Nira Dyn
Abstract
A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C1 for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.
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Index Terms
- A butterfly subdivision scheme for surface interpolation with tension control
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Reviews
Heinrich W. Guggenheimer
The authors have previously studied the convergence of linear interpolatory subdivision schemes for B-spline curves [1]. The schemes investigated generally do not yield smooth (C 2 ) curves. This paper reports on an implementation of a linear interpolatory subdivision scheme for triangulated surfaces (constructing a new subdivision point out of eight neighbors). This scheme depends on a scalar or tensor parameter for which a formal regularity analysis of the limit surface is not available, but it seems to work well (within the narrow limits on the parameters imposed by geometry) on piecewise C 1 surfaces. The usefulness of such a scheme in design experimentation obviously depends on the speed of computation, which in turn depends much more on the internal data structures of the program than on the mathematics of the algorithm. The entire field of CAD would be in much better shape if researchers made their programs available or indicated enough of the crucial technicalities. The bibliography gives a nice survey of the work done in this field.
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