Spherical Functions

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Spherical Geometry (spherical)

Spherical functions for Euler.

Geometry on the Earth

Spherical Geometry

Load this file with "load spherical"

function spoint (pos:vector)

  Get point on the sqhere from [lat,long] with N>0, S<0, E>0, W<0
  Returns a 1x3 vector
  
  File: spherical

function sposprint (pos:vector, sec:integer=0)

  Print [lat,long] in usual form
  sec=1 : use DMS
  Returns a string
  
  File: spherical

function sposition (point:vector)

  Convert a point on the sphere to a position [lat,long]
  Returns a 1x2 vector
  
  File: spherical

function svector (frompos:vector, topos:vector)

  Difference vector of two positions [lat,long] on an ideal ball.
  Note that following the direction will not reach the destination
  exactly.
  Returns [direction,distance], both in radians.
  
  File: spherical
  
  See: 
  saddvector (Spherical Functions)

function sangle (A:vector, B:vector, C:vector)

  Compute the angle ABC at B on a perfect sphere.
  
  File: spherical

function strianglearea (A:vector, B:vector, C:vector)

  Compute the area of a triangle in space.
  
  File: spherical

function sarea (A:vector, B:vector, C:vector)

  Compute the area of a triangle on a perfect sphere.
  
  File: spherical

function esarea (A:vector, B:vector, C:vector)

  Compute the area of a triangle on the earth
  For small triangles this is not very accurate.
  
  File: spherical

function esdist (frompos:vector, topos:vector)

  Distance of two positions [lat,long] on the earth.
  This functions uses an average earth radius between the two points.
  esdist (earth spherical distance).
  Return distance in m
  
  File: spherical

function esdir (frompos:vector, topos:vector)

  Heading between two positions [lat,long] on the earth.
  esdirection (earth spherical direction).
  Return distance in m
  
  File: spherical

function skmprint (x) := print(x/km$,digits=3,unit="km")

function sdegprint (x) := print(deg(x),digits=2,unit="°")

function saddvector (pos:vector, heading:vector)

  Add a vector v to a position, all elements in degrees.
  This would be the position, which you see in that distance
  under that heading from the position pos.
  Returns the new position.
  
  File: spherical
  
  See: 
  svector (Spherical Functions)

function esadd (pos:vector, direction:number, distance:number)

  Add a distance into the direction on the surface of the earth
  This will only work exactly for small distances.
  Returns the new postion
  
  File: spherical
  
  See: 
  saddvector (Spherical Functions)

function navigate (P1:vector, P2:vector, n:index=10)

  Navigate from p1 to p2
  Prints a series of GPS positions and headings to follow.

function plotearth (lat=-90:30:90, long=0:30:330, labels=1)

  Plots the earth with a grid of coordinates
  
  File: spherical

function plotpos (pos:vector, label="", style="o", col=1)

  Plot a postion and a label
  
  File: spherical

function plotposline (pos, thickness=2, color=1)

  Plot a line of positions
  
  File: spherical

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