Module unit_sphere::vector::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 the same (or opposing) great circles.
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 from the cross product of their pole vectors. If the resulting vector is too small to normalize, then the great circles are the same or opposing, in which case they effectively intersect everywhere.

The tricky part is choosing which of the two intersection points to use.
Most of the functions in this module perform that task.

Functions

• calculate_closest_intersection_distances
  Calculate the great circle distances to the closest intersection point from the start points of a pair of great circle arcs, on different great circles.
• calculate_intersection_distances
  Calculate the great circle distances to an intersection point from the start points of a pair of great circle arcs, on different great circles.
• calculate_intersection_point
  Calculate an intersection point between the poles of two Great Circles.
  See: http://www.movable-type.co.uk/scripts/latlong-vectors.html#intersection
• calculate_intersection_point_distances
  Calculate the distances along a pair of Arcs on the same (or reciprocal) Great Circles to their closest (reference) points.
• calculate_same_gc_reference_distances
  Calculate the distances along a pair of Arcs on the same (or reciprocal) Great Circles to their closest (reference) points.
• is_within
  Whether an intersection point is within an arc