Geometric Characteristics:

The NURBS curve shall exhibit the following geometric characteristics:

• Bezier & non-rational b-spline curves are special cases.
• Local Approximation: If control point is moved or a weight is modified, it shall affect the curve only in p = 1 knot spans.
• Strong Convex Hull Property: If u ∉ [u_i , u_{i +1} ] , then C (u) lies in the convex bull of P_{i - p}, . . . , P_i.
• Invariance under affine and perspective transformations.
• The similar differentiability property as with the basic functions.
• If a specific weight is set to zero, then the corresponding control point contain no effect at all on the curve.

                         If w_i  → + ∞,

                         then

NURBS surfaces may be analyzed similarly utilizing the bivariate rational basis functions