Abstract
Filling n-sided regions is an essential operation in shape and surface modeling. Positional and tangential continuities are highly required in designing and manufacturing. We propose a method for filling n-sided regions with untrimmed triangular Coons B-spline patches, preserving G 1 continuity exactly. The algorithm first computes a central point, a central normal, the central, and the corner derivative vectors. Then the region is split into n triangular areas by connecting the central point to each corner of the boundary. These inner curves and all cross-boundary derivatives are computed fulfilling G 1 compatibility conditions. And finally, the triangular patches are generated in the Coons B-spline form, one boundary of which is regressed to the central vertex. Neither positional nor tangential error is introduced by this method. And only one degree elevation is needed.
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Shi, KL., Yong, JH., Sun, JG. et al. Filling n-sided regions with G 1 triangular Coons B-spline patches. Vis Comput 26, 791–800 (2010). https://doi.org/10.1007/s00371-010-0468-4
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DOI: https://doi.org/10.1007/s00371-010-0468-4