Intersection detection between three-dimensional bodies has various applications in computer graphics, video game development, robotics as well as military industries. In some respects, entities do not want to disclose sensitive information about themselves, including their location. In this paper, we present a secure two-party protocol to determine the existence of an intersection between entities. The protocol presented in this paper allows for intersection detection in three-dimensional spaces in geometry. Our approach is to use an intersecting plane between two spaces to determine their separation or intersection. For this purpose, we introduce a computational geometry protocol to determine the existence of an intersecting plane. In this paper, we first use the Minkowski difference to reduce the two-space problem into one-space. Then, the separating set is obtained and the separation of two shapes is determined based on the inclusion of the center point. We then secure the protocol by modifying the separating set computation method as a privacy-preserver and changing the Minkowski difference method to achieve this goal. The proposed protocol applies to any form of convex three-dimensional shape. The experiments successfully found a secure protocol for intersection detection between two convex hulls in geometrical shapes such as the pyramid and cuboid.

中文翻译：

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一种用于两个凸包之间相交检测的安全两方计算协议

三维物体之间的交叉检测在计算机图形学、视频游戏开发、机器人技术以及军事工业中有各种应用。在某些方面，实体不想披露关于他们自己的敏感信息，包括他们的位置。在本文中，我们提出了一种安全的两方协议来确定实体之间是否存在交集。本文中提出的协议允许在几何的三维空间中进行交叉检测。我们的方法是使用两个空间之间的相交平面来确定它们的分离或相交。为此，我们引入了计算几何协议来确定相交平面的存在。在本文中，我们首先使用 Minkowski 差分将双空间问题简化为一个空间。然后，得到分离集，并根据包含的中心点确定两个形状的分离。然后我们通过修改分离集计算方法作为隐私保护器并改变 Minkowski 差分方法来实现这一目标，从而保护协议。提议的协议适用于任何形式的凸三维形状。实验成功地找到了一种安全协议，用于检测金字塔和长方体等几何形状的两个凸包之间的相交。提议的协议适用于任何形式的凸三维形状。实验成功地找到了一种安全协议，用于检测金字塔和长方体等几何形状的两个凸包之间的相交。提议的协议适用于任何形式的凸三维形状。实验成功地找到了一种安全协议，用于检测金字塔和长方体等几何形状的两个凸包之间的相交。