Volume parametrization quantization for hexahedral meshing

Developments in the field of parametrization-based quad mesh generation on surfaces have been impactful over past decade. In this context, an important advance has replacement error-prone rounding integer-grid maps, by robust quantization methods. parallel, hex for volumes advanced. volumetric however, state-of-the-art still relies fragile rounding, not rarely producing defective meshes, especially when targeting a coarse resolution. We present method to robustly quantize volume parametrizations, i.e., determine guaranteed valid choices integers 3D maps. Inspired 2D case, we base our construction non-conforming cell decomposition volume, analogue T-mesh. particular, leverage motorcycle complex, recent generalization graph, purpose. Integer values are expressed differential manner edges enabling efficient formulation conditions required strictly prevent forcing map into degeneration. Applying context hexahedral meshing, demonstrate that meshes can be generated with significantly improved flexibility.