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arXiv · 2606.27235

A unified cell-merge algorithm for generating diverse Voronoi diagrams and new tessellations based on spatial chromatic model

Weining Zhu
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Abstract

As a type of spatial tessellation model and an important spatial structure of computational geometry, Voronoi diagrams (VDs) are widely used in many fields. Due to differences in generation spaces, types of spatial entities, distance metrics, and relationships between entities and Voronoi regions, Voronoi diagrams vary into many types, such as the ordinary VD, VD on spheres, VD for linear entities, weighted VD, and ordered higher-order VD. These VDs also have their own generation algorithms. In this study, we propose a new cell-merge (CM) Voronoi generation algorithm based on the spatial chromatic model. The advantage of the CM algorithm is that it can quickly generate diverse VDs by retrieving and merging cells from a unified database, without requiring the development of specific algorithms for each VD. The CM Voronoi algorithm can be particularly applied in cases where a variety of Voronoi diagrams are frequently required for computation and analysis, such as in location-based spatial analysis. Furthermore, the proposed CM method can also generate some new types of spatial tessellations, such as competition intensity and couple-cell diagrams which are different from classical VDs.

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Weining Zhu. 2026-06-25. A unified cell-merge algorithm for generating diverse Voronoi diagrams and new tessellations based on spatial chromatic model. https://arxiv.org/abs/2606.27235

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