Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices

By Álvaro González. 2009

491 citations recorded by the source corpus.

The area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude–longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead. The latter is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical. Using the Fibonacci lattice would reduce the root mean squared error by at least 40%. If, as is commonly the case, around a million lattice points are used, the maximum error would be an order of magnitude smaller.

Subfields: Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ad1c862d61b84cdbf74ea7b001f31b3f8934dedd

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In Computer Graphics and Computer-Aided Design

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Citations in the corpus

Modeling the formation and growth of atmospheric molecular clusters: A review (2020, unknown): “Using Fibonacci spheres (González, 2009) the grid points can be evenly distributed around the cluster and a new molecule is placed and reoriented to form the 𝑁 cluster (Kildgaard et al., 2018a, 2018b).”
URIEL and lang2vec: Representing languages as typological, geographical, and phylogenetic vectors (2017, methodology): “The fixed points were derived by generating a spherical Fibonacci lattice (González, 2009; Keinert et al., 2015), a technique that approximates with high precision a uniform distribution of points on a sphere.”
Star-convex Polyhedra for 3D Object Detection and Segmentation in Microscopy (2019, methodology): “To that end, we ﬁrst compute the points ( x k , y k , z k ) k =0 ...n − 1 of a spherical Fibonacci lattice [10] where is the golden ratio.”
ClusterNet: Deep Hierarchical Cluster Network With Rigorously Rotation-Invariant Representation for Point Cloud Analysis (2019, methodology): “We can employ the following formulas to As [5] stated, Fibonacci lattice is a mathematical idealization of natural patterns with optimal packing, where the area represented by each point is almost identical.”