The Research Of S-shaped G~2 Hermite Interpolation By Segmented Rational Cubic Bezier Curve Based On TC-Biarcs

Using Hermite interpolation to get smooth curve segment, which satisfies the given boundary conditions is a popular modeling method in computer aided geometric design (CAGD).In particular, (rational) Bezier curve is very common used in modern design system[1], Hermite interpolation of (rational) Bezier curve has been widely studied[1,2,4,5,7].In this paper, uses the idea of segmentation, based on the construct method of the TC-Biarcs and its control polygons, then puts forward the S-shaped of uniform and non-uniform rational cubic Bezier curve of G2 Hermite interpolation algorithm. Then S-shaped G2 Hermite interpolation with segmented rational cubics Bezier curve is construted. And the parameter of curvature K is introduced. The control polygons of TC-Biarcs shoud be calculated which satisfied the C1 Hermite data first. The connected poin is satiifies C1 continuous, then we get the S-shaped Bezier curve which have diverse shapes and better smoothness by adjusting the curvature parameter in this paper.The construct method and algorithm of the S-shaped Bezier curve are given in this paper.The experimental results show that the effectiveness of the algorithm. Comparison is given and implemented different conditions of the advantages and disadvantages of all kinds of situations.