The Interpolation Method Based On Approximation Subdivision Of Triangular Mesh

Subdivision surface interpolation, as a kind of important fitting technology has attratced lots of attention and has important applications in CAGD. In practice, we usually require to achieve the interpolation to the given control points and the shape control for subdivision surface. In order to meet the needs of practical appli-cation, our studies focus on approximating subdivision theory of triangular mesh. On the one hand, with the progressive iteration technology, we study the method of subdivision surface interpolation and shape control; on the other hand, with the normal constraints, we further investigate the shape control for the interpolation subdivision surface. Firstly, we propose a progressive iterative interpolation method based on Loop subdivision and prove the convergence of the method. The method can achieve the limit surface which interpolates the control points. By adjusting the shape control parameters, we can control the shape of the surface effectively. We also prove that the method is localized, which makes local shape control to the surface possible. Secondly, we proposes a new method for two steps Loop subdivi-sion interpolation based on normal constraint. The method can achieve the limit surface which interpolates the control points and normals. Finally, we prove that the progressive iteration technique for (?)3subdivision method is converged and pro-pose a new two-step (?)3subdivision interpolation method based on the progressive iteration technique. The method makes the limit surface interpolate the control points. And by adjusting the shape control parameters, we can control the shape of the surface effectively. In addition, the feasibility of the proposed algorithms in the paper is verified by experiment, and the modelling effect is satisfied.