Adapting Shape Parameters for Cubic Bezier Curves

Bezier curves are an established tool in Computer Aided Geometric Design. One of the drawbacks of the Bezier method is that the curves often bear little resemblance to their control polygons. As a result, it becomes increasingly difficult to obtain anything but a rough outline of the desired shape. One possible solution is tomanipulate the curve itself instead of the control polygon. The standard cubic Bezier curve form has introduced into it two shape parameters, gamma 1 and 2. These parameters give the user the ability to manipulate the curve while the control polygon retains its original form, thereby providing a more intuitive feel for the necessary changes to the curve in order to achieve the desired shape.