دانلود رایگان مقاله انترپولاسیون سطح صاف با استفاده از تکه با آفست منطقی

Abstract

We present a simple functional method for the interpolation of given data points and associated normals with surface parametric patches with rational normal fields. We give some arguments why a dual approach is especially convenient for these surfaces, which are traditionally called Pythagorean normal vector (PN) surfaces. Our construction is based on the isotropic model of the dual space to which the original data are pushed. Then the bicubic Coons patches are constructed in the isotropic space and then pulled back to the standard three dimensional space. As a result we obtain the patch construction which is completely local and produces surfaces with the global G1 continuity.

6. Conclusion

The main goal of this paper was to present a simple functional algorithm for computing piecewise Hermite interpolation surfaces with rational offsets. The obtained PN surface interpolates a set of given points with associated normal directions. The isotropic model of the dual space was used for formulating the algorithm. This setup enables us to apply the standard bicubic Coons construction in the dual space for obtaining the interpolation PN surface in the primal space. The presented method is completely local and yields a surface with G1 continuity. Moreover the method solves the PN interpolation problem directly, i.e., without the need for any subsequent reparameterization, which must be always followed by trimming of the parameter domain. Together with its simplicity, this is a main advantage of the designed technique. It can be used by designers anytime when surfaces with rational offsets are required for modelling purposes.