Two algorithms for volume-preserving approximations of surfaces of revolution

The paper deals with volume-preserving approximations of surfaces of revolution. The approximating surfaces are generated only by line segments and circular arcs of a constant radius r . Further, for r > 0 , the approximating surfaces are visually C1 surfaces. For r = 0 , developable C0 surfaces are obtained (consisting of either congruent cylinders or frustums of cones of revolution). Two algorithms are discussed. The first algorithm preserves the volume enclosed by a surface of revolution and the planes of every two latitude circles; the approximating surface is, however, no longer a surface of revolution. The second algorithm applies an approximating surface of revolution; however, the volume preservation no longer holds globally.