Lyon, MaxCampen, MarcelKobbelt, LeifMitra, Niloy and Viola, Ivan2021-04-092021-04-0920211467-8659https://doi.org/10.1111/cgf.142634https://diglib.eg.org:443/handle/10.1111/cgf142634We present a robust and fast method for the creation of conforming quad layouts on surfaces. Our algorithm is based on the quantization of a T-mesh, i.e. an assignment of integer lengths to the sides of a non-conforming rectangular partition of the surface. This representation has the benefit of being able to encode an infinite number of layout connectivity options in a finite manner, which guarantees that a valid layout can always be found. We carefully construct the T-mesh from a given seamless parametrization such that the algorithm can provide guarantees on the results' quality. In particular, the user can specify a bound on the angular deviation of layout edges from prescribed directions. We solve an integer linear program (ILP) to find a coarse quad layout adhering to that maximal deviation. Our algorithm is guaranteed to yield a conforming quad layout free of T-junctions together with bounded angle distortion. Our results show that the presented method is fast, reliable, and achieves high quality layouts.Computing methodologiesComputer graphicsMesh modelsMesh geometry modelsShape modeling10.1111/cgf.142634305-314