Suppose you have a parametric equation for a surface, for example:
x = 3*cos(s)+cos(t)*cos(s)
y = 3*sin(s)+cos(t)*sin(s)
z = sin(t)
The partial derivative of this wrt s is:
dsx = -3*sin(s)-cos(t)*sin(s)
dsy = 3*cos(s)+cos(t)*cos(s)
dsz = 0
The partial derivative of this wrt t is:
dtx = -sin(t)*cos(s)
dty = -sin(t)*sin(s)
dtz = cos(t)
Which of these is the tangent in the s direction, and which of these is the tangent in the t direction?
I would have thought the tangent in the s direction is the derivative wrt s above and that the tangent in the t direction is the derivative wrt t, but I seem to remember hearing the opposite.
