Level-of-detail quad meshing

The most effective and popular tools for obtaining feature aligned quad meshes from triangular input meshes are based on cross field guided parametrization. These methods are incarnations of a conceptual three-step pipeline: (1) cross field computation, (2) field-guided surface parametrization, (3) quad mesh extraction. While in most meshing scenarios the user prescribes a desired target quad size or edge length, this information is typically taken into account from step 2 onwards only, but not in the cross field computation step. This turns into a problem in the presence of small scale geometric or topological features or noise in the input mesh: closely placed singularities are induced in the cross field, which are not properly reproducible by vertices in a quad mesh with the prescribed edge length, causing severe distortions or even failure of the meshing algorithm. We reformulate the construction of cross fields as well as field-guided parametrizations in a scale-aware manner which effectively suppresses densely spaced features and noise of geometric as well as topological kind. Dominant large-scale features are adequately preserved in the output by relying on the unaltered input mesh as the computational domain.