Let X be a smooth quadric of dimension 2m in P-C(2m+1) and let Y, Z subset of X be subvarieties both of dimension m which intersect transversely. In this paper we give an algorithm for computing the intersection points of Y boolean AND Z based on a homotopy method. The homotopy is constructed using a C*-action on X whose fixed points are isolated, which induces Bialynicki-Birula decompositions of X into locally closed invariant subsets. As an application we present a new solution to the inverse kinematics problem of a general six-revolute serial-link manipulator. (C) 2010 Elsevier Inc. All rights reserved.