Rotational sweep volumes of objects bounded by algebraic curves

An algebraic algorithm is presented for generating the purely rotational sweeping volumes of planar objects bounded by algebraic curves. The boundaries of purely rotational sweep volumes of planar objects are characterized. The sweep volume boundary is related to convolutions consisting of the planar object boundaries at its start and final angles and the circular sweep arcs of radial extreme points. Algebraic algorithms are given to detect radial extreme points and ineffective radial extreme points. Algorithms are also given for the internal representation of algebraic curves, that is, whether they are parametrically or implicitly defined. Redundancies that arise in the effective convolution are treated, and plane sweep methods by which to remove these redundancies and thereby obtain the boundary of the rotational sweep volumes are given