Degenerations of rational Bézier surface with weights in the form of exponential function  

作　　者：ZHANG Yue ZHU Chun-gang GUO Qing-jie 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China [2]School of Mathematics and Physics Science,Dalian University of Technology,Panjin 124221,China.

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2017年第2期164-182,共19页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11671068,11271060,11601064,11290143);Fundamental Research of Civil Aircraft(MJ-F-2012-04);the Fundamental Research Funds for the Central Universities(DUT16LK38)

摘　　要：Rational Bezier surface is a widely used surface fitting tool in CAD. When all the weights of a rational B@zier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bezier surfaces. In this paper, we study on the degenerations of the rational Bezier surface with weights in the exponential function and indicate the difference of our result and the work of Garcia-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bezier surface with weights in the exponential function is defined, which is just the limit of the surface. Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster.Rational Bezier surface is a widely used surface fitting tool in CAD. When all the weights of a rational B@zier surface go to infinity in the form of power function, the limit of surface is the regular control surface induced by some lifting function, which is called toric degenerations of rational Bezier surfaces. In this paper, we study on the degenerations of the rational Bezier surface with weights in the exponential function and indicate the difference of our result and the work of Garcia-Puente et al. Through the transformation of weights in the form of exponential function and power function, the regular control surface of rational Bezier surface with weights in the exponential function is defined, which is just the limit of the surface. Compared with the power function, the exponential function approaches infinity faster, which leads to surface with the weights in the form of exponential function degenerates faster.

关 键 词：rational Bezier surface WEIGHTS regular control surface toric degenerations exponential function. 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]