Shape representations with blossoms and buds

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

1 Citation (Scopus)

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 d ≤ n 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 Xj(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(f). 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.

Original languageEnglish
Title of host publicationGeometric Modeling and Processing, GMP 2006 - 4th International Conference, Proceedings
PublisherSpringer Verlag
Pages397-408
Number of pages12
ISBN (Print)9783540367116
Publication statusPublished - 1 Jan 2006
Event4th International Conference on Geometric Modeling and Processing, GMP 2006 - Pittsburgh, PA, United States
Duration: 26 Jul 200628 Jul 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4077 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference4th International Conference on Geometric Modeling and Processing, GMP 2006
CountryUnited States
CityPittsburgh, PA
Period26/07/0628/07/06

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