ABSTRACT
Bezier curves and surfaces are polynomials that approximate the shape defined by their control points. Nevertheless, Bezier curves and surfaces are not suitable for large-scale industrial design and manufacture. A freeform shape such as the hull of a ship or the fuselage of an airplane or the body of a car cannot be represented accurately by a single polynomial. Moreover, Bezier control points have global effects (see Figure 27.1); adjusting a Bezier control point near the rear of a car would affect the shape near the front of the car. Designers require local control. Adjusting a control point should change the shape of the curve or surface only near the control point; fixing an undesirable artifact in one location should not create a new artifact in a far away location.
