Linear convexity conditions for rectangular and triangular Bernstein-Bézier surfaces

Computer Aided Geometric Design

Volumn 15, Issue 1, 1997, Pages 27-38

  Carnicer, J M ^a   Floater, M S ^b   Pena J M ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b SINTEF   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; DATA PROCESSING; GEOMETRY; INTERPOLATION; SURFACES;

CONVEXITY CONDITIONS;

COMPUTER AIDED DESIGN;

EID: 0031341073     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(97)81783-9     Document Type: Article

References (7)

1. Cavaretta, A.S. and Sharma, A. (1992), Variation diminishing properties and convexity for the tensor product Bernstein operator, Lecture Notes in Mathematics 1511, 18-32.
2. Chang, G. and Davis, P.J. (1984), The convexity of Bernstein polynomial s over triangles, J. Approx. Theory 40, 11-28.
3. Chang, G.Z. and Feng, Y.Y. (1984), An improved condition for the convexity of Bernstein-Bézier surfaces over triangles, Computer Aided Geometric Design 1, 279-283.
4. Chang, G.Z. and Feng, Y.Y. (1985), A new proof for the convexity of Bernstein-Bézier surfaces over triangles, Chinese Annals of Mathematics 6, 171-176.
5. Dahmen, W. (1991), Convexity and Bernstein-Bézier polynomials, in: Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Curves and Surfaces, Vol. 1, Academic Press, Boston, 107-134.
6. Floater, M.S. (1994), A weak condition for the convexity of tensor-product Bézier and B-spline surfaces, Adv. in Comp. Math. 2, 67-80.
7. Lai, M.J. (1990), Some sufficient conditions for convexity of multivariate Bernstein-Bézier polynomials and box spline surfaces, Studia Scient. Math. Hung. 28, 363-374.