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Filling n-sided regions with G1 triangular Coons B-spline patches

Kan-Le Shi 1 Jun-Hai yong 1 Jia-Guang Sun 1, 2 Jean-Claude Paul 2 He-Jin Gu 3 
2 CAD - Computer Aided Design
LIAMA - Laboratoire Franco-Chinois d'Informatique, d'Automatique et de Mathématiques Appliquées, Inria Paris-Rocquencourt
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 G1 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 G1 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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Kan-Le Shi, Jun-Hai yong, Jia-Guang Sun, Jean-Claude Paul, He-Jin Gu. Filling n-sided regions with G1 triangular Coons B-spline patches. The Visual Computer, Springer Verlag, 2010, 26 (6-8), pp.791-800. ⟨10.1007/s00371-010-0468-4⟩. ⟨inria-00517938⟩

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