PROJECT TITLE :
On Linear Spaces of Polyhedral Meshes
Polyhedral meshes (PM)—meshes having planar faces—have enjoyed an increase in popularity lately thanks to their importance in architectural and industrial style. However, they are conjointly notoriously difficult to come up with and manipulate. Previous strategies begin with a smooth surface and then apply elaborate meshing schemes to make polyhedral meshes approximating the surface. During this paper, we tend to describe a reverse approach: given the topology of a mesh, we explore the house of possible planar meshes having that topology. Our approach is predicated on an entire characterization of the maximal linear areas of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear areas can be described as nullspaces of differential operators, a lot of like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and native design of a polyhedral mesh, that totally expose the geometric possibilities and limitations of the given topology.
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