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Rounding Meshes in 3D

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ARTICLE DOWNLOAD

Rounding Meshes in 3D

10.00$

Olivier Devillers, Sylvain Lazard & William J. Lenhart 

Abstract

Let PP be a set of n polygons in R3R3, each of constant complexity and with pairwise disjoint interiors. We propose a rounding algorithm that maps PP to a simplicial complex QQ whose vertices have integer coordinates. Every face of PP is mapped to a set of faces (or edges or vertices) of QQ and the mapping from PP to QQ can be done through a continuous motion of the faces such that: (i) the L∞L∞ Hausdorff distance between a face and its image during the motion is at most 3/2, and (ii) if two points become equal during the motion, they remain equal through the rest of the motion. In the worst case the size of QQ is O(n13)O(n13) and the time complexity of the algorithm is O(n15)O(n15) but, under reasonable assumptions, these complexities decrease to O(n4n−−√)O(n4n) and O(n5)O(n5). Furthermore, these complexities are likely not tight and we expect, in practice on non-pathological data, O(nn−−√)O(nn) space and time complexities.

Only units of this product remain
Year 2020
Language English
Format PDF
DOI 10.1007/s00454-020-00202-2