Applications of Laguerre geometry in CAGD

Autor:	Helmut Pottmann, Martin Peternell
Rok vydání:	1998
Předmět:	Surface (mathematics) Rational surface Dupin cyclide Aerospace Engineering Geometry Computational geometry Computer Graphics and Computer-Aided Design Hidden line removal Geometric design Intersection Medial axis Modeling and Simulation Automotive Engineering Mathematics
Zdroj:	Computer Aided Geometric Design. 15:165-186
ISSN:	0167-8396
DOI:	10.1016/s0167-8396(97)00023-x
Popis:	We briefly introduce to the basics of Laguerre geometry and then show that this classical sphere geometry can be applied to solve various problems in geometric design. In the present part, we focus on applications of the cyclographic model of Laguerre geometry and the cyclographic map. It relates the medial axis and Voronoi curves/surfaces to special surface/surface intersection and the corresponding trimming procedures to hidden line removal. Rational canal surfaces are treated as cyclographic images of rational curves in R 4. This leads to a simple control structure for rational canal surfaces. Its practical use is demonstrated at hand of modeling techniques with Dupin cyclides.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::993e387588ffbd137e2c46a08384f302 https://doi.org/10.1016/s0167-8396(97)00023-x Zobrazit plný text záznamu Full Text from ScienceDirect