---
author:
- Ryan Viertel$^1$
- Braxton Osting$^2$
- Matthew Staten$^1$
bibliography:
- 'partition-simplification.bib'
date: |
     $^1$Sandia National Laboratories, Albuquerque, NM, U.S.A. rvierte@sandia.gov, mlstate@sandia.gov\
    $^2$University of Utah, Salt Lake City, UT, U.S.A. osting@math.utah.edu 
---

Introduction {#sec:intro}
============

Block structured quad meshes are often desirable because of their numerical efficiency [@lindquist_comparison_1989], low memory requirements [@sandia_trilinos_2017], and high mesh quality [@kowalski_pde_2013]. Having such a block structure on a surface is also advantageous for tasks such as spline fitting and isogeometric analysis [@campen_partitioning_2017]. In the past, such meshes have been designed by hand or in an interactive environment [@dlr_megacads_2001]. More recently, researchers have made progress towards fully automating this process [@campen_partitioning_2017]. The problem of coarse quad layout generation can be summarized as determining the placement of irregular nodes of the layout, and determining the connectivity of those nodes in such a way that the resulting layout is topologically valid, coarse, and such that a mapping of the region to a quadrilateral in the plane results in low distortion.

Various approaches have been taken to generate coarse quad partitions of surfaces, each of which address these problems of irregular node placement and determining connectivity in different ways. These methods include medial axis subdivision [@tam_2d_1991; 