Spherical Voronoi Diagram
The article discusses the concept of Voronoi diagrams applied to the surface of a sphere. It describes the use of a randomized incremental algorithm to compute the 3D convex hull of spherical points, which corresponds to the spherical Delaunay triangulation. The implementation is still a work in progress, with tasks remaining to handle coplanar points and display the spherical convex hull.
- ▪A Voronoi diagram divides space into regions based on seed points.
- ▪The implementation uses a randomized incremental algorithm for computation.
- ▪Remaining tasks include handling coplanar points and showing the spherical convex hull.
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Record
| Original publisher | Jasondavies |
| Canonical URL | https://www.jasondavies.com/maps/voronoi/ |
| Publication time | Wed, 03 Jun 2026 15:32:12 +0000 |
| Retrieval time | 2026-06-03T15:42:10.772Z |
| Last seen | 2026-06-03T15:42:10.772Z |
| Headline source | Publisher (no WeSearch rewrite) |
| Excerpt source | publisher body |
| Excerpt method | First ~120 words (~800 chars) of extracted publisher body, fair-use limited. |
| Summary | WeSearch · cerebras-chat (WeSearch summarizer) |
| Summary source text | contentText |
| Citation coverage | Summary is a WeSearch-generated derivative; primary citation is the original publisher URL. |
| Cluster | skie447IT33x |
| Cluster logic | Grouped by semantic title/content similarity across sources within a rolling window. Same-publisher template collisions are excluded from coverage comparison. |
| Ranking reason | Story pages are not engagement-ranked. Hub feeds use recency, with optional source-diversified chronological ordering (cap consecutive stories per source). No personalized ranking. |
| Publisher visit | Yes — open original |
| Substitutes article? | No — link-out required for full text |
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| Snippet | May a short excerpt of the publisher's text be shown? | Allowed |
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| Retrieval / RAG | May the content be exposed for third-party retrieval-augmented generation? | Not asserted |
| Model training | May the content be used to train AI models? | Not asserted |
| Commercial reuse | May the content be reused commercially? | Not permitted |
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Opening excerpt (first ~120 words) tap to expand
A Voronoi diagram for a set of seed points divides space into a number of regions. There is one region for each seed, consisting of all points closer to that seed than any other. In this case, the space is the surface of the globe (approximated as a sphere). This implementation uses a randomised incremental algorithm to compute the 3D convex hull of the spherical points. The 3D convex hull of the spherical points is equivalent to the spherical Delaunay triangulation of these points. A work in progess! Remaining items: Handle coplanar points correctly. Show the spherical convex hull (this is the boundary of the Delaunay triangulation for points ⊆ hemisphere, otherwise the whole sphere). World Airports Voronoi United States of Voronoi World Capitals Voronoi
Excerpt limited to ~120 words for fair-use compliance. The full article is at Jasondavies.
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