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简介:Inthispaper,wepresenttwonewunifiedmathematicsmodelsofconicsandpolynomialcurves,calledalgebraichyperbolictrigonometric(AHT)Béziercurvesandnon-uniformalgebraichyperbolictrigonometric(NUAHT)B-splinecurvesofordern,whicharegeneratedoverthespacespan{sint,cost,sinht,cosht,1,t,...,t~(n-5)},n≥5.ThetwokindsofcurvessharemostofthepropertiesasthoseoftheBéziercurvesandB-splinecurvesinpolynomialspace.Inparticular,theycanrepresentexactlysomeremarkabletranscendentalcurvessuchasthehelix,thecycloidandthecatenary.Thesubdivisionformulaeofthesenewkindsofcurvesarealsogiven.Thegenerationsofthetensorproductsurfacesarestraightforward.Usingthenewmathematicsmodels,wepresentthecontrolmeshrepresentationsoftwoclassesofminimalsurfaces.
简介:Thispaperpresentsanewalgorithmforgenerating3DimagesofB-repsobjectswithtrimmedsurfaceboundaries.The3Dimageisadiscretevoxel-maprepresentationwithinaCubicFrameBuffer(CFB).Thedefinitionof3Dimagesforcurve,surfaceandsolidobjectareintroducedwhichimplytheconnectivityandfidelityrequirements.AdaptiveForwardDifferencingmatrix(AFD-matrix)for1D-3Dmanifoldsin3Dspaceisdeveloped.BysettingrulestoupdatetheAFD-matrix,theforwarddifferencedirectionandstepwisecanbeadjusted.Finally,anefficientalgorithmispresentedbasedontheAFD-matrixconceptforconvertingtheobjectin3Dspaceto3Dimagein3Ddiscretespace.