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1、ConvolutionSurfacesJulesBloomenthalKenShoemakeXeroxPaloAltoResearchCenterPaloAlto,CaliforniaAbstract:SmoothlyblendedarticulatedINTRODUCTIONmodelsareoftendifficulttoconstructusingcurrenttechniques.OursolutioninthisAnimatorsseekmodelsthatflexandpaperistoextendthesurfacesintro
2、ducedbytransform,butwhichareeasytopositionBlinn[Blinn1982]byusingthree-andmold.Designersoftencreatethesedimensionalconvolutionwithskeletonslivelyshapesbyskillfullycombiningcomposedofpolygonsorcurves.Theprimitives,suchasparametricsurfacesresultingconvolutionsurfacespermitflu
3、id(includingpolygons),orimplicitsurfacestopologychanges,seamlesspartjoins,andandsolids.efficientimplementation.AparametricsurfaceisgivenbyaspatialCRCategoriesandSubjectpositionfunction:p(u,v)=[x(u,v),y(u,v),Descriptors:I.3.5[Computerz(u,v)].Inpractice,thefunctionsaresplines
4、Graphics]:ComputationalGeometrydefinedbypiecesofpolynomials,orratiosofandObjectModeling-curve,surface,polynomials[Farin1990],andareshapedbysolid,andobjectrepresentations.asparsesetofcontrolpointswithanAdditionalKeywordsandPhrases:intuitivegeometricrelationtothesurface.AImpl
5、icitSurface,ParametricSurface,singleB-splinesurfaceisnaturallysmooth,Convolution,SolidModeling,Blends.despiteitspiecewiseconstruction.Itisdifficult,however,tocreateasmoothunionofsurfacesautomatically.Animplicitsurfaceisthezero-setofanimplicitfunctionf(p)=f(x,y,z).Includingp
6、ointsforwhichf(p)ispositivegivesasolid.Inpracticethemostcommonfunctionsusedarepolynomials,especiallyquadratics.Theresultingalgebraicsurfacescanrepresentanyrationalpolynomialparametricsurface,asshownbyclassicalalgebraicgeometrytheory[Sederberg1983].Thereverseisnotsmoothblend
7、ingpowerandeasytrue,however,suggestingthatalgebraicmanipulabilityofpotentialsurfaceswhilesurfacesaremorepowerfulthanparametricexpandingtheskeletonsfrompointstolines,surfaces.Unfortunately,quadricsarepolygons,planarcurvesandregions,andinlimitedinshape,higherdegreesurfacespri
8、nciple,anygeometricprimitive.Wemethodsareintheirinfancy[Sederbergexploitproperties
