  We present a new meshing algorithm called guided and augmented meshing,
GAMesh, which uses a mesh prior to generate a surface for the output points of
a point network. By projecting the output points onto this prior and
simplifying the resulting mesh, GAMesh ensures a surface with the same topology
as the mesh prior but whose geometric fidelity is controlled by the point
network. This makes GAMesh independent of both the density and distribution of
the output points, a common artifact in traditional surface reconstruction
algorithms. We show that such a separation of geometry from topology can have
several advantages especially in single-view shape prediction, fair evaluation
of point networks and reconstructing surfaces for networks which output sparse
point clouds. We further show that by training point networks with GAMesh, we
can directly optimize the vertex positions to generate adaptive meshes with
arbitrary topologies.
