Abstract: We studied the parameterization of a kind of GC¹blending of three quadratic surfaces using the ControlSpherebased expression of the blending surface and gave a global parameterization algorithm. At the  same time, we can get the realtime display of the blending surfaces. Different from the parameterization of blending of two quadratic surfaces, it is unnecessary for us to use rotation transformation to reduce the line from the 4thdegree blending surface. We used parallel planes to intersect the cubic curve instead of using radioactive rays.

Key words: implicit algebraic surfaces, blending, parameterization