Weighting adjustable general triangular midpoint subdivision scheme

To select proper weight value in modeling of subdivision surface, the quantitative relationship of limit points and weighting coefficient α was proved with equivalent subdivision mask, and the smoothness of the resulting subdivision surface C¹ when weighting coefficient was negative had also been analyzed. A new weighting coefficient γ which had obvious geometric meaning was proposed. The geometric meaning of weighting coefficient γ was that the limit point of a specific original control point pulled towards the original control point itself on a line as weighting coefficient γ varies from 0.25 to 1. Meanwhile, the limit subdivision surface had lied closer to the control mesh with C¹ continuity when γ gradually became larger. Some typical examples were illustrated to verify the validity of the conclusion at length.