Input Approximation Sphere-Mesh Interpolation

Figure 1: Starting from a surface mesh (left, 200k triangles), we propose an approximation algorithm which generates a sphere-mesh (middle) defining an extremely simplified model (here with 50 spheres) as a sphere interpolation over a set of edges and polygons (right). The input mesh is shown in orange (left), the sphere-mesh is displayed in the middle (spheres in red, edges in yellow, triangles in blue) and the interpolated sphere-mesh geometry is shown on the right (edge interpolation in grey, triangle interpolation in blue). Shape approximation algorithms aim at computing simple geomet-ric descriptions of dense surface meshes. Many such algorithms are based on mesh decimation techniques, generating coarse tri-angulations while optimizing for a particular metric which mod-els the distance to the original shape. This approximation scheme is very efficient when enough polygons are allowed for the sim-plified model. However, as coarser approximations are reached, the intrinsic piecewise linear point interpolation which defines the decimated geometry fails at capturing even simple structures. We claim that when reaching such extreme simplification levels, highl