Shape display devices composed of actuation pixels enable dynamic rendering of surface morphological features, which have important roles in virtual reality and metaverse applications. The traditional pin-array solution produces sidestep-like structures between neighboring pins and normally relies on high-density pins to obtain curved surfaces. It remains a challenge to achieve continuous curved surfaces using a small number of actuated units. To address the challenge, we resort to the concept of surface continuity in computational geometry and develop a C0-continuity shape display device with trichamber fiber-reinforced soft actuators. Each trichamber unit produces three-dimensional (3D) deformation consisting of elongation, pitch, and yaw rotation, thus ensuring rendered surface continuity using low-resolution actuation units. Inspired by human tactile discrimination threshold on height and angle gradients between adjacent units, we proposed the mathematical criteria of C0-continuity shape display and compared the maximal number of distinguishable shapes using the proposed device in comparison with typical pin-array. We then established a shape control model considering the nonlinearity of soft materials to characterize and control the soft device to display C0-continuity shapes. Experimental results showed that the proposed device with nine trichamber units could render typical sets of distinguishable C0-continuity shape sequence changes. We envision that the concept of C0-continuity shape display with 3D deformation capability could improve the fidelity of the rendered shapes in many metaverse scenarios such as touching human organs in medical palpation simulations.
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