UBC Theses and Dissertations

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UBC Theses and Dissertations

Multi-resolution surface approximation for animation Wang, Lifeng


This thesis addresses the problem of approximating a set of gridded data points obtained from a three-dimensional digitizing system to create a representation with a hierarchical bicubic B-spline surface that is suitable for further manipulation and animation. Chord length parameterization is obtained using 2-D deformation technique. A full multigrid (FMG) numerical method is used to solve the surface approximation and the multi-resolution elements created are used directly to define the overlays in a hierarchical B-spline surface. The direct use of FMG multi-resolution data offers reasonable surface shape behaviour, but the number of non-zero offsets is large. Storage cost is reduced either by eliminating offsets whose magnitude is below a certain tolerance or by reducing all offsets in a given level by a user specified amount. The resulting spline surface is modifiable, both locally and globally while retaining surface details of the digitized data. An interactive system based on these methods was created and the results of approximating two large data sets are presented.

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