Modeling the Structureof the SeaAnemone,StomphiaCoccineaand the SeaStar, DermasteriasImbricata Using Implicit Surfaces

Xikun Liangxkliang@cpsc.ucalgary.ca

Mai Ali Nurmnur@cpsc.ucalgary.ca

Brian Wyvillblob@cpsc.ucalgary.ca

Departmentof ComputerScienceUniversityof Calgary

2500UniversityDr. NW, Calgary, Canada

AbstractTheBlobTreeprovidesahierarchicaldatastructurefor

thedefinitionof complex modelsbuilt from implicit sur-faces,CSGBooleanoperationsandspacewarpingfunc-tions. The implicit model within the systemis definedasa hierarchicalcompositionof multiple objects.In thispaper, we describeanapplicationof theBlobTreeto cre-atevisually accuratemodelsof two invertebrates,theseaanemone,StomphiaCoccinea,andtheseastar, Dermas-teriasImbricata.Theseastarwascreatedusinga varietyof parametersthat could be modified to createdifferentvariationsof theDermasteriasImbricataspecies.We usethe phyllotacticmethodto obtainan accurateandvisu-ally pleasingarrangementof theseaanemone’stentacles.Usingahierarchicalconstructionof themodel,wecanre-finethemodellocally anddeformit globallywhile main-tainingtheintegrity of surfacedetails.Takingadvantageof the hierarchicalrepresentationof the object, we caneasilyadjustthemodelby simplychangingsomeparam-etersof thesurfaceor by performingglobaldeformationson theanemoneor local refinementson thetentacles.

Keywords: Implicit surfaces,hierarchical surfaces,mod-eling, local refinement,globaldeformation,marinecrea-tures,spiral phyllotaxis,collision detection.

1 Intr oduction

An implicit surface�

is characterizedasa collectionofpointsin spacewith a potential ������������ equalto somethresholdvaluedenotedby � .������� ���������� �������������������� � �"!

Modeling with Implicit surfacesguaranteesa contin-uoussmoothlyblendedsurfacewhich is relatively easyto deform and intuitive to specify. Since invertebratesareanimalslacking backbonesandmany of themhavesmall, soft, flabby bodies,implicit objectsare ideal tomodelthesespongystructures.We havechosento modelthestructureandbehavior of two suchcreatures,thesea

starandseaanemone.Not only do thesecreatureshavestunninglybeautifulvariationsin structurebut they alsoexhibit interestingbehaviors.

Oneof the beststudiedandmostdramaticescapere-sponsesof marine invertebrateis the detachmentandswimming behavior of Stomphia(S. Coccineaand S.Didemon)in responseto certainspeciesof starfishsuchas DermasteriasImbricata[3]. The escaperesponseoftheStomphiaCoccineafrom DermasteriasImbricatahasbeenof greatinterestto scientistsever sinceit wasfirstdescribedin 1955by YentschandPierce[30] andhasre-sultedin a variety of studieson differentaspectsof theinteraction:behavioral [19] [21], neurophysiological(thediscipline involving the study of the makeupand func-tion of thenervoussystem) [20] morphological(abranchof biology thatdealswith the form andstructureof ani-malsandplants)[17], ecological[16] andchemical.Themainaimbehindthispaperis to createrealisticmodelsofStomphiaCoccineaandDermasteriasImbricatathatcanbeusedto studythestructureandbehavior of thesema-rine creatures.In this paperwe focuson creatingthesestructuresprocedurally. As a result,adjustmentof vari-ousparametersproduceddifferentseastarsandchangedthestructureof theseaanemone.

The tentaclesof theanemonearecorrectlypositionedby usingthe phyllotacticmethod. The hierarchicalrep-resentationof themodelallows thestructureto beeasilyanimatedandlocally andglobally deformed.The paperis organizedasfollows. In section2, we summarizepre-vious work in this area. Section3 provides a detaileddescriptionof the modelsto be developed. We explainthe generalbehavior of the seaanemoneandseastar insection4. Section5 describesthemodelingimplementa-tion details.Section6 presentsourconclusionsandfuturework.

2 Relatedwork

Previous relevantwork will be discussedin this section.The BlobTree and the hierarchicalimplicit surface re-

finementtechnique,usedto build the models,and thecollision-basedspiralphyllotaxisapproachusedto posi-tion theanemone’s tentaclesareoutlined.

2.1 The BlobTreeThe BlobTree [28] provides a hierarchicaldata struc-ture for thedefinitionof complex modelsbuilt from im-plicit surfaces,CSGBooleanoperationsandfield warp-ing functions. The implicit modelwithin the systemisdefinedas the hierarchicalcompositionof multiple ob-jects(Figure1). Thesurfaceof animplicit objectcanalsouseattributessuchas2D textures.TheBlobTreehasbeenextendedto incorporatetexturesasdescribedin [25].

Figure1: Exampleof a modelbuilt up from a BlobTree[28]

2.2 Hierar chical Implicit SurfaceRefinementSincetheimplicit surfacemodelsbuilt from theBlobTreearebasicallystaticmodels.Oncedefined,theBlobTree’sstructurecan’t be easilychanged.To further extendtheuseof theBlobTree, ahierarchicalimplicit surfacerefine-menttechniquehasbeenproposedin [15]. This methodconsistsof hierarchicalrepresentationandconstructionofimplicit objects.# Hierar chical Representationof Implicit Surfaces

For a givenimplicit object,we createa hierarchyofimplicit surfacesrepresentingthe object. In the hi-erarchy, eachsurfaceis a nodein thetree,eitheraninternalnodeat thecoarserlevel or a leaf nodeat afiner level. Eachhierarchycontainsa local surfaceand a set of sub-hierarchies.The surfacedefinedby theBlobTreeis a leaf noderelative to thehigherlevel hierarchy. Eachsub-hierarchyis an internal

nodein the overall structureandit representslocalsurfacedetail. Surfacedetailsrelatedto a specificsurfacebeingrefinedarewithin thesamehierarchi-callevel. With thisrepresentation,implicit objectsateachlevelconsistsof thelocalsurface

�%$&('*)�+-,(' andallthe surfacesof its sub-hierarchies. � $/10�+324/1065�76,981:at level i:� $/1065(7;,<81: �=� $&('*)�+>,?'>@BA 5�:37 $DC :1EF: C�GIH � $/306+24/1065�76,981:6Jwhere@BA 5(:37 $*C :3EK: C�G representstheoperationof thehierarchy.

This hierarchicalstructureof implicit surfacesis il-lustratedby Figure2.

S0

S1Global S1

Hierarchy11... S1

Hierarchy1n

root

Level

1

S21Hierarchy21S21

Global S21Hierarchy2n

...2

3 ...... ...

...

Figure2: Hierarchyof theimplicit object

According to the refinementoperations,four kindsof hierarchiesaredesigned:

– Blending

– ControlledBlending

– PreciseContactModeling

– CSG

They representfour different kinds of operationscombiningtheglobalsurfacewith its details.Blend-ing usessuper-elliptic blending methoddescribedin [1]. Controlledblendingis implementedby themethodproposedin [9]. Precisecontactmodelingcombinesthelocal surfaceandsurfacedetailsusingtheapproachdescribedin [6]. CSGoperationsper-form intersection,difference,or union betweenthelocal surfaceandtherefinedsurface.# SurfaceConstruction

We startwith an initial implicit surfaceandcreatea root hierarchywith the surface. A sequenceofsub-hierarchiescanbe built by recursively refiningtheselectedsurfaces.At eachlevel, a setof refined

surfaces�%$

areintroducedto definelocalsurfacede-tails.

The final implicit object is obtainedby combiningall the leaf surfacesaccordingto thedifferentkindsof hierarchicalproperties.The lower level arepro-cessedfirst. Then the surfaceconstructedat thatlayeriscombinedwith itshigherlevelsurfacesusingblending,controlledblending,precisecontactmod-eling,or CSGoperations.Theprocesscontinuesun-til all theterminalsurfacesareincluded.Dueto thehierarchicalconstructionof therefiningsurface,lo-cal detailscanbe maintainedaccordingto the con-straintsfor eachrefinement.

Theadvantagesof this methodaretheability to ap-ply hierarchicallocal refinementandglobal defor-mationto the models. Local refinementallows theuserto introducemoredetailedsurfacesatany givenlevel. Globaldeformationchangestheoverallshapeof thesurfacewhile maintainingtheintegrity of sur-facedetails.

2.3 The Collision-basedModel of Spiral PhyllotaxisThissectiongivesageneraloverview of spiralphyllotaxisand its applicationto generatecollision-basedmodels.Phyllotaxisis the regulararrangementof organssuchasflowersor leavesoftenseenin many plants.It is charac-terizedby spiralsor parastichies,composedof sequencesof adjacentorgansforming the structure. The numberof parastichiesrunning in oppositedirectionsare usu-ally two consecutive Fibonaccinumbers[5]. The di-vergenceangles,taken from the centerof the structure,measuredbetweenconsecutive formed organsis closeto the Fibonacci angle of L�M�N�O9P 2RQ �TS L U JWV O whereP � � S4XZY V �[]\ . Thequalityof thepatterngeneratedde-pendson this angle[18]. This mathematicalformulahasleadto bothdescriptive andexplanatorymodelsof phyl-lotaxis [12]. Descriptive modelsarelike thoseproposedby Vogel [26] andVan Iterson[4] [11], they attempttocapturethe geometryof phyllotacticpatterns.Explana-tory models,focus on the dynamicprocesscontrollingthe formulationof phyllotacticpatternsin nature.Therearea largenumberof competingtheoriesfor explanatorymodelsandunfortunately, no universallyacceptedmodelhasemerged[12]. In thispaperweusethecollision-basedmodelof phyllotaxisdescribedin [5] whichcombinesthedescriptiveandexplanatorycomponentswith slightmod-ificationstosatisfythepropertiesneededtocreatetheten-tacleson theseaanemone.

The collision-basedmodelof phyllotaxisproposedin[5] is usedto distribute primordiaon the surfaceof thereceptacle.Primordiaarea groupof cellsthatcanbeini-tially identifiedasafuturebodypart.As describedin [5],

Figure3: Thecollision-basedmodelof phyllotaxis. Pri-mordiaaredistributedon thereceptacleusinga fixeddi-vergenceangleof

S L�U JWV O andaredisplacedalongthegen-eratingcurvesto becometangentto their closestneigh-bors.Courtesyimagesof [5]

the receptacleis viewed asa surfaceof revolution, gen-eratedby a curve rotatedarounda verticalaxis. Sphereswhich representprimordiaareaddedto the structurese-quentiallywith a divergenceangleof

S L U JWV O . A horizon-tal ring at thebaseof thereceptacleis formedby this ini-tial groupof primordia. Whena primordiumjust addedcollideswith an existing one,the additionof primordia,to this ring stops. The colliding primordiumaremovedalongthe generatingcurve, tangentto its closestneigh-bor. The next group of primordia are placedsimilarly,on generatingcurvestangentto their closestneighbors,determinedby the divergenceangleasshown in Figure3. The additionof primordiacontinuesuntil thereis nomoreroom to addanotherone. Sincethe anemoneswearemodelinghaveaflower-liketentaclearrangement,weusethis phyllotacticmethodto arrangetentaclesof vary-ing sizeson arbitrarysurfacesof revolution. It canthere-fore beusedto createa widevarietyof seaanemones.

3 Properties of CoccineaStomphia and Dermaste-rias Imbricata

This sectiongives a generaldescriptionof the marinecreaturesto be created,followedby a moredetailedde-scriptionof thespecificspeciesto bemodeled.

3.1 StomphiaCoccineaAnemonesor the flower animalasthey areoftencalled,have a single body cavity that servesasa stomach,in-testineandcirculatory system. They fastenthemselvesto somethingfirm with their basesand have one bodyopening(the mouth), throughwhich everything passes

in or out. The mouth is surroundedby finger-like ten-tacles,studdedwith nematocysts(stingingcells). Nema-tocystsareactive in capturingfood andtransferringit tothemouthfor defense.

The five main componentsof StomphiaCoccineaob-tainedfrom, the textural descriptionsfound in [24] [22]andobservationsof picturesin [10] areexplainedbelow:

1. The column which is cylindrical and not dividedinto regions. It is never as wide as the baseordisk. Theoutermembraneis generallythin andof-ten transparentand always smooth. It can have aseriesof strangeforms. In contraction,the columnis low, firm and dense. In extensionthe body issoft and the skin becomessmoothand translucentwhen sufficiently extended. The color of the col-umnrangesfrom solid orangeto palewhite. Manyare pale orangewith irregular orangeor red areasscatteredon thecolumn.

2. The base which is adherent,slightly irregularandmuch wider than the column is usedto attachtheanemoneto thesubstrate.

3. The upper disk is circularandtransparentwith or-angepatchesscatteredon it. Thereis a largecentralareawhich is free of tentacles,wherethereis a slitfor themouth.Thesurfaceof thedisk is oftenirreg-ular.

4. The tentacleswhichsurroundthemouthmaybeupto 1.5 cm long, conical,andfully coveredwhenre-tracted;therecanbe64 but thereareusually72, al-thoughindividualswith asmany as86canbefound.They are generallyarrangedin four or five cycleswith thoseof the innercyclesbeingslightly longerthanthoseof theouterones.Thesix tentaclesof thefirst or innercycle areusuallyheldpointing inwardoverthedisk,whereasthoseof theoutertwo or threecyclesbenddown over themargin. Thecolor of thetentaclesare white or transparentwith two orangerings encirclingthemanda small white spotat thebaseof each.

The StomphiaCoccineais up to 3 or 4 cm tall withthecolumnbeingusuallylessthan3 cm in diameter. Thedisk of a specimenthis sizewould be about3 cm wideandthebaseabout5 cm.

3.2 Dermaterias ImbricataThis sectiondescribesthegeneralfeaturesof theseastarandfeaturesspecificto DermateriasImbricata.Seastarsvary in shape,sizeandcolor. They canbefrom lessthan1/2 of an inch in diameterto more than 3 feet across.Their shapesvary from regular starswith five or more

armsto pentagonalandalmostcircularseastars[2]. Themostcommoncolorsfound in seastarsareorange,yel-low, pink, or redbut gray, green,blue andpurplecolorscanalsobefound.Thearmsof seastarsareactuallypartof its body ratherthanappendages.If oneof theseani-malsis turnedupsidedown to exposeits mouthsurface,eacharmis seento have a lengthwisegroove filled withmoving tube-feet.Within eacharmthestarhasoneor twobranchesof its reproductiveorgansandoftenextensionsfrom the digestive tract as well. The starfishthat willbemodeledis theDermasteriasImbricataor theLeatherstar. It hasslightly webbedraysusually5 thatareup to12cmin length.It’sskin is smoothandslipperyandfeelslike wet leather. DermasteriasImbricata’sbodycomesina variety of colors. However it is usuallymottled withreddishbrown to orangeblotchesoutlinedwith grey. Itpossessesa large,high disk at thecenterof thebodyandthe tips of its arm arefrequentlyupturned.A ratherun-usualpropertyof it, is the fact that it often hasa strongodorof garlic.

4 The General Behavior of the Anemone andStarfish

This sectiondescribesthe interactionbetweenthe Coc-cineaStomphiaandDermetriasImbricata.Althoughwehave not yet animatedthemodels,it is interestingto ob-serve thevariationsin themodel’s structureover time asillustrated in Figure 4. A numberof parametersasso-ciatedwith our modelswill enableus, in the future, tocreatea realisticanimation. For example,the anemonehasvariouslengths,widthsfor eachcomponentandspac-ing parametersfor thetentacles,andrandombendingan-gles. For thestarfishtheseparametersincludethe lengthof the legs and their anglesand the dimensionsused.By adjustingtheseparametersour structurescould eas-ily beadaptedto differentinteractionsituationsbetweentheanemoneandstarfish.

The general pattern of the swimming behavior inStomphiaCoccineadescribedwas illustrated in detailboth through a diagram,shown in Figure 4 and froma textural descriptiontaken from [3]. The interactionbetweenthe DermasteriasImbricataandStomphiaCoc-cineaconsistsof a numberof phases:

1. Thestimulusphase occurswhenthesurfaceof thestarfishDermasteriasImbricatacomesin brief con-tactwith theanemone’s tentacles.

2. During the initial responsephase, the anemone’stentaclesadhereto thestarfishoncontact.After sev-eralsecondsthetentaclescontract,followedatonceby contractionof thecolumn.

Figure 4: The swimming behavior in Stomphiaof theanemones

3. Theelongationphaseoccurswhenthecolumnelon-gates.Thetentaclesanddisk thenreappearandex-pandto their fullestextent.

4. Thedetachmentphaseoccurswhen the pedaldiskof the anemonebecomesdetached.This phaseisvariable,asananemonemayshow swimmingmove-mentswithoutdetachingfrom thesubstratum.

5. Theswimmingphaseconsistsof a seriesof abruptbending movementsof the column, which maycausetheanimalto ‘swim’.

6. The recovery phase is an inactive period duringwhich the anemoneresumesits normalshape.Thesurfaceof thepedaldiskthenbecomesadhesive,andso it re-attachesto the substratumandthe ordinarypermanentlyattachedpositionis regained.

Althoughtheswimmingresponseof Stomphiais vari-able, nearly all anemoneswhich respondto Dermaste-rias display the initial response,expansionusually fol-lowedby detachmentor theswimmingmovement[3]. Iftheswimmingmovementoccursthenrecovery is thelastphase.Detachmentmayberegardedasa sideeffect anddoesn’t alwaystakeplace.

5 Implementation details

In this section the proceduresused to model the seaanemoneandseastarwill bedescribed.

5.1 Modeling the AnemoneTheanemoneis modeledusinghierarchicalimplicit sur-facerefinementapproach.Themainbodyis first createdastheroothierarchy. ThenaCSGhierarchyis introducedtomodelthemouthwhichtakesthedifferenceof themainbodyfrom aline primitive. Thetentaclesareaddedasthe

third layer. All the tentaclesarecreatedin two consecu-tive layers.TheFirst layermodelsthemainbranchof thetentacleand the secondmodelsthe tip of the tentacles.They arepositionedfollowing thephyllotacticpattern.

When modelingthe tentacleswe have chosento as-sumethatthey surroundthemouthin 4 cycles6,12,18,36= 72 or 6,10,16,32= 64 (with 6 beingthe innermostcy-cle),takenfrom [24]. Theseformulasaresubjectto minorirregularities,affecting the outer tentacleson the wholemorethantheinnerones.Thefollowingsectionsdescribedetailsfor building themodel.

The Main BodyThe mainbody consistsof thebase,the columnandthedisk (components2,1,3 in section3.1). A cylinder wasusedfor the bodyanda toruswasusedfor thebaseandupperdisk. All threeobjectswere blendedtogetherasshown in Figure5 (left).

The mouthof the anemoneis modeledwith the CSGdifferenceoperation.A line primitive is subtractedfromthemainbodyto createamouthin thecenterof theupperdisk (Figure5(right)). The tentacleswill be positionedaroundthismouth.

Figure 5: The main body is a blend of two tori and acylinder andthe mouthwascreatedby applyinga CSGdifferencebetweenthemainbodyanda line primitive

The TentaclesThe tentaclesarecreatedusinga taperedline primitive.They areinitially placedonaplaneandthenshiftedto theimplicit surfaceof themainbodymoving from theoutercycle to innercycles.Basedonthecollision-basedmodelof thespiralphyllotaxisasdescribedin section2.3,anewalgorithmis createdto accuratelyplacethe tentaclesonthe implicit surface. The generalprocedureis outlinedbelow:# Formalization: In order to calculatethe positions

of thetentacles,wefirst assumethatthetentaclesareplacedon theplaneof theanemone’s upperdisk as

Figure6: Tentaclesarepositionedin a circle using themodifiedPhyllotacticapproach

shown in Figure6. The initial positionis describedby theparametricequation:^_ ` � � a%b9c d ��ef ?�� � a%d�g*h ��ef ?�� � i?j�k �mlIn;o>pqlsrwhere

ais the radiusof the circle underconsider-

ation and e is the orientationof the tentaclessepa-ratedwith

S L�U JWV O . Thetentaclesareplacedsequen-tially with anangleof

S L U J V O following the patternillustratedin Figure3.# Formulation of layered tentacle pattern: Withthis simplealgorithm,thenew tentaclemaycollidewith a tentacleat the samelayer. In this case,in-steadof moving thetentacledirectly to thenext in-ner layer, we searchthecurrentlayer for any possi-ble position. If sucha placecannotbe found, it isthenmoved to the next inner layer. This recursiveformulationof thetentaclepatterncanbedescribedasfollows:t e O � Ns�a � u �vrlsnwr j(xyk o3z6{ a�| k o-}zf�^_ ` e C]~�� � e C X�S L U J V O � ��� X�S v� S L U JWV Oa C]~�� � t a C � � j r4� j���� o k n k �a C���� ��� j���� o k n k �

wherea

is the radiusof the currentlayer. Whenacollisionoccurs,anew radius

a C�~�� is obtainby sub-tractingthediameterof thecurrenttentaclefrom

a C .If collision still exists, we simply adjustthe radiusby a predefinedstepsize � .With this algorithm, the angle e at which the newtentaclewill beplacedisat ��� X�S ?� S L U J V O . However,

Theanglevarieswhencollision occurs.Addition oftentaclesto asinglelayerisn’t terminateduntil eachlayerfollowsthepattern6,12,18,36,describedat thebeginningof this section.

Figure7: Tentaclesaremovedtangentto theanemone’stop surface

# Surface searching: Furthermore,the patterngen-eratedso far only providestentaclepositionsat theplaneof theanemone’supperdisk (Figure6). Sincethebodyis asmoothlyblendingsurface,someof thetentaclesmayappearinsideor outsideof thetopsur-face. Thereforethe tentaclesareplacedtangenttothesurface.This is achievedby moving all the ten-taclesto thesurface.We first checkif thetentacle’spositiongivenby thepreviousformulasis insideoroutsideof thesurface. We thenchooseanoppositepointalongthenormalandfind thepointonthesur-face,i.e. ������������ � o3z j � |�� }n . Theassumptionsmadewerethat the surfaceusedfor calculatingthephyllotactictentaclepositionis a sectionof the up-per disk of the anemoneand that the radiusof theintersectionis within the boundingbox. The algo-rithm is outlinedbelow:

1. Calculate the possible tentacle positionA �������R��� accordingto the modifiedphyllao-tacticmodel,

2. Calculatetheboundingboxof thebody,

3. Find the normalof A ��������� on the surface,i.e. � ���������� � �>���q�(���������6 where� is thefield functionof theimplicit sur-faceand � � , � � , and � � arethe partial deriva-tivesof thefield functionat A .

4. Find a point � inside the surfaceif ��� A Z�o3z j ��| � }Rn or a point � outsidethe surfaceif��� A ���o3z j � |�� }Rn . This canbe donesimplyby searchingalongthe surfacenormalwith a

givenstepsize. In this case,an insideor out-sidepoint is guaranteedto befoundaslong asthestepsizeis lessthantheradiusof thebody.

5. Searchthe exact correspondingsurfacepointof A alongtheline betweentheinsideandout-sidepoints A and � . A binarysearchmethodwasimplementedto find thesurfaceposition.

Figure7 showsthetentaclepatternafterthisprocess.Thetentaclesarealsoorientedalongthesurfacenor-mals.

AnemoneDeformationsThis sectiondescribesthe deformationof the tentaclesandthe main body. Anemonetentaclesexhibits variousshapesand deformations. They have slightly differentsizesat eachlayer andall tendto bendin certaindirec-tionsasdescribedin 3.1. This is achievedby placingthetentaclesaccordingto the normalsand the phyllotacticangles.

The outer tentaclesbendover the margins, the inner-mostonesbendinwards,while the restbendrandomly.All tentaclesare orientedbasedon several noisefunc-tions.Thesefunctionswereappliedto thebendingangle,bendingcenter, bendingrange,andorientationsasshownFigure8. Otherfunctionssuchasthe4D noisefunctionsdescribedin [29] couldbeusedto provide bettercontrolover thetentacles’appearance.

Figure8: Bodydeformationwith automaticmaintenanceof tentacleintegrity

An anemone’s body is deformedwhen it is stimu-lated by anotherobject, suchas a starfish. The tenta-clesandbody experiencevariousstagesof deformationas describedin section4. Since the anemoneis con-structedhiearchicallyasstatedat the beginning of sec-tion 5.1,globaldeformationcaneasilybeappliedto anypart of the object. To modelthe bendingcharacteristicsof theanemone,globaldeformationis appliedto themain

body. Thenall thetentaclesareautomaticallyadjustedtomaintainthe integrity of thestructure.Figure8 shows aanemonebodybent270degrees.

Final anemonemodelsTwo anemoneswerecreatedusingour proposedmethod.Textureswereappliedto the anemone’s main body andtentacles.Figure9 showsananemonemodelwith the64tentaclesandfigure10 illustratesthetypical72 tentacles.Bothof theseanemoneshavebeenrotatedby 45degrees.As canbeseen,thetentaclesfollow thephyllotacticpat-tern.Theouterlayertentaclesarebentsharplyagainstthebody andhave an outward orientation. The secondandthird layer tentaclesareslightly bentandrandomlyori-ented. The inner layer tentaclesbendinwards. Overall,the tentaclesarrangementshows the beautyof the phyl-lotatic patternandthe randomnessappliedcreatesmorelively lookingseaanemones.

Figure9: An anemonewith 64tentaclesaroundtheupperdisk

Figure10: An anemonewith 72 tentaclesaroundtheup-perdisk

5.2 Modeling the StarfishThestarfishwasmodeledasdescribedbelow:-

1. Fiveconeswerecreatedfor thearms.

2. Thestar’s armswere rotatedand translated to thecorrectpositions. They were rotatedto lie in the� ��� planeandweretranslatedto lie in a circle.The initial position is describedby the parametricequation: ^_ ` � � a%b9c d ��ef ?�� � a%d�g*h ��ef ?�� � i?j�k �mlIn;o>pqlsrWhere

ais theradiusof starfishsurface.Theangles

usedweremeasuredfrom apictureof thestarfish.

3. A texturewasappliedto thecones(Figure11(left)).

Figure11: Starfishlegsarecreatedusingconeprimitivesandthecorrecttexturewasapplied(left). A bumpsurfacewascreatedusingpointprimitives(right)

4. Smallbumpswerecreatedalongtheconeprimitives.Thetopsurfaceof thestarfishwechoosehadaratherunusualtexture that requiredtheuseof point prim-itives to achieve the surfacetexture. Unlike somestarfish,ourexamplehada irregularsurface.To cre-atethetexture,a grid like patternof pointswascre-atedon eachcone(Figure11 (right)). The spheresweremovedto thesurfaceof theconeusingthesur-facesearchingmethoddescribedin section5.1. ARandomoffsetwassubtractedfrom the positionofthespheresothatsomesphereswould behiddeninthe surface. Thereforethe final texturewould con-sistof someirregularitiesto achieve morereallisticmodel. The sphereswereblendedwith eachotherand control blendedwith the surface. Controlledblendingof thesphereswith thesurfaceallowedtheshapeandtextureto beclearlyobservedasshown inFigure12.

5. Randomcolors were appliedto all point primitivesselectedfrom 6 brown colorsthatwerefoundon thestarfish(Figure12).

Figure12: Thefinal bumptexturewascreatedby movingthepoint primitivestangentto thesurfacewith a randomnoisefunctionapplied

A similar approachwas applied to create anotherleatherstar, that hada very differenttexture. The pointprimitivesweremovedtangentto thesurfacebut thistimeonly afew wereaddedto thecenter. They wereaddedus-ing randomanglesandrandomradiusvalues. The finalmodelof this seastar’s legswereslightly bentasin Fig-ure13.

Figure13: AnotherLeatherStarfishwith a differentsur-faceappearance

6 Conclusionsand Futur ework

In this paperwe have presenteda methodto modeltwoinvertebrates,theseaanemone,StomphiaCoccinea,and

theseastar, DermasteriasImbricataasan applicationofthe BlobTree . The model combinesimplicit surfaces,CSG,controlledblending,2D texture mappingand thecollision-basedmodelof phyllotaxis. The resultsshowimplicit surfacesbeingcapableof modelingcomplex seacreaturesusinga proceduralapproach.We arecurrentlyworking on generatingmorerealistic imagesusing ren-deringtechniquessuchasPhotonmaps[13, 14] to cor-rectly reproducethe effect of transparency and translu-cency, observedin someof thesecreatures.We arelook-ing towardscreatingarealisticsimulationof thebehaviorof thesemarinecreatures,usinga physically basedap-proach. We have found that the BlobTree provides anexcellent structureon which to basesuchmodels. Us-ing thetechniquesof Cani-GascuelandDesbrun,[8], weintendto simulatethe interactionsbetweentheseobjectsandtheirenvironment.Weareinvestigatingtheextensionof the BlobTree to incorporatethesefeaturesto providebettertoolsfor implicit modeling.

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