Geodesics on Some Surfaces

select surface

monkey saddle

Parameters of surface

a

1

b

1

c

1

opacity

1

parameters of initial point

x

0

0.5

y

0

0.5

parameters of geodesics

number of geodesics

10

length

1

Or

parameters of direction

specify direction

direction

0.5

This Demonstration shows geodesic curves on some selected surfaces. Mathematica's built-in function NDSolve is used to solve the appropriate differential equation and functions are defined to calculate Christoffel coefficients and the second fundamental form (not actually needed, but it could be used for possible extensions for asymptotic curves). You can choose from 11 surfaces; the program is easily extendable to other surfaces.