메뉴 건너뛰기




Volumn 164, Issue 1, 2012, Pages 77-104

Q-Blossoming: A new approach to algorithms and identities for q-Bernstein bases and q-Bézier curves

Author keywords

Marsden's identity; Q B zier curve; Q Bernstein basis; Q blossom; Subdivision

Indexed keywords


EID: 81555202511     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2011.09.006     Document Type: Article
Times cited : (46)

References (22)
  • 1
    • 34250793932 scopus 로고    scopus 로고
    • A generalization of rational Bernstein-Bézier curves
    • Disibuyuk C., Oruç H. A generalization of rational Bernstein-Bézier curves. BIT 2007, 47:313-323.
    • (2007) BIT , vol.47 , pp. 313-323
    • Disibuyuk, C.1    Oruç, H.2
  • 2
    • 0001836480 scopus 로고
    • Pólya's urn model and computer aided geometric design
    • Goldman R. Pólya's urn model and computer aided geometric design. SIAM J. Algebr. Discrete Methods 1985, 6:1-28.
    • (1985) SIAM J. Algebr. Discrete Methods , vol.6 , pp. 1-28
    • Goldman, R.1
  • 3
    • 1542301130 scopus 로고    scopus 로고
    • Pyramid Algorithms, A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling
    • Elsevier Science
    • Goldman R. Pyramid Algorithms, A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling. The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling 2003, Elsevier Science.
    • (2003) The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling
    • Goldman, R.1
  • 4
    • 34249956850 scopus 로고
    • Recursive polynomial curve schemes and computer-aided geometric design
    • Goldman R., Barry P. Recursive polynomial curve schemes and computer-aided geometric design. Constr. Approx. 1990, 6:65-96.
    • (1990) Constr. Approx. , vol.6 , pp. 65-96
    • Goldman, R.1    Barry, P.2
  • 5
    • 0039050000 scopus 로고
    • Shape parameter deletion for Pólya curves
    • Goldman R., Barry P. Shape parameter deletion for Pólya curves. Numer. Algorithms 1991, 1:121-137.
    • (1991) Numer. Algorithms , vol.1 , pp. 121-137
    • Goldman, R.1    Barry, P.2
  • 6
    • 33644949358 scopus 로고    scopus 로고
    • Classical and Quantum Orthogonal Polynomials in One Variable
    • Cambridge University Press
    • Ismail M.E.H. Classical and Quantum Orthogonal Polynomials in One Variable. Encyclopedia of Mathematics and its Applications 2005, vol. 98. Cambridge University Press.
    • (2005) Encyclopedia of Mathematics and its Applications , vol.98
    • Ismail, M.E.H.1
  • 7
    • 0037675743 scopus 로고    scopus 로고
    • Quantum Calculus
    • Springer-Verlag
    • Kac V., Cheung P. Quantum Calculus. Universitext Series 2002, vol. IX. Springer-Verlag.
    • (2002) Universitext Series , vol.9
    • Kac, V.1    Cheung, P.2
  • 8
    • 4043127644 scopus 로고    scopus 로고
    • Generalized Bernstein polynomials
    • Lewanowicz S., Wozny P. Generalized Bernstein polynomials. BIT 2004, 44:63-78.
    • (2004) BIT , vol.44 , pp. 63-78
    • Lewanowicz, S.1    Wozny, P.2
  • 9
    • 54149117988 scopus 로고    scopus 로고
    • Approximation properties for generalized Bernstein polynomials
    • Nowak G. Approximation properties for generalized Bernstein polynomials. J. Math. Anal. Appl. 2009, 350:50-55.
    • (2009) J. Math. Anal. Appl. , vol.350 , pp. 50-55
    • Nowak, G.1
  • 10
    • 81555216265 scopus 로고    scopus 로고
    • Halil Oruç, Generalized Bernstein Polynomials and Total Positivity, Ph.D. Thesis, School of Mathematical and Computational Sciences, University of St. Andrews
    • Halil Oruç, Generalized Bernstein Polynomials and Total Positivity, Ph.D. Thesis, School of Mathematical and Computational Sciences, University of St. Andrews, 1998.
    • (1998)
  • 11
    • 0042235532 scopus 로고    scopus 로고
    • A de Casteljau algorithm for generalized Bernstein polynomials
    • Phillips G.M. A de Casteljau algorithm for generalized Bernstein polynomials. BIT 1997, 37:232-236.
    • (1997) BIT , vol.37 , pp. 232-236
    • Phillips, G.M.1
  • 12
    • 0009553236 scopus 로고    scopus 로고
    • Bernstein polynomials based on the q-integers
    • Phillips G.M. Bernstein polynomials based on the q-integers. Ann. Numer. Math. 1997, 4:511-518.
    • (1997) Ann. Numer. Math. , vol.4 , pp. 511-518
    • Phillips, G.M.1
  • 13
    • 76549126480 scopus 로고    scopus 로고
    • A survey of results on the q-Bernstein polynomials
    • Phillips G.M. A survey of results on the q-Bernstein polynomials. IMA J. Numer. Anal. 2010, 30:277-288.
    • (2010) IMA J. Numer. Anal. , vol.30 , pp. 277-288
    • Phillips, G.M.1
  • 14
    • 26844461332 scopus 로고    scopus 로고
    • Interpolation and Approximation by Polynomials
    • Springer-Verlag, New York
    • Phillips G.M. Interpolation and Approximation by Polynomials. CMS Books in Mathematics 2003, Springer-Verlag, New York.
    • (2003) CMS Books in Mathematics
    • Phillips, G.M.1
  • 15
    • 81555216269 scopus 로고
    • Blossoming: A Connect-the-Dots Approach to Splines, Digital Equipment Corp., Systems Research Center, Technical Report No. 19
    • L. Ramshaw, Blossoming: A Connect-the-Dots Approach to Splines, Digital Equipment Corp., Systems Research Center, Technical Report No. 19, 1987.
    • (1987)
    • Ramshaw, L.1
  • 16
    • 0000396670 scopus 로고
    • Bézier and B-splines as multiaffine maps
    • Springer-Verlag, New York, R.A. Earnshaw (Ed.) Theoretical Foundations of Computer Graphics and CAD
    • Ramshaw L. Bézier and B-splines as multiaffine maps. NATO ASI Series F 1988, vol. 40:757-776. Springer-Verlag, New York. R.A. Earnshaw (Ed.).
    • (1988) NATO ASI Series F , vol.40 , pp. 757-776
    • Ramshaw, L.1
  • 18
    • 81555216266 scopus 로고    scopus 로고
    • On Multiplying Points: The Paired Algebras of Forms and Sites, Compaq Systems Research Center, SRC Research Report 169
    • L. Ramshaw, On Multiplying Points: The Paired Algebras of Forms and Sites, Compaq Systems Research Center, SRC Research Report 169, 2001.
    • (2001)
    • Ramshaw, L.1
  • 20
    • 81355142066 scopus 로고    scopus 로고
    • h-blossoming: a new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves, Computer Aided Geometric Design
    • in press, doi:10.1016/j.cagd.2011.09.003
    • P. Simeonov, V. Zafiris, R. Goldman, h-blossoming: a new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves, Computer Aided Geometric Design, in press (). doi:10.1016/j.cagd.2011.09.003.
    • Simeonov, P.1    Zafiris, V.2    Goldman, R.3
  • 21
    • 0000385289 scopus 로고
    • Approximation of functions by a new class of linear polynomial operators
    • Stancu D. Approximation of functions by a new class of linear polynomial operators. Rev. Roum. Math. Pures Appl. 1968, 13:1173-1194.
    • (1968) Rev. Roum. Math. Pures Appl. , vol.13 , pp. 1173-1194
    • Stancu, D.1
  • 22
    • 81355144643 scopus 로고
    • Generalized Bernstein approximating operators, Itinerant seminar on functional equations, approximation and convexity
    • Stancu D. Generalized Bernstein approximating operators, Itinerant seminar on functional equations, approximation and convexity. Cluj-Napoca 1984, 185-192.
    • (1984) Cluj-Napoca , pp. 185-192
    • Stancu, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.