Regular algebraic curve segments (I)—Definitions and characteristics

Guoliang Xu, Chandrajit L. Bajaj*, Weimin Xue

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

13 Citations (Scopus)


In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular algebraic curves (real, nonsingular and connected). Several discriminating families are obtained which yield different characterizations of the Bernstein–Bézier (BB) bivariate polynomials over the plane triangle and the quadrilateral domain such that their zero contours are smooth and connected. These regular curve segments in BB basis can be smoothly joined together to form algebraic curve splines or A-splines. Algorithms for the efficient graphics display of these new A-spline families are also provided.
Original languageEnglish
Pages (from-to)485-501
Number of pages17
JournalComputer Aided Geometric Design
Issue number6
Early online date15 May 2000
Publication statusPublished - Jul 2000
Externally publishedYes

Scopus Subject Areas

  • Modelling and Simulation
  • Automotive Engineering
  • Aerospace Engineering
  • Computer Graphics and Computer-Aided Design


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