Abstract
An algorithm for determining if any given point,P, on the surface of a sphere is located inside, outside, or along the border of an arbitrary spherical polygon,S, is described. The polygon is described by specifying coordinates of its vertices, and coordinates of some pointX which is known to lie withinS. The algorithm is based on the principle that an arc joiningX andP will cross the border ofS an odd number of times ifP lies outsideS, and an even number of times ifP lies withinS. The algorithm has been implemented as a set of FORTRAN subroutines, and a listing is provided. The algorithm and subroutine package can be used with spherical polygons containing holes, or with composited spherical polygons.
Similar content being viewed by others
References
Bevis, M., and Cambareri, G., 1987, Computing the Area of a Spherical Polygon of Arbitrary Shape: Math. Geol., v. 19, p. 335–346.
Chatelain, J. L., Isacks, B. L., Cardwell, R. K., Prévot, R., and Bevis, M., 1986, Patterns of Seismicity Associated with Asperities in the Central New Hebrides Island Arc: J. Geophys. Res., v. 91, p. 12497–12519.
Davis, M. W., and David, M., 1980, An Algorithm for Finding the Position of a Point Relative to a Fixed Polygonal Boundary: Math. Geol., v. 12, p. 61–68.
Hall, J. K., 1975, PTLOC: A FORTRAN Subroutine for Determining the Position of a Point Relative to a Closed Boundary: Math. Geol., v. 7, p. 75–79.
Salomon, K. B., 1978, An Efficient Point-in-polygon Algorithm: Comput. Geosci., v. 4, p. 173–178.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bevis, M., Chatelain, JL. Locating a point on a spherical surface relative to a spherical polygon of arbitrary shape. Math Geol 21, 811–828 (1989). https://doi.org/10.1007/BF00894449
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00894449