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This paper describes a generalization of the god-object method for haptic interaction between rigid bodies. Our approach separates the computation of the motion of the six degree-of-freedom god-object from the computation of the force applied to the user. The motion of the god-object is computed using continuous collision detection and constraint-based quasi-statics, which enables high-quality haptic interaction between contacting rigid bodies. The force applied to the user is computed using a novel constraint-based quasi-static approach, which allows us to suppress force artifacts typically found in previous methods. The constraint-based force applied to the user, which handles any number of simultaneous contact points, is computed within a few microseconds, while the update of the configuration of the rigid god-object is performed within a few milliseconds for rigid bodies containing up to tens of thousands of triangles. Our approach has been successfully tested on complex benchmarks. Our results show that the separation into asynchronous processes allows us to satisfy the different update rates required by the haptic and visual displays. Force shading and textures can be added and enlarge the range of haptic perception of a virtual environment. This paper is an extension of [1].