A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Mathematical methods in computer aided geometric design II
Blossoming off the diagonal
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
De Boor-Fix dual functionals for transformation from polynomial basis to convolution basis
ACM Communications in Computer Algebra
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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 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(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.