دانلود رایگان مقاله درون یابی هرمیت هندسی توسط مجموعه منحنی مسطح

َAbstract

This paper proposes techniques of interpolation of intrinsically defined planar curves to Hermite data. In particular, a family of planar curves corresponding to which the curvature radius functions are polynomials in terms of the tangent angle are used for the purpose. The Cartesian coordinates, the arc lengths and the offsets of this type of curves can be explicitly obtained provided that the curvature functions are known. For given G 1 or G 2 boundary data with or without prescribed arc lengths the free parameters within the curvature functions can be obtained just by solving a linear system. By choosing low order polynomials for representing the curvature radius functions, the interpolating curves can be spirals that have monotone curvatures or fair curves with small numbers of curvature extremes. Several examples of shape design or curve approximation using the proposed method are presented.

8. Conclusions and discussions

This paper has proposed to define and control the shapes of a family of planar curves via predefined curvature radius functions. The defined curves together with their arc lengths and the offsets can be explicitly computed when the curvature radius is given by a wide class of elementary functions. By choosing the curvature radius functions as polynomials, the curvature radius functions can be obtained by solving linear systems under the constraint of interpolating given boundary data or having prescribed arc lengths. Particularly, G 1 Hermite interpolation with or without the constraint of arc length and G 2 Hermite interpolation by the proposed curves have been given. The potential applications of the proposed technique include fair shape design as well as CNC machining tool path generation, etc.