Coudert‐Osmont, YoannYoannCoudert‐OsmontDesobry, DavidDavidDesobryHeistermann, MartinMartinHeistermann0000-0002-1757-7661Bommes, DavidDavidBommes0000-0002-3190-1341Ray, NicolasNicolasRaySokolov, DmitryDmitrySokolov2024-10-252024-10-252023-09-17https://boris-portal.unibe.ch/handle/20.500.12422/170204Grid 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.en000 - Computer science, knowledge & systems500 - Science::510 - Mathematicsarticle10.48350/18658110.1111/cgf.14928