Reference Work Entry

Encyclopedia of Algorithms

pp 2174-2177

Date:

Surface Reconstruction

  • Nina AmentaAffiliated withDepartment of Computer Science, University of California Email author 

Keywords

Delaunay triangulation Local feature size Medial axis Surface reconstruction Voronoi diagram

Years and Authors of Summarized Original Work

  • 1999; Amenta, Bern

  • 2000; Amenta, Choi, Dey, Leekha

  • 2001; Amenta, Choi, Kolluri

  • 2004; Dey, Goswami

https://static-content.springer.com/image/prt%3A978-1-4939-2864-4%2F19/MediaObjects/978-1-4939-2864-4_19_Part_Fig1-713_HTML.jpg
Surface Reconstruction, Fig. 1

The medial axis of an object; the Voronoi diagram of a set of samples from the object boundary; the set of polar balls, with those inside the object shaded; the corresponding cells of the weighted Voronoi diagram, again with those inside the object shaded

Problem Definition

Surface reconstruction, here, is the problem of producing a piecewise-linear representation of a two-dimensional surface S in \(\mathbb{R}^{3}\), given as input a set P of point samples from the surface. Very sparse sets of point samples clearly do not convey much about S, so in order to prove correctness, we need to assume that the sample P is somehow sufficiently dense. The minimum required density could vary across the surface, with more detailed areas requiring denser sampling. This idea is captured in the following definition [2]. Let S be a two ...

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