N-way blending problem of circular quadrics
A method of blending circular quadrics with parametric patches is proposed in this paper. It needs n rational bi-cubic B,zier patches and two S-patches to blend n (n > 2) quadrics. Bi-cubic rational B,zier patches are used to G (1)-continuously blend each pair of adjacent base surfaces. These patches enclose two n-sided holes. And an S-patch is used to fill each hole, which keeps nearly G (1)-continuity. Explicit formulas of control points for both B,zier patches and S-patches are derived from their constraint conditions, which make modeling by blending quadrics very simple and convenient. In addition, the shapes of the blending surfaces can be intuitively adjusted by free parameters.
n-way blending circular quadrics s-patch