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Tessellations are an important tool to model the microstructure of cellularand polycrystalline materials. Classical tessellation models include theVoronoi diagram and Laguerre tessellation whose cells are polyhedra. Due to theconvexity of their cells, those models may be too restrictive to describe datathat includes possibly anisotropic grains with curved boundaries. Severalgeneralizations exist. The cells of the generalized balanced power diagram areinduced by elliptic distances leading to more diverse structures. So far,methods for computing the generalized balanced power diagram are restricted todiscretized versions in the form of label images. In this work, we derive ananalytic representation of the vertices and edges of the generalized balancedpower diagram in 2d. Based on that, we propose a novel algorithm to compute thewhole diagram.

An Analytical Representation of the 2d Generalized Balanced Power Diagram