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