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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.

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Metadaten
Author:Géraldine Morin, Ron Goldman
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49920
Serie (Series number):Interner Bericht des Fachbereich Informatik (306)
Document Type:Report
Language of publication:English
Publication Date:2017/10/30
Year of Publication:2001
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/30
Number of page:21
Faculties / Organisational entities: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)