| We present a real-time, physically based simulation method for animating high-resolution elastic deformations with a focus on haptic interaction. To achieve interactive rates without losing accuracy, the reduced material stiffness matrix is precomputed by removing the equations that correspond to the internal nodes of the system. In addition, we employ linear modal analysis to precompute the natural vibration modes of the system. We introduce a deformation-coupling technique in order to achieve the reduced dynamic behaviour while keeping the high-resolution local deformations. During real-time simulation, the high-spatial-frequency static deformations are coupled with the low-spatial-frequency dynamics, by projecting the reduced coordinate deformations onto an orthogonal basis constructed from natural vibration modes. To explore the implications of the coupling system, we describe different integration techniques to time-step the reduced dynamic solution in addition to evaluating the force feedback. Moreover, we show how we handle multiple contact points for non-sticky materials. To improve the contact-handling procedure, we employ our sliding technique to include friction. We compare our proposed method to the previously existing techniques in terms of run-time complexity and deformation properties using 3D meshes embedded in finite elements. |
