{
  "id": "1708.06800",
  "version": "v1",
  "published": "2017-08-22T20:01:54.000Z",
  "updated": "2017-08-22T20:01:54.000Z",
  "title": "On a discretization of confocal quadrics. II. A geometric approach to general parametrizations",
  "authors": [
    "Alexander I. Bobenko",
    "Wolfgang K. Schief",
    "Yuri B. Suris",
    "Jan Techter"
  ],
  "comment": "48 pp, 20 figures",
  "categories": [
    "math.DG",
    "math.MG"
  ],
  "abstract": "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 (IC) nets and a generalized Euler-Poisson-Darboux system are established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-22T20:01:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric approach",
      "general parametrizations",
      "discretization",
      "discrete confocal coordinate system",
      "novel discrete analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}