In our daily lives, we interact with fluids by touching them directly with our hands. Fluids produce a pressure field against the surface of our hands, and we experience fluid dynamics over our skin temporally and spatially at varying pressure distributions depending on fluid properties as well as on the interacting hand's poses and motions. To improve the realism of fluid simulation together with user interaction, we propose a real-time fluid tactile rendering technique that computes the pressure field on a virtual hand surface to be delivered to the user's actual hand via ultrasound-based mid-air haptic display. Our haptic rendering algorithm computes the feedback force in two stages: First, the pressure distribution of the rigid-fluid interaction is computed from a real-time Lagrangian fluid simulation, and then a set of focal points that reflects the generated pressure field is extracted by using a hill-climbing method which gives the local extrema of the pressure field of simulation. We implement a real-time smoothed-particle hydrodynamics fluid simulator and the proposed haptic rendering algorithm using adaptive amplitude modulation approach to demonstrate the effectiveness of our method in fluid tactile rendering in various scenarios.

中文翻译：

---

用于超声波空中触觉的 SPH 流体触觉渲染

在我们的日常生活中，我们通过直接用手触摸液体来与它们互动。流体对我们的手表面产生压力场，我们在时间和空间上体验我们皮肤上的流体动力学，根据流体特性以及相互作用的手的姿势和运动，在不同的压力分布下。为了提高流体模拟和用户交互的真实性，我们提出了一种实时流体触觉渲染技术，该技术计算虚拟手表面上的压力场，通过基于超声波的空中触觉显示传递给用户的实际手。我们的触觉渲染算法分两个阶段计算反馈力：首先，根据实时拉格朗日流体模拟计算刚性流体相互作用的压力分布，然后使用爬山法提取一组反映所产生的压力场的焦点，该方法给出了模拟压力场的局部极值。我们使用自适应调幅方法实现了实时平滑粒子流体动力学流体模拟器和提出的触觉渲染算法，以证明我们的方法在各种场景中的流体触觉渲染中的有效性。