procedurally representing lofted surfaces

《procedurally representing lofted surfaces》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、IProcedurallyRepresentingLoftedSurfacesDanielJ.FilipRasnaThomasW.BallAutomationTechnologyProductsInthisarticlewediscussamethodfordeterminingThesurfaceshouldnotcontainanyunnecessaryandevaluatingaloftedsurfaceinparametricform.undulationsnotimpliedbythecu

2、rves.Loftingisatechniquewherebyauserspecifiesase-Thesurfaceshouldbeinvariantunderaffinetrans-quenceofcurves,arbitrarilypositionedinmodelformationsofthecurves.space,andthedesignsystemgeneratesasurfacethatThethirdrequirementmeansthatifthesetofcurvesinter

3、polatesthecurves.Thistechniqueiswellknownisrigidlytransformedtoadifferentlocationinmodelforformingrelativelycomplexsurfacesfromasetofspaceandthesurfaceisreconstructed,therecon-cross-sectionalcurves.'Althoughconceptuallythestructedsurfaceisidenticalwith

4、thesurfacethatissurfaceseemsrathersimple,manypracticalissuesobtainedbyapplyingthesamerigidtransformtothemustberesolvedforaparametricdescriptionoftheoriginalsurface.Affineinvariancealsoimpliesthatifresultingsurfacetosatisfyengineeringrequirementsthesurf

5、aceisdesignedinadifferentscale(forexam-aswellastobeaestheticallypleasing.ple,Englishinsteadofmetric),therelativegeometry(ignoringscaling)shouldnotchange.FortheloftedsurfacetobeusedinaproductionThemostpopularwayofrepresentingsurfacesmechanicaldesignsyst

6、em,thesurfaceshouldsatisfytodayiswithtensor-productnonuniformrationalandatleastthefollowingrequirements:integralB-splinesurfaces.2ForsimplicitywerefertoThesurfacemustbevisuallysmoothifallofthebothasjustB-splinesurfaces.Inthenextsectionwecurvesarevisual

7、lysmooth.introducethepossibilityofusingsurfacesthatcannotNovember19890272-17-16/89/1100-0027501.0081989IEEE27practicallyberepresentedasB-splines.WealsoshowWhenfittingthesplinesinthesecondstep,becausethatseveralproblemsmustbeovercomeifB-splineofthetenso

8、r-productrepresentation,asingleknotsurfacesaretobeusedinlofting.Wethendevoteavectormustbechosenforallthesplines.Thisknotsectiontodescribingaproceduralrepresentationthatvectorwillthenbecomethev-directionknotvectorinpracticeseemstosatisfy