Module intersection 

The intersection module contains functions for calculating great-circle intersections using vectors.

A pair of great circles intersect at two points unless they are coincident.
For example, points u and v in Figure1.

Figure 1 A pair of intersecting great circles

A great circle intersection point can simply be calculated by normalizing the cross product of their pole vectors.
If the resulting vector is too small to normalize, then the great circles are coincident, in which case they effectively intersect everywhere.

If a pair of Arcs are on coincident great circles, the mormalized centroid of the arc midpoints is used instead of the intersection point.

Otherwise closest_intersection_point calls use_antipodal_pointto determine which intersection point is closer to the centroid of the Arcs midpoints.

Functions

calculate_arc_reference_distances_and_angle

Calculate signed great circle distances from two arc mid points to their closest intersection point or normalized centroid if the arcs are on coincident great circles.

calculate_intersection

Calculate an intersection point between the poles of two Great Circles. See: http://www.movable-type.co.uk/scripts/latlong-vectors.html#intersection

calculate_reference_point_and_angle

Determine the reference point of a pair of arcs. I.e. the closest intersection point if they intersect or the centroid normalized to lie on the unit sphere if they don’t.

closest_intersection_point

Return the closer intersection point to the centroid of the Arcs.

use_antipodal_point

Determine whether the antipodal point is closer to the centroid of the Arcs.