By means of direct analysis of the connection between Loop subdivision surface and its control mesh and the computation of the basis functions,we obtain a bound on the distance between Loop subdivision surface patch and its control mesh.The bound can be used to compute the numbers of subdivision for a given tolerance.Finally,two examples are listed in this paper to demonstrate the applications of the bound.
In this paper,we derive some equalities and inequalities about g-continuous frames,which are an extension to g-frames and continuous frames.We also discuss the stability of the perturbation of a g-continuous frame.
XIAO XiangChun & ZENG XiaoMing Department of Mathematics,Xiamen University,Xiamen 361005,China
