A Tangent Vector Based Nonlinear Subdivision Scheme without Self-Intersection for Curve Design

In this paper, we proposed a nonlinear subdivision scheme based on tangent vector, with the purpose of offsetting the deficiencies of Dyn´s 4-point method and other classical linear subdivision schemes in the control of shape of subdivision curves. This method has a clear geometric meaning and the property of convexity preserving. Theoretical analysis show that the limit curve of this method is G1 continuous without self-intersection. Several examples are given to show the effectiveness of the scheme.