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Shape Representations with Blossoms and Buds

  • L. Yohanes Stefanus
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4077)

Abstract

Polynomials, either on their own or as components of splines, play a fundamental role for shape representations in computer-aided geometric design (CAGD) and computer graphics. This paper shows that any polynomial p(t) of degree dn can be represented in the form of a blossom of another polynomial b(t) of degree d evaluated off the diagonal at the linear functions X j (t), j=1, ..., n, chosen under some conditions expressed in terms of the elementary symmetric functions. The polynomial b(t) is called a bud of the polynomial p(t). An algorithm for finding a bud b(t) of a given polynomial p(t) is presented. Successively, a bud of b(t) can be computed and so on, to form a sequence of representations. The information represented by the original polynomial is preserved in its buds. This scheme can be used for encoding/decoding geometric design information.

Keywords

Computer Graphic Geometric Design Decode Process Shape Representation Control Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • L. Yohanes Stefanus
    • 1
  1. 1.Faculty of Computer ScienceUniversity of IndonesiaDepokIndonesia

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