
;
if (UseParallel)
{
// can process each x-row in parallel
AxisAlignedBox2i box = new AxisAlignedBox2i(0, 0, nj, nk);
gParallel.ForEach(box.IndicesExclusive(), (vi) => {
if (CancelF())
{
return;
}
int j = vi.x, k = vi.y;
int total_count = 0;
for (int i = 0; i < ni; ++i)
{
total_count += intersection_counts[i, j, k];
if (isInsideF(total_count)) // if parity of intersections so far is odd,
{
distances[i, j, k] = -distances[i, j, k]; // we are inside the mesh
}
}
});
}
else
{
for (int k = 0; k < nk; ++k)
{
if (CancelF())
{
return;
}
for (int j = 0; j < nj; ++j)
{
int total_count = 0;
for (int i = 0; i < ni; ++i)
{
total_count += intersection_counts[i, j, k];
if (isInsideF(total_count)) // if parity of intersections so far is odd,
{
distances[i, j, k] = -distances[i, j, k]; // we are inside the mesh
}
}
}
}
}
}
} // end make_level_set_3
// sweep through grid in different directions, distances and closest tris
void sweep_pass(Vector3f origin, float dx,
DenseGrid3f distances, DenseGrid3i closest_tri)
{
sweep(distances, closest_tri, origin, dx, +1, +1, +1);
sweep(distances, closest_tri, origin, dx, -1, -1, -1);
sweep(distances, closest_tri, origin, dx, +1, +1, -1);
sweep(distances, closest_tri, origin, dx, -1, -1, +1);
sweep(distances, closest_tri, origin, dx, +1, -1, +1);
sweep(distances, closest_tri, origin, dx, -1, +1, -1);
sweep(distances, closest_tri, origin, dx, +1, -1, -1);
sweep(distances, closest_tri, origin, dx, -1, +1, +1);
}
// single sweep pass
void sweep(DenseGrid3f phi, DenseGrid3i closest_tri,
Vector3f origin, float dx,
int di, int dj, int dk)
{
int i0, i1;
if (di > 0)
{
i0 = 1; i1 = phi.ni;
}
else
{
i0 = phi.ni - 2; i1 = -1;
}
int j0, j1;
if (dj > 0)
{
j0 = 1; j1 = phi.nj;
}
else
{
j0 = phi.nj - 2; j1 = -1;
}
int k0, k1;
if (dk > 0)
{
k0 = 1; k1 = phi.nk;
}
else
{
k0 = phi.nk - 2; k1 = -1;
}
for (int k = k0; k != k1; k += dk)
{
for (int j = j0; j != j1; j += dj)
{
for (int i = i0; i != i1; i += di)
{
Vector3d gx = new Vector3d(i * dx + origin[0], j * dx + origin[1], k * dx + origin[2]);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i - di, j, k);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i, j - dj, k);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i - di, j - dj, k);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i, j, k - dk);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i - di, j, k - dk);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i, j - dj, k - dk);
check_neighbour(phi, closest_tri, ref gx, i, j, k, i - di, j - dj, k - dk);
}
}
}
}
public void Initialize()
{
// figure out origin & dimensions
AxisAlignedBox3d bounds = Mesh.CachedBounds;
float fBufferWidth = (float)Math.Max(4 * CellSize, 2 * MaxOffsetDistance + 2 * CellSize);
grid_origin = (Vector3f)bounds.Min - fBufferWidth * Vector3f.One - (Vector3f)ExpandBounds;
Vector3f max = (Vector3f)bounds.Max + fBufferWidth * Vector3f.One + (Vector3f)ExpandBounds;
int ni = (int)((max.x - grid_origin.x) / CellSize) + 1;
int nj = (int)((max.y - grid_origin.y) / CellSize) + 1;
int nk = (int)((max.z - grid_origin.z) / CellSize) + 1;
UpperBoundDistance = (float)((ni + nj + nk) * CellSize);
grid = new DenseGrid3f(ni, nj, nk, UpperBoundDistance);
MaxDistQueryDist = MaxOffsetDistance + (2 * CellSize * MathUtil.SqrtTwo);
// closest triangle id for each grid cell
if (WantClosestTriGrid)
{
closest_tri_grid = 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 (ComputeSigns == true)
{
compute_intersections(grid_origin, CellSize, ni, nj, nk, intersection_count);
if (CancelF())
{
return;
}
// then figure out signs (inside/outside) from intersection counts
compute_signs(ni, nj, nk, grid, intersection_count);
if (CancelF())
{
return;
}
if (WantIntersectionsGrid)
{
intersections_grid = intersection_count;
}
}
}
void check_neighbour(DenseGrid3f phi, DenseGrid3i closest_tri,
ref Vector3d gx, int i0, int j0, int k0, int i1, int j1, int k1)
{
if (closest_tri[i1, j1, k1] >= 0)
{
Vector3d xp = Vector3f.Zero, xq = Vector3f.Zero, xr = Vector3f.Zero;
Mesh.GetTriVertices(closest_tri[i1, j1, k1], ref xp, ref xq, ref xr);
float d = (float)point_triangle_distance(ref gx, ref xp, ref xq, ref xr);
if (d < phi[i0, j0, k0])
{
phi[i0, j0, k0] = d;
closest_tri[i0, j0, k0] = closest_tri[i1, j1, k1];
}
}
}
static void check_neighbour(DMesh3 mesh,
DenseGrid3f phi, DenseGrid3i closest_tri,
Vector3f gx, int i0, int j0, int k0, int i1, int j1, int k1)
{
if (closest_tri[i1, j1, k1] >= 0)
{
Index3i tri = mesh.GetTriangle(closest_tri[i1, j1, k1]);
int p = tri.a, q = tri.b, r = tri.c;
Vector3f xp = (Vector3f)mesh.GetVertex(p);
Vector3f xq = (Vector3f)mesh.GetVertex(q);
Vector3f xr = (Vector3f)mesh.GetVertex(r);
float d = point_triangle_distance(gx, xp, xq, xr);
if (d < phi[i0, j0, k0])
{
phi[i0, j0, k0] = d;
closest_tri[i0, j0, k0] = closest_tri[i1, j1, k1];
}
}
}
// fill the intersection grid w/ number of intersections in each cell
void compute_intersections(Vector3f origin, float dx, int ni, int nj, int nk, DenseGrid3i intersection_count)
{
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
double invdx = 1.0 / dx;
bool cancelled = false;
// this is what we will do for each triangle. There are no grid-reads, only grid-writes,
// since we use atomic_increment, it is always thread-safe
Action <int> ProcessTriangleF = (tid) => {
if (tid % 100 == 0 && CancelF() == true)
{
cancelled = true;
}
if (cancelled)
{
return;
}
Vector3d xp = Vector3d.Zero, xq = Vector3d.Zero, xr = Vector3d.Zero;
Mesh.GetTriVertices(tid, ref xp, ref xq, ref xr);
bool neg_x = false;
if (InsideMode == InsideModes.ParityCount)
{
Vector3d n = MathUtil.FastNormalDirection(ref xp, ref xq, ref xr);
neg_x = n.x > 0;
}
// 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;
// recompute j/k integer bounds of triangle w/o exact band
int j0 = MathUtil.Clamp((int)Math.Ceiling(MathUtil.Min(fjp, fjq, fjr)), 0, nj - 1);
int j1 = MathUtil.Clamp((int)Math.Floor(MathUtil.Max(fjp, fjq, fjr)), 0, nj - 1);
int k0 = MathUtil.Clamp((int)Math.Ceiling(MathUtil.Min(fkp, fkq, fkr)), 0, nk - 1);
int k1 = MathUtil.Clamp((int)Math.Floor(MathUtil.Max(fkp, fkq, fkr)), 0, nk - 1);
// and do intersection counts
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.atomic_incdec(0, j, k, neg_x);
}
else if (i_interval < ni)
{
intersection_count.atomic_incdec(i_interval, j, k, neg_x);
}
else
{
// we ignore intersections that are beyond the +x side of the grid
}
}
}
}
};
if (UseParallel)
{
gParallel.ForEach(Mesh.TriangleIndices(), ProcessTriangleF);
}
else
{
foreach (int tid in Mesh.TriangleIndices())
{
ProcessTriangleF(tid);
}
}
}
} // 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
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 process_version1(DenseGrid3f supportGrid, DenseGridTrilinearImplicit distanceField)
{
int ni = supportGrid.ni, nj = supportGrid.nj, nk = supportGrid.nk;
float dx = (float)CellSize;
Vector3f origin = this.GridOrigin;
// sweep values down, column by column
for (int k = 0; k < nk; ++k) {
for (int i = 0; i < ni; ++i) {
bool in_support = false;
for (int j = nj - 1; j >= 0; j--) {
float fcur = supportGrid[i, j, k];
if (fcur >= 0) {
Vector3d cell_center = new Vector3f(i * dx, j * dx, k * dx) + origin;
if (in_support) {
bool is_inside = distanceField.Value(ref cell_center) < 0;
if (is_inside) {
supportGrid[i, j, k] = -3;
in_support = false;
} else {
supportGrid[i, j, k] = -1;
}
}
} else {
in_support = true;
}
}
}
}
// skeletonize each layer
// todo: would be nice to skeletonize the 3D volume.. ?
DenseGrid3i binary = new DenseGrid3i(ni, nj, nk, 0);
foreach (Vector3i idx in binary.Indices())
binary[idx] = (supportGrid[idx] < 0) ? 1 : 0;
for (int j = 0; j < nj; ++j)
skeletonize_layer(binary, j);
// debug thing
//VoxelSurfaceGenerator voxgen = new VoxelSurfaceGenerator() {
// Voxels = binary.get_bitmap()
//};
//voxgen.Generate();
//Util.WriteDebugMesh(voxgen.makemesh(), "c:\\scratch\\binary.obj");
// for skeleton voxels, we add some power
for (int j = 0; j < nj; ++j) {
for (int k = 1; k < nk - 1; ++k) {
for (int i = 1; i < ni - 1; ++i) {
if (binary[i, j, k] > 0)
supportGrid[i, j, k] = -3;
//else
// supportGrid[i, j, k] = 1; // clear non-skeleton voxels
}
}
}
// power up the ground-plane voxels
for (int k = 0; k < nk; ++k) {
for (int i = 0; i < ni; ++i) {
if (supportGrid[i, 0, k] < 0)
supportGrid[i, 0, k] = -5;
}
}
#if true
DenseGrid3f smoothed = new DenseGrid3f(supportGrid);
float nbr_weight = 0.5f;
for (int iter = 0; iter < 15; ++iter) {
// add some mass to skeleton voxels
for (int j = 0; j < nj; ++j) {
for (int k = 1; k < nk - 1; ++k) {
for (int i = 1; i < ni - 1; ++i) {
if (binary[i, j, k] > 0)
supportGrid[i, j, k] = supportGrid[i, j, k] - nbr_weight / 25.0f;
}
}
}
for (int j = 0; j < nj; ++j) {
for (int k = 1; k < nk - 1; ++k) {
for (int i = 1; i < ni - 1; ++i) {
int neg = 0;
float avg = 0, w = 0;
for (int n = 0; n < 8; ++n) {
int xi = i + gIndices.GridOffsets8[n].x;
int zi = k + gIndices.GridOffsets8[n].y;
float f = supportGrid[xi, j, zi];
if (f < 0) neg++;
avg += nbr_weight * f;
w += nbr_weight;
}
if (neg > -1) {
avg += supportGrid[i, j, k];
w += 1.0f;
smoothed[i, j, k] = avg / w;
} else {
smoothed[i, j, k] = supportGrid[i, j, k];
}
}
}
}
supportGrid.swap(smoothed);
}
#endif
// hard-enforce that skeleton voxels stay inside
//for (int j = 0; j < nj; ++j) {
// for (int k = 1; k < nk - 1; ++k) {
// for (int i = 1; i < ni - 1; ++i) {
// if (binary[i, j, k] > 0)
// supportGrid[i, j, k] = Math.Min(supportGrid[i, j, k], - 1);
// }
// }
//}
}