Optimized Refinable Surface Enclosures

An enclosure of a composite spline surface is a pair of simpler approximations that sandwich the surface. In particular, we are interested in efficiently constructing two triangulations, so that matched triangle pairs enclose a piece of the curved surface. The width of the enclosure, i,e. the distance between inner and outer hull, can be easily measured, because it is taken on at a vertex. Enclosures are therefore approximate implicitizations with known error; such bounding constructs are useful to support, say, collision detection, re-approximation for format conversion, meshing with tolerance, or silhouette detection. The surface enclosure developed in this paper is effective, because it is optimized and refinable: an optimization specific to a given geometry representation is done off-line and tabulated once and for all. Moreover, given an enclosure of a smooth surface, the number and location of refinement steps can be announced that guarantee that the distance to the object falls below a given tolerance, because the width generically shrinks to 1/4 under subdivision at midpoints. CR Categories: I.3.5 [surface representation, splines]: I.3.6— graphics data structures