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Calculating areas of box spline surfaces

โœ Scribed by TNT Goodman; BH Ong

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
642 KB
Volume
27
Category
Article
ISSN
0010-4485

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โœฆ Synopsis

Suppose that S is a linear combination of integer translates of a box spline on a 3-direction mesh that is restricted to a bounded region. The paper shows that the surface area of the control net decreases under subdivision and converges linearly to the surface area of S. A lower bound is also given for the surface area of S which increases under subdivision and converges quadratically. Both upper and lower bounds can be easily calculated from certain coefficients that are computed by a simple, recursive averaging algorithm.

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