Techniques are disclosed for generating a consensus mesh to cover a received set of points. In one embodiment, a meshing application generates multiple meshes that cover the received point set by varying parameters of an interpolating meshing technique, such as the ball-pivoting technique, tangent-space Delaunay triangulation, and the like. Different values for the one or more parameters are used to generate each of the meshes. After generating the multiple meshes, the meshing application may sort triangles in the meshes based on the frequency in which the triangles appear in the meshes. The meshing application may then iteratively add next-best triangles which are also compatible with the current consensus mesh to the consensus mesh, with the next-best triangle being a most frequently occurring triangle which has not yet been added to the consensus mesh. Compatibility may be defined using various criteria, such as producing a manifold and orientable triangulation.