In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.

翻译：本文提出了一种利用有限域约束求解器自动求解三角尺规作图问题的方法。该约束模型采用MiniZinc建模语言描述，并基于自动规划技术。与传统开发专用工具相比，使用通用约束求解器的主要优势在于：我们可以直接利用求解器中已实现的高效搜索机制，从而将精力聚焦于问题的几何层面。此外，我们还可借助求解器内置的优化功能，搜索最短可能的作图方案。我们基于Wernick列表中的74个可解问题对方法进行了评估，并将其与专用三角作图求解器ArgoTriCS进行对比。结果表明，我们的方法在达到与专用工具相当性能的同时，实现所需工作量显著减少。得益于约束求解器提供的优化能力，我们的模型往往能发现更短的作图方案。