On Quad Mesh Extraction From Messy Grid Preserving Maps

TL;DR

This paper clarifies the differences between typical inputs and ideal grid preserving maps for quad mesh extraction, proposing a framework to handle deviations and paving the way for more robust algorithms.

Contribution

It introduces a formal understanding of deviations from grid preserving maps and models these differences through operations on discrete structures, enabling improved quad mesh extraction methods.

Findings

Identifies common deviations in real inputs from ideal grid maps

Models deviations as operations on discrete structures

Suggests directions for developing robust quad extraction algorithms

Abstract

Extracting a quad mesh from a grid preserving map is straightforward in theory, but typical inputs are not exactly grid preserving maps. Previous works can manage minor deviations from grid preserving maps, but without a clear specification of what is acceptable. This work clarifies how typical inputs differ from a grid preserving map, and shows how the differences with a grid preserving map can be reflected by a sequence of operations acting on a discrete structure. It opens research opportunities for the design of a robust quad extraction algorithm.