static void smooth(DenseGrid3f grid, DenseGrid3f tmp, float alpha, int iters, int min_j = 1)
{
if (tmp == null)
{
tmp = new DenseGrid3f(grid);
}
int ni = grid.ni, nj = grid.nj, nk = grid.nk;
for (int iter = 0; iter < iters; ++iter)
{
for (int j = min_j; j < nj - 1; ++j)
{
for (int k = 1; k < nk - 1; ++k)
{
for (int i = 1; i < ni - 1; ++i)
{
float avg = 0;
foreach (Vector3i o in gIndices.GridOffsets26)
{
int xi = i + o.x, yi = j + o.y, zi = k + o.z;
float f = grid[xi, yi, zi];
avg += f;
}
avg /= 26.0f;
tmp[i, j, k] = (1 - alpha) * grid[i, j, k] + (alpha) * avg;
}
}
}
grid.swap(tmp);
}
}
void make_grid_dense(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f scalars)
{
scalars.resize(ni, nj, nk);
bool abort = false; int count = 0;
gParallel.ForEach(scalars.Indices(), (ijk) =>
{
Interlocked.Increment(ref count);
if (count % 100 == 0)
{
abort = CancelF();
}
if (abort)
{
return;
}
var gx = new Vector3d((float)ijk.x * dx + origin[0], (float)ijk.y * dx + origin[1], (float)ijk.z * dx + origin[2]);
scalars[ijk] = (float)ScalarF(gx);
});
} // end make_level_set_3
} // end make_level_set_3
void fill_spans(int ni, int nj, int nk, DenseGrid3f scalars)
{
gParallel.ForEach(gIndices.Grid3IndicesYZ(nj, nk), (idx) =>
{
int j = idx.y, k = idx.z;
float last = scalars[0, j, k];
if (last == float.MaxValue)
{
last = 0;
}
for (int i = 0; i < ni; ++i)
{
if (scalars[i, j, k] == float.MaxValue)
{
scalars[i, j, k] = last;
}
else
{
last = scalars[i, j, k];
if (last < IsoValue) // propagate zeros on outside
{
last = 0;
}
}
}
});
}
void make_grid_dense(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f winding)
{
winding.resize(ni, nj, nk);
MeshSpatial.WindingNumber(Vector3d.Zero);
bool abort = false; int count = 0;
gParallel.ForEach(winding.Indices(), (ijk) =>
{
Interlocked.Increment(ref count);
if (count % 100 == 0)
{
abort = CancelF();
}
if (abort)
{
return;
}
var gx = new Vector3d((float)ijk.x * dx + origin[0], (float)ijk.y * dx + origin[1], (float)ijk.z * dx + origin[2]);
winding[ijk] = (float)MeshSpatial.WindingNumber(gx);
});
} // end make_level_set_3
public void Generate()
{
// figure out origin & dimensions
AxisAlignedBox3d bounds = Mesh.CachedBounds;
if (ForceMinY != float.MaxValue)
{
bounds.Min.y = ForceMinY;
}
// expand grid so we have some border space in x and z
float fBufferWidth = 2 * (float)CellSize;
Vector3f b = new Vector3f(fBufferWidth, 0, fBufferWidth);
grid_origin = (Vector3f)bounds.Min - b;
// need zero isovalue to be at y=0. right now we set yi=0 voxels to be -1,
// so if we nudge up half a cell, then interpolation with boundary outside
// value should be 0 right at cell border (seems to be working?)
grid_origin.y += (float)CellSize * 0.5f;
Vector3f max = (Vector3f)bounds.Max + b;
int ni = (int)((max.x - grid_origin.x) / (float)CellSize) + 1;
int nj = (int)((max.y - grid_origin.y) / (float)CellSize) + 1;
int nk = (int)((max.z - grid_origin.z) / (float)CellSize) + 1;
volume_grid = new DenseGrid3f();
generate_support(grid_origin, (float)CellSize, ni, nj, nk, volume_grid);
}
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);
}
void generate_mesh(DenseGrid3f supportGrid, DenseGridTrilinearImplicit distanceField)
{
DenseGridTrilinearImplicit volume = new DenseGridTrilinearImplicit(
supportGrid, GridOrigin, CellSize);
BoundedImplicitFunction3d inputF = volume;
if (SubtractMesh)
{
BoundedImplicitFunction3d sub = distanceField;
if (SubtractMeshOffset > 0)
{
sub = new ImplicitOffset3d()
{
A = distanceField, Offset = SubtractMeshOffset
}
}
;
ImplicitDifference3d subtract = new ImplicitDifference3d()
{
A = volume, B = sub
};
inputF = subtract;
}
ImplicitHalfSpace3d cutPlane = new ImplicitHalfSpace3d()
{
Origin = Vector3d.Zero, Normal = Vector3d.AxisY
};
ImplicitDifference3d cut = new ImplicitDifference3d()
{
A = inputF, B = cutPlane
};
MarchingCubes mc = new MarchingCubes()
{
Implicit = cut, Bounds = grid_bounds, CubeSize = CellSize
};
mc.Bounds.Min.y = -2 * mc.CubeSize;
mc.Bounds.Min.x -= 2 * mc.CubeSize; mc.Bounds.Min.z -= 2 * mc.CubeSize;
mc.Bounds.Max.x += 2 * mc.CubeSize; mc.Bounds.Max.z += 2 * mc.CubeSize;
mc.Generate();
SupportMesh = mc.Mesh;
}
}
public void GenerateContinuation(IEnumerable <Vector3d> seeds)
{
Mesh = new DMesh3();
int nx = (int)(Bounds.Width / CubeSize) + 1;
int ny = (int)(Bounds.Height / CubeSize) + 1;
int nz = (int)(Bounds.Depth / CubeSize) + 1;
CellDimensions = new Vector3i(nx, ny, nz);
GridBounds = new AxisAlignedBox3i(Vector3i.Zero, CellDimensions);
if (LastGridBounds != GridBounds)
{
corner_values_grid = new DenseGrid3f(nx + 1, ny + 1, nz + 1, float.MaxValue);
edge_vertices = new Dictionary <long, int>();
corner_values = new Dictionary <long, double>();
if (ParallelCompute)
{
done_cells = new DenseGrid3i(CellDimensions.x, CellDimensions.y, CellDimensions.z, 0);
}
}
else
{
edge_vertices.Clear();
corner_values.Clear();
corner_values_grid.assign(float.MaxValue);
if (ParallelCompute)
{
done_cells.assign(0);
}
}
if (ParallelCompute)
{
generate_continuation_parallel(seeds);
}
else
{
generate_continuation(seeds);
}
LastGridBounds = GridBounds;
}
IEnumerable <int> down_neighbours(Vector3i idx, DenseGrid3f grid)
{
yield return(grid.to_linear(idx.x, idx.y - 1, idx.z));
yield return(grid.to_linear(idx.x - 1, idx.y - 1, idx.z));
yield return(grid.to_linear(idx.x + 1, idx.y - 1, idx.z));
yield return(grid.to_linear(idx.x, idx.y - 1, idx.z - 1));
yield return(grid.to_linear(idx.x, idx.y - 1, idx.z + 1));
yield return(grid.to_linear(idx.x - 1, idx.y - 1, idx.z - 1));
yield return(grid.to_linear(idx.x + 1, idx.y - 1, idx.z - 1));
yield return(grid.to_linear(idx.x - 1, idx.y - 1, idx.z + 1));
yield return(grid.to_linear(idx.x + 1, idx.y - 1, idx.z + 1));
}
protected override void SolveInstance(IGH_DataAccess DA)
{
Point3d pt = Point3d.Origin;
int ni = 0;
int nj = 0;
int nk = 0;
double cellSize = 0;
DA.GetData(0, ref pt);
DA.GetData(1, ref ni);
DA.GetData(2, ref nj);
DA.GetData(3, ref nk);
DA.GetData(4, ref cellSize);
DenseGrid3f grid = new DenseGrid3f(ni, nj, nk, 0);
DenseGridTrilinearImplicit grd = new DenseGridTrilinearImplicit(grid, pt.ToVec3d(), cellSize);
DA.SetData(0, grd);
}
void fill_vertical_spans(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 = get_cell_center(i, j, k);
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;
}
}
}
}
}
public void Compute()
{
// figure out origin & dimensions
AxisAlignedBox3d bounds = Mesh.CachedBounds;
float fBufferWidth = 2 * BufferCells * (float)CellSize;
grid_origin = (Vector3f)bounds.Min - fBufferWidth * Vector3f.One;
Vector3f max = (Vector3f)bounds.Max + fBufferWidth * Vector3f.One;
int ni = (int)((max.x - grid_origin.x) / (float)CellSize) + 1;
int nj = (int)((max.y - grid_origin.y) / (float)CellSize) + 1;
int nk = (int)((max.z - grid_origin.z) / (float)CellSize) + 1;
scalar_grid = new DenseGrid3f();
if (ComputeMode == ComputeModes.FullGrid)
{
make_grid_dense(grid_origin, (float)CellSize, ni, nj, nk, scalar_grid);
}
else
{
make_grid(grid_origin, (float)CellSize, ni, nj, nk, scalar_grid);
}
}
/// <summary>
/// Run MC algorithm and generate Output mesh
/// </summary>
public void Generate()
{
Mesh = new DMesh3();
int nx = (int)(Bounds.Width / CubeSize) + 1;
int ny = (int)(Bounds.Height / CubeSize) + 1;
int nz = (int)(Bounds.Depth / CubeSize) + 1;
CellDimensions = new Vector3i(nx, ny, nz);
GridBounds = new AxisAlignedBox3i(Vector3i.Zero, CellDimensions);
corner_values_grid = new DenseGrid3f(nx + 1, ny + 1, nz + 1, float.MaxValue);
edge_vertices = new Dictionary <long, int>();
corner_values = new Dictionary <long, double>();
if (ParallelCompute)
{
generate_parallel();
}
else
{
generate_basic();
}
}
void make_grid(Vector3f origin, float dx,
int ni, int nj, int nk,
DenseGrid3f scalars)
{
scalars.resize(ni, nj, nk);
scalars.assign(float.MaxValue); // sentinel
if (DebugPrint)
{
System.Console.WriteLine("start");
}
// Ok, because the whole idea is that the surface might have holes, we are going to
// compute values along known triangles and then propagate the computed region outwards
// until any iso-sign-change is surrounded.
// To seed propagation, we compute unsigned SDF and then compute values for any voxels
// containing surface (ie w/ distance smaller than cellsize)
// compute unsigned SDF
var sdf = new MeshSignedDistanceGrid(Mesh, CellSize)
{
ComputeSigns = false
};
sdf.CancelF = this.CancelF;
sdf.Compute();
if (CancelF())
{
return;
}
DenseGrid3f distances = sdf.Grid;
if (WantMeshSDFGrid)
{
mesh_sdf = sdf;
}
if (DebugPrint)
{
System.Console.WriteLine("done initial sdf");
}
// compute values at surface voxels
double ox = (double)origin[0], oy = (double)origin[1], oz = (double)origin[2];
gParallel.ForEach(gIndices.Grid3IndicesYZ(nj, nk), (jk) =>
{
if (CancelF())
{
return;
}
for (int i = 0; i < ni; ++i)
{
var ijk = new Vector3i(i, jk.y, jk.z);
float dist = distances[ijk];
// this could be tighter? but I don't think it matters...
if (dist < CellSize)
{
var gx = new Vector3d((float)ijk.x * dx + origin[0], (float)ijk.y * dx + origin[1], (float)ijk.z * dx + origin[2]);
scalars[ijk] = (float)ScalarF(gx);
}
}
});
if (CancelF())
{
return;
}
if (DebugPrint)
{
System.Console.WriteLine("done narrow-band");
}
// Now propagate outwards from computed voxels.
// Current procedure is to check 26-neighbours around each 'front' voxel,
// and if there are any sign changes, that neighbour is added to front.
// Front is initialized w/ all voxels we computed above
AxisAlignedBox3i bounds = scalars.Bounds;
bounds.Max -= Vector3i.One;
// since we will be computing new values as necessary, we cannot use
// grid to track whether a voxel is 'new' or not.
// So, using 3D bitmap intead - is updated at end of each pass.
var bits = new Bitmap3(new Vector3i(ni, nj, nk));
var cur_front = new List <Vector3i>();
foreach (Vector3i ijk in scalars.Indices())
{
if (scalars[ijk] != float.MaxValue)
{
cur_front.Add(ijk);
bits[ijk] = true;
}
}
if (CancelF())
{
return;
}
// Unique set of 'new' voxels to compute in next iteration.
var queue = new HashSet <Vector3i>();
var queue_lock = new SpinLock();
while (true)
{
if (CancelF())
{
return;
}
// can process front voxels in parallel
bool abort = false; int iter_count = 0;
gParallel.ForEach(cur_front, (ijk) =>
{
Interlocked.Increment(ref iter_count);
if (iter_count % 100 == 0)
{
abort = CancelF();
}
if (abort)
{
return;
}
float val = scalars[ijk];
// check 26-neighbours to see if we have a crossing in any direction
for (int k = 0; k < 26; ++k)
{
Vector3i nijk = ijk + gIndices.GridOffsets26[k];
if (bounds.Contains(nijk) == false)
{
continue;
}
float val2 = scalars[nijk];
if (val2 == float.MaxValue)
{
var gx = new Vector3d((float)nijk.x * dx + origin[0], (float)nijk.y * dx + origin[1], (float)nijk.z * dx + origin[2]);
val2 = (float)ScalarF(gx);
scalars[nijk] = val2;
}
if (bits[nijk] == false)
{
// this is a 'new' voxel this round.
// If we have an iso-crossing, add it to the front next round
bool crossing = (val <IsoValue && val2> IsoValue) ||
(val > IsoValue && val2 < IsoValue);
if (crossing)
{
bool taken = false;
queue_lock.Enter(ref taken);
queue.Add(nijk);
queue_lock.Exit();
}
}
}
});
if (DebugPrint)
{
System.Console.WriteLine("front has {0} voxels", queue.Count);
}
if (queue.Count == 0)
{
break;
}
// update known-voxels list and create front for next iteration
foreach (Vector3i idx in queue)
{
bits[idx] = true;
}
cur_front.Clear();
cur_front.AddRange(queue);
queue.Clear();
}
if (DebugPrint)
{
System.Console.WriteLine("done front-prop");
}
if (DebugPrint)
{
int filled = 0;
foreach (Vector3i ijk in scalars.Indices())
{
if (scalars[ijk] != float.MaxValue)
{
filled++;
}
}
System.Console.WriteLine("filled: {0} / {1} - {2}%", filled, ni * nj * nk,
(double)filled / (double)(ni * nj * nk) * 100.0);
}
if (CancelF())
{
return;
}
// fill in the rest of the grid by propagating know values
fill_spans(ni, nj, nk, scalars);
if (DebugPrint)
{
System.Console.WriteLine("done sweep");
}
}
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);
// }
// }
//}
}
void process_version2(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 layer by layer
DenseGrid2f prev = supportGrid.get_slice(nj - 1, 1);
DenseGrid2f tmp = new DenseGrid2f(prev);
Bitmap3 bmp = new Bitmap3(new Vector3i(ni, nj, nk));
for (int j = nj - 2; j >= 0; j--)
{
// skeletonize prev layer
DenseGrid2i prev_skel = binarize(prev, 0.0f);
skeletonize(prev_skel, null, 2);
//dilate_loners(prev_skel, null, 2);
if (j == 0)
{
dilate(prev_skel, null, true);
dilate(prev_skel, null, true);
}
for (int k = 1; k < nk - 1; ++k)
{
for (int i = 1; i < ni - 1; ++i)
{
bmp[new Vector3i(i, j, k)] = (prev_skel[i, k] == 1) ? true : false;
}
}
smooth(prev, tmp, 0.5f, 5);
DenseGrid2f cur = supportGrid.get_slice(j, 1);
cur.set_min(prev);
for (int k = 1; k < nk - 1; ++k)
{
for (int i = 1; i < ni - 1; ++i)
{
float skelf = prev_skel[i, k] > 0 ? -1.0f : int.MaxValue;
cur[i, k] = Math.Min(cur[i, k], skelf);
if (cur[i, k] < 0)
{
Vector3d cell_center = new Vector3f(i * dx, j * dx, k * dx) + origin;
if (distanceField.Value(ref cell_center) < -CellSize)
{
cur[i, k] = 1;
}
}
}
}
for (int k = 1; k < nk - 1; ++k)
{
for (int i = 1; i < ni - 1; ++i)
{
if (is_loner(prev_skel, i, k))
{
foreach (Vector2i d in gIndices.GridOffsets8)
{
float f = 1.0f / (float)Math.Sqrt(d.x * d.x + d.y * d.y);
cur[i + d.x, k + d.y] += -0.25f * f;
}
}
}
}
for (int k = 1; k < nk - 1; ++k)
{
for (int i = 1; i < ni - 1; ++i)
{
supportGrid[i, j, k] = cur[i, k];
}
}
prev.swap(cur);
}
VoxelSurfaceGenerator gen = new VoxelSurfaceGenerator()
{
Voxels = bmp
};
gen.Generate();
Util.WriteDebugMesh(gen.Meshes[0], "c:\\scratch\\binary.obj");
}
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);
}
});
}
public static void test_marching_cubes_topology()
{
AxisAlignedBox3d bounds = new AxisAlignedBox3d(1.0);
int numcells = 64;
double cellsize = bounds.MaxDim / numcells;
Random r = new Random(31337);
for (int ii = 0; ii < 100; ++ii)
{
DenseGrid3f grid = new DenseGrid3f();
grid.resize(numcells, numcells, numcells);
grid.assign(1);
for (int k = 2; k < numcells - 3; k++)
{
for (int j = 2; j < numcells - 3; j++)
{
for (int i = 2; i < numcells - 3; i++)
{
double d = r.NextDouble();
if (d > 0.9)
{
grid[i, j, k] = 0.0f;
}
else if (d > 0.5)
{
grid[i, j, k] = 1.0f;
}
else
{
grid[i, j, k] = -1.0f;
}
}
}
}
var iso = new DenseGridTrilinearImplicit(grid, Vector3f.Zero, cellsize);
MarchingCubes c = new MarchingCubes();
c.Implicit = iso;
c.Bounds = bounds;
//c.Bounds.Max += 3 * cellsize * Vector3d.One;
//c.Bounds.Expand(2*cellsize);
// this produces holes
c.CubeSize = cellsize * 4.1;
//c.CubeSize = cellsize * 2;
//c.Bounds = new AxisAlignedBox3d(2.0);
c.Generate();
for (float f = 2.0f; f < 8.0f; f += 0.13107f)
{
c.CubeSize = cellsize * 4.1;
c.Generate();
c.Mesh.CheckValidity(false);
MeshBoundaryLoops loops = new MeshBoundaryLoops(c.Mesh);
if (loops.Count > 0)
{
throw new Exception("found loops!");
}
}
}
//c.Mesh.CheckValidity(false);
//TestUtil.WriteTestOutputMesh(c.Mesh, "marching_cubes_topotest.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
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);
}