Geodesic
t-Design Curves and Mobile Sampling on the Sphere
Forum of Mathematics, Sigma, Tome 11 (2023)

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In analogy to classical spherical t-design points, we introduce the concept of t-design curves on the sphere. This means that the line integral along a t-design curve integrates polynomials of degree t exactly. For low degrees, we construct explicit examples. We also derive lower asymptotic bounds on the lengths of t-design curves. Our main results prove the existence of asymptotically optimal t-design curves in the Euclidean $2$-sphere and the existence of t-design curves in the d-sphere. 
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     author = {Martin Ehler and Karlheinz Gr\"ochenig},
     title = {t-Design {Curves} and {Mobile} {Sampling} on the {Sphere}},
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Martin Ehler; Karlheinz Gröchenig. t-Design Curves and Mobile Sampling on the Sphere. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.106

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