Morphing

Cutting

A curve is defined by a series of points. The points on the curve are described as a range of values. The limits of this range are defined by the two end points on the curve. In the parametric equations that follow, there are two parameters (u, v), which control these end points. The u-parameter ‘sees’ only the local curves, which define a particular shape, while the v-parameter ‘sees’ the elevations of the entire shape. For example, in the case of the cylinder, the v-parameter would see a rectangle, while the u-parameter would see a circle. Limiting the numerical range of the parameters (u and v) will effectively cut the shape.