메뉴 건너뛰기




Volumn 16, Issue 4, 1999, Pages 287-300

Subharmonicity and convexity properties of Bernstein polynomials and Bezier nets on triangles

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER AIDED DESIGN; POLYNOMIALS;

EID: 0033548977     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(98)00050-8     Document Type: Article
Times cited : (4)

References (20)
  • 1
    • 85031619770 scopus 로고
    • Geometric properties on Bernstein polynomials over simplices
    • Lyche, T. and Schumaker, L.L., eds., Academic Press, Boston
    • Beśka, M. (1992), Geometric properties on Bernstein polynomials over simplices, in: Lyche, T. and Schumaker, L.L., eds., Mathematical Methods in CAGD and Image Processing, Academic Press, Boston, 1-8.
    • (1992) Mathematical Methods in CAGD and Image Processing , pp. 1-8
    • Beśka, M.1
  • 2
    • 0026915632 scopus 로고
    • Convexity preserving interpolation and Powell - Sabin elements
    • Carnicer, J.M. and Dahmen, W. (1992), Convexity preserving interpolation and Powell - Sabin elements, Computer Aided Geometric Design 9, 279-289.
    • (1992) Computer Aided Geometric Design , vol.9 , pp. 279-289
    • Carnicer, J.M.1    Dahmen, W.2
  • 3
    • 0031341073 scopus 로고    scopus 로고
    • Linear convexity conditions for rectangular and triangular Bernstein - Bézier surfaces
    • Carnicer, J.M., Floater, M.S. and Peña, J.M. (1997), Linear convexity conditions for rectangular and triangular Bernstein - Bézier surfaces, Computer Aided Geometric Design 15, 27-38.
    • (1997) Computer Aided Geometric Design , vol.15 , pp. 27-38
    • Carnicer, J.M.1    Floater, M.S.2    Peña, J.M.3
  • 4
    • 0001834679 scopus 로고
    • The convexity of Bernstein polynomials over triangles
    • Chang, G.Z. and Davis, P.J. (1984), The convexity of Bernstein polynomials over triangles, J. Approx. Theory 40, 11-28.
    • (1984) J. Approx. Theory , vol.40 , pp. 11-28
    • Chang, G.Z.1    Davis, P.J.2
  • 5
    • 0009400943 scopus 로고
    • Converse theorems of convexity for Bernstein polynomials over triangles
    • Chang, G.Z. and Zhang, J.Z. (1990), Converse theorems of convexity for Bernstein polynomials over triangles, J. Approx. Theory 61, 265-278.
    • (1990) J. Approx. Theory , vol.61 , pp. 265-278
    • Chang, G.Z.1    Zhang, J.Z.2
  • 6
    • 0002671799 scopus 로고
    • Convexity and Bernstein - Bézier polynomials
    • Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Academic Press, Boston, MA
    • Dahmen, W. (1991), Convexity and Bernstein - Bézier polynomials, in: Curves and Surfaces, Laurent, P.J., Le Méhauté, A. and Schumaker, L.L., eds., Academic Press, Boston, MA, 107-134.
    • (1991) Curves and Surfaces , pp. 107-134
    • Dahmen, W.1
  • 7
    • 0001261671 scopus 로고
    • Convexity of multivariate Bernstein polynomials and box spline surfaces
    • Dahmen, W. and Micchelli, C.A. (1988), Convexity of multivariate Bernstein polynomials and box spline surfaces, Studia Sci. Math. Hungar. 23, 265-287.
    • (1988) Studia Sci. Math. Hungar. , vol.23 , pp. 265-287
    • Dahmen, W.1    Micchelli, C.A.2
  • 8
    • 0028374478 scopus 로고
    • The invariance of weak convexity conditions of B-nets with respect to subdivision
    • Feng, Y.Y., Chen, F.L. and Zhou, H.L. (1994), The invariance of weak convexity conditions of B-nets with respect to subdivision, Computer Aided Geometric Design 11, 97-107.
    • (1994) Computer Aided Geometric Design , vol.11 , pp. 97-107
    • Feng, Y.Y.1    Chen, F.L.2    Zhou, H.L.3
  • 9
    • 0031143851 scopus 로고    scopus 로고
    • A counterexample to a theorem on Powell - Sabin elements
    • Floater, M. (1997), A counterexample to a theorem on Powell - Sabin elements, Computer Aided Geometric Design 14, 383-385.
    • (1997) Computer Aided Geometric Design , vol.14 , pp. 383-385
    • Floater, M.1
  • 10
    • 0001020447 scopus 로고
    • Shape preserving representations
    • Lyche, T. and Schumaker, L.L., eds., Academic Press, Boston, MA
    • Goodman, T.N.T. (1989), Shape preserving representations, in: Mathematical Methods in Computer Aided Geometric Design, Lyche, T. and Schumaker, L.L., eds., Academic Press, Boston, MA, 333-351.
    • (1989) Mathematical Methods in Computer Aided Geometric Design , pp. 333-351
    • Goodman, T.N.T.1
  • 11
    • 0009460030 scopus 로고
    • Shape criteria of Bernstein - Bézier polynomials over simplexes
    • He, T.-X. (1995), Shape criteria of Bernstein - Bézier polynomials over simplexes, Comput. Math. Appl. 30, 317-333.
    • (1995) Comput. Math. Appl. , vol.30 , pp. 317-333
    • He, T.-X.1
  • 12
    • 0009353691 scopus 로고    scopus 로고
    • On convexity and subharmonicity of some functions on triangles
    • Le Méhauté, A., Rabut, C. and Schumaker, L.L., eds., Vanderbilt University Press
    • Lorente-Pardo, J., Sablonnière, P. and Serrano-Pérez, M.C. (1997), On convexity and subharmonicity of some functions on triangles, in: Curves and Surfaces with Applications in CAGD, Le Méhauté, A., Rabut, C. and Schumaker, L.L., eds., Vanderbilt University Press, 271-278.
    • (1997) Curves and Surfaces with Applications in CAGD , pp. 271-278
    • Lorente-Pardo, J.1    Sablonnière, P.2    Serrano-Pérez, M.C.3
  • 13
    • 0009418175 scopus 로고    scopus 로고
    • On the convexity of Powell - Sabin finite elements
    • Chen, Z., Li, Y., Micchelli, C.A. and Xu, Y., eds., Marcel Dekker, Inc.
    • Lorente-Pardo, J., Sablonnière, P. and Serrano-Pérez, M.C. (1998), On the convexity of Powell - Sabin finite elements, in: Advances in Computational Mathematics, Chen, Z., Li, Y., Micchelli, C.A. and Xu, Y., eds., Marcel Dekker, Inc., 395-404.
    • (1998) Advances in Computational Mathematics , pp. 395-404
    • Lorente-Pardo, J.1    Sablonnière, P.2    Serrano-Pérez, M.C.3
  • 15
    • 0009346389 scopus 로고
    • Some remarks on nonnegative polynomials on polyhedra
    • Anderson, T., Athreya, K. and Iglebert, D., eds., Academic Press, New York
    • Micchelli, C.A. and Pinkus, A. (1989), Some remarks on nonnegative polynomials on polyhedra, in: Prob. Stat. and Math. Papers in Honor of Samuel Karlin, Anderson, T., Athreya, K. and Iglebert, D., eds., Academic Press, New York, 163-186.
    • (1989) Prob. Stat. and Math. Papers in Honor of Samuel Karlin , pp. 163-186
    • Micchelli, C.A.1    Pinkus, A.2
  • 16
    • 0009436920 scopus 로고
    • Sur les fonctions convexes et les fonctions sousharmoniques
    • Montel, P. (1928), Sur les fonctions convexes et les fonctions sousharmoniques. J. Math. Pures Appl., Series 9, Vol. 7, 29-60.
    • (1928) J. Math. Pures Appl., Series 9 , vol.7 , pp. 29-60
    • Montel, P.1
  • 18
    • 0026406596 scopus 로고
    • Multivariate Bernstein polynomials and convexity
    • Sauer, T. (1991), Multivariate Bernstein polynomials and convexity, Computer Aided Geometric Design 8, 465-478.
    • (1991) Computer Aided Geometric Design , vol.8 , pp. 465-478
    • Sauer, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.