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 s

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 which consists

of classes 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 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 the negative jet motion is only

Table Energy consumption during one jet cycle for Polyorchis

Figure Pressurevolume lo op for the lo comotor cycle of Polyorchis

empirical data reveal that the p ositive jet force exceeds the negative jet force by to times

The same conclusion can b e drawn from the pressurevolume diagram Fig for Polyorchis

jellysh under exp eriment in As shown in the plot Fig the maximum pressure in

the b ell cavity results in the p ositive jet propulsion pressure b eing around Pa while the

maximum pressure results in the negative jet propulsion pressure of only Pa

The ab ove analysis and empirical data illustrate mechanical prop erties of a jellyshs

lo comotor system and explain the jet propulsion mechanism during swimming In the next

section the relevant animation techniques for mo deling and simulating a jellysh are exam

ined

Animation Techniques

To animate a soft b oneless ob ject such as a jellysh a springmass mo del SMM is an

appropriate choice SMMs are used in animation as sp ecial representations of elastically

deformable mo dels describ ed in A deformable mo del can have elasticity ie there are

internal elastic forces generated when the ob ject is deformed The forces are prop ortional to

the degree of deformation Also this mo del dissipates energy The Lagrange equation for

motion for any p oint p on an elastically deformable mo del is as follows

r t r t P r t

f r tt

t t t r t

where r t is the p osition of p oint p at time t is the mass densityat p is the damping

densityatp and P r t is the elastic p otential energy that p oint p hasattimet f r tt

represents the net externally applied force at p osition r tattimet On the left hand side

of equation the rst term is the force used to overcome the inertial of the p oint mass

at p the second term is the damping force at p and the third term is the elastic force

caused by deformation at pGoverned by the Lagrange equations of motion the elastically

deformable system can successfully mo del ob jects such as string rubb er cloth pap er and

exible metals

SMM is a subset of the elastically deformable mo dels It contains a discrete set of mass

p oints that are connected through springs The Lagrange equation for any mass p ointwith

index i is as follows



X

dx t d x t

i i

s e

f t f t i N m

i i

ij i



dt dt

j N

i

where N is the numb er of mass p oints in the SMM x t is the p osition of the mass p oint

i

with index i at time t m is its mass is its damping factor N is the index set of its

i i i

s e

neighb ouring mass p oints f is the spring force p oint j applys on p oint i at time tand f t

ij i

is the external force acting on p oint i at time t Comparing to equation the terms on

the left hand side play the same functions but are signicantly simplied due to the discrete

nature of SMM These equations of motion are thus much easier to simulate and implement

A semiimplicit Euler metho d is used to numericallyintegrate the ab ove group of equations

where the internal spring forces on the left hand side are implicitlyintegrated and the

external forces on the right hand side are explicitly integrated

Using the SMM to mo del is rst done by Miller where animated snakes

caterpillars and worms are created These animals have the ability of deforming elastically

under external forces making SMM an ideal representation for them In order to achieve

realistic motions each animals anatomy and mechanics of motion are rst studied and then

mo deled Their complex internal structures are simplied and mo deled as a sequence of cub es

of masses with springs along each edge and across the diagonal of each face The internal

forces such as those generated bymuscle contractions are mo deled as spring tensions The

external forces such as directional friction due to their surface structure are also mo deled

As an example from the results snake motions such as rectilinear progression horizontal

undulatory progression and sidewinding are animated by giving snake mo dels dierent

typ es of control over their muscle springs Further successes of using SMM are shown in

Tus sh mo del The exing b o dies of swimming sh again give a go o d application of

using SMMs for animation These sh mo dels not only can swim forward make turns but

also can demonstrate lifelike b ehaviors suchasscho oling eating and mating Based on the

snake mo del in and sh mo del in Grzeszcauk designed SMMs for coral snakes

leopard sharks dolphins and stingrays Given meticulously selected control these animals

can p erform stunning tasks such as a dolphin jumping out of the water and using its nose

to b ounce a b each ball These fantastic results prop ose a natural choice of using SMM for

designing another sea creature the jellysh

Design of an Animated Jellysh

Under the combined understanding of a jellyshs general anatomy its mechanics for swim

ming and the appropriate animation techniques for such animals the principal features of

real jellysh are extracted and mo deled to create Jel ly Its physical mo del is constructed

ternal control as a SMM where springs functioning as muscles are commanded byanin

mo del Jellys interaction with its environment is determined by its force mo del Finally

it is dressed up by a NURB surface whose control p oints are tied to the SMM through a

mapping technique Chains of cylinders are used to represent its tentacles Details of these

mo dels are presented in the following sections

SpringMass Mo del

Fig illustrates Jel lys physical mo del whose shap e roughly resembles the cylindrical

structure of a real jellysh It consists of mass no des and springs Points to

represent the upp er half of the jellysh and p oints to represent the lower half Since

the thickness of the b ell of a real jellysh is greater at the top than the b ottom p oints to

are heavier than p oints to Sp ecically the individual mass for eachpoint from to

is and for eachpoint from to is

Constructed as a truncated cone structure Jel ly has p oints to on a circle with 2 3 1

4 0

5 6 7

10 11 9

12 8

13 15

14

Figure SpringMass Mo del SMM

radius and p oints to on a circle units down with radius Springs connecting

these p oints are categorized as circular springs horizontal cross springs vertical springs and

vertical cross springs Eight springs form one circle which resembles the muscle ring on the

real jellysh These springs need to b e relatively sti to simulate the muscle contraction

Horizontal cross springs are used to maintain horizontal structural stabilityAt the same

time they mo del the elastic b ers in the b ell mesoglea while energy can b e stored in them

as the muscle rings contract These springs do not need to b e very sti otherwise to o much

energy will b e stored and cause rapid recovery of the b ell during the relling pro cess The

vertical springs and vertical cross springs provide vertical structural stability during Jel lys

motion as the b ellshap ed b o dy of a real jellysh hardly changes its length during swimming

These springs are therefore kept very strong to maintain the structure The spring constant

for circular muscles is for horizontal cross springs is for vertical springs and vertical

cross springs is All these springs have a damping factor of

The Lagrange equation for this SMM system is the same as equation which is rep eated

as the following



X

dx t d x t

i i

s e

f t f t i N m

i i

ij i



dt dt

j N

i

In particular the spring force is calculated as following

de t

ij

s

tk e t f r tkr tk

ij ij ij ij ij

ij

dt

where k is the elastic constant and is the damping factor of the spring connecting p oint

ij ij

i and j r tx x and e tkr kl l is the natural length of the spring

ij j i ij ij ij ij

A summary on the parameters used for Jellys SMM during simulation is as following

N

i

m

i

i

i

if spring is a muscle spring

if spring is a horizontal cross spring k

ij

if spring is a vertical spring or vertical cross spring

ij

The mechanism of using springs to control muscles is to mo dify their rest lengthes For





k l l example bychanging a static spring with rest length l to l a p otential energy of

   



is intro duced into the spring This spring is either contracted l l or extended l l

   

and has to move to its new rest length p osition to seek equilibrium Motion is thus generated

Control of the muscle springs are discussed in the next section

Internal Control Mo del

Two circular muscles exist in Jel ly eachofwhich contracts uniformly So Jel ly can only

swim upward but can not turn Because of the uniform contraction each ring of springs

only need one function to control Control functions determine howmucheachmuscle ring

should contract or recover at every time instance Designing the control functions requires

the knowledge of how these muscle rings b ehave

One metho d used is by examining the motion of a real jellysh Because muscle rings

contraction and recovery are directly related to their diameters jellyshs shap e changes can

reveal its muscle rings p erformance A video recording of Cassiopeia andromeda jellysh

swimming is studied frame by frame Fig shows one sequence extracted Toinvestigate

the muscle rings b eing mo deled b ell diameters at the top and b ottom are traced to imagine

ery As seen from Fig the b ellshap ed jellysh narrows its their contraction and recov

top rst frame to then a waveofcontraction passes down the b o dy frame to

As the jellysh shrinks to its minimum volumeit maintains the compact shap e for a short

time frame to and then recovers to its resting shap e frame to Examining these

frames and sp ecifying the control functions based on the measurementofeachmuscle ring

mo deled in every frame remind one of the keyframing animation technique Exp eriments

show that given enough damping in the springs in Jel lys SMM the muscle rings can contract

to certain dimensions and recover exactly following the sp ecication of the control functions

This reveals the p ossibilityofachieving keyframing control in physicsbased animation and

combing these two opp osing animation techniques b eautifully

Besides the video recording of real jellysh motion biomechanics literature addressing

jellysh muscle b ehavior is also of great help It is sp ecied in that swimming muscles

of jellysh contract slowly at the early stage Then the rate of contractions increases signif

icantly and the jellysh maximally accelerates After this aggressivemovement stage the

b ell continues to contract but at a slower rate It should achieve at least a reduction

Figure One sequence of frames for the swimming of Cassiopeia andromeda jellysh 0 5 10 15 20 t

u 0.0 1

-0.2

0.0 u 2

-0.4

Figure Internal control mo del

in its average diameter during the contraction When the recovery phase b egins the b ell

extends very slowly to its resting dimension As indicated in in general the recovery

phase of the swimming cycle takes ab out to longer than the contraction All the

ab ove information gives many helpful hints in designing the control functions

The rough idea of how Jellys swimming muscles should b ehave during its swimming

results in the control graph shown in Fig The horizontal axis represents time and the

vertical axis records the change of rest length change of rest length current rest length

initial rest length for the muscle springs u t for springs in the rst muscle ring and u t

 

for the ones in the second To obtain this control graph the simulation time is divided into

intervals and the changes of rest length are sp ecied at every time instance from to

Function values at other time sp ots are linearly interp olated The resulting control graph

presented in Fig shows the following considerations in order to match the understanding

of howrealmuscle rings b ehave from the previous motion investigations First u t declines



earlier than u t so that the rst muscle ring contracts so oner than the second and thus



pro duce the wavy eect of contraction from the top of the b o dy to the b ottom Second the

recovery phase is designed to hav e a longer duration than the contraction phase Third the

second muscle ring contracts much more than the rst one to create the signicant shrinking

eect at the b ottom part of the b ell during the contraction phase

This control graph can b e mo died by optimization algorithms These techniques are

addressed in great detail in The optimization pro cess is referred to as training to the

animal mo dels Before the training starts the mo deled animals SMM mo dels for shark

dolphin snake and stingray havenoknowledge as to howtheirmuscles should contract

over time ie the control functions are set to initial values For the training of these

animals goals are set such as reaching a certain target turning at a certain angle keeping

balance minimizing energy and so on As training starts forward simulation is carried and

optimization techniques such as simulated annealing and simplex metho ds are used to

mo dify the control functions to achieve these goals

In summary the internal control mo del directs muscles on howtocontract and recover

over time Internal forces are thus created to give Jel ly power to move Howitmoves

nonetheless is not only governed bytheinternal forces but also determined by the external nv

Hydrodynamic forces on the surfaces: n n f f f vv

(side view)

(a)

f Jet propulsion force:

V 1 V 2 S (side view) v t { V m v

f’ t t+ t

(b)

Figure External force mo del

forces which are describ ed in the next section

External Force Mo del

We imgine Jel ly in a world of full of water Collision with other ob jects are not considered

at present since the currentgoalistomake Jel ly swim All the external forces are therefore

gravityandhydro dynamic forces

Gravity is considered since according to Polyochis jellysh has a gravity slightly

greater than that of sea water They would sink slowly when not swimming Jel ly is mo deled

to have the same prop erty a slightgravity force is designed to act on every mass p oint

on Jel ly The gravitational accelaration is set to

Hydro dynamic forces that Jel ly exp eriences during swimming are categorized into several

groups and mo deled separately The rst group includes the hydro dynamic forces exerted

on anypatch of surface on Jel ly as that surface moves in the water As describ ed in

when a patch of surface moves and displaces a volume of water the inertia of the discharged

water exert a reaction force normal to the surface and prop ortional to the volume of that

water displaced p er unit time Under certain simplications the instantaneous force on the

R

surface S of a b o dy in a viscous uid is prop ortional to n v ndS where n is the

S

normal of the surface and v is the relativevelo citybetween the surface and the uid Each

surface on Jel ly is broken into triangles Assuming A is the area of a triangular surface the

force on the surface is An v n and is equally distributed to the three mass p oints that

form the triangle Fig a presents a lateral view of Jellys SMM It shows one of the

surface normals for each side and the top of the b ell Also shown are the forces acting on

these surfaces as jellysh is contracting and swimming upward

The second group of external forces which is crucial for Jel lys swimming consists of the

jet propulsion forces As depicted in Fig b imagine Jel ly stays still at time t and prop els

avolume of water with mass m during a short time interval tIfitssubumbrel lar cavity

volume changes from V to V then the exp elled water should havea volume V where

 

V V V Let the average jet propulsion force acting on Jel ly be f and the average

 

 

prop elling force acting on water b e f then f f according to Newtons Third Law Let



v b e the average velo city of the emitted water By Newtons Second Law f t mv during

an instantaneous interval of time Since m V where is the density of the water and

v tS V where S is the op ening area of the b ell cavity the following relationship can

b e derived



V

kf k



t S

Because V tandS are all known at each time step during the simulation the jet

propulsion force can b e calculated This force is then prop ortionally distributed according

to the mass of eachpointinSMM

Equation do es not only calculate the p ositive jet propulsion force that prop els the

animal upward f but also compute the negative jet force that the animal endures

positiv e

when the b ell relaxes and water p ours into the b ell cavityf

neg ativ e



V

kf k k

positiv e positiv e



t S

and



V

kf k k

neg ativ e neg ativ e



t S

where k and k are scaling factors Given the reasons discussed in section

positiv e neg ativ e

these two factors are not the same During the simulation

k k

neg ativ e positiv e

The third group of external forces include the drag forces caused bythewater contained

in the b ell cavity As the jellysh moves it has to carry along the water inside of its internal

cavity The eect of this water is mo deled by increasing the mass for all the p oints in SMM

During the contraction phase the mass of the SMM system is chosen as times bigger

than the net mass and during the recovery phase the mass of SMM system is chosen as

times bigger than the net mass These factors are selected based on the prediction made in

which indicates that the eective mass in the jellysh should b e b etween and times

larger than the mass of the animal Jellysh is heavier during the recovery phase b ecause it

has a bigger cavity and contains more water

The last group of external forces contains the friction forces b etween the water of the

b ell surface These forces are mo deled as damping on the spring which dissipates energy

Given the springmass mo del control mo del and force mo del Jel ly is able to swim To

give Jel ly a realistic app earance a NURB surface is employed for decorating the underlying

springmass mo del The details are describ ed in the next section

Geometric Mo del

In creating the geometric mo del of Jel ly a D picture of Polyorchis penicil latus jellysh Fig

is rst scanned in Then a D curvewhich outlines the b ellshap ed b o dy on the picture is

TM

revolved in Alias to construct a NURB surface In the end this NURB surface is resized

to match the dimensions of Jel lys SMM Fig shows a snapshot of the nal lo ok of this

mo del with Jellys SMM mo del emb eded inside The dangling lines are added to the fringe

of the NURB surface to represent tentacles Eachtentacle has line segments and their end

p oints are randomly p erturb ed to a small amountover time to show exible motion

To attach the NURB surface mo del to the SMM each control p oint on the NURB surface

is mapp ed to the closest mass p oint or face center on the SMM bykeeping its distance to

the mapp ed p oint As simulation pro ceeds the p ositions of the mass p onts on the SMM are

up dated ob eying the equations of motion discussed in section Though maintaining the

distance to its lo cked p oint on the SMM every control p oint on the NURB surface is moved

along The tentacles are also dragged along by the NURB surface

TM

The geometric mo del is nally rendered in Rrenderman with the b ellshap ed b o dy

rendered as a translucent NURB surface and each tentacle as a sequence of cylinders

Conclusion and Future Work

Given the springmass mo del internal control mo del external force mo del and geometric

mo del describ ed in the earlier sections Jel ly is able to swim with two distinct phases con

traction and recovery Moreover it swims at a reasonable sp eed ab out one b ell length

swimming distance during one swimming cycle Given enough damping in the springs mus

cle ring contraction and recovery can follow the sp ecications in the control graph This

accomplishes kinematic control in physicsbased animation and repro duces naturallo oking

motion Possible future work is explored in the following sections physicsbased tentacles

turning and light tracking interactive control graph and jet propulsion mo deling on other

animals

Figure Geometric mo del and embeded SMM

Physicsbased Tentacles

Currently tentacles are rendered kinematically by hanging series of cylinders down the b ell

fringe An attempt of implementing each tentacle as strings of springs has b een made and

the physicsbase tentacles swim reasonably well given that p oint damping is added to the

tentacle mass p oints in SMM Dynamically simulated tentacles will give more realistic results

when Jel ly is able to make fancier moves than swimming straightupward

Moreover literatures show that jellysh tentacles are not completely passive dragging

along by the b ellshap ed b o dy For example in as Aglantha digitale jellysh extend

their tentacles the tentacles show considerable indep endentmovement icking curling at

their tips and swaying up and down These active asp ects of tentacles can b e examined and

mo deled

Turning and LightTracking

Jel ly can only swim upward at present The uniform contraction of every muscle ring do es

not allow it to turn However in real jellysh turning phenomena such as deecting o

water surfaces turning upside down and light tracking are often observed Deecting o

jellysh as they swim toward the water water surfaces is noted in Polyorchis montereyensis

surface strike it and reb ound in an approximately reection angle Turning upside down

is seen in Alglantha ditale jellysh as they slowly turn around and stretch out their tentacles

when they are not swimming The widely spreaded tentacles increase the probability

of catching prey Light tracking phototropism is observed in Polyorchis montereyensis as

they o ccasionally turn and swim to the b ottom of a lit chamb er o or during exp eriments

These jellysh would continue to swim in this inverted p osition for a while but as so on

as they stop swimming they will quickly return to their upright p ositions Turning during

light tracking is facilitated by the contraction of the radial muscles RM in Fig and the

function of the velume Velume in Fig and V in Fig In order to turn the radial

muscles contract to distort the b ell shap e esp ecially the velum shap e to direct the water jet

at angles to the longitudinal axis of the b ell These intricate mechanics can b e investigated

and mo deled to equip Jel ly for turning

Interactive Control Graph

As mentioned in the rep ort earlier if Jellys SMM is given enough damping factor the

animation can achievekeyframing control for the contraction and recovery of the swimming

muscles whose action directly aects the shap e of the jellysh mo del over time At present

the control function is implemente d as a piecewise linear curve and user can only sp ecify

the value of the control function at some discrete time step in a script le A b etter user

interface can b e implemented so that we are able to plot a curve to sp ecify the demanded

control function and thus reach smo other and b etter control

Jet Propulsion Mo deling on Other Animals

The jet propulsion force mo del for Jel ly can b e extended to more animals that use jet

propulsion as a mechanism for swimming These animals include the Nautilus and Squid

describ ed in To animate these animals same design pro cedures can b e followed by rst

studying their anatomies and lo comotor structures then lo oking for approp eriate animation

techniques and in the end coming up with the mo deled animals bycombining knowledge

from b oth

Acknowledgement

First I would like to thank Radek Grzeszczuk for his great help To get me started he

gave me his wonderful set of C programs which can b e nicely mo died and extended I

would also like to thank Xiaoyuan Tu for her detailed demo and valuable suggestions Dr

Dale Calder professor in Royal Ontario Museum has given me warm help in answering my

jellysh questions He also provided me great pap ers that I could not nd in the libraries

Last but not the least I would like to givemy sp ecial thanks to Victor NgThowHing for

his great supp ort and inspiring discussions phylum Cnidaria

Hydrozoa Scyphozoa Anthozoa (e.g. Aurelia/Common ) other hydromedusae siphonophoes (e.g. Polyorchis) (e.g. Physalia/Potuguese man_of_war)

Jellyfish

Figure Jellysh family

App endix A Various Sp ecies of Jellysh

Figure Various sp ecies of jellysh x

a

h

b

Figure Volume calculation

App endix B Volume Calculation

In calculating the volume of the SMM sp ecied in Fig the SMM is approximated by

a truncated cone shown in Fig The volume of the truncated cone is the dierence of

the two cones Given a b e the radius of the top circle b b e the radius of the b ottom circle

x b e the height of the top cone and h b e the height of the truncated cone

 

b x h a x V

tr uncated

where

a a x

ie x h

x h b b a

In conclusion

 

V a ab b

tr uncated

References

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san jellysh Polyorchis p enicillatus I Mechanical prop erties of the lo comotor structure

J exp Biol

Demont M E and Gosline J M b Mechanics of jet propulsion in the hydrome

dusan jellysh Polyorchis p enicillatus I I Energetics of the jet cycle J exp Biol

Demont M E and Gosline J M b Mechanics of jet propulsion in the hydrome

dusan jellysh Polyorchis p enicillatus I I I A natural resonating b ell the presence and

imp ortance of a resonant phenomenon in the lo comotor structure J exp Biol

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Shih C T A Guide to the Jellysh of Canadian Atlantic Waters National Museum of

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No

Sherman IW Sherman VG The Invertebrates Function and Form a Lab oratory

Guide nd edition Macmillan Publishing Co Inc New York Collier Macmillan Pub

lishers London

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p edia Britannica Inc ChicagoAucklandGenevaLondonManilaParisRomeSeoul

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Keeton WT Illustrated byPaula di santo Bendadoun Biological Science nd edition

New York WWNorton and CompanyInc

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Chester Melb ourne Sydney

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Computer Graphics Volume Number July

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Hydrozoa Trachylina and their Control

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