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- W4385489968 abstract "In this paper we disprove the belief widespread within the computer graphics community that Catmull-Clark subdivision surfaces cannot be evaluated directly without explicitly subdividing. We show that the surface and all its derivatives can be evaluated in terms of a set of eigenbasis functions which depend only on the subdivision scheme and we derive analytical expressions for these basis functions. In particular, on the regular part of the control mesh where Catmull-Clark surfaces are bi-cubic B-splines, the eigenbasis is equal to the power basis. Also, our technique is both easy to implement and efficient. We have used our implementation to compute high quality curvature plots of subdivision surfaces. The cost of our evaluation scheme is comparable to that of a bi-cubic spline. Therefore, our method allows many algorithms developed for parametric surfaces to be applied to Catmull-Clark subdivision surfaces. This makes subdivision surfaces an even more attractive tool for free-form surface modeling." @default.
- W4385489968 created "2023-08-03" @default.
- W4385489968 creator A5063366011 @default.
- W4385489968 date "2023-08-01" @default.
- W4385489968 modified "2023-09-27" @default.
- W4385489968 title "Exact Evaluation of Catmull-Clark Subdivision Surfaces at Arbitrary Parameter Values" @default.
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- W4385489968 doi "https://doi.org/10.1145/3596711.3596728" @default.
- W4385489968 hasPublicationYear "2023" @default.
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