PH-CPF

We present a new approach for computing planar hexagonal meshes that approximate given surface, represented as triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields , which are pair of tangent vector fields the surface fulfill certain continuity constraint. prove fulfillment this constraint guarantees existence seamless parameterization with quantized rotational jumps, then use to regularly remesh surface. additionally propose an optimization framework finding Fields, also additional constraints, such alignment, sizing and bijectivity. Second, build upon address challenging meshing problem: meshing. To end, suggest combination conjugacy, scaling alignment together lead planarizable hexagons. demonstrate our variety surfaces, automatically generating complicated meshes, were not achievable existing methods.