Geometric Constraint Solving in R² and R³

Geometric constraint solving has applications in a wide variety of fields, such as mechanical engineering, chemical molecular conformation, geometric theorem proving, and surveying. The problem consists of a given set of geometric elements and a description of geometric constraints between the elements. The goal is to find all placements of the geometric entities which satisfy the given constraints. In two-dimensions, several different approaches have been examined and implemented, while the three-dimensional problem has been much less explored in previous literature. In light of the diverse applicability of the problem, we have three objectives in this paper. First, we provide a brief overview of the basic approaches to geometric constraint solving. Second, we review a specific solution to constraint solving for two-dimensional geometric problems. Finally, we present developing work in extending the solution technique for the two-dimensional problem to geometric constraint solving for..