Computing Non-Obtuse Triangulations with Few Steiner Points

TL;DR

This paper introduces an algorithm that efficiently computes non-obtuse triangulations of planar regions with minimal Steiner points by employing local search on constrained Delaunay triangulations.

Contribution

It presents a novel local search-based method for minimizing Steiner points in non-obtuse triangulations under given constraints.

Findings

Achieved the best results in the CG:SHOP 2025 challenge.

Successfully minimized Steiner points while ensuring non-obtuse angles.

Demonstrated effectiveness of local search in constrained triangulation optimization.

Abstract

We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints consisting of extra vertices and edges that must be part of the triangulation. The goal was to minimize the number of introduced Steiner points. Our approach is to maintain a constrained Delaunay triangulation, for which we repeatedly remove, relocate, or add Steiner points. We use local search to choose the action that improves the triangulation the most, until the resulting triangulation is non-obtuse.