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 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.
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© 2006 Springer-Verlag Berlin Heidelberg
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Stefanus, L.Y. (2006). Shape Representations with Blossoms and Buds. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_28
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DOI: https://doi.org/10.1007/11802914_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36711-6
Online ISBN: 978-3-540-36865-6
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