期刊
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
卷 2020, 期 24, 页码 10180-10230出版社
OXFORD UNIV PRESS
DOI: 10.1093/imrn/rny279
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资金
- Deutsche Forschungsgemeinschaft [TRR 109]
- Australian Research Council [DP1401000851]
We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system may be constructed geometrically via polarity with respect to a sequence of classical confocal quadrics. Various sequences correspond to various discrete parametrizations. The coordinate functions of discrete confocal quadrics are computed explicitly. The theory is illustrated with a variety of examples in two and three dimensions. These include confocal coordinate systems parametrized in terms of Jacobi elliptic functions. Connections with incircular nets and a generalized Euler-Poisson-Darboux system are established.
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