2-Manifold Tests for 3D Delaunay Triangulation-Based Surface Reconstruction

Abstract : This is a companion paper of a previous work on the surface reconstruction from a sparse cloud of points, which are estimated by Structure-from-Motion. The surface is a 2-manifold sub-complex of the 3D Delaunay triangulation of the points. It is computed as the boundary of a list of tetrahedra, which grows in the set of Delaunay tetrahedra. Here we detail the proofs for the 2-manifold tests that are used during the growing: we show that the tetrahedron-based test and the test for adding (or subtracting) one tetrahedron to (or from) the list are equivalent to standard tests based on triangles.
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Maxime Lhuillier. 2-Manifold Tests for 3D Delaunay Triangulation-Based Surface Reconstruction. Journal of Mathematical Imaging and Vision, Springer Verlag, 2015, 51 (1), pp.98-105. ⟨10.1007/s10851-014-0508-1⟩. ⟨hal-01635381⟩

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