The Occlusion challenge

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To answer Dev's terminology question...

A mesh is convex if all of its faces point outward and none of them, when extended to form infinite planes, intersect with any other faces in the mesh. Here's the test: if a 3d line can intersect the object in more than two places, it's not convex.

Of course, concave is the same thing but with all of the faces pointing inward.

Brush geometry refers to mesh details added on top of the occlusion geometry and usually parented to it as part of the visibility scheme. Think of it as furniture inside the room.