Measurement of areas on a sphere using Fibonacci and latitude-longitude lattices - Mathematics > Metric GeometryReport as inadecuate




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Abstract: The area of a spherical region can be easily measured by considering whichsampling points of a lattice are located inside or outside the region. Thispoint-counting technique is frequently used for measuring the Earth coverage ofsatellite constellations, employing a latitude-longitude lattice. This paperanalyzes the numerical errors of such measurements, and shows that they couldbe greatly reduced if the Fibonacci lattice were used instead. The latter is amathematical idealization of natural patterns with optimal packing, where thearea represented by each point is almost identical. Using the Fibonacci latticewould reduce the root mean squared error by at least 40%. If, as is commonlythe case, around a million lattice points are used, the maximum error would bean order of magnitude smaller.



Author: Álvaro González

Source: https://arxiv.org/



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