Arts & Sciences Events
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Arts & Sciences
[PAST EVENT] Computational Topology for Modeling & Visualization
November 15, 2013
3pm - 4pm
Abstract:
Topological equivalence between geometric objects is not only theoretically fundamental, but also computationally useful. In many practical situations, such as modeling and visualizing the writhing of macro-molecular structures, complex shapes can only be approximated in a high performance computing environment. For these visualization approximations, establishing topological equivalence (in a broad sense including homeomorphism and ambient isotopy) plays a crucial role for both theoretical correctness and algorithmic efficiency. This topic lies in the emerging area of Computational Topology. I will start with an introduction for general audiences. Then I will present my research that provides the equivalence for knots, and for splines between their smooth and the associated piecewise linear structures.
Topological equivalence between geometric objects is not only theoretically fundamental, but also computationally useful. In many practical situations, such as modeling and visualizing the writhing of macro-molecular structures, complex shapes can only be approximated in a high performance computing environment. For these visualization approximations, establishing topological equivalence (in a broad sense including homeomorphism and ambient isotopy) plays a crucial role for both theoretical correctness and algorithmic efficiency. This topic lies in the emerging area of Computational Topology. I will start with an introduction for general audiences. Then I will present my research that provides the equivalence for knots, and for splines between their smooth and the associated piecewise linear structures.
Contact
Sarah Day