and
surface
rendering
techniques
Erhan
Okuyan
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U˘gur
Güdükbay
a,∗,
Ceyhun
Bulutay
b,
Karl-Heinz
Heinig
caDepartmentofComputerEngineering,BilkentUniversity,06800Ankara,Turkey bDepartmentofPhysics,BilkentUniversity,06800Ankara,Turkey
cHelmholtz-ZentrumDresden–Rossendorf,BautznerLandstr.400,01328Dresden,Germany
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Articlehistory: Accepted23March2014 Availableonline30March2014 PACS: 07.05.Rm 61.72.−y 81.07.Ta 61.43.Dq 61.66.Bi Keywords: Materialvisualization
Embeddednano-structurevisualization Directvolumerendering
Unstructuredtetrahedralmeshes Crystaldefects
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Visualizationofthematerialsisanindispensablepartoftheirstructuralanalysis.Wedevelopeda visual-izationtoolforamorphousaswellascrystallinestructures,calledMaterialVis.Unliketheexistingtools, MaterialVisrepresentsmaterialstructuresasavolumeandasurfacemanifold,inadditiontoplainatomic coordinates.Bothamorphousandcrystallinestructuresexhibittopologicalfeaturesaswellasvarious defects.MaterialVisprovidesawiderangeoffunctionalitytovisualizesuchtopologicalstructuresand crystaldefectsinteractively.Directvolumerenderingtechniquesareusedtovisualizethevolumetric featuresofmaterials,suchascrystaldefects,whichareresponsibleforthedistinctfingerprintsofa spe-cificsample.Inaddition,thetoolprovidessurfacevisualizationtoextracthiddentopologicalfeatures withinthematerial.Togetherwiththerichsetofparametersandoptionstocontrolthevisualization, MaterialVisallowsuserstovisualizevariousaspectsofmaterialsveryefficientlyasgeneratedbymodern analyticaltechniquessuchastheAtomProbeTomography.
©2014ElsevierInc.Allrightsreserved.
1. Introduction
Extractingtheunderlyingatomic-levelstructureofnaturalas wellassyntheticmaterialsisvitalformaterialsscientists,working inthefieldssuchaselectronics,chemistry,biology,andgeology. However,asthetopologyandotherimportantpropertiesareburied undera vastnumberofatomspiledontopofoneanother,this inevitablyconcealsthetargettedinformation.Withoutanydoubt, thevisualizationofsuchembeddedmaterialscanhelpto under-standwhat makes a certain sample uniquein how it behaves. However, rudimentary visualization of atoms would fall short becauseitwillnotrevealanytopologicalstructureorcrystalline defects.
Inordertovisualizethematerialtopology,thedatamustbe rep-resentedasasurfacemanifold,whereas,visualizationofcrystalline defectsrequireextractingandquantifyingdefectsand represent-ingthedatavolumetrically.Currentvisualizationtoolslacksuch features,andhence,theyarenotveryeffectiveforvisualizingthe materialtopologyandcrystallinedefects.
∗ Correspondingauthor.Tel.:+903122901386;fax:+903122664047. E-mailaddress:gudukbay@cs.bilkent.edu.tr(U.Güdükbay).
Materialvisualizationtoolsrequireatomiccoordinatesofthe materialsasinput.Acquisitionofreal-spaceatomiccoordinatesof asamplehasbeenamajorobstacle,untilrecentlymainlyrestricted tothesurfaces.Onecancallthisperiodasthedarkagesof mate-rialvisualization.However,recenttechniques,suchasAtomProbe Tomography[1],canextractatomiccoordinatesmucheasierthan before.Thisisalsoaveryactiveresearchfield,withthepromise ofmanynewadvancesinthenearfuture.Accordingly,asthedata acquisitionphaseformaterialsgetsmoreefficientandaccurate, thenecessityforsophisticatedmaterialvisualizationtoolsbecomes self-evident.
OurmotivationonMaterialVisistoprovidesuchavisualization toolthatcanrevealtheunderlyingstructureandvarious proper-tiesofmaterialsthroughseveralrenderingmodesandvisualization options.Inthisway,weintendtoprovideagoodmaterialanalysis toolthatwillbeusefulinawiderangeofrelateddisciplines. Mate-rialVissupportsvisualizationofboth amorphousandcrystalline structures.Amorphousstructuresonlypresentthetopological fea-tureswhilecrystallinestructurespresentbothtopologicalfeatures anddefects.Thestructureofamaterialcanbebestvisualizedusing surfacerenderingmethods.Theunderlyingsurfacesofthe mate-rialshouldbeextractedandvisualized.Ontheotherhand,defects suchasthe disposition ofsomeatoms, vacancies orinterstitial http://dx.doi.org/10.1016/j.jmgm.2014.03.007
impurityatomsinthestructure,cannotbevisualizedbysimply drawingtheatomsorrenderingthesurfaceofthecrystal.These defectscanbebestvisualizedusingdirectvolumerendering tech-niques.MaterialVissupportsdirectvolumerenderingandsurface rendering,aswellascombiningtheminthesamevisualization.It providesthefunctionality-drivenvisualizationofthesame struc-turewithseveraltechniques;thusithelpstheusertoanalyzethe materialstructurebycombiningtheoutputofindividualrendering modes.
Wetestedthetoolwiththreereal-worldandsevensynthetic datasetswithvariousstructuralproperties,sizesanddefects.For instance,thespongedataset[2]isamaterialproducedfromsilicate, whichhasinterestingnano-technologicalproperties.Veryrecently, ithasbeenexperimentallyshownthatasilicon-richoxidefilmcan decayintoasiliconnanowirenetworkembeddedinSiO2by
spin-odaldecompositionduringrapidthermaltreatment[3],whichhas alsobeenconfirmedbyaccompanyingkineticMonte Carlo sim-ulations[4].Theunderlyinggoalinsuchalineofresearchisto achieveanano-scalefeaturecontrolandtransferittoinexpensive large-scalethin-filmtechnologyforsilicon-basedoptoelectronics through growth kinetics. However, the direct imaging of such structuresthroughtransmissionelectronmicroscopyhasnotbeen satisfactoryduetolowcontrastbetweenSiandSiO2regions.We
believethatitformsanidealcandidatefordemonstratingtheneed foradirectvolumeimagingtool.
Theorganizationofthepaperisasfollows.First,inSection2we discussrelatedworkstoaddresswhereourcontributionlieswithin thecontextofexistingtoolsandsimilarstudies.InSection3we out-linethegeneralframeworkofMaterialVis,followedbytwosections onthepreprocessing andrendering steps.In thesesectionsthe mainalgorithmsarepresentedintheformofpseudo-codes, leav-ingtechnicaldetailstotheaccompanyingSupplementaryMaterials document.Someofthecapabilitiesofthetoolaredemonstratedin Section6usinganembeddedquantumdotdataset.Eventhough ourprimaryemphasisinMaterialVisisonfunctionality,butnotthe speed,neverthelessinSection7weprovideperformance bench-marksforawiderangeofdatasets.Finally,abriefconclusionis given.
2. Relatedwork
Therearemanycommercialandfreecrystalvisualizationtools. CrystalMaker[5],ShapeSoftware[6],XtalDraw[7],Vesta[8], Dia-mond[9]andMercury[10]aresomeexamples.Therearealsosome studiesontheanalysisofcrystalsthatalsoprovidesome visualiza-tionfunctionality,suchastheworkofbyUshizimaetal.[11].These toolsareessentiallycrystalanalysistools,whichalsoprovidesome visualizationfunctionality.Theirvisualizationcapabilitiesarenot veryadvanced.Theymostlyofferjustatom-ballmodelswithsome variations.Someofthetoolssupportprimitivesurfacerendering, whichallowsexaminingthecrystalontheunitcelllevel. How-ever,theyarenotsufficienttoexaminetheunderlyingtopologyof adataset.
TherearealsogeneralvisualizationtoolssuchasAtomEye[12], VisIt [13],and XCrySDen [14].These tools providesophisticated visualizationcapabilitiesbuttheylacktheabilitytocreate volu-metricrepresentationsofmaterials,cannotusedirectvolumetric renderingtechniques,andcannotquantifydefectsofcrystal struc-tures.
Iso-surfacerenderingtechniquesprovidefastsurfacerendering ofthevolumedata.Theyareespeciallyusefulwhenthesurfacesare theregionsofinterestforthevolumetricdata.DoiandKoide[15] proposeanefficientmethodfortriangulatingequi-valuedsurfaces byusingtetrahedralcellsbasedontheMarchingCubesalgorithm [16].
MaterialVisisprimarilybasedondirectvolumerendering.There aremainlytwotypesofvolumedata.Thefirsttypeisthe regu-largridrepresentation,whichiswidelyusedinmedicalimaging. Mostlytexture-basedtechniquesareusedforthevisualizationof regulargrids.Earlierapproachesusesamplingthevolumealong theviewdirectionwithparallelplanes[17,18].Newgraphicscards allowstoringthevolumedataas3DtexturesintheGPU.Ertletal. [19,20]usea pre-integrationmechanism torender thevolume using3Dtextures.Regulargridrepresentationcanberendered effi-ciently,butthedatasetsusingthisrepresentationareverylarge. Thesecondtypeofdata,unstructuredgridrepresentation,canbe significantlycompacted,soitcangivemuchhigherdetaillevelsfor thesamesize.
Visibility orderingis animportant partof volumerendering algorithms.Cooketal.[21]andKrausandErtl[22]proposemethods forperformingvisibilitysortingefficiently.ShirleyandTuchman proposedaprojectedtetrahedraalgorithm[23]forvisibility sor-ting.Wylieetal.[24]later extendthisalgorithm toGPUsusing vertexshaders.
Garrity[25]andKoyamada[26]useconnectivityinformationto traversethemeshefficiently.Weileretal.[27]extendthisapproach toGPU.Callahanetal.proposeavisibilityorderingalgorithm,HAVS [28],whichperformsanapproximatesortingontheCPUandrefines thesortingintheGPU.Silvaetal.[29]presentanextensivesurvey ofvolumerenderingtechniques.
3. Generalframework
Fig.1illustratestheframeworkofMaterialViswhichhastwo mainstages:preprocessingandrendering.Thepreprocessingstage takes the raw inputand constructs the volumetric representa-tion.For(poly)crystallinestructuresthepreprocessingstepfurther continues and assignserror values toatoms representing crys-taldefects.Therenderingstagevisualizestheconstructedvolume representation.Theinputreadermodulereadsthevolumetric rep-resentationandinitializestherenderers.Atanytime,oneoffive renderersisselectedbytheuserandthevisualizationisperformed. Theserenderers usetheOpenGL-baseddrawingmoduleto dis-playthevolumetricdata.Therenderingtoolisaninteractivetool. Theuserinteractivelyprovidesvariousinputstorenderers,suchas cameraandlightinformationandseveralrenderer-specific param-eters.
4. Preprocessing
MaterialVisoperatesonaverysimpleinputformat.For amor-phousmaterials,thetypesandatomiccoordinatesofeachatom inthematerialissufficient.However,forcrystallinestructures,the toolalsorequiresprimitiveandbasisvectorinformationofthe crys-talstructure.Ifthisinformationisnotreadilyavailable,ourearlier work,BilKristal[30,31],couldbeutilizedtoextracttheunitcell informationfromthecrystalstructure.
MaterialVis construct a volumetric representation using the coordinates of a setof pointsrepresenting atoms in the mate-rial.There aretwo types ofvolumetric representations: regular andunstructuredgrids.Regulargridrepresentationiswidelyused inmedicalimaging fieldswheretheinputdataisfixedin reso-lution.For materialvisualization,interest pointsaretheatoms; crystallinedefectsareattributedtothemandtheyconstitutethe surfacestructure.Becausetheregulargridrepresentationisdefined independenttoatoms,afairlyhighgridresolutionmustbeusedin ordertocapturecrystaldefectsandsurfacestructuresinhighdetail. Ontheotherhand,unstructuredgridrepresentationusesatomsas vertices.Accordingly,despiteusingtheconnectivityinformation, theunstructuredgridrepresentationismorecompactandsuited
Fig.1. TheoverallframeworkofMaterialVis.
betterfor materialvisualization.Becausethetetrahedraarethe simplest3Dprimitives,weperformtetrahedralizationtoconvert atomiccoordinatesintoanunstructuredvolumetric representa-tion.
Aftertetrahedralization,weextractthesurfacepolygonsofthe createdvolume.Thesurfacepolygonsarerequiredbythesurface renderingmodes.MaterialVisfocusesonvisualizingcrystaldefects; thus,forthecrystalstructuresthedefectsmustbequantifiedfor eachatominthecrystal.Thepreprocessingstageperformsthese tasksandproducesadatafilestoringthevolumetricrepresentation ofthematerial.Forcrystalstructures,quantifiedcrystaldefectsare alsoincluded.Inourexperiments,weobservedthatthedatasets withsizesuptohalfamillionatomscouldbepreprocessedinless thantwentyminutes.Thepreprocessingstagedataflowis summa-rizedinFig.2.
4.1. Constructionofthevolumetricrepresentation
Theconstructionofthevolumerepresentationstartswith tetra-hedralizationofatoms.Eachatomisrepresentedasapointin3D space.Tetrahedracannot overlap withothertetrahedra and all partsofthevolumemustbecoveredbyexactlyonetetrahedra. Thegeneratedtetrahedramustbeasclosetoaregulartetrahedron aspossible(all sidesareequilateraltriangles)becausevolumes containingmanysliver tetrahedra donot representthevolume accuratelyandmaycauserenderingartifacts.Delaunay tetrahe-dralizationis theapproach that generatessuchtetrahedra and itisthedefaulttetrahedralizationschemeinMaterialVisbecause itproducessuperiorresults. WeadaptBowyer-Watson Delaunay triangulation [32,33] to generate Delaunay tetrahedra. Because Delaunaytetrahedralizationisnotscalablefordatasets contain-ingmillionsofpoints,wedevisedapattern-basedtetrahedralization algorithm.
Ourpattern-basedtetrahedralizationalgorithmisbasedonthe factthatthecrystalstructureshaveregularrepeatingpatterns.The
algorithmtetrahedralizes aunit cellofthecrystaland searches fortheoccurrenceofthispatternintheactualdatasetcontaining atoms.Hence,itcannothandlearbitrarilyunstructuredpointsets orhighlydeformedcrystals.Itdoesnotworkonamorphous mate-rials.Itcantoleratesmalldeformations,someinterstitialimpurity atomsand somevacancies.It canhandle cavitiesin thecrystal structures,aslong asthecrystalremains asa singlepiece.The volumetricrepresentationconstructedbythepattern-based tetra-hedralizationisnotasgoodastheoneobtainedbytheDelaunay tetrahedralization,thusmayproduceinferiorrenderingresults;but thepattern-basedtetrahedralizationismuchfasterforlargerinput sizes.MaterialVisonlyswitchestopattern-basedtetrahedralization forverylargeinputdatasets,whichotherwisewouldtakehours topre-process.ForthedetailsofDelaunaytetrahedralizationand pattern-basedtetrahedralization,pleaserefertothe supplemen-tarymaterialsprovidedonline.
Afterthe tetrahedralization, the preprocessing stage contin-ueswithsurfaceextraction.Thesurfaceextractionprocesssimply extracts faces of tetrahedra which are not shared by another tetrahedra.Foreachface,thenormalvaluesarecalculated.Theface normalsareusedinflatshading.Forsmoothshading,thevertex normalsshouldbecomputedbyaveragingthenormalsofthefaces sharingthevertex.
4.2. Quantifyingcrystaldefects
Weclassifycrystaldefectsintothreegroups.Thefirstgroupof defectsisthepositionaldefects,whicharecausedbythedeviation ofatomsfromtheirperfectpositionsrelativetotheirneighbors.The graphitecrystalwithslightlyshiftedlayersisanexample.Atoms intheseshiftedlayershavepositionaldefects.Thesecondgroupof defectsiscausedbyvacantpositionsincrystalswheresomeatoms shouldexist.Thethirdgroupofdefectsiscausedbyextra (intersti-tialimpurity)atomswheresomeforeignatomscouldbefoundat off-latticesites.Themajorityofcrystaldefectscanberepresented asoneoftheseoracombinationofthem.
(Primitive, Basis Vectors)
Defect Quantification Computation Normal Extraction Surface Tetrahedralization Atomic Errors Face and Atom Normal s Surface Mesh Tetrahedral Mesh Atomic Coordinates, Unit Cell Info
Cl Na Cl Na Cl Na Cl NaH Cl Na Na Cl Na Cl Na Cl Na Na Cl Cl Na Na Na Na Cl Cl Na Na Cl Cl Na Na Cl Cl
of the center Na atom
Cl Na Na
Local neighborhood vector Na Na Na Na Cl Cl Na Na Cl Na Na Na Cl K
Unit cell of the NaCl crystal PV 0
PV 1
Feature vector of the central Na atom Defects affecting the central Na atom
Positional defect Vacancy
Substitutional impurity Interstitial impurity atom Cl
Cl
Fig.3. IllustrationofthedefectquantificationfortheNaClcrystal.
MaterialViscalculatesdefectvalues ofatomsforeachtypeof defect.Theyarecalculatedusingthelocalneighborhoodofatoms; anydefectinthelocalneighborhoodofanatomcontributestothe atom’sdefect.Inthisway,thedefectsarerepresentedand visual-izedproperlybecausealargevolumetricregionisaffected.
Fig.3illustratesasamplecrystalstructurewithvariousdefects. TheunitcellandtheprimitivevectorsoftheNaClcrystalareshown ontheleft.Althoughtherearesimplerprimitivevectorsforthe NaClstructure,weusethegivenprimitivevectorsfor demonstra-tionpurposes.Inthemiddlepart,thefeaturevectorofaNaatomis given.Itincludeseveryatomwithinthemaximumprimitive vec-torlengthdistancetoitinaperfectcrystal.Ontherightpartof thefigure,asamplecrystalsegmentdemonstratesvarioustypes ofcrystaldefects.Thelocalneighborhood(theyellowbackground region)vectoroftheatomiscomparedwiththefeaturevectorof theatomandtheerrorvaluesthatwillbeassignedtotheatomare computedaccordingly.
ThedefectquantificationprocessisdescribedinAlgorithm1. Defectquantificationisperformedforeveryatominthecrystal. Firstthelocalneighborhoodvector(LNV)oftheatomisextracted. LNVincludesalltheatomswithinacertaindistancetotheatom.We usedthemaximumprimitivevectorlengthasthedistance, how-everthisvaluecanbetunedbytheuser.Thenthefeaturevector, whichisthelocalneighborhood vectorof theatomin aperfect crystaliscomputed.
Lastly,thelocalneighborhoodandthefeaturevectorsare com-paredtoquantifythedefectvalue.Thecomparisonprocessmatches eachatominthelocalneighborhoodvectortoitscorresponding atominthefeaturevector.Hence,itfindsanypositionaldifferences betweencorresponding atoms and any vacanciesor interstitial impurity atoms in thelocal neighborhood vector. The detailed descriptionofthedefectquantificationalgorithmcanbefoundin thesupplementarymaterialsprovidedonline.
4.3. Losslessmeshsimplification
Inordertocapturesmallmaterialfeatures,likesurfacetopology andcrystallinedefects,MaterialVisusehighlydetailed tetrahedral-ization where each atom is represented witha vertex. On the otherhand,thisrepresentation isusually over-detailedfor uni-formregionsinthematerialstructures.Crystaldefectsconstitute thevolumetric features of materialsfor visualization purposes. MaterialVisaimstousevolumerenderingtechniquestovisualize suchdefects.Amorphousmaterialsorperfectcrystallinestructures donotcontainanydefects;hence,theirstructureismostly uni-form.Moreover, many materialscontaining crystal defects still containa significantportionofuniformstructure. Representing suchuniformregionsatalowlevelofdetailwouldreducethemesh
sizesignificantly.Weproposealosslessmeshsimplification algo-rithmthatwouldsimplifythevolumetricallyuniformregionsin thematerialimprovingtherenderingperformance,without affect-ingthesurfacestructureandtheregionsbearingsomecrystalline defects.
Thelosslessmeshsimplificationalgorithmis basedon edge-collapse-based reduction techniques. This algorithm was first proposedbyHoppe[34]fortriangularmeshes.Weextendedthe simplificationalgorithmtotetrahedralmeshes[35].Edge-collapse techniqueworksbyrepeatedlycollapsingedgesintonewvertices. Anedge-collapsewouldeliminatetetrahedrausingthecollapsed edgeandstretchthetetrahedrausingonlyonevertexofthe col-lapsededge.Wespecifytheconstraintsforselectingtheedgesto collapseinsuchawaytoensurelosslesscompression.Thedetails aregiveninAlgorithm2.Inordertopreservesurfacedetails,no surfaceedgecanbecollapsed.Also,anedgewithavertexonthe surfacecanonlybecollapsedontothesurfacevertex.Afteranedge collapse,varioustetrahedraareaffectedbyeitherbeingdeletedor beingstretched.Ifanyoftheseaffectedtetrahedracontainanatom withanon-zerodefectvalue,theedge isnotcollapsedbecause itwillmodifythevisualoutput.Thesimplificationratiodepends highlyonthedataset.Withthetestdatasetsweused,weachieved simplificationratiosofupto30%oftheoriginalsize.Thedetailed descriptionofthelossless meshsimplificationalgorithm canbe foundinthesupplementarymaterialsprovidedonline.
5. Rendering
MaterialVisprovidesrenderingfunctionalitywithvariousmodes and display options, suchaslighting and cut-planes. It utilizes graphics accelerationviaOpenGLgraphics application program-ming interface (API). The rendering tool supports five modes: volume and surface rendering, volume rendering, surface ren-dering, XRAY rendering, and atom-ball model rendering. Each renderingmodeisusefulforsomeaspectofmaterialanalysis.A user-friendlygraphicalinterfaceisprovided,allowingusersto con-trolthetooleasily.For detailedexplanationaboutfeatures and functionalitiesoftheMaterialVistool,pleaserefertotheusers man-ualprovidedonline.
5.1. VolumeandSurfaceRendering
Volumeandsurfacerenderingaimstovisualizeboththe mate-rialtopologyand thecrystaldefects.It istheslowestbut most flexiblerenderingmode.Theusercansetmanypropertiesofthe visualization.Thevolumerenderingisbasedonthecell-projection algorithm that we used inour earlierwork [35]. We extended the mentioned algorithm to handle surfaces. We selected the
Fig.4. Theraycastingframework.
cell-projection algorithm for several reasons. First of all, cell-projectionisaveryrobustandflexiblealgorithm.Itcanbemodified tosupportadvancedfeatureseasily.Itdoesnotrequireany auxil-iarydatasuchasneighboringinformation.Itsexecutionflowand memoryaccesspatternsaremostlyuniform,makingitidealfor parallelimplementations[36].Ourimplementationutilizes multi-coreCPUhardware.Wecanachievealmostlinearspeed-ups[36]; i.e.,3.0-to3.5-foldspeed-upsforquad-coreCPUs.
We decided not to use GPU-based implementation for two reasons. First, the conventional GPU based volume rendering algorithms, albeit being fast, cannot support features, such as surfaceprocessing,multi-variablevisualization,advanced trans-ferfunctions,becausetheyrelyonlimitedshaderprogramming techniques.Secondly, althoughtheCUDAorOpenCLbasedGPU implementationsarecapabletosupportrequiredfeatures,theyare notveryrobustandtheyarehighlyhardwaredependent.
Thecellprojectionalgorithmisaray-casting-basedrendering technique.Fig.4demonstratestheprocessingofasinglepixel.The visualizationparametersarethecameraposition,orientationand theprojectionangle.Aray iscastforeverypixelonthescreen image,travelingthevolumeandhittingthecenter ofthepixel. Theraystartswithfullintensity.Whiletheraytraversesthe vol-ume,itscolorisaffectedbythevolumeitvisitedanditsintensity isreduced.Thefinalcolorthattherayassumesafterexitingthe volumedefinesthepixelcolor.Algorithm3presentsourversionof thecell-projectionalgorithm.
Thecell-projectionalgorithmprojectseachtetrahedronandface ontotheimageasthefirststep.Allthepixelsthatlieunderthe pro-jectionsofeachfaceandtetrahedraarefoundandassociatedwith thosefacesand tetrahedra.The algorithmconstructs theimage pixelbypixel.First,thelistoftetrahedraandfacesassociatedwith thecurrentpixelareextracted.Thenintersectioncontributionsare calculatedforeach faceortetrahedrainthelist.While calculat-ingthecontributions,tetrahedraandfaceintersectionsaretreated differently.Theintersectioncontributionstructurecontains two piecesofdata.Thefirstoneisthecameradistancetotheentry pointofthetetrahedronorthefacewhichisusedinvisibility sor-tingofintersectionrecords.Thesecondpieceofdataisthecolorand intensityofafullintensityraythattravelsthroughthetetrahedron ortheface.
Aftertheintersectioncontributionsarecomputed,theresults aresortedaccordingtothecameradistance.Thenstartingfrom neartofar,theintersectioncontributionsarecompositedintoa singleintensityvalue,whichisassignedasthepixelcolor.
Thecalculationoftetrahedronintersectioncontributionsstarts byfindingtheentryandexitpointsoftherayonthetetrahedron (cf.Fig.5(a)).Ittakesseveralsamplesonthelinesegmentbetween theentryandexitpoints.Thecolorandtransparencyofeach sam-pleiscalculatedbyinterpolation.Thesampledcolorsarecombined intoasinglecolor.Whilecombiningthecolors,front-to-back alpha-blendingisusedandthealphachannelvalueiscorrectedforeach sample.Thecontributionofeachcolorisproportionaltothe seg-mentlengthofthesample.Thelargerthetetrahedron,thehigher itscontributionwillbe.Theremaininglightintensityisdirectly proportionaltothecontribution.Forexample,forafully-opaque volume,onlytheentrycolormattersbecausetheraywillloseallof itsintensityatthebeginning.
Volumetricfeaturesaregenerallyrevealedbytheuseof appro-priatetransferfunctions.Thetransferfunctionsaresimplymapping functionsthatcomputethecolorandintensityvaluesforeachset ofattributes.Theyareverycriticalfortheperception.The trans-ferfunctionshouldbedefinedinawaytohighlightthefeaturesof primeinterest.Defectsincrystalstructurescanbeanexampleof suchinterestedfeatures.Usually,interestingfeaturesarepresentin asmallfractionofthevolumedata.Inthatcase,verytransparent colorsshouldbeassignedtotheattributesthatoneisnot inter-estedinandarangeofrelativelyopaquecolorsshouldbeassigned tointerestingfeatures.Thus,theinterestingfeaturescanbe visu-alizedinhighdetailwhiletheotherpartsarebarelyrepresented. Althoughgeneralprinciplescanbelaidouteasily,defininggood transferfunctionsisanimportantresearcharea.
MaterialVisusesasimplebutflexibleapproachfordefiningthe transfer function.The colors of vertices are determined bythe defectsassociatedwiththeatomdefiningthevertex.The quan-tifieddefectvaluesofanatomaareconvertedintocolorvalues usingthedefectparametersoftheatomasfollows:
a.Color=BaseColor+a.positionalDefect×PositionalDefectColor ×PositionalDefectMultiplier+a.extraAtomDefect
×ExtraAtomColor×ExtraAtomMultiplier+a.vacancyDefect ×VacancyColor×VacancyDefectMultiplier
Thecoloranderrormultipliersusedintheequationaretunable bytheuser.Thefaceintersectionsareusedtohandletheeffectsof thesurface.Thecalculationofthefaceintersectioncontributions
Ray Tetrahedron Exit Point Entry Point Sample Points Face Normal Light Normal−Light Angle Ray Intersection Point
a)
b)
Fig.5. (a)Tetrahedron-rayintersectionandsamplepoints,and(b)face-rayintersectionandnormal-lightangle.
handlesthelightingeffectsthataremissinginpurevolume ren-derers.Thecolorandtransparencyofthefacesandthelighting parametersaretunablebytheuser.
Lightingeffectsunderlinethesurfacestructurewithouthiding thevolumevisualization.Thefaceintersectioncontribution calcu-lationstartsbyfindingtheintersectionpointbetweenthefaceand theray.Thedistancefromthecameratotheintersectionpointis computed.Thecolorofintersectioniscomputedusing interpola-tionofthecolorsoffacevertices.Thenormalfortheintersection pointiscalculated.Iftheshadingmodeisflat,thanthefacenormal isused.Ifshadingmodeissmooth,thevertexnormalsare inter-polated.Fig.5(b)demonstratesthefacerayintersectionandthe light-normalangle.
We use Phong illumination model for this rendering mode becausethespecificationofanexcessivenumberoflighting param-etersusedbycomplexilluminationmodelsputstheburdenonthe user.The mainfocusinthis renderingmodeisstillthevolume renderingpart;hence,asimplerlightingmodelworkswellandis moreuser-friendly.Moredetailedexplanationsaboutvolumeand surfacerenderingalgorithm canbefoundinthesupplementary materialsprovidedonline.
Fig.6showsthevisualizationofsomematerialdatasetsusing thismode. We tunedtherenderingparameterstofocus onthe defectsinthecrystalvolumeandthesurfacerelatedparameters togiveanimpressionofthestructureitselfbutnotoverwhelmthe volumevisualization.Sincethevolumeandsurfacerenderingmode isflexible,theusercanvisualizethematerialinvariouswaysand analyzevariousaspectsofthedataefficiently.
5.2. Volumerendering
Volumerenderingaimstovisualizethedefectsinthecrystal. Sincesurfacesarenotrepresented,itgivesonlyaveryroughidea aboutthetopologyofthematerial.WeuseHardwareAssisted Vis-ibilitySorting (HAVS) forvolume rendering [28].The algorithm performssomeofthecomputationsandrenderingonthegraphics hardware;hence,itispartiallyGPUaccelerated.Itisnotasfastas surfacerendering.Fig.7presentsthevisualizationofsomedatasets withthismode.
ThehighperformanceoftheHAVSalgorithmisduetoitsuseof thegraphicshardware.Thealgorithmconvertsthevolume render-ingproblemintoasimplerversionthatcanbesolvedontheGPU. Althoughthisapproachisfast,italsohasdrawbacks.Thefirst prob-lemisinvisibilitysorting.HAVSperformsaroughbutfastvisibility sortingontheCPU,whichmayhaveerrors.Thealgorithmrelieson ashaderprogramrunningintheGPUtocorrecttheseerrorsbefore rendering.Duetothelimitationsinthegraphicshardware,allof theerrorsmightnotbecorrected,leadingtovisualartifacts.This situationisveryparticularforirregulartetrahedralizations. Luck-ily,materialstructureshavefairlyregulartetrahedralization,thus HAVSworkwellwithMaterialVis.
Thesecondproblemisthelimitationsoncolorcomputations. HAVSuseapre-integrationtableintermsof3Dtexturesto com-putethecontributionsoftetrahedra.Thisbringsarestrictionon colorcomputationssothatthevisualizationattributeofthe vol-ume,thequantifieddefectvalueinourcase,canonlybeascalar. Inthedefectquantificationstage,weassignthreedefectattributes
Fig.7.Volumerenderingmode:(a)NaClcracked,(b)Acenters(substitutionalnitrogen-pairdefects)indiamond,(c)Palladiumwithhydrogen.
toeachvertex:positional,vacancy,andextra(interstitialimpurity) atomdefects.HAVScannothandlethreeattributes;thusthesedefect valuesmustbemergedasasingledefect.Wecomputeaweighted sumusingtheuser-specifiedweights:positionaldefectmultiplier, extraatom multiplier,andvacancydefectmultiplier.Wecalculate thescalardefectvalueofatomausingthedefectparametersofthe atomasfollows:
a.scalar=a.positionalDefect×PositionalDefectMultiplier +a.extraAtomDefect×ExtraAtomMultiplier
+a.vacancyDefect×VacancyDefectMultiplier
Afteralldefectvaluesarecomputed,theyarenormalizedtothe range[0,1].
Thescalar-to-colorconversionsareperformedusingasimple colormapspecifiedbytheuser.Thecolormapisasetofentries mappingacertainscalarvaluetoacertaincolorandintensity.The colorsandintensitiesofintermediatescalarvaluesarefoundusing linearinterpolationbetweenthecolormapentries.Fig.8showsa samplecolormap wherefiveentriesaredefinedandthewhole scalarrange iscomputed fromtheseentries.Theexample map focusesonthescalarrange[0.4,0.6];thus,itcandistinguishscalar valuesinthisrangemuchbetterthantheotherparts.
5.3. Surfacerendering
Surfacerenderingaimstovisualizethetopologicalstructureof thematerialandissuitedtovisualizedatasetswithanunderlying topologicalstructure.Thespongedatasetisoneexample.Fig.9(a) presentstherenderedoutputofspongedatasetwiththis mode. Forregulardatasetswithoutanyspecificshape,thismodecannot providemuchinformation.
Wecaneasilyrenderthesurfaceofthematerialbecausethe surfacedataispresentinthevolumerepresentation.Cut-planes changethesurfacestructurebutwiththesurfacereconstruction algorithm,thecurrentsurfacedataismaintained.Therendering isperformedusingOpenGLrenderingfunctionality.Thetriangular meshthatrepresentsthesurfaceisrenderedbyOpenGLdirectly.
Fig.8. Anexamplecolormap.(Forinterpretationofthereferencestocolorinthis figurelegend,thereaderisreferredtothewebversionofthisarticle.)
Vertexorfacenormalsarefedtotheshaders,dependingonthe selectedshadingmodelbeingsmoothorflat,respectively.Thecolor andtheshininessofthesurfacematerialcanbespecifiedbythe user.BecausesurfacedataisdirectlyrenderedwithOpenGL, sur-facerenderingisGPUaccelerated.Thesurfacedataisonlyasmall portionofthevolumedata;hence,surfacerenderingisafast ren-deringmode,comparedtotheotherrenderingmodes.
5.4. XRAYrendering
XRAYrenderingmodecanbeconsideredasasimplifiedvolume visualizationtechnique. Its outputresembles theXRAY images, henceitisnamedafterit.Fig.9(b)presentsamaterialrenderedin thismode.Thisrenderingmodeisparticularlyusefulforvisualizing theinternalstructureofcrystals.Itisaimedtofillasmallgapthat otherrenderingmodescannotaddresswell.XRAYrenderingmode doesnotvisualizetheerrorsinthestructureofacrystal.Similarto thesurfacerenderingmode,itfocusesonthetopology.However, unlikethesurfacerenderingmode,itdoesnotjustvisualizethe outersurfacebutvisualizesthevolume.
Thealgorithm is a simplified version of volumeand surface renderingalgorithm. Basically,foreach thrownray,thefacesit intersectswitharefoundandsortedwithintersectionorder.The oddnumberedfaceswouldbetheentryfaces,whererayenters insidethematerialandevennumberedfaceswouldbetheexit faces.Thesefacesareusedtocalculatethedistancethattheray travelsinsidethematerial.Thecalculateddistanceisthenusedas theopacitycoefficientforthepixelthatrayisthrownfor.Because thealgorithmusessurfacepolygonstovisualizethevolume,the inputsizeismuchsmallerthanthemodesthatusetetrahedra.This modeisrelativelyfasteventhoughtheimplementationisnotGPU accelerated.
5.5. Atom-ballmodelrendering
Atom-ballmodelrenderingmodevisualizesthematerialasa groupofatoms.Itdoesnotconsiderthevolumetricpropertiesand thesurfacestructureofthematerial.Thismodeisusefulto under-standtherelationsbetweenatomsandtoexaminesmalldatasets. Itistheonlymodethatdistinguishesbetweendifferenttypesof atomsin thematerialbecauseit treatsthematerial asa setof atoms,ratherthanasavolumeorasurface.Atomsaredrawnas spheres.Theusercansetthecolorsofeachatomtype.Theatom radiigivenintheinputfileareusedastheradiiofthespheres rep-resentingatoms.However,theuserisallowedtosetaparameter, whichscalesdowntheradii.Inthisway,theusercanvisualizethe crystalwithactualatomradiiinaverycompactform,orscaledown
Fig.9.Examples:(a)Surfacerenderingmode–Spongedataset,(b)XRAYrenderingmode–CaCuO2spiraldataset,(c)Atom-ballmodelrenderingmode–NaClcracked
dataset.
theradiitoobtainaspaciousversionwhereindividualatomscan bedistinguishedeasily.
Atom-ballmodelrenderingcanvisualizethecrystaldefectsin arestrictedway.Theusercansetthetransparencyofatomsthat donotcontainanydefects,whichmakestheatomswithdefects distinguishedeasily.However,this modecannot help toassess themagnitudeofdefectsanddifferentiatedifferentdefectclasses. Fig.9(c)depictsthevisualizationofNaClcrackeddatasetwiththis renderingmode.
TherenderingisdoneusingbasicOpenGLfunctionalitytodraw spheresrepresentingatoms.However,inordertohandle trans-parency,theatomsshouldbesortedinvisibilityorder.Thismodeis alsoGPUaccelerated;itisafastmodeandcanbeusedinteractively.
6. Demonstration:embeddedquantumdotdatasets
Inordertodemonstratetheusageandvariouscapabilitiesof MaterialVis,wedescribethestepsofhowwehaveusedthetool forthestructuralanalysisoftworeal-worldquantumdotdatasets thatwehavebeenworkingon.Quantumdotsaresemiconductors withbuilt-instructuralirregularities.Suchirregularitiesprovide thesemiconductoruniqueelectricalproperties.Quantumdotshave possibleusesinvariousareassuchasquantumcomputing,solar cells,medicalimaging,LEDsandtransistors.BiasiolandHeun[37] andUlloaetal.[38]presentin-depthinformationaboutthe struc-tureandphysicalpropertiesofquantumdots.
We used two InGaAs type quantum dot datasets, one with randomalloying among thecationsand one without.Thebase semiconductoristheGaAscompound.Thequantumdotisgrown layerbylayer.Theatomsbelongingtoeachlayeraredepositedonto existinglayers.Depositedatomsusetheexistinglatticestructure tobind.Whenthequantumdotlayersaretobegrown,indium atomsaredepositedinsteadofgalliumatomsatcertainregions. Althoughtheindiumatomsarelargerthanthegalliumatoms,they stillfillthebindingsitesforgalliumatoms.Theresultingcrystal structurebecomeshighlystressed.Eventually,indiumatomscause deformationsinthecrystalstructure,relaxingtostablepositions. Thecrystalregionswithsuchdeformationshavesignificantly dif-ferentelectricalproperties.Bymanagingthedepositionofindium atoms,buildingquantumdotswithvariousshapesandproperties ispossible.
Bothofthequantumdotdatasetscontainjustunder1.5million atoms.Duetothedeformationsinthecrystalstructure, pattern-basedtetrahedralizationcannotbeusedforquantumdotdatasets. Theymust betreated asamorphous materialswhere Delaunay tetrahedralizationmustbeused;hence,itiscrucialtokeepinput sizeslow.However,inordertosimplifyourtask,wecanmaskthe Arsenicatomsfromthedataset.Arsenicisthecommonatomthatis
foundthroughoutthewholematerialmoreorlesshomogeneously. Whatwearereallyinterestedinisthedistributionofgalliumand indiumatoms.IfArsenicatomsareincluded,theywillhave sig-nificanteffectonthevolumevisualization,reducingtheeffectsof interestedpropertiesofthematerial.Secondly,maskingtheArsenic atomsreducesthesizeofthedatasetssignificantly.Thishelpsto keeppre-processingtimeslow.
Wecanalsoemployanotherinputsimplificationtechnique. Vol-umerenderingtechniquesmainlyvisualizethegalliumandindium distributionsinthematerial.Itdoesnotdependonthedensityof atomsinacertainregion.Forexample,inInGaAsquantumdots, certainpartsofthematerialwillbemadeofjustregularGaAsalloy andcertainpartswillbemadeofjustInAsalloy.Becausewemasked theArsenicatoms,thosepartswillbecomposedofjustsingletype ofatoms.Forvolumerenderingpurposes,itdoesnotmatterifwe representsuchregionswithalltheatomsorjustafractionofthem; hence,wecanreducetheinputsizesignificantly.
Weemployedasimpledatasizereductiontechnique.First,we includedtheatomsbelongingtothesurfaceofthematerial.Because ourdatasetshaverectangularprismshape,determiningthe bound-aryatomswasstraightforward.Secondly,weuniformlysampled thewholematerialandincludedthesampledatoms,whichhelps tokeepthetetrahedralizationregular.Finally,weincludedevery atom that hasanother atom of different type within a certain distance.Withthis technique, wecancapturetheregions with gallium–indiumtransitionswithhighdetail.Wealsoreducedthe sizesofourtwodatasetsto5.8%and8.5%totheiroriginalsizes, withoutlosinganyinformationregardingthevisualization.
Thenextstepisscalarassignment.Becauseweareonly inter-estedingallium–indiumtransitions, weassigned 0.0togallium atomsand 1.0toindiumatoms.However,users canassignany scalar values depending on the properties they want to visu-alize. After scalar assignments, the datasets are ready to be pre-processed.Becausethedatasizesarekeptlow,pre-processing takesjustafewminutes.Afterpre-processing,wetunedthe ren-deringparameters.Weusedvolumeandsurfacerendering.Weset thesurfacelightingparameterssothatthematerialsurfacesare justidentifiable.Weassignedagreen,hightransparencycoloras thebasecolor.Thiscolorrepresentsthegalliumatomsbearing0.0 scalarvalue.Thescalarvaluesareusedasthepositionaldefect. Weusedahighopacityredcolortopositionaldefect.Accordingly, weobservedtheindiumatomsinred.Fig.10depictstherendered imagesofoursampledatasets.
7. Benchmarks
Minimum hardware requirements of MaterialVis are rather modest.Wetestedthetoolwithoutanyproblemsonvariouslow
Fig.10.InGaAsquantumdots:(a)withoutrandomalloying,(b)withrandomalloying.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferred tothewebversionofthisarticle.)
Table1
Preprocessingandrenderingtimesofeachdataset(inms).
Numberof atoms
Pre-processing Volumeand surfacerendering Volume rendering Surface rendering XRAY rendering Atom-ball rendering NaClcracked 25,725 9254 707 66 11 275 28 Culinedefect 173,677 171,559 1329 269 15 302 187
Diamondvacancydefect 44,982 17,824 891 109 14 266 49
ACenters(SubstitutionalNitrogen-pair Defects)inDiamond
45,005 18,072 879 112 15 265 49
Graphiteslided 66,576 140,563 1405 138 13 284 72
Palladiumwithhydrogen 137,549 103,399 1471 254 14 298 148
CaCuO2spiral 199,764 114,221 1484 305 16 337 216
Sponge 534,841 602,869 2748 1015 22 471 578
Quantumdotwithoutrandomalloying 86,338 84,376 611 145 16 175 114
Quantumdotwithrandomalloying 125,595 1,161,757 730 196 16 182 181
endcomputers.On theotherhand,therenderingtimesheavily dependonavailablecomputationalpower.Theperformanceofthe volumeandsurfacerenderingandtheXRAYrenderingmodesdepend ontheCPUpower.Theycanalsobenefit frommulti-coreCPUs. OtherrenderingmodesareGPUboundmodes;high-end graph-icscardswillincreasetheperformancesignificantly.Theminimal configurationshouldhaveagraphicscardwithOpenGL1.5support. Stand-alonegraphicscardswithprivatememoryisrecommended. Memoryrequirementsheavilydependontheinputsize.Inour tests,webarelyreached1GBofmemoryusage.Astandard per-sonalcomputerwithastand-alonegraphicscardcouldrunthetool withoutanysignificantlatency.
Wetestedthetoolwithvariousdatasets.Inthespongedataset [2],whichwasalreadymentionedintheintroductionsection,we tackledthevolumetricimagingofahighlycomplicatedstructure. Inthedatasetweused,thestoichiometryofSiOxwasfixedtox=1,
i.e.,SiObysettingthesiliconexcessto30vol.%.Therearemorethan halfamillionatomsintotal.
Thequantumdotrepresentsaself-assembledInGaAsquantum dotembeddedinaGaAsmatrix.Itcontainsalens-shaped quan-tumdotplacedonanInAshalf-monolayer-thickwettinglayer.The randomalloyvarianthas20%indiumand80%gallium composi-tionalalloyingbetweenthecationatoms.Bothstructuresarefirst preparedinthezincblendesitesoftheGaAscrystal,followedby strainrelaxationusing molecularstatics asimplemented inthe LAMMPScode[39].Here,theinteratomicforcefieldsaredescribed bytheAbell-Tersoffpotentials[40,41].Thespongeandquantum dotdatasetsarereal-worlddatasetsthatareresearchedactively.
TheNaClCrackeddatasetrepresenta NaClcrystalwithsome positional defects. The atoms with defects represent a crack. The datasets Cu Line Defect, Diamond Vacancy Defect, ACenters
(Substitutional Nitrogen-pair Defects) in Diamond, and Graphite Slidedrepresentcrystalswithsomewell-knowndefects.The Palla-diumwithHydrogendatasetrepresentsablockofpalladiummetal absorbinghydrogenfromoneofitsfaces.TheCaCuO2Spiraldataset
presentsacylinder-shapedcrystalwithaspiralsculpturedfrom inside.Thesedatasetsaresyntheticdatasetsandtheyare specifi-callydesignedtoshowcasevariouscrystaldefectsandinteresting topologicalstructuresusingthefeatures and capabilitiesof our renderingtool.
Table1presentsthepreprocessingandrenderingtimesofeach datasetonamiddle-endPCwith3.2GHzquad-coreCPUandnVidia GTX560GPU.Thelongestpreprocessingtimeislessthan20min. Despitethehighcomputationalcostofvolumeandsurface render-ingmode,thehighestrenderingtimeis2.7sfortesteddatasets. With other rendering modes, interactive rendering rates were achievedforalltesteddatasets.
8. Conclusions
MaterialVisisafunctionalvisualizationtool,whichcaneasily processmillion-atomdatasets.Itsupportsmanyrenderingmodes toaccentuateboththetopologyandthedefectswithinthe nano-structures.WhatdistinguishesMaterialVisfromothervisualization toolsisthatitcanhandlethematerialsasavolumeorasurface manifold,aswellasasetofatoms. WebelievethatMaterialVis willbeaninstrumental softwareforcrystallographers, polymer and macromolecule researchers,solid state physicists, or more generally material scientists in need to analyze nanostructures embeddedwithinamatrixofatoms.Althoughonlyasmallpart ofitsvisualizationcapabilitiescouldbedemonstratedthroughout thiswork,theusercaneasilytunetherenderingparameterswith
theuser-friendlyinterfacetoobtaincustomvisualrepresentations ofmaterials.Thetoolwithsourcecodes,executables,datasetsand usermanualisprovidedasa supplementarymaterialforonline publication.
Algorithm1. Defectquantificationalgorithm.
DefectQuantification(AtomsA)
begin
foreach(AtomainA)do
//Extract all atoms within a certain distance to atom a LNV=extractLocalNeighborhoodVector(a);
//Extract all atoms within a certain distance to atom a in a perfect crystal
FV=computeFeatureVector(a.type);
//Assign defect upon feature comparisons a.defect=compareFeatures(FV,LNV);
end
Algorithm2. Losslessmeshsimplificationalgorithm.
LosslessMeshSimplification(AtomsA,TetrahedraT)
begin
//Extract and sort all non-surface edges with no defect EdgeList=ExtractEdgeList(T);
whileEdgeListisnotemptydo
e=EdgeList.getShortestEdge()
ifNotetrahedronwithavertexhavingnon-zerodefectwillbeaffected fromthecollapseofedgeethen
//Collapse edge einto newly created vertex v v=collapse(e);
//Delete tetrahedra that use edge eand update tetrahedra that use a vertex of edge eto use vinstead
UpdateTetrahedra(T,e,v);
//Update the edge list upon tetrahedral changes UpdateEdgeList(EdgeList,e,v);
end
Algorithm3. Thecell-projectionalgorithm.
VolumeAndSurfaceRenderer()
begin
//Associate the tetrahedra and the faces with the pixels that they are projected onto
ProjectTetrahedraOntoImageSpace(); ProjectFacesOntoImageSpace(); //Process pixel by pixel
foreachPixelpdo
//Extract the faces and tetrahedra that are projected upon p
list=getProjectedFacesAndTetrahedra(p);
foreachFaceorTetrahedrafotinlistdo
//Compute the contibution of foton the ray cast from p CalculateIntersectionContributions(fot,p);
SortByEyeDistance(list); p.color={0,0,0,0};
//Combine the intersection contributions with alpha blending and alpha correction to compute p’scolor
foreachFaceorTetrahedrafotinlistdo
CompositeColor(p.color,fot);
end
AppendixA. SupplementaryData
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.jmgm.2014.03.007.
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