2D quad mesh generation using divide and conquer poly-square maps

We develop a structured quad meshing algorithm for large-scale 2D geometric regions based on solving a low-distorted poly-square map. The poly-square map is constructed through a divide-and-conquer strategy in a distributed way. First, a geometry-aware partitioning is performed to decompose the geometric region into solvable subparts. Then, parameterizations and meshing are computed on subregions under certain boundary constraints. The local results are merged and refined through a multi-pass optimization until the global convergence of the polysquare map is achieved. We demonstrate that our algorithm can process huge geometric model effectively on high performance clusters.