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Re: bounding boxes for loop's subdivision patches

Posted by Ray on September 14, 2005 at 13:44:15:

In Reply to: Re: bounding boxes for loop's subdivision patches posted by Scott Schaefer on September 14, 2005 at 11:07:17:

: : I am working on ray tracing Loop's subdivision surface, and I wonder if there is a fast way to compute the bounding box of each subdivided patch (a patch is a single triangle in the base mesh). Ideally I would like to compute these bounding boxes from the base mesh, NOT the finely subdivided mesh, which is expensive. They don't have to be exact but should be fairly tight for fast ray tracing. Thanks!!

: Yes there is. Loop subdivision (as well as many other subdivision schemes) has the convex hull property. That is, the surface lies in the convex hull of its control points. So if you take a triangle from the base surface and consider all triangles that touch that triangle, the convex hull of those control points bounds that patch. You can then compute an axis-aligned or non-axis-aligned bounding box from those control points.

Thanks Scott! I am curious if there is any tighter estimation than this. Take a cube for example, the bounding box for any base patch is actually the whole cube, which seems too conservative. Any thoughts?

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Re: bounding boxes for loop's subdivision patches Scott Schaefer 10:18:11 09/15/05 (0)

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: : : I am working on ray tracing Loop's subdivision surface, and I wonder if there is a fast way to compute the bounding box of each subdivided patch (a patch is a single triangle in the base mesh). Ideally I would like to compute these bounding boxes from the base mesh, NOT the finely subdivided mesh, which is expensive. They don't have to be exact but should be fairly tight for fast ray tracing. Thanks!! : : Yes there is. Loop subdivision (as well as many other subdivision schemes) has the convex hull property. That is, the surface lies in the convex hull of its control points. So if you take a triangle from the base surface and consider all triangles that touch that triangle, the convex hull of those control points bounds that patch. You can then compute an axis-aligned or non-axis-aligned bounding box from those control points. : Thanks Scott! I am curious if there is any tighter estimation than this. Take a cube for example, the bounding box for any base patch is actually the whole cube, which seems too conservative. Any thoughts?

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