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 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, calculate_coincident_arc_distances calculates the distances between Arc ends, zero if the Arcs overlap.

Otherwise closest_intersection_point determines which intersection point is closer to the centroid of the Arcs midpoints, normalized to lie on the surface of the sphere. calculate_intersection_distances then calculates great-circle distances along the Arcs to the intersection point.

Functions

• calculate_coincident_arc_distances
  Calculate the great-circle distances along a pair of Arcs on coincident Great Circles to their closest (reference) points.
• 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 great-circle distances along a pair of arcs to their closest intersection point or their coincident arc distances if the Arcs are on coincident Great Circles.
• closest_intersection_point
  Determine the closest intersection point to the centre of the Arcs.
• is_within
  Whether an intersection point is within an Arc.