Continuous collision detection (CCD) between parametric surfaces is typically formulated as a five-dimensional constrained optimization problem. In the field of CAD and computer graphics, common approaches to solving this problem rely on linearization or sampling strategies. Alternatively, inclusion-based techniques detect collisions by employing 5D inclusion functions, which are typically designed to represent the swept volumes of parametric surfaces over a given time span, and narrowing down the earliest collision moment through subdivision in both spatial and temporal dimensions. However, when high detection accuracy is required, all these approaches significantly increases computational consumption due to the high-dimensional searching space. In this work, we develop a new time-dependent inclusion-based CCD framework that eliminates the need for temporal subdivision and can speedup conventional methods by a factor ranging from 36 to 138. To achieve this, we propose a novel time-dependent inclusion function that provides a continuous representation of a moving surface, along with a corresponding intersection detection algorithm that quickly identifies the time intervals when collisions are likely to occur. We validate our method across various primitive types, demonstrate its efficacy within the simulation pipeline and show that it significantly improves CCD efficiency while maintaining accuracy.

中文翻译：

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一种基于时间依赖夹杂物的参数化表面之间连续碰撞检测方法


参数化表面之间的连续碰撞检测 （CCD） 通常被表述为五维约束优化问题。在 CAD 和计算机图形学领域，解决此问题的常见方法依赖于线性化或采样策略。或者，基于包含的技术通过使用 5D 包含函数来检测碰撞，这些函数通常旨在表示给定时间跨度内参数化表面的扫描体积，并通过在空间和时间维度上进行细分来缩小最早的碰撞时刻。然而，当需要高检测精度时，由于高维搜索空间，所有这些方法都会显著增加计算消耗。在这项工作中，我们开发了一种新的基于时间依赖的包含体 CCD 框架，该框架消除了对时间细分的需要，并且可以将传统方法的速度提高 36 到 138 倍。为了实现这一目标，我们提出了一种新的瞬态包含函数，该函数提供移动表面的连续表示，以及相应的交叉点检测算法，该算法可以快速识别可能发生碰撞的时间间隔。我们在各种基元类型中验证了我们的方法，在仿真管道中证明了其有效性，并表明它在保持精度的同时显著提高了 CCD 效率。