基于_基有理可展曲面的参数化_英文_

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1、第29卷第3期中国科学院研究生院学报Vol．29No．32012年5月JournalofGraduateUniversityofChineseAcademyofSciencesMay2012ArticleID:1002-1175(2012)03-0289-05Parametrizationofarationaldevelopablesurface*usingtheμ-basisCHENXiao-Hua，CHENYu

2、-Fu，SHENLi-Yong(SchoolofMathematicalSciences，GraduateUniversity，ChineseAcademyofSciences，Beijing100049，China)(Received14January2011;Revised13April2011)ChenXH，ChenYF，ShenLY．Parametrizationofarationaldevelopablesurfaceusingtheμ-basis［J］．JournalofGraduateUniver

3、sityofChineseAcademyofSciences，2012，29(3):289-293．AbstractFindingparametrizationofagivencurveorsurfaceisanessentialprobleminCAGDandCG．Itisstillopentodesignanalgorithmforageneralgivencurveorsurface．Inthispaper，wefocusonrationaldevelopablesurfaceswhicharewidel

4、yusedinmanufacturing．Keywordsparametrization;μ-basis;zerodecompositionCLCTP391.7Incomputeraidedgeometricdesign(CAGD)andcomputergraphics(CG)，parametricandimplicitformsaretwomainrepresentationsofgeometricobjects．Thenanaturalproblemistoconvertthetwoformsfromone

5、totheother．Inthispaper，wewillfocusontheprocessofconvertingtheimplicitformtotheparametricone．Thisprocessisknownasparametrizationanditisstillanopenproblemfortodeterminingandparameterizingageneralgivensurface．Asanalternativeprogress，peopletriedtodesignsomeparam

6、etrization［1］algorithmforsomespecialsurfaceswhicharecommonlyused．Forexample，Chen，etal．presentedamethodtodealwiththeimplicitizationandparametrizationofquadraticandcubicsurfacesbytheμ-basis．Asknownthatthedevelopablesurfaceisanothercommonlyusedsurfaceincomputer

7、aideddesignandgeometricmodeling．Ithassomeniceproperties，forinstance，thedevelopablesurfacecanpreservelengthsunderanisometricmap．Thispaperfocusesonthedevelopablesurfacessincetherehavebeennootherparametrizationmethodsforthem．Thepaperisorganizedasfollows．InSecti

8、on1，somepreliminarynotationsaboutrationalruledsurfacesanddevelopablesurfacesarepresented．InSection2，analgorithmtodeterminewhetherasurfaceisdevelopableornotisgiven．InSection3，theprocessofparametr