Constructions And Continuity Analysis Of Subdivision Curves

Subdivision scheme is an important technology in curves and surfaces modeling,and subdivision scheme has been widely used in Computer Aided Geometric Design,Computer Graphics and related areas.Its basic idea is: giving the initial control mesh,defining a subdivision rule,and inserting new points into the given initial grid constantly,until eventually producing a smooth curve or surface.If the mask of the scheme does not vary with subdivision level,then it is termed as stationary or else non-stationary.Similarly,if the limiting curve(surface)passes through initial control points,then subdivision scheme is called interpolating,otherwise approximating.In recent years,most research of curve subdivision focus on the construction of subdivision scheme,the proof of the convergence and continuity,the symmetry of basic limit function,and the calculation of the support width and so on.As we all know,some special curves,such as conics,can be generated by the non-stationary subdivision schemes,which greatly enhance the modeling ability.Approximating methods can yield curves with higher continuity order,while interpolating methods yields the limit curve which passes through the original control points.These two methods have been combined recently,thus the limit curve can interpolate part of the points as the designer wants,while the others can be approximated.In view of this,main works are as follows:1.A new family of(2p-1)-point binary non-stationary approximating subdivision schemes with shape parameter ? is presented with the help of the sine function.With the changing of p,theoretical analysis of some important properties of the proposed schemes such as symmetry of basic limit function andkC continuity have been discussed,and the support width also has been calculated.2.A family of hyperbolic forms of 4-point m-ary non-stationary approximating subdivision scheme is presented using the hyperbolic functions for even positive integer m.The asymptotic equivalence is used to investigate the convergence and smoothness of the non-stationary subdivision scheme.3.A multi-parameter combined 5-point ternary subdivision scheme is presented,and the continuity of the scheme is proved by exploiting the joint spectral radius.