简介:Asimplerobust'strutalgorithm'ispresentedwhich,whengivenagraphembeddedin3Dspace,thickensitsedgesintosolidstruts.Variousapplications,crystallographicandsculptural,areshowninwhichsmoothhigh-genusformsaretheoutput.Atoolboxofalgorithmictechniquesallowforavarietyofnovel,visuallyengagingformsthatexpressamathematicalaesthetic.Insculpturalexamples,hyperbolictessellationsinthePoincaréplanearetransformedinseveralwaystothree-dimensionalnetworksofedgesembodiedwithinaplausiblyorganicorganization.Bytheuseofdifferenttransformationsandadjustableparametersinthealgorithms,avarietyofattractiveformsresult.Thetechniquesproducewatertightboundaryrepresentationsthatcanbebuiltwithsolidfreeformfabricationequipment.Thefinalphysicaloutputsatisfiesthe'coolnesscriterion,'thatpassersbywillpickthemupandsay'Wow,that'scool!'
简介:Thispaperpresentsanewalgorithmforgenerating3DimagesofB-repsobjectswithtrimmedsurfaceboundaries.The3Dimageisadiscretevoxel-maprepresentationwithinaCubicFrameBuffer(CFB).Thedefinitionof3Dimagesforcurve,surfaceandsolidobjectareintroducedwhichimplytheconnectivityandfidelityrequirements.AdaptiveForwardDifferencingmatrix(AFD-matrix)for1D-3Dmanifoldsin3Dspaceisdeveloped.BysettingrulestoupdatetheAFD-matrix,theforwarddifferencedirectionandstepwisecanbeadjusted.Finally,anefficientalgorithmispresentedbasedontheAFD-matrixconceptforconvertingtheobjectin3Dspaceto3Dimagein3Ddiscretespace.