Advantages of NURBS Surfaces

The Quotient Rule

NURBS are a form of curves and surfaces that are expressed quotients (fractions). When you want to find the slope on a NURBS curve, you need a way of finding the derivative of a quotient. There is a simple rule that can be applied when differentiating quotients, which is appropriately called "the quotient rule." You can express the numerator and denominator as separate functions, find the derivatives of each, and then put them together as shown in Equation A.8.

(A.8) The quotient rule. 

The quotients shown in this book are relatively straightforward. Both the numerator and denominator are simple polynomials . Although the results are sometimes ugly, the quotient rule gives you a useful and straightforward tool to divide and conquer quotients.