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A Voronoi diagram of a set of sites partitions a bounded space into regions of different areas. A capacity-constrained Voronoi diagram is a partition in which the area for each Voronoi region is predefined. In this paper, we present two approaches for computing such capacity-constrained Voronoi diagrams in continuous spaces. Our first approach is based on ordinary (non-weighted) distance functions and achieves the capacity constraint by a general optimization of the site locations. Our second approach is based on weighted distance functions and optimizes the weights of the sites. Both approaches are iterative methods that start with an initial set of sites and then optimize the area of one Voronoi region at a time. As a consequence, the dimensionality of the individual optimization problem is minimal, which enables a reliable and fast convergence even for large sets of sites.