pisp4bae

Under active development. A suite of tools that demonstrate the Projection-Winding-Orientation algorithm framework for great elliptic polygons on ellipsoids, including spherical polygons on spheres, that decide if a point is on the boundary, inside, or outside the ellipsoidal region.

• PiSP: Point-in-Spherical-Polygon
• PiGEP: Point-in-Great-Elliptic-Polygon
• PiGP: Point-in-Geodesic-Polygon

What is an AEB-gon (antipodally extreme SP/GEP)?

A AEB-gon is a spherical polygon (SP) or a great elliptic polygon (GEP) whose boundary does not contain antipodal points. The following SPs or GEPs are AEB-gons:

• A spherical triangle (ST) or a great elliptic triangle (GET) that is not a closed hemisphere

• SPs or GEPs contained within any open hemisphere (HCed; hemispheric)

• SPs or GEPs whose interior contains a closed hemisphere (HCing)

• BAE-gons: A ST/GET that does not intersect its antipode

  • A BAE-gon is an antipodally small SP/GEP

• BAI-gons: A ST/GET that is complementary to a BAE-gon

  • A BAI-gon is an antipodally large SP/GEP

  • Two STs/GETs are complementary if they share the same topological boundary and their union is the entire sphere/ellipsoid

Note: No support is currently provided for compound SPs/GETs.

Usage Example

Please review test.m for the PiSP problem. Call pisp_shear.m for the more optimal algorithm out of the two (compared to pisp.m).

Please review test_pigp_via_pigep.m (under review) for the PiGP problem.

Functions not described in this README.md are under active research or review.

Current State

The PiSP manuscript is published in Mathematical Geosciences. If you have found it useful, please consider citing it.

@article{Li2026Winding,
  Author  = {Li, Z. and Sun, J.},
  Title   = {Winding-based Point-Inclusion Tests for Spherical Polygons},
  Journal = {Mathematical Geosciences},
  Year    = {2026},
  DOI     = {10.1007/s11004-026-10282-0}
}

The PiGP-via-PiGEP manuscript is under review.

More manuscripts are under way.

Reference & Attributions

• pip is based on Sunday (2021).

• states.mat is sourced from tl_2012_us_state.shp.

• institutions.mat is sourced manually from (a previous version of) List of research universities in the United States and Apple Maps.