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UBC CS TR-92-36 Summary

Multi-Resolution Surface Approximation for Animation, October 30, 1992 David Forsey and LiFeng Wang, 11 pages

This paper considers the problem of approximating a digitized surface in R3 with a hierarchical bicubic B-spline to produce a manipulatable surface for further modeling or animation. The 3D data's original mapping from R3 (multiple rows of cylindrical scans) is mapped into the parametric domain of the B-splice (also in R3) using a modified chord-length parameterization. This mapping is used to produce a gridded sampling of the surface, and a modified full multi-grid (FMG) technique is employed to obtain a high-resolution B-spline approximation. The intermediate results of the FMG calculations generate the component overlays of a hierarchical spline surface reconstruction. Storage requirements of the hierarchical representation are reduced by eliminating offsets wherever their removal will not increase the error in the approximation by more than a given amount. The resulting hierarchical spline surface is interactively modifiable (modulo the size of the dataset and computing power) using the editing capabilities of the hierarchical surface representation allowing either local or global changes to surface shape while retaining details of the scanned data.

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