Haptic rendering involving deformable objects has seen many applications, from surgical simulation and training, to virtual prototyping, to teleoperation, etc. High quality rendering demands both physical fidelity and real-time performance, which are often conflicting requirements. In this paper, we simulate contact force between a held rigid body and an elastic object and the corresponding shape deformation of the elastic object efficiently and realistically based on a nonlinear physical model

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... and a novel beam-skeleton model, taking into account friction, compliant motion, and multiple contact regions. Our approach is able to achieve a combined update rate of over 1 kHz in realistic, smooth, and stable rendering, as demonstrated by our implemented examples.