The Existence For Vector-valued Rational Interpolation And Its Application In CAGD

This thesis consists of four chapters. In the first chapter, We outline the background and the main results abtained in this thesis.In the second chapter, We state some basic concepts and properties of the vector rational interpolation, the main computation methods and results on the vector rational interpolation.In the third chapter, We give a method to judge the existence for the vector rational interpolation by use of Newton interplating polynomial,and present a concrete expression of the corresponding rational interpolation when the latter exists.In the fourth chapter, the vector rational interpolation have been used in CAGD. We present two methods for generating a segmant of circular arc by the vector continued frations. Based on this method we construct a parametric rational arc spline that is GC1 continuity. By adjusting the given tangent vector, the parametric rational arc spline also has convexity preserving property and monotonicity preserving property.