translateUVN Deformer - Unlimited Range (Part 2)
So in order to make sure I'm scaling the tangents correctly we need to calculate the basis function for the first CV. That ends up being:
W = (1-U)^3
which can expanded to
W = 1 - 3U + 3U^2 - x^3
So if we want the "speed" of the point we need to take the derivative of this function. Keep in mind this isn't the derivative of Weight with respect to Parameter, this is parameter with respect to time. The derivative is:
dW/dU = -3 + 6U - 3U^2
So if we evaluate that function for the U value of 0 (since we're dealing with the start of the curve) we get -3. Which lines up with what we observed in Maya. I actually double checked this methodology for quadratic curves too, and it holds up, for quadratic curves the tangent is twice the distance to the second CV, very interesting!
So this suggests I shouldn't divide the tangent to keep the speed constant, I should leave it as is. The basis function for the first CV just falls off really quickly so it makes sense that the point would be travelling quickly at that point.