Ray tracing objects defined by sweeping a sphere

The basic calculation underlying ray tracing is that of the intersection of a line with the surfaces of an object. A method is presented here for performing this calculation for a new and powerful class of objects, those defined by sweeping a sphere of varying radius along a 3D trajectory. When polynomials are used for the parametrization of the centre and radius of the sphere, the intersection problem reduces to the location of the roots of a polynomial. An implementation is presented, together with sample applications.