Interpolating given tangent vectors or curvatures by preprocessed incenter subdivision scheme

This paper introduces a preprocessed incenter subdivision scheme to make the limit curves interpolate G1 or G2 Hermite data. The key idea is to add a preprocessed step, changing the compute rule of new inserted points and their corresponding tangent vectors in the first subdivision step of the incenter subdivision scheme[4]. Moreover, we prove that the limit curves generated by our algorithm interpolate given tangent vectors or curvatures at given points, with some mathematical analyses techniques. Numerical examples elucidate the validity of our approach.