[1] A problem to be solved consists of a given set of geometric elements and a description of geometric constraints between the elements, which could be non-parametric (tangency, horizontality, coaxiality, etc) or parametric (like distance, angle, radius).
A general scheme of geometric constraint solving consists of modeling a set of geometric elements and constraints by a system of equations, and then solving this system by non-linear algebraic solver.
For the sake of performance, a number of decomposition techniques could be used in order to decrease the size of an equation set:[8] decomposition-recombination planning algorithms,[9][10] tree decomposition,[11] C-tree decomposition,[12] graph reduction,[13] re-parametrization and reduction,[14] computing fundamental circuits,[15] body-and-cad structure,[16] or the witness configuration method.
[17] Some other methods and approaches include the degrees of freedom analysis,[18][19] symbolic computations,[20] rule-based computations,[21] constraint programming and constraint propagation,[21][22] and genetic algorithms.
[21] Geometric constraint solving has applications in a wide variety of fields, such as computer aided design, mechanical engineering, inverse kinematics and robotics,[24] architecture and construction, molecular chemistry,[25] and geometric theorem proving.