partial derivatives of sphere


x = r sin v cos u
y = r cos v
z = r sin v sin u

u in [0, 2pi]
v in [0, pi]

Now when I take dp/dv, the tangent vector will be tilted in the -y direction
because v (which comes from the spherical coordinates) is an angle measured
from +y down towards -y. So if we move a small increment dv, we are rolling
down the sphere so to speak.

However, I actually want the tangent vector to go the other way to be
consistent with the direction my texturing v-axis goes. For example, if v =
pi/2, I want dp/dv = (0, 1, 0). It seems to obtain this all
I need to do is negate dp/dv. Does this always work for every dp/dv on the
sphere?

I suppose another way to achieve my goal would be measure v from the -y up
towards +y and redo the spherical to rectangular coordinates based on this
to get a different parameterization of the sphere.



.

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