非正则变距偏置曲线曲面研究与应用

项目名称： 非正则变距偏置曲线曲面研究与应用

项目编号： No.61262044

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 邱泽阳

作者单位： 兰州交通大学

项目金额： 46万元

中文摘要： 非正则问题是偏置（offset）曲线曲面中经常遇到的问题，本项目拟拓展非正则等距偏置曲线曲面的理论，开展非正则变距偏置曲线曲面的研究，从而完善偏置曲线曲面理论。 其算法思想以偏置距离为半径构造扫描圆盘，让圆盘的圆心沿基曲线移动进行圆盘扫描，选出自交区域,再用基曲线上圆心点处的法线与偏置曲线求交点,找出候选自交点 ,并将圆盘内的点作为真实自交点。实际操作时，通过求解一系列多项式方程的解空间来探测、去除非正则变距偏置曲线中的自交区域，从而消除非正则变距偏置曲线中的自交现象。然后，将非正则变距偏置曲线的处理算法拓展到非正则变距偏置曲面中，形成非正则变距偏置曲面自交探测、去除算法。 最后，用得到的非正则变距偏置曲线曲面自交点去除算法来处理Hwan Pyo Moon提出的Equivolumetric偏置曲线、曲面以及Equivolumetric管道曲面的非正则问题。

中文关键词： 非正则曲线曲面；变距偏置曲线曲面；Equicolumetric曲线曲面；Equicolumetric管道曲面；圆盘扫描算法

英文摘要： Irregular problems often occur in the offset curves and surfaces. In order to expand the theory of equidistance offset curves and surfaces, this project will do some irregular work in vari-distance offset curves and surfaces, and make it perfect in the theory of offset curves and surfaces. Its main idea is to construct a disk, which radius is offset distance of vari-distance offset curves, and let the disk to move along the original curve. If some offset curves occur in the disk, call it self-intersect area. Then find the points, from the self-intersect area, on the normal of the original curves as alternative points, the self-intersect points are those interior the disk. In fact, by solving a series of polynomial equations, to detect and remove the self-intersection area of local and global in vari-distance offset curves. Then, Extend the algorithm for vari-distance offset curves to vari-distance offset surfaces. At last, using the algorithm for vari-distance offset curve and surface to solve irregular problem in Equivolumetric offset curves, surface and Equivolumetric tubular cylinders, which promoted by Hwan Pyo Moon.

英文关键词： Irregular curve or surface；var-distance offset curve or surface；Equicolumetric curve or surface；Equicolumetric tubular surface；Disc scanning algorithm