Integral computation relating to rational curves based on approximate degree reduction  

作　　者：陈国栋 王国瑾 

机构地区：[1]State Key Laboratory of CAD & CG and Department of Mathematics, Zhejiang University, Hangzhou 310027, China

出　　处：《Progress in Natural Science:Materials International》2000年第11期53-60,共8页自然科学进展·国际材料（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No.69673029), Natural Science Foundation of Zhejiang Province (Grant No. 698025)and the Foundation of State Key Basic Research 973 Item (Grant No. G1998030600).

摘　　要：A new algorithm is presented for computing the volume of revolution, moment of area and centroid etc. , which are related to the integration of rational curves. In this algorithm rational curve with high degree is firstly approximated by those with lower degree through endpoint interpolation. And finally the closed form integration solution is derived for quadratic rational curve. The diminishing rate of the minimum norm of the perturbation vector needed by degree reduction is 0(2-n) when the interval is subdivided at the midpoint. Combining the subdivision with the degree reduction, we can obtain a faster convergence of integration approximation. A series of integral error bound functions which are fairly simple to compute are derived. The examples given in this paper show that this algorithm is a simple and time-saving method in computing with small tolerance.A new algorithm is presented for computing the volume of revolution, moment of area and centroid etc. , which are related to the integration of rational curves. In this algorithm rational curve with high degree is firstly approximated by those with lower degree through endpoint interpolation. And finally the closed form integration solution is derived for quadratic rational curve. The diminishing rate of the minimum norm of the perturbation vector needed by degree reduction is 0(2-n) when the interval is subdivided at the midpoint. Combining the subdivision with the degree reduction, we can obtain a faster convergence of integration approximation. A series of integral error bound functions which are fairly simple to compute are derived. The examples given in this paper show that this algorithm is a simple and time-saving method in computing with small tolerance.

关 键 词：degree reduction RATIONAL CURVES INTEGRAL error BOUNDS subdivision. 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]