I''m looking at Bezier surfaces and need to calculate the tangents needed to find the normals at a point. I''m trying to do the maths on paper first, not worried about implementation. But I got stuck with a slight differentiation problem. My minds gone blank!!! How do I differentiate 4t(1-t)^3 ? Is there a rule? I tried the chain rule, but am not sure about how the 4t part fits into it. Any mathematicians know what to do? Thanks in advance.

A straightforward, brute force way to do it is to expand it out and differentiate the resulting polynomial. You might want to check out the books listed below, they both cover this topic.

Author, "Real Time Rendering Tricks and Techniques in DirectX", "Focus on Curves and Surfaces"

Product rule first, then chain rule. You apply the chain rule for the derivative of (1-t)^3 as you apply the product rule. So if f(t)=4t, g(t)=t^3 and h(t)=1-t then d/dt f(t)*g(h(t)) = f(t)*g'(h(t))*h'(t)+f'(t)*g(h(t)) = 4t*3(1-t)^2*-1+4(1-t)^3.

[edited by - LilBudyWizer on January 12, 2003 8:04:25 PM]

ah ha! Cool... thanks guys.