论文信息 - On the convexity of Bézier nets of quadratic Powell—Sabin splines on 12-fold refined triangulations

On the convexity of Bézier nets of quadratic Powell—Sabin splines on 12-fold refined triangulations

Abstract In this paper, we give a geometrical characterization of the convexity of Bezier nets of some piecewise quadratic Powell–Sabin surfaces. This condition also guarantees the convexity of the underlying surfaces. We first study the local problem for the Powell–Sabin finite element decomposed into 12 triangles (the PS2 finite element). Then, we extend our results to surfaces obtained by assembling these finite elements.

Paul Sablonnière | J. Lorente-Pardo | María C. Serrano-Pérez

[1] Paul Sablonnière,et al. Error Bounds for Hermite Interpolation by Quadratic Splines on an α-Triangulation , 1987 .

[2] Wolfgang Dahmen,et al. Convexity preserving interpolation and Powell-Sabin elements , 1992, Comput. Aided Geom. Des..

[3] Philip J. Davis,et al. The convexity of Bernstein polynomials over triangles , 1984 .

[4] Geng-zhe Chang,et al. An improved condition for the convexity of Bernstein-Bézier surfaces over triangles , 1984, Comput. Aided Geom. Des..

[5] Malcolm A. Sabin,et al. Piecewise Quadratic Approximations on Triangles , 1977, TOMS.

[6] Michael S. Floater. A counterexample to a theorem about the convexity of Powell-Sabin elements , 1997, Comput. Aided Geom. Des..

[7] Aidi Li,et al. Convexity preserving interpolation , 1999, Comput. Aided Geom. Des..

[8] Paul Dierckx,et al. Surface fitting using convex Powell-Sabin splines , 1994 .

[9] Thomas A. Grandine,et al. On convexity of piecewise polynomial functions on triangulations , 1989, Comput. Aided Geom. Des..