On the domain of constructive geometric constraint solving techniques

We study the domain of two constructive geometric constraint solving techniques. Both deal with constraints represented by a geometric constraint graph. The first technique analyses the graph bottom-up, from the edges to the whole graph. The second technique analyses the graph top-down, from the whole graph to the individual edges. We describe these techniques using abstract reduction systems which simplifies the study of their properties. We present an abstract description of the domain of each technique. Finally, we show that both techniques have the same domain, that is, they solve the same kind of problems defined by geometric constraints.