摘要
one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.
one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.
