Quad Mesh Quantization Without a T-Mesh

Yoann Coudert-Osmont, David Desobry, Martin Heistermann, David Bommes, Daniele Panozzo, Dmitry Sokolov
Computer Graphics Forum

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.

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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},