A Functional Optimization Based Approach for Continuous 3D Retargeted Touch of Arbitrary, Complex Boundaries in Haptic Virtual Reality

Yiwei Zhao, Sean Follmer

Passive or actuated physical props can provide haptic feedback, leading to a satisfying sense of presence and realism in virtual reality. However, the mismatch between the physical and virtual surfaces (boundaries) can diminish user experience. Haptic retargeting can overcome this limitation by utilizing visio-haptic effects. Previous investigations in haptic retargeting have focused on methods for point based position retargeting and techniques for remapping 2D shapes or simple 3D shape changes. Our approach extends haptic retargeting to complex, arbitrary shapes that provide a continuous mapping across all points on a boundary. This new approach also allows for multi-finger interaction. We describe a functional optimization to find the ideal spatial warping function with different goals: a maximum mapping smoothness, a minimum mismatch between the real and virtual world, or the combination of the two. We report on a preliminary user study of different optimization goals and elaborate potential applications through a set of demonstrations.

The mathematical description of the physical space, warped virtual space, boundaries and spatial warp function.

1D results of our method for retargeting to a different line length ($\partial \Omega_2$ to $\partial \Omega'_2$). When $\lambda = 0$, the mapping is linear and the offset between the physical hand and the virtual hand increases linearly with displacement. As $\lambda$ increases the mapping becomes more exponential.

2D results of remapping a square to a circle and changing the orientation of a rectangle. (a) Euclidean norm of the gradient. (b) x displacement. (c) y displacement.