NumGCS is a library that uses numerical optimization methods for Geometric Constraint Solving (GCS). It is build on top of the nlopt library for numerical, nonlinear local and global optimization.

NumGCS implements a set of primitive spatial relations for points, lines and circles:

As described in [1], the primitive relations can be used to encode a large set of high-order spatial relations:

[1] Carl Schultz and Mehul Bhatt. A numerical optimisation based characterisation of spatial reasoning. In RuleML, 2016.