We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch.
In this paper, we study a new method in shape adjustment ofS-λcurves. By examples of finite and infinite degree generation function, we get the conclusion thatS-λcurves can be adjusted by perturbation of generation functionS（t）while the control points and parameters hold.
In this paper, we propose a face recognition approach-Structed Sparse Representation-based classification when the measurement of the test sample is less than the number training samples of each subject. When this condition is not satisfied, we exploit Nearest Subspaee approach to classify the test sample. In order to adapt all the eases, we combine the two approaches to an adaptive classification method-Adaptive approach. The adaptive approach yields greater recognition accuracy than the SRC approach and CRC_RLS approach with low ~ample rate on the Extend Yale B dataset. And it is more efficient than other two approaches.
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 demon- strate the applications of the bound.
