CISE-TR-01-003: Surface envelopes
نویسنده
چکیده
Surface envelopes are tight, two-sided enclosures of composite spline surfaces. This paper shows how to construct the two hulls of the enclosure so that matched triangle pairs sandwich a given nonlinear, curved surface consisting of tensor-product Bézier patches. The main cost of the hull computation are 12 transversal line-plane intersections per vertex. 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. A one-time precomputation and optimization guarantees that the width is minimal for a set of basic splines, and the width shrinks to 1/4 under midpoint subdivision (uniform knot insertion). Surface envelopes yield easier point classification and intersection testing and an improved rule with error bound for approximately rendering curved surfaces as triangulations. CR Categories: I.3.5 [surface representation, splines]: I.3.6— graphics data structures
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