This paper proposes a method for simulating real-time haptic interaction with deformable objects. The deformable model consists of regular hexahedrons of a single type. This homogeneity is exploited to improve the efficiency in deformation computations. Model boundaries are approximated using a moving-least-squares function reflecting the deformation results of the hexahedrons. A method for adaptively approximating the model boundaries is presented for efficient collision handling in the haptic loop. The proposed method can simulate a model of 16,481 nodes in less than 1 ms, which is a significant improvement over the previous methods in the literature. Small gap between the model boundary and the hexahedrons can cause errors in the proposed method. Numerical examples considering the characteristics of human tissues show that the errors are less than just-noticeable difference of human.

中文翻译：

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使用基于 GPU 的并行计算和齐次六面体元素实时模拟与可变形物体的触觉交互的方法

本文提出了一种模拟与可变形物体的实时触觉交互的方法。可变形模型由单一类型的正六面体组成。这种均匀性被用来提高变形计算的效率。使用反映六面体变形结果的移动最小二乘函数近似模型边界。提出了一种自适应逼近模型边界的方法，用于在触觉循环中进行有效的碰撞处理。所提出的方法可以在不到 1 ms 的时间内模拟出一个包含 16,481 个节点的模型，这比以往文献中的方法有了显着的改进。模型边界和六面体之间的小间隙会导致所提出方法的错误。