Chapter 3 - B-spline curves

Abstract

A curve generated by using the vertices of a control polygon is dependent on some interpolation or approximation scheme to establish the relationship between the curve and the control polygon. The global nature of the Bernstein basis affects the shape of the total curve. Another basis called the B-spline basis contains the Bernstein basis as a special case. The B-spline basis is generally nonglobal. The nonglobal behavior of B-spline curves is due to the fact that each vertex is associated with a unique basis (support) function. Thus, each vertex affects the shape of a curve only over a range of parameter values where its associated basis function is nonzero. The B-spline basis also allows changing the order of the basis function, and hence the degree of the resulting curve, without changing the number of control polygon vertices. Because of the flexibility of B-spline basis functions and the resulting B-spline curves, different types of control handles are used to influence the shape of B-spline curves.