Module unit_sphere::vector

The vector module contains functions for performing great circle calculations using vectors to represent points and great circle poles on a unit sphere.

Modules

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

Constants

• MIN_LENGTH
  The minimum length of a vector to normalize.
• MIN_NORM
  The minimum norm of a vector to normalize.
• MIN_SQ_DISTANCE
  The minimum value of the square of distance.

Functions

• along_track_distance
  The Great Circle distance of a point along the arc relative to a, (+ve) ahead of a, (-ve) behind a.
• are_orthogonal
  Determine whether two Vector3ds are orthogonal (perpendicular).
• calculate_atd_and_xtd
  Calculate Great Circle along and across track distances.
• calculate_azimuth
  Calculate the azimuth at a point on the Great Circle defined by pole.
• calculate_direction
  Calculate the direction vector along a Great Circle from an initial position and an azimuth.
  See: Panou and Korakitis equations: 30, 31, & 32a https://arxiv.org/abs/1811.03513
• calculate_pole
  Calculate the right hand pole vector of a Great Circle from an initial position and an azimuth.
  See: http://www.movable-type.co.uk/scripts/latlong-vectors.html#distance
• cross_track_distance
  The across track distance of a point relative to a Great Circle pole.
• delta_longitude
  Calculate the relative longitude of point a from point b.
• direction
  Calculate the direction vector of a Great Circle arc.
• distance
  Calculate the shortest (Euclidean) distance between two Points.
  @post for unit vectors: result <= 2
• is_unit
  Determine whether a Vector3d is a unit vector.
• is_west_of
  Determine whether point a is West of point b.
  It calculates and compares the perp product of the two points.
• latitude
  Calculate the latitude of a point.
• longitude
  Calculate the longitude of a point.
• mean_position
  Calculate the mean position of a slice of points on a unit sphere.
• position
  Calculate the position of a point along a Great Circle arc.
• rotate
  Calculate the direction vector of a Great Circle rotated by angle.
• rotate_position
  Calculate the position of a point rotated by angle at radius.
• sin_atd
  The sine of the along track distance of a point along a Great Circle arc.
  It is the triple product of the pole, a and the point: (pole X a) . point = pole . (a X point)
• sq_along_track_distance
  Calculate the square of the Euclidean along track distance of a point from the start of an Arc. It is calculated using the closest point on the plane to the point.
• sq_cross_track_distance
  The square of the Euclidean cross track distance of a point relative to a Great Circle pole.
• sq_distance
  Calculate the square of the Euclidean distance between two points. Note: points do NOT need to be valid Points.
  @post for unit vectors: result <= 4
• to_point
  Convert a latitude and longitude to a point on the unit sphere. @pre |lat| <= 90.0 degrees.