Haptic rendering of interacting dynamic deformable objects simulated in real-time at different frequencies

The dynamic response of deformable bodies varies significantly in dependence on mechanical properties of the objects: while the dynamics of a stiff and light object (e. g. wire or needle) involves high-frequency phenomena such as vibrations, much lower frequencies are sufficient for capturing the dynamic response of an object composed of a soft tissue. Yet, when simulating mechanical interactions between soft and stiff deformable models, a single time-step in the time integration is usually employed to compute the dynamics of both objects. However, this can be a serious issue when the haptic rendering of complex scenes composed of various bodies is considered. In this paper, we present a novel method allowing for the haptic simulation of a scene composed of colliding objects modeled at different frequencies: typically, the dynamics of soft objects is calculated at a frequency of about 50Hz, while the dynamics of stiff object is simulated at 1 kHz, being directly connected to the computation of the haptic force feedback. The collision response is performed at both low and high frequencies employing data structures which describe the actual constraints and are shared between the high and low frequency loops. We show that during the simulation we show that the objects behave according to two mechanical principles: non-inter-penetration and action-reaction principles. Examples showing the scenes involving different bodies in interaction are given, demonstrating the benefits of the proposed method.