Using invariance under the similarity group to solve geometric constraint systems

In the area of Computer Aided Design (CAD), the main feature of geometric constraint systems lies in their invariance under the direct isometry group. Several researchers have developed methods, which take advantage of this fact to decompose such systems into smaller sub-systems. In this paper, we show that considering the invariance under the direct similarity group leads to a new constructive method to solve geometric constraint systems encountered in CAD.