Mathematical Methods in Computer Aided Geometric Design II by Tom Lyche, Larry L. Schumaker

By Tom Lyche, Larry L. Schumaker

This quantity relies on a global convention held in June 1991, and includes instructional and unique research-level papers on mathematical equipment in CAGD and snapshot processing. top researchers (Barnsley, Chui, Seidell, de Casteljau) have authored invited survey papers on spline and Bezier tools for curve and floor modeling, visualization, and information becoming in addition to connections with wavelets and fractals, and their functions in photograph processing. it is a very winning sector with the twin machine graphics/applied arithmetic marketplace

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Discussion of T h e s e M o d e l i n g S c h e m e s All the methods presented have different strengths and weaknesses. In each case, by present day technology, one has to choose the "right" scheme ac­ cording to the relevance of its strengths and weaknesses to the application at hand. In this section we would like to present briefly these differences, and explore their interactions, defining in the passing the space that we feel the new model presented in Section 6 can fill. In the next three subsections, we do this by focusing on three central issues: corner compatibility problems, geometric interrogations and set operations.

Computer Aided Geom. Design 6 (1989), 235-247. 9. CatmuU, E. , and J. H. Clark, Recursively generated B-spUne surfaces on arbitrary topological meshes, Comput. Aided Design 10 (1978), 350355. 10. Chaikin, G. , An algorithm for high speed curve generation. Comp. Graphics and Image Proc. 3 (1974) 346-349. 11. , and F. Kimura, A new surface interpolation method for irregular curve models. Comp. Graph. Forum 3 (1984) 209-218. 12. , Extended free-form deformation: a sculpturing tool for 3D geometric modeling, SIGGRAPH'90 24 (1990), 187-196.

Chiyokura, Boolean operations on sets using surface data. Proceedings of the Symposium on Solid Modeling Foundations and CAD/CAM Applications, Texas, 1991, J. Rossignac and J. ), ACM Press, 1991, 119-127. 31. Sederberg, T. , Piecewise algebraic surface patches. Computer Aided Geom. Design 2 (1985), 53-59. 32. Sederberg, T. , and S. R. Parry, Free-form deformation of solid models, SIGGRAPH'86 20 ACM, 1986, 151-160. 33. Van Wijk, J. , Bicubic patches for approximating non-rectangular control-point meshes.

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