Finite elements on point based surfaces

  • Authors:
  • U. Clarenz;M. Rumpf;A. Telea

  • Affiliations:
  • Institut für Mathematik, Duisburg University, Germany;Institut für Mathematik, Duisburg University, Germany;Department of Mathematics and Computer Science, Eindhoven University of Technology, the Netherlands

  • Venue:
  • SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
  • Year:
  • 2004

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Abstract

framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. Our method is based on the construction of local tangent planes and a local Delaunay triangulation of adjacent points projected onto this plane. The definition of tangent spaces relies on moment-based computation with proven scaling and stability properties. Once local couplings are obtained, we are able to easily assemble PDE-specific mass and stiffness matrices and solve corresponding linear systems by standard iterative solvers. We demonstrate our framework by different classes of PDE-based surface processing applications, such as texture synthesis and processing, geometric fairing, and segmentation.