Spectral Quadrangulation with Boundary Conformation

Existing spectral quadrangulation methods are effective only for closed surfaces, because they cannot satisfactorily handle surfaces with boundaries or feature lines that need to be respected. We propose an extension to the spectral quadrangulation approach that ensures boundary/feature conformation. Our contributions include the formulation of a set of new boundary conditions and the introduction of quasi-eigenfunctions that are solutions of a PDE with the new boundary conditions. We also develop algorithms for computing the quasi-eigenfunctions and extracting their MorseSmale complexes to generate desired quadrangulation. We further extend the method to generating adaptive quadrangulation observing a pre-specified density function. Experiments show that our method produces better quadrilateral meshes with conforming boundaries/features and varying element size than existing methods do.