Voronoi diagrams describe half-way points between neighbours. Some recommended general introductory links:
The standard text is the excellent Spatial tessellations: Concepts and Applications of Voronoi Diagrams by Atsuyuki Okabe, Barry Boots, Kokichi Sugihara and Sung Nok Chiu.
Voronoi diagrams have many uses throughout the sciences but have seemingly not been applied much to music. I’ve only found two papers so far;
- Masatoshi Hamanaka and Keiji Hirata, Applying Voronoi Diagrams in the Automatic Grouping of Polyphony, 2002
- Ross Bencina, The Metasurface – Applying Natural Neighbour Interpolation to Two-to-Many Mapping, 2005
My own contribution is the essay Voronoi Diagrams of Music, 2006. It has an On-line appendix.
