Spherical Vector Field and its Flow

The following components of a vector field in R³ at any point (x,y,z) of the 2-sphere S² will be projected to the tangent space of S² at this point and normalized to get unit speed integral curves. That's the way we construct a vector field on S² based on the field in R³!
Please use standard C notation for math, x, y and z for the coordinates. Any other notation will produce an unknown variable error!

• First component of the vector field
• Second component of the vector field
• Third component of the vector field

Initial points of integral curves need not lie on the 2-sphere S²; they will be normalized by radial projection.

• 1 3 5 10 16 20 Choose number of integral curves (trajectories)
• 1 2 3 5 10 Run-time (equals length of the curve)
• First coordinate of initial point
• Second coordinate of initial point
• Third coordinate of initial point
• Increment coordinate of initial point by
• first second third Increment first, second or third coordinate
• -90 0 90 180 Longitude of point of view (London: 0, New York: -74, Dehli: 77)
• -60 -30 0 30 60 Latitude of point of view (Equator: 0, S. Pole: -90, N. Pole: 90)