三次B样条反求控制点

反求工程作为复杂工业产品设计与制造的重要技术手段之一,深受CAD/CAM领域的广泛重视,特别是自由曲面重构技术作为复杂曲面产品反求工程中的＂瓶颈＂问题,是今后一个时期的研究热点.反求工程中最为关键的技术就是曲面重构技术.目前主要有两大重构方法：NURBS曲面重构和三角Bezier曲面重构.本文围绕NURBS曲面重构展开研究,提出一种反算三次B样条曲线、曲面控制顶点的简便算法.该算法适用于准均匀和非均匀B样条曲线、曲面的反算.算法采用非节点边界条件,不需要由用户提供,从而使反算过程得以简化.

Calculating Control Points of NURBS

Reverse engineering（RE）is a key technology of advanced manufacturing.As one of important technical ways to design and manufacture complex industrial products,reverse engineering is taken into a account widely in the field of CAD/CAM.Especially,free-form surface reconstruction is a challenging task and will catch more attention in future work.Surface reconstruction is the most important technology in RE.There are two prevailing surface reconstruction methods.They are NURBS surface reconstruction method and triangle surface reconstruction method.This thesis makes some research work on NURBS surface reconstruction.Our paper proposed a simple method which can calculate the control points in NURBS curves and surfaces.This arithmetic applies to quasi-uniform B-spline and non-uniform B-spline.The arithmetic uses non-node boundary conditions and does not need interaction,which can simplify the operation process.