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Revista Ingenierías Universidad de Medellín

Print version ISSN 1692-3324

Abstract

MATEUS, Sandra. Quadrilateralization of a triangular net using spectral analysis and Morse theory. Rev. ing. univ. Medellin [online]. 2008, vol.7, n.12, pp.158-167. ISSN 1692-3324.

Reparametrization of triangular nets is one of the basic processes used by almost all geometric processing systems. Most works have been focused on the triangular netting. A problem which is also important about triangled surface reparametrization in quadrilaterals has gone adrift for a long time. In spite of a relative lack of attention, a need for quality quadrilateral reparametrization methods is extremely important in several areas such as graphic computation and computer visualization. This article shows an approach to the trIangle net quadrilateraliization issue. By applying Morse theory to Laplace’s net own values, a logarithm which quadrilateralizes triangular surfaces is implemented. Due to the properties of Laplace’s operator, resulting quadrilateral patches are appropriately formed and directly lifted from intrinsic properties of the surface.

Keywords : quadrilateralization; Morse theory; spectral analysis; triangular nets.

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