In this paper, we present an approach towards approximating configuration spaces of 2D and 3D rigid objects. The approximation can be used to identify caging configurations and establish path non-existence between given pairs of configurations. We prove correctness and analyse completeness of our approach. Using dual diagrams of unions of balls and uniform grids on SO(3), we provide a way to approximate a 6D configuration space of a rigid object. Depending on the desired level of guaranteed approximation accuracy, the experiments with our single core implementation show runtime between 5–21 s and 463–1558 s. Finally, we establish a connection between robotic caging and molecular caging from organic chemistry, and demonstrate that our approach is applicable to 3D molecular models. The supplementary material for this paper can be found at https://anvarava.github.io/publications/wafr-2018-supplementary-material.pdf.