A Case Study in Geometric Constructions

The geometric constructions problem is often studied from a combinatorial point of view: a pair data structure + algorithm is proposed, and then one tries to determine the variety of geometric problems which can be solved. Conversely, we present here a different approach starting with the definition of a simple class of geometric construction problems and resulting in an algorithm and data structures. We show that our algorithm is correct, complete with respect to the class of simply constrained polygons, and has a linear complexity. The presented framework is very simple, but in spite of its simplicity, this algorithm can solve non-trivial problems.