Synchronous haptic-visual-audio multi-sensory feedback should be rendered to realize an interactive simulation of music instrument playing. For the haptic feedback

a 6-DoF haptic rendering of multi-region contacts between a rigid hand and the surface of the instrument is a fundamental requirement. In this study

we proposed a hybrid model to simulate the various parts of the instrument through collision response

i.e.

analytic model for the thin-sized components (i.e.

a line segment) and a sphere-tree for the other parts. We proposed a discrete collision detection method to detect the collision pairs between the sphere-tree of the virtual hand and the analytic model of the strings. A model based on constraint optimization is solved by using an active set method to obtain the non-penetrated configuration of the held hand. To simulate string deformation

a cylindrical volume with variable diameters is defined with the response to the real-time interaction force applied by the hand. Different force feelings can be rendered to reflect hand collision with a static or vibrating string. Experimental results based on Phantom Premium 3.0 illustrated that the proposed method could simulate single-and multi-region contacts between the virtual hand and the strings. Six-dimensional force and torque can be stably simulated. Users can sense the subtle feeling of coming in contact with a vibrating string. This study performs several multi-region contact instances with the use of a discrete collision detection method. No penetration occurs in these instances

and the stacked frequency is above 1 kHz in the loop circuit of collision detection

constraint optimization

and deformation simulation. The penalty-method may cause a distinct torque jump because of the transformation of contact position and normal

thus causing a discrepancy between force feeling and visual feeling. The proposed constraint optimization-based method can improve computational precision.