Incenter subdivision scheme for curve interpolation

A new geometry driven subdivision scheme for curve interpolation is presented in this paper. Given a sequence of points and associated tangent vectors, we get a smooth curve interpolating the initial points by inserting new points iteratively. The new point corresponding to an edge is the incenter of a triangle, which is formed by the edge and the two tangent lines of the two end points, so we call such scheme incenter subdivision scheme. The limit curves are proved to be shape preserving and G1 continuous, but many numerical examples show that they are G2 continuous and fair. Generating spiral from two-vertices G1 Hermite data by the incenter subdivision scheme is also introduced. If all the initial points and their initial tangent vectors are sampled from a circular arc segment, the circular arc segment is reproduced. Several examples are given to demonstrate the excellent properties of the scheme.