## Section: New Results

### Formal study of a triangulation algorithm

Participant : Yves Bertot.

In work from 2010, a formal description of Delaunay triangulations was presented where the input was a triangulation not satisfying the Delaunay criterion and where the output was a triangulation satisfying this criterion.

In this work, we wish to complete the previous work by describing an algorithm that produces the initial triangulation. We plan this work in several phases, where the first phase only uses simple data-structures, more advanced structures being introduced only later. This work was presented partially in an invited talk at the ICTAC conference [10].