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Accelerating visual communication of mathematical knot deformation


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.

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This work was supported in part by National Science Foundation Grant #1651581 and the 2016 ORAU’s Ralph E. Powe Junior Faculty Enhancement grant.

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Correspondence to Hui Zhang.

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Lin, J., Zhang, H. Accelerating visual communication of mathematical knot deformation. J Vis 23, 913–929 (2020).

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  • Knot untanglement
  • View selection
  • Least squares fitting
  • Parallelization