Subdivision Schemes With Several Geometric Parameters For Geometric Modeling

Subdivision is one important technology in curves and surfaces modeling, and subdivision has been widely used in Computer Aided Geometric Design and Computer Graphics. A class of subdivision schemes with multi-geometric parameters is discussed in this thesis. Compared with the other existing methods, the proposed schemes can exactly reproduce conic section arcs of arbitrary length, and create a variety of shape like bumps and flat edges. And in this thesis we also propose a new subdivision scheme, which is different from the traditional interpolating subdivision scheme in which all the points at each refinement level are changed, but in our scheme the generated limit curve only passes through the initial data points. The numerical experiments show our approach combines the advantages of approximating schemes with the precise control of interpolating schemes. This thesis is structured as follows:First of all, a three-point scheme with a local tension parameter, a local bias parameter and a global tension parameter to control the tightness and offset of the limit curve, respectively. By choosing appropriate parameters, the subdivision scheme is shape-preserving, such as, flat edges preserving, convexity-preserving. And then we propose a non-stationary subdivision scheme can reproduce circles or conic sections by choosing appropriate parameters.At last, in this article we propose two four-point interpolating subdivision schemes which is designed in traditional way. Firstly, a stationary subdivision scheme which with a global tension parameter and a local bias parameter is presented. Furthermore, based on the stationary subdivision scheme, we propose a non-stationary subdivision scheme, which is much more smooth.