Classification and solving of merge patterns in geometric constraint solving

A basic idea of geometric constraint solving is to divide a large geometric constraint problem into several subproblems according to certain patterns and then to merge these subproblems to obtain a solution to the original problem. In this paper, we give a classification of the basic merge patterns in 2D when solving a constraint problem with generalized construction sequences. We also obtain the analytical solutions to all eleven cases of merge patterns, which is to assemble two rigid bodies connected with three constraints. We also give conditions to solve these patterns with ruler and compass constructions.