Error-bounded compatible remeshing

We present a novel method to construct compatible surface meshes with bounded approximation errors. Given two oriented and topologically equivalent surfaces and a sparse set of corresponding landmarks, our method contains two steps: (1) generate compatible meshes with bounded approximation errors and (2) reduce mesh complexity while ensuring that approximation errors are always bounded. Central to the first step is a parameterization-based remeshing technique, which is capable of isotropically remeshing the input surfaces to be compatible and error-bounded. By iteratively performing a novel edge-based compatible remeshing and increasing the compatible target edge lengths, the second step effectively reduces mesh complexity while explicitly maintaining compatibility, regularity, and bounding approximation errors. Tests on various pairs of complex models demonstrate the efficacy and practicability of our method for constructing high-quality compatible meshes with bounded approximation errors.