Abstract: A geometric 4-points interpolatory subdivision scheme with a parameter is
proposed to overcome the deficiency of traditional 4-points interpolatory subdivision scheme that
it can not generate non-polynomial curve, for example, circle. As three adjacent points confirm a
circle, there are two arcs between every two adjacent points. The new generating point is
determined by weighted average of two midpoints on the arcs. Interpolation formula and
algorithm are described. This subdivision scheme can be convexity-preserving and restore a circle
if all initial knots are on the same circle. Examples show the difference between this scheme and
some traditional schemes. As the parameter becomes smaller, limit curve gets closer to initial
controlling polygon.

Key words: geometric interpolation, convexity preserving, subdivision, circle-restoring