In Virtual Reality, visuo-haptic illusions such as hand redirection introduce a discrepancy between the user's hand and its virtual avatar. This visual shift can be used, for instance, to provide multiple virtual haptic objects through a single physical proxy object. This lowcost approach improves the sense of presence, however, it is unclear how these illusions impact the hand trajectory and if there is a relationship between trajectory and the detection of illusion. In this paper, we present an empirical model predicting the hand trajectory as a function of the redirection. It relies on a cubic Bézier curve with 4 control points. We conduct a two alternative forced choice (2AFC) experiment to calibrate and validate our model. Results show that (1) our model predicts well the hand trajectory of each individual using a single parameter; (2) the hand trajectory better explains the detection of the illusion than the amplitude of the redirection alone; (3) a user specific calibration allows to predict per-user redirected trajectories and detection probabilities. Our findings provide a better understanding of visuo-haptic illusions and how they impact the user's movements. As such they may provide foundations to design novel interaction techniques, e.g. interacting in a scene with multiple physical obstacles.

Hand redirection is a visuo-haptic illusion offering rich haptic feedback in Virtual Reality while using a limited number of physical objects. This technique relies on a redirection function which determines the virtual hand position depending on the physical hand position. In this paper, we extend the design space of the Handredirection technique by generalizing this redirection function. A user study compares 6 redirection functions. Our results suggest that the redirection function does not deteriorate the illusion offering more flexibility and control to designer over the hand trajectory and avoid collisions. CCS CONCEPTS• Human-centered computing → HCI theory, concepts and models; Pointing.

Visuo-haptic illusions, such as Hand Redirection, offer rich haptic feedback in Virtual Reality while using a limited number of physical objects. In this paper, we extend the design space for these illusions by generalizing the redirection function. A user study compares 6 redirection functions. Our results suggest that the redirection function has no influence on the illusion breakup. They also suggest that the designer can freely manipulate the redirection function for example to avoid collisions. RÉSUMÉLes illusions visuo-haptiques, telles que la redirection de la main (Hand Redirection) offrent un retour haptique riche en réalité virtuelle bien qu'utilisant un nombre limité d'objets physiques. Dans cet article, nous élargissons l'espace de conception de ces illusions en généralisant la fonction de redirection. Une étude utilisateur compare 6 fonctions de redirections. Nos résultats suggèrent que la fonction de redirection n'a pas d'influence sur la rupture de l'illusion. Ils suggèrent également que le concepteur peut manipuler librement la fonction de redirection par exemple pour éviter des collisions. CCS CONCEPTS• Human-centered computing → HCI design and evaluation methods; Virtual reality.