# A Simple Algorithm for Higher-order Delaunay Mosaics and Alpha Shapes

arXiv: https://arxiv.org/abs/2011.03617 · HTML: https://mlsanity.com/paper/2011.03617/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2020.

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

- [AiGAS-dEVL-RC: An Adaptive Growing Neural Gas Model for Recurrently Drifting Unsupervised Data Streams](https://mlsanity.com/paper/2504.05761/) (2025)

## Abstract (arXiv)

We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-k mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-k mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order α-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.