GEODESIC solves geodesic problems concerning three types of surface.

By using variational method

(1) a right cylinder with a circular cross section
(2) a right cone with a circular base
(3) a sphere

The parametric expression and the length of the geodesic can be obtained. The results are displayed in 3-D plots. Generally, two curve can be obtained: one is the correct geodesic; the other is the conjugate geodesic which is longer than the correct one.

r, h: geometry of the surface.
surface: surface type.
theta1, z1, xi1: the first ending points in local coordinates
theta2, z2, xi2: the second ending points in local coordinates
x, y, z: parametric expression of the geodesic
cx,cy,cz: parametric expression of the conjugate geodesic

Note:
1. Symbolic Toolbox is necessary to this program for solving the constants in the parametric expression of conical or spherical geodesic