Computation of Algebraic Polynomial Parametric Surface Intersections

摘要

In the work the authors present the basic elements of a new algorithm to trace a planar algebraic curve f(u,v)=0 within a rectangular parallelogram arising in the context of automatic interrogation of intersections of algebraic surfaces and piecewise continuous rational polynomial parametric surface patches. The method combines the advantageous features of analytic representation of the governing equation in the Bernstein basis with adaptive subdivision techniques and the a priori computation of turning and singular points to provide the basis for a reliable and efficient solution procedure. Representative results from the application of the method in tracing well known algebraic curves and in computing intersections of typical algebraic and rational polynomial surfaces are also presented.