TY - JOUR

T1 - Measure of overlap between two arbitrary ellipses on a sphere

AU - Gnidovec, Andraž

AU - Bozic, Anze

AU - Jelercic, Urska

AU - Copar, Simon

N1 - Funding Information:
We acknowledge support by Slovenian Research Agency (ARRS) under contracts no. P1-0099 and no. J1-9149. The work is associated with the COST action no. CA17139.
Publisher Copyright:
© 2022 Royal Society Publishing. All rights reserved.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - collision detection

KW - curved substrate

KW - dense packing

KW - hard ellipse repulsion

UR - http://www.scopus.com/inward/record.url?scp=85130371643&partnerID=8YFLogxK

U2 - 10.1098/rspa.2021.0807

DO - 10.1098/rspa.2021.0807

M3 - Article

C2 - 35601962

AN - SCOPUS:85130371643

VL - 478

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2261

M1 - 20210807

ER -