**Martin Maňák**

## NTIS Research Centre

SAT morning

This workshop will introduce the participants to tessellations useful for the spatial analysis of a set of points or balls, namely to Voronoi diagrams and their weighted variants. These diagrams have many applications. They can be used to solve proximity queries, volume computations, finding collision-free paths for a spherical probe of flexible radius, etc. Workshop participants will gain a theoretical insight into the area of Voronoi diagrams. Application principles will be explained and practically demonstrated.

- Simple math?
- Inscribed circle (Voronoi vertex position)
- Catching a unicorn (Apollonius 10th problem)

- Introduction to Voronoi diagrams and their dual structures

- Delaunay triangulation
- Finding k nearest neighbors of a point

- Regular triangulation
- Union of balls – volume computation

- Additively weighted Voronoi diagrams and the quasi-triangulation
- Analysis of empty spaces in protein models

*Martin Maňák* s a researcher at the NTIS Research Centre in Pilsen. He received a PhD in Computer Science and Engineering from the University of West Bohemia in 2017. He spent some nice time with additively weighted Voronoi diagrams, computational geometry, and the computational analysis of molecular structures. He likes people, architecture, 8-bit computers, old books and poetry. A cup of coffee in the morning with a bit of Carolina Reaper is his secret recipe to instant happiness.