Rigid body dynamic simulation with line and surface contact

In this paper, we develop a principled method to model line and surface contact with point contacts that is consistent with physics-based models of surface (line) contact. We solve the contact detection and dynamic simulation step simultaneously by formulating the problem as a mixed nonlinear complementarity problem. This allows us to simultaneously compute the centre of pressure as well as the forces at the centre of pressure (consistent with the friction model) along with the configuration and velocities of the rigid objects. We present a geometrically implicit time-stepping scheme for dynamic simulation for contacts between two bodies with convex contact area, which includes 2D line contact, 3D surface contact, and 3D line contact. We prove that for surface and line contact, for any value of the velocity of center of mass of the object, there is a unique solution for contact point and contact wrench that satisfies the discrete-time equations of motion. For pure translation and pure rotation, we show that there is a closed form solution for each discrete time-step if the contact mode does not change. Simulation examples are shown to demonstrate the validity of our approach and show that with our approach we can seamlessly transition between point, line, and surface contacts.