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1、Seediscussions,stats,andauthorprofilesforthispublicationat:https://www.researchgate.net/publication/46284312ComputingtheminimumdistancebetweentwoplanaralgebraiccurvesArticleinJisuanjiFuzhuShejiYuTuxingxueXuebao/JournalofComputer-AidedDesignandComputerGraphics·April2008Sourc
2、e:OAICITATIONSREADS2563authors,including:Xiao-DiaoChenJun-HaiYongHangzhouDianziUniversityTsinghuaUniversity44PUBLICATIONS293CITATIONS106PUBLICATIONS1,160CITATIONSSEEPROFILESEEPROFILESomeoftheauthorsofthispublicationarealsoworkingontheserelatedprojects:SolidModelingViewproje
3、ctgeometricmethodforsolvingnon-linearequationsystemViewprojectAllcontentfollowingthispagewasuploadedbyXiao-DiaoChenon22October2015.Theuserhasrequestedenhancementofthedownloadedfile.第20卷第4期计算机辅助设计与图形学学报Vol120,No142008年4月JOURNALOFCOMPUTER2AIDEDDESIGN&COMPUTERGRAPHICSApr1,2008
4、平面代数曲线间最近距离的计算1)2)3)陈小雕雍俊海汪国昭1)(杭州电子科技大学计算机学院杭州310018)2)(清华大学软件学院北京100084)3)(浙江大学数学系计算机图象图形研究所杭州310027)(xiaodiao@nit.zju.edu.cn)摘要通过几何观察,指出一条曲线上的最近点是另一条曲线的等距曲线与该曲线的切点这一事实,同时提出基于等距思想的方法来求解2条平面代数曲线间的最近距离1该方法几何意义明显,可同时用来计算代数曲线P参数曲线间的最近距离1对于平面二次曲线,采用文中方法得到的单变量多项式方程次数比已有类似方法中结果方
5、程的次数更低,从而可以降低方程求解的计算复杂度或提高求解的稳定性1关键词最近距离;平面代数曲线;等距方法中图法分类号TP391172ComputingtheMinimumDistancebetweenTwoPlanarAlgebraicCurves1)2)3)ChenXiaodiaoYongJunhaiWangGuozhao1)(CollegeofComputer,HangzhouDianziUniversity,Hangzhou310018)2)(SchoolofSoftware,TsinghuaUniversity,Beijing1000
6、84)3)(InstituteofComputerGraphicandImageProcessing,DepartmentofMathematics,ZhejiangUniversity,Hangzhou310027)AbstractThroughgeometricobservation,itisfoundthatthenearestpointonacurveisatangentpointbetweenthecurveandanoffsetcurveoftheothercurve1Basedonthisobservation,anoffset
7、methodispresentedforcomputingtheminimumdistancebetweentwoplanaralgebraiccurves1Thenewmethodisgeometricallyinstructive,andcanbeusedforcomputingtheminimumdistancebetweenanalgebraiccurveandaparametriconeonthesameplane1Forplanarquadraticcurves,thedegreeoftheresultingunivariatep
8、olynomialequationbyourmethodismuchlowerthanthatoftheequationsinpreviouscomparablem
