{
  "annotation_id": "00b61893-0fdf-4676-9600-e845b5917783",
  "date_created": "2026-03-02T18:00:42.283000Z",
  "date_modified": "2026-03-02T18:00:42.283000Z",
  "file_hash": "c6e33015ab68f695086e6b87999e819c941ec75d710a0b3ec15f0579dd3d5850",
  "private": false,
  "record": {
    "abstract": "We describe the implementation of algorithms to construct and maintain\nthree-dimensional dynamic Delaunay triangulations with kinetic vertices using a\nthree-simplex data structure. The code is capable of constructing the geometric\ndual, the Voronoi or Dirichlet tessellation. Initially, a given list of points\nis triangulated. Time evolution of the triangulation is not only governed by\nkinetic vertices but also by a changing number of vertices. We use\nthree-dimensional simplex flip algorithms, a stochastic visibility walk\nalgorithm for point location and in addition, we propose a new simple method of\ndeleting vertices from an existing three-dimensional Delaunay triangulation\nwhile maintaining the Delaunay property. The dual Dirichlet tessellation can be\nused to solve differential equations on an irregular grid, to define partitions\nin cell tissue simulations, for collision detection etc.",
    "arxiv_id": "physics/0302018",
    "authors": [
      "Gernot Schaller",
      "Michael Meyer-Hermann"
    ],
    "categories": [
      "physics.bio-ph",
      "physics.comp-ph"
    ],
    "doi": "10.1016/j.cpc.2004.06.066",
    "journal_ref": "Computer Physics Communications 162, 9-23 (2004)",
    "title": "Kinetic and Dynamic Delaunay tetrahedralizations in three dimensions",
    "url": "https://arxiv.org/abs/physics/0302018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0289b561-4f6b-4df8-baaf-a1e4fc54e778",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}