Adaptive Surface Meshes from Harmonic Maps

Abstract: We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given function over a planar domain. Our algorithm, in contrast, optimizes the mesh's approximation of a curved surface; surfaces can be represented in various formats, such as a signed distance field. The optimization is achieved by continuously flowing the mesh without altering its topology, making the implementation simpler compared to other adaptive surface meshing techniques. The resulting optimal mesh can be interpreted as a harmonic map with respect to a metric using the shape operator. Furthermore, our approach can be tailored to target height fields by utilizing isotropic geometry.