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Extracting good views from a large sequence of visual frames is quite difficult but a very important task across many fields. Fully automatic view selection suffers from high data redundancy and heavy computational cost, thus fails to provide a fast and intuitive visualization. In this paper we address the automatic viewpoint selection problem in the context of 3D knot deformation. After describing viewpoint selection criteria, we detail a brute-force algorithm with a minimal distance alignment method in a way to not only ensure the global best viewpoint but also present a sequence of visually continuous frames. Due to the intensive computation, we implement an efficient extraction method through parallelization. Moreover, we propose a fast and adaptive method to retrieve best viewpoints in real-time. Despite its local searching nature, it is able to generate a set of visually continuous key frames with an interactive rate. All these combine provide insights into 3D knot deformation where the critical changes of the deformation are fully represented. 

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, a number of challenges arise when visualizing mathematical knot's static and changing structures during topological deformation. In this paper we focus on computational methods to visually communicate the mathematical knot's dynamics by computationally simulating the topological deformation and capturing the critical changes during the entire simulation. To further improve our visual experience, we propose a fast and adaptive method to extract key moments where only critical changes occur to represent and summarize the long deformation sequence. We conduct evaluation study to showcase the efficacy and efficiency of our methods.