二次NURBS曲线下的面积的精确计算公式

摘要

NURBS method is one of the most important methods in CAGD,and has been widely used in industrial product form design.However,Some of algorithms for NURBS,such as integration,are not set,which limits the application.This paper presents an algorithm for computing area of regions bounded by quadratic NURBS curves by using NURBS matrix representation.Thus the area can be directly obtained by the knot points,coordinates of control points and weights.This algorithm makes important sense in application.It also gives numerical examples.%非均匀有理B样条(NURBS)方法是CAGD的重要方法之一，已被广泛应用于工业产品外形设计中.但NURBS的有些算法，比如积分算法，还不够成熟，因此给实际应用带来了限制.文中利用二次NUBRS曲线的矩阵表达式，给出了二次NURBS曲线下的面积的精确计算公式，所求面积可用曲线的节点、控制顶点坐标和权因子一步代入直接求得，对实际应用具有十分重要的意义.并给出了数字算例.