球面上等距线的构造  

Offset of Curves on Spherical Surfaces

作　　者：余正生[1] 杨章通[1] 

机构地区：[1]杭州电子科技大学图形图象研究所,杭州310018

出　　处：《系统仿真学报》2008年第17期4630-4632,4642,共4页Journal of System Simulation

基　　金：浙江省自然科学基金(Y106166);国家教育部回国人员启动基金;国家级留学人员科研活动资助项目

摘　　要：提出了球面上等距线的构造方法。首先,用有理二次Bézier曲线生成球面上的圆弧[1],实现不同圆弧间的拼接,使其达到C1连续,来构造球面上的组合曲线,然后对该组合曲线利用测地线技术求其在球面上的等距线,并通过点与点求交方法来检测所生成等距线的自相交现象,同时去除自交情况。仿真结果表明,该方法能生成球面上的等距线,并基于以下原理:球面上圆弧的球面等距线仍然为圆弧,而圆弧本身不会自相交,从而能快速消除球面上等距线自相交现象。An algorithm was put forward to construct the offset of curves on spherical surfaces. Firstly, the Rational Quadric Bezier spline curves was adopted to build the arc on spherical surfaces, then two or more above mentioned curves were C^1 assembled to construct the combined curve with C^1 continuity, The offset of combined curves on spherical surfaces was got by the technology of geodesic. The way of intersecting between point and point was introduced to judge whether the offset has the loops on which the curve intersected with itself. Based on the principle that the offset of an arc on spherical surfaces is still an arc, and the arc itself has no loops which intersected with the curve itself, the algorithm can wipe off the loops fast.

关 键 词：球面上的等距线 球面上的曲线 自相交 测地线 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]