Cálculo de linhas de curvatura sobre malhas de triângulos sem parametrização usando geodésicas discretas

Abstract

Lines of curvature are objects of great importance in several areas of knowledge, such as architecture, engineering, arts, and Visual Computing itself, where they are useful to perform geometry analysis and remeshing, for example. This work describes a method to compute lines of curvature on triangle meshes without requiring a parameterization. Based on the work of Alliez et al. [1], which uses approximately conform parameterizations to compute lines of curvature, concepts involving geodesics and parallel transport of vectors were applied to calculate and smooth curvature tensors, and integrating lines of curvature in the geometry of the surface. Experiments were performed to demonstrate that the method is able to compute lines of curvature on surfaces of arbitrary genus, and avoid problems caused by distortions of parameterizations.