Surface representations using blossoms and buds

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Shape representations using polynomials in computer-aided geometric design (CAGD) and computer graphics are ubiquitous. This paper shows that any bivariate polynomial p(t,u) of total degree d ≤ n can be represented in the form of a blossom of another bivariate polynomial b(t,u) of total degree d evaluated off the diagonal at the linear function pairs (Xj(t),Yj(u)), j = 1, . . ., n, chosen under some conditions expressed in terms of symmetric functions. The bivariate polynomial b(t,u) is called a bud of the bivariate polynomial p(t,u). An algorithm for finding a bud b(t,u) of a given bivariate polynomial p(t,u) is presented. Successively, a bud of b(t,u) can be computed and so on, to form a sequence of representations. The information represented by the original bivariate polynomial is preserved in its buds. This scheme can be used for encoding/ decoding geometric design information. The objects in the encoding/decoding sequence can be rendered graphically and manipulated geometrically like the usual parametric representations. Examples concerning triangular Bézier patches are provided as illustrations.

Original languageEnglish
Title of host publicationIEEE International Conference on Shape Modeling and Applications 2008, Proceedings, SMI
Pages139-145
Number of pages7
DOIs
Publication statusPublished - 9 Sep 2008
EventIEEE International Conference on Shape Modeling and Applications 2008, SMI - Stony Brook, NY, United States
Duration: 4 Jun 20086 Jun 2008

Publication series

NameIEEE International Conference on Shape Modeling and Applications 2008, Proceedings, SMI

Conference

ConferenceIEEE International Conference on Shape Modeling and Applications 2008, SMI
Country/TerritoryUnited States
CityStony Brook, NY
Period4/06/086/06/08

Keywords

  • Algorithm
  • Bivariate polynomial
  • Blossom of a bivariate polynomial
  • Bud of a bivariate polynomial
  • Encoding-decoding
  • Geometric design
  • Sequence of representations
  • Shape representation
  • Surface representation
  • Triangular Bézier patch

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