基于共形几何代数的圆拟合方法实现  

Realization of Circle Fitting Algorithm Based on Conformal Geometric Algebra

作　　者：白志鹏[1] 刘超[2] 李茂宽[3] 

机构地区：[1]中国人民解放军61741部队 [2]总参气象水文局 [3]海军航空工程学院

出　　处：《现代电子技术》2009年第16期140-142,145,共4页Modern Electronics Technique

基　　金：国家自然科学基金资助项目(60672140;60802088);教育部新世纪优秀人才支持计划资助项目(NCET-05-0912)

摘　　要：提出一种基于共形几何代数的圆拟合算法,通过将欧式空间嵌入到共形空间,圆可以表示为向量形式,共形空间中点与圆的内积,则表示了点与圆的位置关系。可以证明,通过附加两个变量,圆就可以表示为平面,用圆代替超平面作为决策面,可以降低某些问题的计算复杂度。针对Visual Basic数值计算能力的不足,不利于系统开发;介绍基于共形几何代数圆拟合算法及其基于VB和Matrix VB的实现,该方法将Matlab的强大计算功能与VB的Windows用户界面开发方面的优势结合起来,充分发挥了各自优势,缩短了软件的开发周期。软件测试结果表明,计算方法正确,计算速度快,系统资源消耗少,操作简便易行,能满足数据拟合的要求。A circle fitting algorithm based on conformal geometric algebra is introduced. By embedding Euclidean space in a conformal space, circles can be expressed as vectors. The inner product of points and circles in conformal space, which expresses position between points and circles. It shows that a circle may be implemented as a plane with another two inputs. By using circles instead of planes as decision surfaces,a reduction in computational complexity can be achieved for certain types of problems. According to the situation that Visual Basic is insufficient in numerical computation ability,and is weak in algorithm development. The theory of circle fitting algorithm based on conformal geometric algebra is introduced firstly,then the realization of circle fitting algorithm based on conformal geometric algebra by incorporating VB and MatrixVB. The incorporated advances of Matlab＇s powerful calculation function and Visual Basic＇s friendly graphic user interface shorten the period of software development by taking the advantages of both. It has been demonstrated by the instance that the calculating procedure is accurate. The software interface is friendly. Beside this, resource expenditure of computer is low and calculating speed is quick, the software is convenient to use. It can fulfill the circle fitting problem well.

关 键 词：VISUAL Basic MATRIXVB 圆拟合 共形几何代数 

分 类 号：TQ015.9[化学工程] TP391[自动化与计算机技术—计算机应用技术]