Measure of overlap between two arbitrary ellipses on a sphere

Andraž Gnidovec, Anze Bozic, Urska Jelercic, Simon Copar

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a spherical surface, curvature and compactness lead to nontrivial behaviour that finds uses in physics, computer science and geometry. A well-known idealized isotropic example is the Tammes problem of finding optimal non-intersecting packings of equal hard disks. The anisotropic case of elliptic particles remains, on the other hand, comparatively unexplored. We develop an algorithm to detect collisions between ellipses constrained to the two-dimensional surface of a sphere based on a solution of an eigenvalue problem. We investigate and discuss topologically distinct ways two ellipses may touch or intersect on a sphere, and define a contact function that can be used for construction of short- A nd long-range pair potentials.

Original languageEnglish
Article number20210807
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2261
StatePublished - 1 Jan 2022


  • collision detection
  • curved substrate
  • dense packing
  • hard ellipse repulsion

ASJC Scopus subject areas

  • Mathematics (all)
  • Engineering (all)
  • Physics and Astronomy (all)


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