Some applications of scalar and vector fields to geometric processing of surfaces

  • Authors:

  • Jaime Puig-Pey;Akemi Gálvez;Andrés Iglesias;José Rodríguez;Pedro Corcuera;Flabio Gutiérrez

  • Affiliations:

  • Department of Applied Mathematics and Computational Sciences, University of Cantabria, Av. de los Castros, s/n, 39005 Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Av. de los Castros, s/n, 39005 Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Av. de los Castros, s/n, 39005 Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Av. de los Castros, s/n, 39005 Santander, Spain;Department of Applied Mathematics and Computational Sciences, University of Cantabria, Av. de los Castros, s/n, 39005 Santander, Spain;Department of Mathematics, National University of Piura, Campus Universitario s/n. Urbanizacion Miraflores, Piura, Perú

  • Venue:
  • Computers and Graphics
  • Year:
  • 2005

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Abstract

In this paper, two geometric processing problems are considered: (1) point on a surface nearest to an external point, and (2) silhouette curve of a surface when observed from a given point. Problem (1) is solved by constructing gradient curves on the surface associated with a distance scalar field. Problem (2) appears as the intersection of surfaces (implicit case), or as tracing a plane curve (parametric case). Formulations are geometric-differential, and lead to explicit, first-order systems of ordinary differential equations (ODEs), with initial conditions that can be efficiently integrated by standard numerical methods. The methodology allows us to deal with both implicit and parametric representations, these having any functional structure for which the differential statements are meaningful.