Chapter 1: Three Point Stationary and Non-stationary Subdivision Schemes

We present a family of 3-point binary approximating C
^-1
stationary subdivision schemes. The Chaikin 2-point scheme and a known 3-point scheme belong to this family of schemes. We also present a 3-point C
^-1
non-stationary subdivision scheme. This non-stationary scheme reproduces functions spanned by {1, sin(alphax), cos(alphax)}, 0 < alpha < pi/2 and, in particular, circles, ellipses and so on.