Abstract: We present a surface representation and a set of algorithms that allow interactive placement of curved parametric objects without interpenetration. Using these algorithms, a modeler can place an object within or on top of other objects, find a stable placement for it, and slide it into new stable placements. Novel algorithms are presented to track points of contact between bodies, detect new points of contact, and delete vanishing contacts. Interactive speeds are maintained even when the moving body touches several bodies at many contact points. We describe a new algorithm that quickly brings a body into a stable configuration with respect to a set of external forces, subject to the constraint that it not penetrate a set of fixed bodies. This algorithm is made possible by sacrificing the requirement that a body behave physically over time. Intuitive control is still achieved by making incremental, "pseudo-physical" changes to the body's placement, while enforcing the non-interpenetration constraint after each change.