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Visualization and Minima Finding of Multidimensional Hypersurface
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Author(s): Eugene Vladimirovich Popov (Nizhegorodsky State Architecture and Civil Engineering University, Russia), Anatoliy Aleksandrovich Batiukov (Nizhegorodsky State Architectural and Civil Engineering University, Russia), Natalja Vogt (Lomonosov Moscow State University, Russia), Tatyana Petrovna Popova (National Research University Higher School of Economics, Russia)and Jürgen Vogt (University of Ulm, Germany)
Copyright: 2020
Pages: 28
Source title:
Interactivity and the Future of the Human-Computer Interface
Source Author(s)/Editor(s): Pedro Isaias (Information Systems and Technology Management School, The University of New South Wales, Australia)and Katherine Blashki (Victorian Institute of Technology, Australia)
DOI: 10.4018/978-1-7998-2637-8.ch015
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Abstract
Analysis of multidimensional function properties is required for industrial applications. The solution of its problems is a challenge in economics, sociology, chemistry, biology, biochemistry, and other sciences. For example, the study of the potential energy surface (PES) of a free molecule is of fundamental importance in structural chemistry because it is necessary to determine the stable conformations of a molecule and the ways of interconversion between them. However, if the PES is a function of more than three rotational coordinates, the costs of its quantum-chemical calculation rapidly increases and the problem of its graphical visualization can be hardly solved for a large number of variables. This work describes how a specially developed multidimensional interpolation procedure can contribute to solve these problems. To visualize a five dimensional (5D) hypersurface, the authors applied a special coordinate system.
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