| To construct a curve that satisfies the conditions of given endpoint conditions is a basic problem.Geometric hermite interpolation that satisfies the given data consisting of two points, two unit tangent vectors at those points, and two signed curvatures at those points,is widely used in geometric structure and curves and surfaces smooth processing.In order to make the surface more smooth,we usually use this kind of traditional hermite curve instead of regional highlights line of irregular parts and make some adjustments. Based on the summary of the existing research results, This papar proposes a new optimization algorithm. This paper includes three parts.The first chapter is the introduction part,simply introducing the origin, development, application of computer aided geometric, and the interpolation algorithm and the study of the smoothing problems of curves and surfaces at home and abroad,and the research state of geometric hermite interpolation curve. At the same time,it introduces some useful curve theory including parametric norm, the nature of the cubic spline curve, the geometric meaning of curvature and flexible rate,and the smooth standards of curves.The second chapter gives a method of generating the basis function of cubic interpolation curve. In consideration of the traditional geometric hermite interpolation curve may produce cuspidal points, curunde, inflection point, this papar proposes a method of generating cubic interpolation curve based on adjusting the length of the endpoint tangent modulus. In consideration of the factors of curvature and torsion,this paper gaves the value of the parameter of the formula with minimum energy.The third chapter gaves a new method of generating geometric hermite interpolation curve by Joining a quadratic curves and a circular arc together instead of cubic interpolation curve.This kind of combination curve can also satisfy the interpolation properties,and is more easily to control the shape of the interpolation curves. |
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