Capacity constrained blue-noise sampling on surfaces

We present a novel method for high-quality blue-noise sampling on mesh surfaces with prescribed cell-sizes for the underlying tessellation (capacity constraint). Unlike the previous surface sampling approach that only uses capacity constraints as a regularizer of the Centroidal Voronoi Tessellation (CVT) energy, our approach enforces an exact capacity constraint using the restricted power tessellation on surfaces. Our approach is a generalization of the previous 2D blue noise sampling technique using an interleaving optimization framework. We further extend this framework to handle multi-capacity constraints. We compare our approach with several state-of-the-art methods and demonstrate that our results are superior to previous work in terms of preserving the capacity constraints. Graphical abstractWe present a new method for blue noise sampling on mesh surfaces under capacity constraints and extend this framework to handle multi-capacity constraints.Multi-capacity constrained sampling on Dragon model.Display Omitted HighlightsA new approach for blue-noise sampling on mesh surfaces under capacity constraints.The derivation of the gradient of the new formulation on mesh surfaces.A novel extension to handle multi-capacity constraints.