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Algebraic Point Set Surfaces

Abstract : In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our approach compared to existing planar MLS include significantly improved stability of the projection under low sampling rates and in the presence of high curvature. The method can approximate or interpolate the input point set and naturally handles planar point clouds. In addition, our approach provides a reliable estimate of the mean curvature of the surface at no additional cost and allows for the robust handling of sharp features and boundaries. It processes a simple point set as input, but can also take significant advantage of surface normals to improve robustness, quality and performance. We also present an novel normal estimation procedure which exploits the properties of the spherical fit for both direction estimation and orientation propagation. Very efficient computational procedures enable us to compute the algebraic sphere fitting with up to 40 million points per second on latest generation GPUs.
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Contributor : Gaël Guennebaud Connect in order to contact the contributor
Submitted on : Wednesday, January 21, 2009 - 4:32:32 PM
Last modification on : Thursday, May 27, 2021 - 1:54:05 PM


  • HAL Id : inria-00354998, version 1


Gael Guennebaud, Markus Gross. Algebraic Point Set Surfaces. ACM Transactions on Graphics, Association for Computing Machinery, 2007, Proceedings of Siggraph 2007, 26 (3), pp.23-9. ⟨inria-00354998⟩



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