This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.
['Xiao-Shan Gao', 'Lei-Dong Huang', 'Kun Jiang']
Geometric constraint solving with geometric transformation