Hello!

I’ve got a few 3d-models which aren’t drawn very cleanly - that is: There are some faces which are never visible from any point of view - as for example two intersecting spheres.

Having given up googling for an answer I was searching for a clean way to remove the hidden faces but didn’t come to a “clean” (that is: mathematically correct) solution.

Such a solution would mean to find all triangles for which it is impossible to cast a ray from anywhere of it’s surface to a point sufficiently far away without intersecting any other triangle.

Having thought about this this would form an (in-)equation system that contains different equations as well as inequalities: First one knows the ray is originated on the triangle to test for invisibility:

```
P = A + a*AB + b*AC , a>=0, b>= 0, a+b <= 1
```

and the ray cast from it

```
R = P + c * D
```

may not intersect with any triangle

```
T = Q + s*S + r*R, s+r <= 1, s>=0, r>= 0
```

.

which leads to:

```
R != T, for any (valid) a,b,c,D,T (in all other triangles)
```

.

Can this be solved efficiently? Is there software performing perfect non-realtime face removal?