Abstract: Some groups of blending functions consisting of n (n≥3) functions are given. They have
non-negativity, normalization, symmetry and special endpoint property. The curves defined by them
possess convex hull property, geometric invariance, symmetry. The starting and ending points of the
curves are the midpoints of the first and last edges of their control polygons. At the starting points of
the curves, both the first order and the second order derivative vectors are parallel to the first edge of
the control polygon. And at the ending points, the first order and the second order derivative vectors
are parallel to the last edge of the control polygon. Given m (m > 3) control points, we define one
curve segment, and a composite curve consists of several segments. Each segment can be determined
by different number of control points. So the same control points can be used to define a variety of
shapes. The composite curve is G2 continuous at the piecewise points. The tensor product surfaces
defined by the function groups also have many good properties similar to the curves.

Key words: curve and surface design, Bézier method, B-spline method, piecewise combination, continuity