An ultralight geometry processing library for parallel mesh refinement

In applications such as parallel mesh refinement, it remains a challenging issue to ensure the refined surface respects the original Computer-Aided Design (CAD) model accurately. In this paper, an ultralight geometry processing library is developed to resolve this issue effectively and efficiently. Here, we say the kernel is ultralight because it has a very small set of data-structures and algorithms by comparison with industrial-level geometry kernels. Within the library, a simplified surface boundary representation (B-rep) and a radial edge structure are developed respectively to depict the geometry model and the surface mesh, plus hash tables that record the connections between the geometry model and the surface mesh. Based on these data structures, a set of efficient algorithms are developed, which initializes the connection tables, projects a point back to the original geometry, etc. With these data-structure and algorithmic infrastructures set up, the callings of eight well-designed Application Programming Interfaces (APIs) are powerful enough to enable the parallel mesh refinement algorithm outputs a mesh respecting the input CAD model accurately. Numerical experiments will be finally presented to evaluate the performance of the overall parallel mesh refinement algorithm and the algorithms in relation with the developed library.