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Reports (Research Report) Year : 2004

Variational Shape Approximation

Pierre Alliez
Mathieu Desbrun


Achieving efficiency in mesh processing often demands that overly verbose 3D datasets be reduced to more concise, yet faithful representations. Despite numerous applications ranging from geometry compression to reverse engineering, concisely capturing the geometry of a surface remains a tedious task. In this paper, we present both theoretical and practical contributions that result in a novel and versatile framework for geometric approximation of surfaces. We depart from the usual strategy by casting shape approximation as a variational geometric partitioning problem. Using the concept of geometric proxies, we drive the distortion error down through repeated clustering of faces into best-fitting regions. Our approach is entirely discrete and error-driven, and does not require parameterization or local estimations of differential quantities. We also introduce a new metric based on normal deviation, and demonstrate its superior behavior at capturing anisotropy.
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Dates and versions

inria-00070632 , version 1 (19-05-2006)


  • HAL Id : inria-00070632 , version 1


David Cohen-Steiner, Pierre Alliez, Mathieu Desbrun. Variational Shape Approximation. [Research Report] RR-5371, INRIA. 2004, pp.29. ⟨inria-00070632⟩
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