# An Analytical Representation of the 2d Generalized Balanced Power Diagram

arXiv: https://arxiv.org/abs/2303.15275 · HTML: https://mlsanity.com/paper/2303.15275/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Fitting Generalized Power Diagrams to 3D Image Data: A Prerequisite for Virtual Materials Testing](https://mlsanity.com/paper/2507.14268/) (2025)

## Abstract (arXiv)

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.