Cubic Spline Based Sweep Surface:

Additionally to open curves, closed polygons and curves are utilized to make sweep surfaces. If the end surfaces are involved, then the sweep surface encloses a finite volume. Several geometric modeling systems makes primitive volumes in this way. A square or rectangle swept along with a straight path yields a rectangular parallelepiped. A circle swept along with a straight path yields a cylinder. A circle of reducing radius swept along with a straight path yields a cone. Rotation around the sweep axis is also possible. Figure illustrated the sweep surface resulting from a plane square perpendicular to and centred on the x-axis being swept along with and simultaneously rotated through 90° around the x-axis. In sweeping a planar polygon or closed curve along an arbitrary path there are two significant considerations. The primary is what point in the polygon continuously lies on the path? Generally, any point in a polygon or on a closed curve can continuously lie on the path. For different points, the resulting surfaces are different.