A parametric algorithm for drawing pictures of solid objects composed of 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 on 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 coordinates 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.