Chapter 9: NURBS Surfaces

Finding the Derivative of NURBS Curves

Finding the derivative at any point along a NURBS curve is conceptually the same as finding the derivative on a B-spline. Again, you must find the derivative of the curve with respect to t using the derivatives of the basis functions. For NURBS, the derivative of the basis functions is the following equation.

(5.3) The derivative of a NURBS basis function. 

Students of calculus will notice that this is the result of finding the derivative of Equation 5.1 using the quotient rule. This equation can be used to find the derivative of any point along the curve. In the next section, I will show you how to actually compute the derivative in code.