In this paper, we develop a new approach to blending of
constant and varying parametric surfaces with curvature
continuity. We propose a new mathematical model consisting of a
vector-valued sixth-order partial differential equation (PDE) and
time-dependent blending boundary constraints, and develop an
approximate analytical solution of the mathematical model. The
good accuracy and high computational efficiency are
demonstrated by comparing the new approximate analytical
solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on
the continuity at trimlines, and apply the new approximate
analytical solution in blending of constant and varying parametric
surfaces with curvature continuit
