Efficient and Robust Algorithm for Overlaying Nonmatching Surface Meshes

This paper describes an efficient and robust algorithm for computing a common refinement of two meshes modeling a common surface of arbitrary shape by overlaying them on top of each other. A common refinement is an important data structure for transferring data between meshes that have different topological structures. Our algorithm is optimal in time and space, with linear complexity. Special treatments are introduced to handle discretization and rounding errors and to ensure robustness with imprecise computations. It also addresses the additional complexities caused by degeneracies, sharp edges, sharp corners, and nonmatching boundaries. The algorithm has been implemented and demonstrated to be robust for complex geometries from real-world applications.