Abstract: A geometric subdivision method based on double parameters is proposed in this paper.
Firstly, the new control points are determined by the original control points and their tangents: using
the quadratic rational Bézier curves formula in which the parameter t is 0.5, let two adjacent points
and the intersecting point of their tangents be the control points of Bézier curves, and take its weight
as the first parameter  to calculate new points. Then we calculate new tangent vectors of all points:
after define provisional tangent vectors, the circle-tangent of this point is computed by the point and
its two adjacent points; whereafter define the formula of new tangents for all points by introducing
the second parameter  related to tangent vectors. Theoretical analyses show its convexity preserving
and convergence. If the second parameter =0, and next step we define a new factor by the initial
parameter , its limit curve is a piecewise rational quadratic C1 curve. The circle preserving of this
scheme can be obtained by computing new points with different parameters  in every step under =1.
The effectiveness of this approach is verified by some numerical examples.

Key words: quadratic rational Bézier curves, geometric subdivision method, convexity preserving, C1
continuity, circle preserving