Study On Hermite-type Interpolation Subdivision Method

With the rapid development and wide application of computer science, subdivision has become a powerful tool in the fields of computer aided design(CAD) and computer graphics(CG).Through nearly three decades'development, subdivision becomes more mature day after day and most classical subdivision methods have established a more systematic theory of knowledge. The Hermite-type interpolation subdivision scheme has firstly proposed in 1992 by J.L.Merrien, from that on, the Hermite-type interpolation subdivision has a rapid development. With this, in a short time, the results from the subdivision scheme which generates the C1 or C2 curve on a one-dimensional interval to the subdivision scheme that generates the smooth surface on a rectangular meshes can be shown. However the smooth surface that generated by subdivision scheme has a big difference from the sample function surface. This paper introduces a new method which can get a more precise surface. This thesis reviews the general situation and history of subdivision at first, and then introduces several kinds of classic subdivision schemes, depicts the Hermite-type interpolation subdivision schemes on one-dimensional interval and rectangular mesh and introduces the definitions and theorems in subdivision analysis theory.In this paper, at first the main work refines a large rectangle and manipulates the refinement operation on each smaller rectangle based on the Hermite interpolation subdivision scheme proposed by Merrien. In light of this, this paper combining the Merrien's algorithm and the Hermite interpolatory subdivision scheme with tension gives a Hermite interpolatory subdivision scheme with tension on rectangle meshes. This subdivision scheme can also generate smooth subdivision surface(such as a similar part of sphere and paraboloid) and generate different subdivision surfaces when the tension parameter takes different values. And moreover when the tension parameter's absolute value given greater, the subdivision surface generated by this scheme increasingly close to initial control mesh.