Plus curves and surfaces

The formulations for parametric curves and surfaces that are based on control points are revised to use control lines and control planes instead. Curves defined by control lines are called control-line curves or plus curves, and surfaces defined by control planes are called control-plane surfaces or plus surfaces; the plus implies that in addition to the control points, gradient vectors at the control points are used to design curves and surfaces. The new curve and surface formulations provide more flexibility than traditional formulations in geometric design. Properties of plus curves and surfaces are investigated and an application of plus surfaces in smooth parametric representation of polygon meshes is introduced.