Meshless Geometric Subdivision

Abstract

Point-based surface processing has developed into an attractive alternative to mesh-based processing techniques for a number of geometric modeling applications. By working with point clouds directly, any processing is based on the given raw data and its underlying geometry rather than any arbitrary intermediate representations and generally artificial connectivity relations. We extend this principle into the area of subdivision surfaces by introducing the notion of meshless, or point cloud, geometric subdivision. Our meshless subdivision approach replaces the role of mesh connectivity with intrinsic point proximity thereby avoiding a number of limitations of widely-used mesh-based surface subdivision schemes. Apart from introducing this idea of meshless subdivision, we put forward a first intrinsic meshless subdivision scheme and present a new method for the computation of intrinsic means on euclidean manifolds.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2004
Accession Number
ADA525792

Entities

People

  • Carsten Moenning
  • Facundo Mémoli
  • Guillermo Sapiro
  • Neil A. Dodgson
  • Nira Dyn

Organizations

  • University of Minnesota

Tags

Communities of Interest

  • Biomedical
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computations
  • Computer Graphics
  • Computer Science
  • Data Sets
  • Differential Equations
  • Engineering
  • Equations
  • Geodesics
  • Geometry
  • Graphics
  • Mathematics
  • Partial Differential Equations
  • Point Clouds
  • Three Dimensional
  • Visualizations

Readers

  • Computational Fluid Dynamics (CFD)
  • Distributed Systems and Data Platform Development
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)