PH-CPF: Planar Hexagonal Meshing using Coordinate Power Fields

05/06/2021 ∙ by Kacper Pluta, et al. ∙ 0

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.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 3

page 4

page 5

page 6

page 10

page 17

page 18

page 20

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.