Modeling Wireframe Meshes With Discrete Equivalence Classes

We study a problem of modeling wireframe meshes where the vertices and edges fall into a set of discrete equivalence classes, respectively. This problem is motivated by the need of fabricating large wireframe structures at lower cost and faster speed since both nodes (thickened vertices) and rods (thickened edges) can be mass-produced. Given a 3D shape represented as a wireframe mesh, our goal is to compute a set of template vertices and a set of template edges, whose instances can be used to produce a fabricable wireframe mesh that approximates the input shape. To achieve this goal, we propose a computational approach that generates the template vertices and template edges by iteratively clustering and optimizing the mesh vertices and edges. At the clustering stage, we cluster mesh vertices and edges according to their shape and length, respectively. At the optimization stage, we first locally optimize the mesh to reduce the number of clusters of vertices and/or edges, and then globally optimize the mesh to reduce the intra-cluster variance for vertices and edges, while facilitating fabricability of the wireframe mesh. We demonstrate that our approach is able to model wireframe meshes with various shapes and topologies, compare it with three state-of-the-art approaches to show its superiority, and validate fabricability of our results by making three physical prototypes.