Matthew Strom BormanDepartment of Mathematics, Stanford UniversityYakov EliashbergDepartment of Mathematics, Stanford UniversityEmmy MurphyDepartment of Mathematics, Massachusetts Institute of Technology
Geometric Analysis and Geometric Topologymathscidoc:1701.15002
We establish a parametric extension$h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the 3-dimensional result from . It implies, in particular, that any closed manifold admits a contact structure in any given homotopy class of almost contact structures.
We introduce a novel approach for the polygonization of Multi-view Stereo (MVS) meshes of buildings,
which results in compact and topologically valid models. The main characteristic of our method is structure
awareness, i.e., the recovery and preservation of the initial mesh primitives and their adjacencies. Our proposed
methodology consists of three main stages: (a) primitive detection via mesh segmentation, (b) encoding of
primitive adjacencies into a graph, and (c) polygonization. Polygonization is based on the approximation of
the original mesh with a candidate set of planar polygonal faces. On this candidate set, we apply a binary
labelling formulation to select and assemble an optimal set of faces under hard constraints that ensure that
the final model is both manifold and watertight. Experiments on various building models demonstrate that
our simplification method can produce simpler representations for both closed and open building meshes.
Furthermore, these representations highly conform to the initial structure and are ready to be used for
spatial analysis. The source code of this work is freely available at https://github.com/VasileiosBouzas/MeshPolygonization.