robust cross-sections

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I have some complex, highly concave geometry that consist of a thin volume enclosed by a pair of surfaces (loaded from two .obj files; these surfaces are very close together but do not intersect). I want to render the cross-section of this volume, i.e. intersect the volume with a plane.

The way I'm trying to do this now is by taking the two .obj meshes, inverting the normals on one of them, merging them together, and then using Cookie intersect on this object and a plane (created using an isosurface using the equation aX + bY + cZ + d = 0).

It… kind of works. But Cookie seems to be very buggy/non-robust and so I get artifact triangles from the plane that aren't actually inside the volume, pieces of the “cap” in the interstitial space that are missing, etc. Playing around with the “3D tolerance” helps a bit but doesn't actually fix the problem completely (in fact setting it too small is disastrous). Jitter doesn't seem to help at all.

Is there a more robust way of doing boolean operations, for the special case where I just need the cross-section with a plane?
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What about the Clip SOP?
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