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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Shape Representations with Blossoms and Buds
verfasst von : L. Yohanes Stefanus
Erschienen in: Geometric Modeling and Processing - GMP 2006
Verlag: Springer Berlin Heidelberg
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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.