An improved ternary subdivision interpolation scheme was developed for computer graphics ap- plications that can manipulate open control polygons unlike the previous ternary scheme, with the resulting curve proved to be still C2-continuous. Parameterizations of the limit curve near the two endpoints are given with expressions for the boundary derivatives. The split joint problem is handled with the interpolating ter- nary subdivision scheme. The improved scheme can be used for modeling interpolation curves in computer aided geometric design systems, and provides a method for joining two limit curves of interpolating ternary subdivisions.
