A parametric algorithm for drawing pictures of solid objects bounded by quadric surfaces

Abstract

An algorithm for drawing pictures of three-dimensional objects, with surfaces made up of patches of quadric surfaces, is described.The emphasis of this algorithm is calculating the intersections of quadric surfaces. A parameterization scheme is used. Each quadric surface intersection curve (QSIC) is represented as a set of coefficients and parameter limits. Each value of the parameter represents at most two points, and these may easily be distinguished. This scheme can find the co-ordinates of points of even quartic (fourth-order) intersection curves, using equations of no more than second order.Methods of parameterization for each type of QSIC are discussed, as well as surface bounding and hidden surface removal.