The Application Of Hybrid Computational Methods In CAGD

The implicitization of parametric curves and surfaces is the main researchobject. In the paper, the optimization algorithms of the implicitization ofparametric curves and surfaces are given by the hybrid computational methods.The major research methods of the implicitization of parametric curves andsurfaces are Groebner bases, resultant theory, Wu-method and the movingcurves and surfaces provided by Sederberg, and so on. We mainly get twooptimization methods of the implicitization of parametric curves and surfacesin the base of the Lagrange and Newton interpolation and the resultant theoryfrom this paper. The principal research results are as follows:The method of the implicitization of parametric curves has been improvedthrough the Newton interpolation algorithm and Bezout matrix, Comparedwith the way that parametric curve is implicated via Lagrange interpolation, itsaves the time and space, therefore greatly improves the operation speed whenfinding the implicitization of polynomial parametric curves. And according tosome examples, it proves the effectiveness and accuracy of this method.The algorithm of Dixon’s matrix is given in the paper. Secondly, a methodof the implicitization of parametric surfaces, which is based on Dixon matrixand Lagrange interpolation, is given. This method not only reduces thecomputational cost, but also saves the time and space cost. What’s more, itspeeds up the implicitization of the parametric surfaces. Finally, someexamples are provided to prove the accuracy and efficiency of the algorithm.