Normal based subdivision scheme for curve design

In this paper we propose a new kind of nonlinear and geometry driven subdivision scheme for curve interpolation. Instead of using linear combination of old vertexes, displacement vector for every new vertex is given by normal vectors at old vertexes. The normal vectors are computed adaptively for each time of subdivision, and the limit curve is G1 smooth with wide ranges of free parameters. With this new scheme, normal vectors at selected vertexes can be interpolated efficiently. A shape preserving subdivision scheme with explicit choices of all free parameters is also presented.