Algorithm-Level Citations

In addition to the package-level Zenodo citation, several spherical geometry and regridding algorithms in UXarray implement methods from peer-reviewed publications. Please cite the corresponding publication(s) below, in addition to the UXarray software citation, if your work depends directly on the details of one of these algorithms, for example describing the algorithm in detail or comparing it against other algorithms. This does not apply to typical use of these APIs as part of an analysis workflow, such as tutorials, internal tools, or research that simply relies on UXarray’s computed outputs.

The definitions and geometric conventions for nodes, edges, and faces used throughout UXarray are based on:

Chen, H., Ullrich, P. A., Panetta, J., Marsico, D., Hanke, M., Jain, R., Zhang, C., and Jacob, R. L. (2026). “Accurate and Robust Geometric Algorithms for Regridding on the Sphere.” Geoscientific Model Development, 19(14), 6545-6570. doi:10.5194/gmd-19-6545-2026 (BibTeX)

Several of the intersection and geometry operators are additionally based on:

Chen, H., Ullrich, P. A., and Panetta, J. (2026). “Fast and Accurate Intersections on a Sphere.” SIAM Journal on Scientific Computing, 48(2), B208-B232. doi:10.1137/25M1737614 (BibTeX)

Algorithm-to-Publication Mapping

Documentation section	API or implementation	Required citation(s)
Descriptors	bounds face_bounds_lon face_bounds_lat	Chen, H., Ullrich, P. A., Panetta, J., Marsico, D., Hanke, M., Jain, R., Zhang, C., and Jacob, R. L. (2026). “Accurate and Robust Geometric Algorithms for Regridding on the Sphere.” Geoscientific Model Development, 19(14), 6545-6570. doi:10.5194/gmd-19-6545-2026 (BibTeX)
Zonal Average	All zonal-average remapping implementations (e.g. zonal_mean())	Chen, H., Ullrich, P. A., and Panetta, J. (2026). “Fast and Accurate Intersections on a Sphere.” SIAM Journal on Scientific Computing, 48(2), B208-B232. doi:10.1137/25M1737614 (BibTeX)
Spherical Geometry: Intersections	All spherical-intersection APIs in this section (gca_gca_intersection(), gca_const_lat_intersection(), get_number_of_intersections())	Cite both: Chen, H., Ullrich, P. A., Panetta, J., Marsico, D., Hanke, M., Jain, R., Zhang, C., and Jacob, R. L. (2026). “Accurate and Robust Geometric Algorithms for Regridding on the Sphere.” Geoscientific Model Development, 19(14), 6545-6570. doi:10.5194/gmd-19-6545-2026 (BibTeX) Chen, H., Ullrich, P. A., and Panetta, J. (2026). “Fast and Accurate Intersections on a Sphere.” SIAM Journal on Scientific Computing, 48(2), B208-B232. doi:10.1137/25M1737614 (BibTeX)
Spherical Geometry: Arcs	in_between() point_within_gca()	No new citation required. Expected to be removed in a future release.
Spherical Geometry: Arcs	extreme_gca_latitude()	Chen, H., Ullrich, P. A., Panetta, J., Marsico, D., Hanke, M., Jain, R., Zhang, C., and Jacob, R. L. (2026). “Accurate and Robust Geometric Algorithms for Regridding on the Sphere.” Geoscientific Model Development, 19(14), 6545-6570. doi:10.5194/gmd-19-6545-2026 (BibTeX)
Spherical Geometry: Arcs	orient3d_on_sphere() on_minor_arc()	Shewchuk, J. R. (1997). “Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates.” Discrete & Computational Geometry, 18, 305-363. doi:10.1007/PL00009321 (BibTeX)
Compensated Arithmetic	two_sum()	Knuth, D. E. (1997). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed.). Addison-Wesley, Section 4.2.2, Theorem B. (BibTeX)
Compensated Arithmetic	two_prod()	Dekker, T. J. (1971). “A Floating-Point Technique for Extending the Available Precision.” Numerische Mathematik, 18, 224-242. doi:10.1007/BF01397083 (BibTeX)
Compensated Arithmetic	diff_of_products()	Cite both: Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms (2nd ed.). Society for Industrial and Applied Mathematics. doi:10.1137/1.9780898718027 (BibTeX) Jeannerod, C.-P., Louvet, N., and Muller, J.-M. (2013). “Further Analysis of Kahan’s Algorithm for the Accurate Computation of 2 × 2 Determinants.” Mathematics of Computation, 82, 2245-2264. doi:10.1090/S0025-5718-2013-02679-8 (BibTeX)
Compensated Arithmetic	accucross() accucross_pair()	Chen, H., Ullrich, P. A., Panetta, J., Marsico, D., Hanke, M., Jain, R., Zhang, C., and Jacob, R. L. (2026). “Accurate and Robust Geometric Algorithms for Regridding on the Sphere.” Geoscientific Model Development, 19(14), 6545-6570. doi:10.5194/gmd-19-6545-2026 (BibTeX)
Compensated Arithmetic	acc_sqrt_re()	Rump, S. M. (2023). “Fast and Accurate Computation of the Euclidean Norm of a Vector.” Japan Journal of Industrial and Applied Mathematics, 40. doi:10.1007/s13160-023-00593-8 (BibTeX)