The Analytic Blossom
- Blossoming is a powerful tool for studying and computing with Bézier and B-spline curves and surfaces - that is, for the investigation and analysis of polynomials and piecewise polynomials in geometric modeling. In this paper, we define a notion of the blossom for Poisson curves. Poisson curves are to analytic functions what Bézier curves are to 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.
Author: | Géraldine Morin, Ron Goldman |
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URN: | urn:nbn:de:hbz:386-kluedo-49920 |
Series (Serial Number): | Interner Bericht des Fachbereich Informatik (306) |
Document Type: | Report |
Language of publication: | English |
Date of Publication (online): | 2017/10/30 |
Year of first Publication: | 2001 |
Publishing Institution: | Technische Universität Kaiserslautern |
Date of the Publication (Server): | 2017/10/30 |
Page Number: | 21 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Informatik |
DDC-Cassification: | 0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik |
Licence (German): | Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0) |