Transfinite Interpolation Surface Using Blending Method

This thesis focuses on transfinite interpolation surface modeling problem in CAGD and CAM field via blending approach. The main contents include:traditional transfinite interpolation theory, the transfinite interpolation on the rectangle with single direction and two directions via blending approach, etc.Firstly, the existing methods of the transfinite interpolation are discussed, and the idea of the transfinite interpolation spline modeling via blending approach is given.Secondly, transfinite interpolation theory and its development in surface modeling are discussed and summarized. The advantage of the proposed approach in transfinite interpolation methods is shown, that is, our method don't need the differential information of the given edge curves in smoothing joining.Thirdly, blending-based transfinite interpolation method in rectangle field is discussed. The transfinite spline surfaces are constructed to interpolate the one direction border curves and both direction border curves, respectively, and a few meshes are proposed to construct G1/G2 interpolation spline surface. Numerical experiments show the proposed method is effective.