IEEE Transactions on Visualization and Computer Graphics

IEEE Transactions on Visualization and Computer Graphics (TVCG) is a monthly journal that publishes research on subjects related to computer graphics and visualization techniques, systems, software, hardware, and user interface issues. Read the full scope of TVCG.

From the May 2015 issue

On Linear Spaces of Polyhedral Meshes

By Roi Poranne, Renjie Chen, and Craig Gotsman

Featured articlePolyhedral meshes (PM)—meshes having planar faces—have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes having that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology.

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           TVCG is indexed in MEDLINE®/PubMed® & ISI

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