Cone Geodesics

cone slope

3

distance R

2

angle β

0

surface transparency

0

Geodesics on a cone are easily found using the fact that the surface is isometric to the plane. The left image shows a line specified by two parameters,

R

(distance from the origin) and

β

(angle between the normal vector and the horizontal axis). The right part shows a cone together with the geodesic that represents an isometric image of the given line.