Convex Hull to Voxel Grid

Question

I have a given 3D mesh which is constructed by taking a set of random points and finding the convex hull of those points. I then use open3d and trimesh to convert the conex hull into a mesh. I want to know how I can convert this mesh or the convex hull itself into a filled boolean voxel grid.

I can use trimesh to get a voxel grid of some sort but it seems the insides are hollow. I want a boolean voxel grid which gives true for the volume inside the convex hull and false otherwise.

Spektre Spektre · Accepted Answer · 2020-05-18T06:53:42

Simply rasterize your convex polygon volume ...

compute any inside point c

for convex hull its enough to compute avg point so sum all n points together an divide by n
compute per face normals

each triangle face has 3 points p0,p1,p2 so
```
nor = cross( p1-p0 , p2-p0 );
```
and chose direction so it points out of the convex hull so:
```
if ( dot( p0-c , nor ) < 0) nor = -nor;
```
loop through all voxels

so 3 nested for loops going through your grid. Lets call the actual iterated point q
test inside convex hull

the q is inside your convex hull if all dot products between q-face_point and face_normal is negative or zero... So loop through all triangles/faces and test... after that either fill the voxel or not ...

If you want something faster (in case you got too many triangles) there are ways like:

Rasterize the triangles and floodfill
Tetrahedronize volume and rasterize each tetrahedron separately
render depth maps from 6 sides of outscribed cube and infill

Convex Hull to Voxel Grid

2 Answers