Dancing Jellysh Xiaohuan Corina Wang Septemb er Intro duction Jellysh are lovely creatures In the Seattle Aquarium I have seen their soft translucent b o dies dancing elegantly in a darklit tank It was as fascinating as watching a ballet p erformance Designing a jellysh mo del and teaching it how to lo comote are eorts to recreate the jellyshs natural graceful movement Mo deling live creatures and animating their movements have b een long studied Two broad categories of techniques include traditional animation and physicsbased animation Traditional animation uses keyframing where the animator has to repro duce an animals p oses at eachpoint along the time line Although this metho d lets the animators imagination y it is timeconsuming to create the animated sequences and these sequences are usually not reusable Physicsbased animation op ens up a new approach for creating animal motion Applying this technique the animator is able to assign the mo deled creature similar physical structures as those of its live counterpart Moreover the interaction b etween the real creature and its environment is mo deled and simulated Both the internal and external forces that a real animal exp eriences during its motion are applied to its mo del This greatly automate the animation pro cess In short physicsbased animation provides interactive automation to the animated creature instead of manually regenerating the app earance of the animal in sequence as done in the traditional animation Using physicsbased animation to achieve realistic motion the real animals general anatomy and mechanical prop erties for motion should b e investigated Of the same imp or tance is the examination of the approp oriate computer mo deling and animation techniques for the sp ecic animal under study A general pro cedure of mo deling and animating a crea ture is describ ed as following First study the animal to b e mo deled Second investigate the animation techniques suitable for that animal Third combine knowledge from b oth domains and create the mo deled animal and simulate its motion This rep ort describ es the pro cess of applying the ab ove pro cedure in designing a jellysh mo del The result is a mo deled jellysh named Jel ly designed as a D springmass structure emb eded in a D NURB surface It lo comotes bycontracting its circular swimming muscles commanded by the muscle controllers During its lo comotion Jel ly exp eriences hydro dy namic forces including a jet propulsion force which prop els it forward This mo del is designed based on the background work discussed in section which is divided into two domains the Figure General structure of a hydromedusa investigation of jellysh and the examination of animation techniques Section presents Jel ly in detail including its springmass mo del internal control mo del external force mo del and geometric mo del Section gives the conclusion and prop oses some future work that can turn Jel ly into a skillful dancer Background Two domains of background knowledge are presented in this section one for jellysh and one for the appropriate animation techniques which are b oth imp ortant in designing a computer mo deled jellysh The rst part is mostly based on biological and biomechanics researchon jellysh and the second part is a survey on the animation techniques suitable for animating soft deformable ob jects such as jellysh Jellysh Jellysh are not always like the ones we see in aquariums They have a big family with around sp ecies In biological terms jellysh b elong to phylum Cnidaria which consists of classes Hydrozoa Scyphozoaand Anthozoa Jellysh include all the marine members of Scyphozoa and certain Hydrozoa memb ers suchas hydromedusae and siphonophones Figure Lo comotor b ell structure in hydromedusan Polyorchis An example of Scyphozoa is Aurelia common jellysh of hydromedusae is Polyorchis and of siphonophoes is Physalia Portuguese manofwar Their pictures are presented in App endix A to illustrate their signicant dierences in shap es Jel ly is mo deled after a hydromedusan Polyorchis jellysh App endix A Therefore the structure of hydromedusan jellysh esp ecially Polyorchis is studied in detail Fig presents the general structure of a hydromedusan jellysh and Fig p ortraits the lo comotor b ell structure of a hydromedusan Polyorchis jellysh The general shap e of a hydromedusan jellysh is like a b ell The outer surface of the b ell is named as exumbrel lar surface the inner surface of the b ell is called subumbrel lar surface and the b ell cavity is referred to as subumbrel lar cavity as seen in Fig The b ell is mostly comp osed of noncellular and transparent mesoglea Fig whichistraversed bynumerous radially arranged b ers shown as RF radial b ers in Fig These radial b ers are capable of sustaining energy when they are pulled and thus give the b ell structure certain elasticityAt the fringe of the b ellshap ed b o dy there are tentacles dangling as seen from the picture of Polyorchis in App endix A also shown as marginal tentacle in Fig These tentacles are helpful in catching fo o d stinging aw ay enemies and keeping balance On the subumbrel lar surface of the b ell b o dy line circular muscles indicated as CM in Fig These muscles are the engines for the movement of the jellysh Their contractions initiate jellysh swimming Swimming of a jellysh is p erio dic and consists of two distinct phases the contraction phase and the relling phase or recovery phase as referred to in The contraction of the circular muscles starts the rst phase As they contract their diameters reduce and the b ellshap ed b o dy narrows Water contained in the subumbrel lar cavity is pushed out as its volume shrinks The ejected water gains momentum from the jellysh and exerts reaction forces on the b ell b o dy prop elling it to the opp osite direction As the b ellshap ed b o dy shrinks to its minimum volume and starts to recover the relling phase b egins Water p ours into the b ell cavity and negative jet forces slowdown the jellysh Fig shows the plots of the volume of the b ell cavityover time the distance traveled over time and the velo city over time The jellysh under study is Gonionemus vertensone of the hydrozoan medusae Notice that the volume initially decreases during contraction then maintains a certain level for a short time and then increases Also notice that the animal is accelerated during the contraction phase from the p ositive jet propulsion force and then decelerated during the relling phase A p otential paradox regarding to jet propulsion arises if one realizes that water b eing squeezed out of the b ell cavity during the contraction phase is the main cause for jellysh ater is lled in again during the relling swimming but also notices that same amountofw phase Whywould not the eect of the negative jet propulsion force cancel out the eect of the p ositive one The answer lies in the dierence b etween the momentum changes of the water for the two phases During the contraction phase of the swimming cycle as illustrated in Fig a the b ell narrows and water is ejected Assuming m is the mass w of the amountofwater b eing pushed out and v is the average velo city of the water the w momentum change of the water is m v given that jellysh is static b efore the contraction w w starts During the relling pro cess depicted in Fig b jellysh exp ends and the same amountofwater lls back to the b ell cavityandcatches the sp eed of the jellysh Assuming jellyshs average swimming sp eed during the relling phase is v the momentum change j Figure Volume distance and velo cityover time m w v w (a) contraction phase vj m w (b) refilling phase Figure Jet propulsion of the water is then m v Comparing the momentum change of water during two phases w j ie m v and m v we only need to lo ok at the sp eed of the ejected water jet sp eed v w w w j w with the average swimming sp eed of a jellysh swimming sp eed v As observed in squid j the jet sp eed is much greater than the swimming sp eed Literatures also record that jellysh are slow swimmers So the conclusion is that the same amountofwater gains much higher momentum in the contraction phase than in the relling phase According to the Conservation Law of Momentum the momentum that jellysh attains in the contraction phase is much bigger than the momentum it loses in the relling phase The net motion of the jellysh results with a direction opp osite to the emitted water The ab ove explanation can b e further understo o d by comparing the energy sp ent during the contraction phase and the recovery phase According to all the energy required for jellysh swimming are pro duced by the swimming muscles during the contraction phase They are divided into comp onents The rst part of the energy is used to generate the pressure in the subumbrella cavity This pressure creates the thrust that prop els the jellysh The second part of the energy is used to overcome the inertia of the movement of the b ell The third part of the energy is used to deform the b ers traversing the mesoglea This last fragment of the energy is stored as elastic strain energy and used for the relling pro cess during whichnomuscles are activated for the recoil of the b ell to its resting dimension Water is drawn bac kinto the b ell by the release of this stored energyTable reveals the various comp onents of energy generated bythemuscles in the jet cycle of Polyorchis jellysh As seen from this table the energy used for pro ducing the p ositive jet motion is J J These while the energy consumed in overcoming