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We present a new approach for computing planar hexagonal meshes thatapproximate a given surface, represented as a triangle mesh. Our method isbased on two novel technical contributions. First, we introduce CoordinatePower Fields, which are a pair of tangent vector fields on the surface thatfulfill a certain continuity constraint. We prove that the fulfillment of thisconstraint guarantees the existence of a seamless parameterization withquantized rotational jumps, which we then use to regularly remesh the surface.We additionally propose an optimization framework for finding Coordinate PowerFields, which also fulfill additional constraints, such as alignment, sizingand bijectivity. Second, we build upon this framework to address a challengingmeshing problem: planar hexagonal meshing. To this end, we suggest acombination of conjugacy, scaling and alignment constraints, which togetherlead to planarizable hexagons. We demonstrate our approach on a variety ofsurfaces, automatically generating planar hexagonal meshes on complicatedmeshes, which were not achievable with existing methods.

PH-CPF: Planar Hexagonal Meshing using Coordinate Power Fields