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Some Popular Algorithms for Distributing Points on \(S^2\)

  • Sergiy V. BorodachovEmail author
  • Douglas P. Hardin
  • Edward B. Saff
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  • 285 Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

From star-charts to golf-ball dipples to testing radar in aircraft, well-placed points on the two-dimensional sphere \(S^2\subset \mathbb {R}^{3}\) have a vast number of practical applications. In this chapter, we describe the properties (such as equidistribution, covering, separation, quasi-uniformity, etc.) of such point configurations generated by commonly used methods, namely zonal equal-area points, generalized spiral points, Fibonacci points, HEALPix nodes, octahedral points, icosahedral points, cubed sphere nodes, Hammersley nodes, minimizing Coulomb and logarithmic energy points, radial icosahedral points, equal-area icosahedral nodes, maximal determinant nodes, and random points.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sergiy V. Borodachov
    • 1
    Email author
  • Douglas P. Hardin
    • 2
  • Edward B. Saff
    • 2
  1. 1.Department of MathematicsTowson UniversityTowsonUSA
  2. 2.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA

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