Quad Mesh Quantization Without a T‐Mesh

Coudert‐Osmont, Yoann; Desobry, David; Heistermann, Martin; Bommes, David; Ray, Nicolas; Sokolov, Dmitry (2023). Quad Mesh Quantization Without a T‐Mesh. Computer graphics forum, 43(1) Wiley 10.1111/cgf.14928

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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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