While often a requirement for geometric models, there has been little research in resolving the interaction of deforming surfaces during real-time modeling sessions. To address this important topic, we introduce an interference algorithm specifically designed for the domain of geometric modeling. This algorithm is general, easily working within existing modeling paradigms to maintain their important properties. Our algorithm is fast, and is easily able to maintain interactive rates on complex deforming meshes of over 75K faces, while robustly resolving intersections. Lastly, our method is controllable, allowing fine-tuning to meet the specific needs of the user. This includes support for minimum separation between surfaces, elastically-deforming surfaces, and control over the relative rigidity of interacting objects. The talk is tailored for a general audience and contains a short introduction to classical geometric modeling algorithms.