Subdivision Curves on Surfaces and Applications

Authors:
Dimas Martínez Morera;Luiz Velho;Paulo Cezar Carvalho
Affiliations:
Instituto Nacional de Matemática Pura e Aplicada---IMPA, Brazil;Instituto Nacional de Matemática Pura e Aplicada---IMPA, Brazil;Instituto Nacional de Matemática Pura e Aplicada---IMPA, Brazil
Venue:
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
Year:
2008

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Abstract

Subdivision curves have great importance for many CAD/CAM applications.. In this paper we propose a simple method to define subdivision schemes on triangulations. It works by translating to the triangulation a perturbation of a planar binary subdivision. To reproduce this perturbation in the surface we use both, shortest and straightest geodesics, so we call this strategy intrinsic projection method.It can reproduce any binary subdivision scheme, regardless whether it is linear or not.