Blending Subdivision Curves and Their Applications

This paper designs two families of blending subdivisions based on known approximatory subdivisions.One is a binary blending subdivision based on the cubic B-splines,the other is a ternary blending subdivision based on the ternary 3-point subdivision.The approach provides a way to control the length of generated curves by introducing a blending parameter.Continuity analysis based on generating functions demonstrates that two families of blending subdivisions are C² continuous in most cases.As an application, a length-preserving subdivision strategy is also proposed in the paper.