Higher Order Geometric Continuous Transition Surface Modeling Applications

Blending surface plays an important role in CAD/CAM, and the problem of blending surface with high-degree geometric continuity is a key question. The paper concerns how to construct a blending surface between two surfaces.(a) It summarizes geometric modeling on its development, its new methods, and further trend, and gives the theory of geometric continuity and blending surface.(b) It systematically introduces main blending method, and points out the defect of blending algorithm in general.(c) G1, G2 and G3 blending surfaces have successfully been constructed by combining rescaling continuity with geometric blending methods.(d) From the relation of geometric invariant with blending surface, a sufficient and necessary condition is derived. Then a high-degree geometric continuity blending surface is obtained with transfinite interpolate method.(e) G3 blending surface with approximation can be constructed by lofting if geometric invariant errors are given, the surface can be converted to B-spline, NURBS form for the purpose of system aggregation.