# Quad Mesh Quantization Without a T-Mesh

## Materials

## Abstract

Grid preserving maps of triangulated surfaces were introduced for quad meshing because the 2D unit grid in such maps corresponds to a sub-division of the surface into quad-shaped charts. These maps can be obtained by solving a mixed integer optimization problem: Real variables define the geometry of the charts and integer variables define the combinatorial structure of the decomposition. To make this optimization problem tractable, a common strategy is to ignore integer constraints at first, then to enforce them in a so-called quantization step. Actual quantization algorithms exploit the geometric interpretation of integer variables to solve an equivalent problem: They consider that the final quad mesh is a sub-division of a T-mesh embedded in the surface, and optimize the number of sub-divisions for each edge of this T-mesh. We propose to operate on a decimated version of the original surface instead of the T-mesh. It is easier to implement and to adapt to constraints such as free boundaries, complex feature curves network etc.

## BibTeX

@article{quantization-without-tmesh, author = {Coudert-Osmont, Yoann and Desobry, David and Heistermann, Martin and Bommes, David and Ray, Nicolas and Sokolov, Dmitry}, title = {Quad Mesh Quantization Without a T-Mesh}, journal = {Computer Graphics Forum}, doi = {https://doi.org/10.1111/cgf.14928}, }