PH-CPF: Planar Hexagonal Meshing using Coordinate Power Fields

TL;DR

This paper introduces Coordinate Power Fields for seamless surface parameterization, enabling automatic generation of planar hexagonal meshes on complex surfaces, advancing meshing techniques with novel mathematical and optimization tools.

Contribution

The paper presents a new framework using Coordinate Power Fields and an optimization approach to produce planar hexagonal meshes from arbitrary surfaces, addressing limitations of previous methods.

Findings

Successfully generates planar hexagonal meshes on complex surfaces

Guarantees seamless parameterization with quantized rotational jumps

Outperforms existing methods in meshing complicated geometries

Abstract

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