Ultrasound mid-air haptic (UMH) devices are a novel tool for haptic feedback, capable of providing localized vibrotactile stimuli to users at a distance. UMH applications largely rely on generating tactile shape outlines on the users' skin. Here we investigate how to achieve sensations of continuity or gaps within such two-dimensional curves by studying the perception of pairs of amplitude-modulated focused ultrasound stimuli. On the one hand, we aim to investigate perceptual effects that may arise from providing simultaneous UMH stimuli. On the other hand, we wish to provide perception-based rendering guidelines for generating continuous or discontinuous sensations of tactile shapes. Finally, we hope to contribute toward a measure of the perceptually achievable resolution of UMH interfaces. We performed a user study to identify how far apart two focal points need to be to elicit a perceptual experience of two distinct stimuli separated by a gap. Mean gap detection thresholds were found at 32.3-mm spacing between focal points, but a high within- and between-subject variability was observed. Pairs spaced below 15 mm were consistently (>95) perceived as a single stimulus, while pairs spaced 45 mm apart were consistently (84) perceived as two separate stimuli. To investigate the observed variability, we resort to acoustic simulations of the resulting pressure fields. These show a non-linear evolution of actual peak pressure spacing as a function of nominal focal point spacing. Beyond an initial threshold in spacing (between 15 and 18 mm), which we believe to be related to the perceived size of a focal point, the probability of detecting a gap between focal points appears to linearly increase with spacing. Our work highlights physical interactions and perceptual effects to consider when designing or investigating the perception of UMH shapes.
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