Three Geometric Hermite Interpolation And Optimization

Geometric Hermite interpolation is to find a curve which interpolates position, tangent vectors, curvatures and other conditions at the end. It has widely application in geometric structure and engineering design. In this paper, we presented a new constructive algorithm on the basis of the existing algorithm. This paper includes three parts.In first chapter, we simply introduce provenience and development of the Computer Aided Geometric Design and the current research situation at home and aboard, then summarize geometric continuous, cubic splines curve and the nature of Bézier curves.In second chapter, we presented a scheme for a class of GHI curve which is G~1 continuous through bringing in a new knot, gave the parameters formula when the strain energy of curve is minimum. The formulas reserve rational adjustable parameters. In order to accessing smooth curves, we discuss how to choose free parameters in various interpolation conditions. Then we analyze the pros and cons of algorithm, and propose two corresponding improved algorithm according to advantages and disadvantages of algorithm.In third chapter, we gave a scheme for a class of GHI curve which is G~2 continuous through bringing in two new knots and the parameters formula when the strain energy of curve is minimum. The algorithm contains 6 free parameters, These parameters could control the length of tangent vector and curvature vector of GHI curve, and we can have local modify to the interpolation curveIn the paper, we also give some specific example, these examples are drawn by Matlab according to the algorithm of paper. The method is effective in generating smooth curve.