Mathematical knots are different from everyday ropes, in that they are infinitely stretchy and flexible when being deformed into their ambient isotopic. For this reason, challenges of visualization and computation arise when communicating mathematical knot’s static and changing structures during its topological deformation. In this paper, we focus on visual and computational methods to facilitate the communication of mathematical knot’ dynamics by simulating the topological deformation and capturing the critical changes during the entire simulation. To improve our visual experience, we design and exploit parallel functional units to accelerate both topological refinements in simulation phase and view selection in presentation phase. To further allow a real-time keyframe-based communication of knot deformation, we propose a fast and adaptive method to extract key moments where only critical changes occur to represent and summarize the long deformation sequence in real-time fashion. We conduct performance study and present the efficacy and efficiency of our methods. Graphic abstract .

中文翻译：

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加速数学结变形的视觉传达

数学结与日常绳索的不同之处在于，当它们变形为周围的同位素时，它们具有无限的弹性和柔韧性。出于这个原因，当在拓扑变形期间传达数学结的静态和变化结构时，会出现可视化和计算的挑战。在本文中，我们专注于视觉和计算方法，通过模拟拓扑变形和捕获整个模拟过程中的关键变化来促进数学节点动力学的交流。为了改善我们的视觉体验，我们设计和利用并行功能单元来加速模拟阶段的拓扑细化和呈现阶段的视图选择。为了进一步允许基于实时关键帧的结变形通信，我们提出了一种快速且自适应的方法来提取仅发生关键变化的关键时刻，以实时表示和总结长变形序列。我们进行性能研究并展示我们方法的功效和效率。图形摘要。