Computer Aided Geometric Design
de Boor—fix functionals and polar forms
Computer Aided Geometric Design
Computer Aided Geometric Design
The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
Proceedings of the international conference on Curves and surfaces in geometric design
Journal of Approximation Theory
The rational Bernstein bases and the multirational blossoms
Computer Aided Geometric Design
A subdivision scheme for Poisson curves and surfaces
Computer Aided Geometric Design
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
s-power series: an alternative to Poisson expansions for representing analytic functions
Computer Aided Geometric Design
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Blossoming is a powerful tool for studying and computing with Bzier and B-spline curves and surfaces --- that is, for the investigation and analysis of polynomials and piecewise polynomials in geometric curves. Poisson curves are to analytic functions what Bzier curves are the polynomials --- a representation adapted to geometric design. As in the polynomial setting, the blossom provides a simple, powerful elegant and computationally meaningful way to analyze Poisson curves. Here, we define the analytic blossom and interpret all the known algorithms for Poisson curves --- subdivision, trimming, evaluation of the function and its derivatives, and conversion between the Taylor and the Poisson basis --- in terms of this analytic blossom.