Improve Proposal with Vissarion's comment.

[Rylynnn]

• List some algorithms from Boost Geometry that need to compare distances.
• A similar problem we could study is the compare azimuths. Given p1, p2, q1, q2 we want to compare azimuth(p1,p2) vs. azimuth (q1,q2). The result again will be {larger than, less than, equal}. This problem appear in relational operations in Boost Geometry.Find places in the library that need to compare two azimuths.
• Read and learn a Link, which not directly related but a useful reference for filtering in computational geometry is the following:

[Rylynnn]

• See for example where we test if two points are on the same side of some geodesic segment.
• Learn Spherical trigonometry.
• Learn Geographic coordinate system
• Learn Haversine formula.

[Rylynnn]

• Learn Andoyer distance with Geographic Distance and Azimuth Calculations
• We can not Calculate with The Area of a Sector of an Ellipse for:

On the surface of a sphere, geodesics lie along great circles (i.e. a circle with its center at the center of the sphere). An ellipsoid geodesic is a minimum-distance path on an ellipsoid, and you might be tempted to think it's a great-ellipse (an ellipse where the center of the ellipse is located at the center of the Earth). If you think it's a great-ellipse, you are right in some cases; in other cases, it is not an ellipse but an ill-defined oval of some sort.