The document evaluates CAE tools in Solid Edge using the example of designing a steering wheel. It discusses parametric modelling which allows dimensions to change and regenerate the model. Assemblies can be created using relationships and exploded for visualization. Finite element analysis is used to simulate stresses and optimize designs. Curves are drawn using techniques like Bezier and B-splines to approximate shapes.

1. AVANESSOVA Nadezda
11-24-2016
University of Edinburgh
CAE Evaluation

2. Table of Contents
Introduction.................................................................................................................................2
Parametric modelling.................................................................................................................... 3
Assemblies...................................................................................................................................8
Finite Element Analysis and Optimization..................................................................................... 11
Convergence .......................................................................................................................... 14
Singularity.............................................................................................................................. 14
Optimization........................................................................................................................... 15
Curves and Surfaces.................................................................................................................... 16
Curves.................................................................................................................................... 16
Continuity .............................................................................................................................. 19
Surfaces................................................................................................................................. 20
Direct Modelling......................................................................................................................... 22
Standard Parts........................................................................................................................ 25
Rendering and Animation............................................................................................................ 26
Drafting..................................................................................................................................... 27
References................................................................................................................................. 27

3. Introduction
Solid Edge (SE) is an engineering software that allows modelling mechanical products in 3D
and analysing them. The purpose of this report is to evaluate CAE tools with the help of SE
using the example of designing a steering wheel for the Formula Student Car. The simplified
approach of design is introduced in Figure 1.
Figure 1
All steps of modelling in SE are shown in order (first steps on top, last in the bottom) in the
history tree of the design. It also allows to suppress or unsuppress the features of the model or
completely delete them (Figure 2). The history tree of simulation commands works in the
similar manner.
3D Part
Model
Assembly
Drawings
Rendered
image
Animations
FEA

4. Figure 2
The most commonly used tools for 3D design are the protrusion tools (Figure 3). The input for
every protrusion is a sketch and some other parameters to satisfy a design idea. The output is
the addition of material in a desired
way. Cut-outs work the same way
however the output is removing a
material.
Parametric modelling
The name parametric modelling refers to the fact that models are built of parts with dimensions
and other variables (i.e. parameters) that can be later changed and the models re-generated [1].
Parametric modelling can be also called a history based modelling because the model is built
using a series of commands that are kept in an ordered way so that if one parameter is changed
the SE system re-generates the model’s features starting from the command where the
parameter changes were done. With the help of this if the relations between lines in the sketches
are manually applied then changing the dimensions (or parameters) can be easy and fast.
However, the relations between lines in the sketch should be done before starting the next
command, otherwise an error may occur (Figure 6). It is still most suitable for the design of a
steering wheel, so that if the limits for steering wheel have changed it is possible to fit the
designed wheel into new size without changing all dimensions. Besides the sketch dimensions,
parameters also include [2]:
Figure 3

5. • Extent dimensions – in Figure 4 the cutout is made through the whole part, however
using the extent button the extent distance can be chosen.
• Feature parameters (e.g. hole specs)
• Offset values (common in assemblies)
• User defined variables
• Variables from other models (peer variables)
Figure 4
Figure 5

6. • Product and Manufacturing Information (PMI) i.e. surface finish, material properties
which can be chosen manually or using the materials list in SE
It is a useful tool if it is required to keep a ratio or position of any feature in the part or a relation
between the parts in assembly.
One example of parametric modelling can be shown using a pattern command. This command
will be used for a steering wheel design to repeat a particular feature over some surface. An
example is shown in Figure 1 where there is a part of a quick release mechanism for a steering
wheel. One tooth was repeated 14 times following a path of a blue sketched circle. A user can
edit the number of reiterations, the path and remove a feature (a tooth) where needed by
clicking on the green dot. If the design of a reference tooth is changed, the pattern command
edits all of them simultaneously.
Part Families allow a user to have several parts in one file which have similar features but
different dimensions. The user should separate features into synchronous which are the same
for all parts and ordered which user can choose to be present for particular parts. This tool is
convenient if the steering wheel must be manufactured several times but with insignificant
differences. The example can be designing steering wheels with common features but different
Figure 6
Figure 7

7. sizes of the screen (Figure 8,9), then to change a size
of a hole for the screen it is only needed to select a
required member and click apply. If the screen must
be absent then all commands related to designing a
hole can be suppressed, after clicking the Apply
button the hole for the screen will be vanished.
However, choosing the right screen should be done
before creating an assembly, because transfer from
one to another design will create an error in the
assembly.
Figure 9
The main disadvantage of parametric modelling is the speed of modelling. It is required to
apply relations listed in Figure 10 to get a successful design (as it was done in Figure 11 for a
spindle) where changing one parameter affects the other in an expected way.
Figure 8

8. Figure 10

9. Figure 11
Assemblies
The CAD of any device isnotcompletedwithoutthe assembly.Itisimportanttoputall partstogether
into assembly which can be later used for the final project as a product definition. Art CAD system
allowsbuildingassemblieswithmore thanmillionpartswhichare still able to be managedwhile still
enhancingthe individualpartdesignprocess [3].DoinganFIE analysisonthe assemblywill givemore
realisticresultsratherthandoingitseparatelyoneachindividual part.
Assembliesare made byusingthe relations similartothose forsketching.The exampleof PlanarAlign
is showninFigure 5. Two planesare selectedandthe distance betweenthemcanbe chosen.For the
circularparts, whichdonot have the revolutionaxisitisbettertoapplytangential relationship,asfor
ball bearingsanda springinthiscase (Figure 12).
Figure 12

10. Assembliescanbe usedtocreate part explosionsas
shown in the Figure, which will allow to see the
arrangement of all parts in the Assembly. It will be
easier to construct a device with the help of this
view. The explosion view can either be made
automatically using an Auto Explode button or
manually (using Explode) by clicking on the parts
desiredtobe exploded.Shownexplosionwasmade
with a use of Auto Explode command and then
modified with the help of Reposition and Drag
Component tools. Manual explosion is useful for
complicated designs with much more components
where only some parts of the device must be
emphasised. If an assembly was made of several
smaller assemblies, then Auto Explode will only
explode the device into these assemblies and
separation into individual parts must be done
manually.
Animations can be very useful for project
presentation. In Solid Edge the creation of
animations is very convenient and simple withthe
helpof AnimationEditor.InAnimationEditorthere
are several optionsforanimation,whichcanbe seen
inthe Figure. The explosionanimationcouldbe used
as an instruction video for the steering wheel
construction. Animations can also be created. To
create that you only need to edit definition of
Explosion and select an explosion configuration of
the interest among those which were created in
using explode commands. The fly-through can be
done byselectingseveralviewsof the steeringwheel
and naming them (f.e. Angle1-6), the animation is
These tools
remove/ad
d arrows
Figure 13
Figure 15
Figure 14

11. thenautomaticallydone as if camera wouldslide aroundthe wheel alongthe path lyingalongthese
viewpoints. However, it does not allow to see parts hiddeninside the assembly. If visibility of these
parts isrequired,itisneededtochange the viewingsettingtotransparentusingthe tool inFigure
Assemblies can also be used to create 2D drawings of the collided view, of the exploded view or of
everyindividual partof the assembly.SEMetric Draft allowsa userto create any view of 2D drawing
togetherwiththe table of assemblyparts,whichcellscanbe editedandnamesof parts changed.An
example of the collidedviewisshownbelow. Itisaveryusefultool forcreatingaconstructionmanual
for the device.
Figure 16
Figure 17

12. Item
Number
FileName(noextension) Author Quantity
1 Boss s1449529 1
2 Ball Bearing s1449529 4
3 Sealing s1449529 1
4 Spindle s1449529 1
5 Helix s1449529 1
6 Ring s1449529 1
7 SteeringWheel s1449529 1
8 Button s1449529 6
9 Bolt s1449529 3
10 LCDScreen s1449529 1
11 Micro-controller s1449529 1
12 Screw jmrobins 4
Figure 18
Finite Element Analysis and Optimization
As any other device the steering wheel
can be subject to stresses, strains,
vibrations, heat transfer, fluid flow,
electric/magnetic fields etc. These
systems are commonly modelled by
differential equations that are difficult
to solve.One approachistobreakdown
the complex geometry into small
regularly shaped elements. Thus every
element transfers physical phenomena
to its neighbours through nodes and
these inturn be solved.The setof these
elements is called a mesh and it may
consistof differentshapes(Figure19)
Figure 19 [4]

13. SE as any other engineering software allows a user to run a Finite Element Analysis on the Part or
Assembly i.e. to allow a user to see the behaviour of the device at different conditions. An example
FIE wasdone on the Spindle. The approachwas [4]:
The geometry of a spindle was simplifiedto make the analysis faster and simpler: Teeth Cutout and
Pattern were supressed. All sharp edges were rounded with 1mm rounding command to minimise
singularity (Figure 21).Howeverforabigmesh(greaterthan1mm) the singularitymaystilloccur.The
Torque of 100Nm was appliedonapartof a Spindle whichhasteeth.The reactionforcescomingfrom
the wallsof the Boss were assumedtobe 100N and were appliedtothe same part’ssurface.
Material
Selection
Start the study,
select the
geometry
Loads
Constrains
Mesh size
Solve
Analysis of
result
Figure 20

14. Simulationresultsare shown belowfordifferentmeshsizes fromcoarsertofiner:The maximumstress
convergestoaround295MPa. For the meshesbiggerthan1.7mmthe resultvaluesjumpupanddown
because of a singularity:forbetterresultsall sharpedgesshouldbe roundedwith2-3mmRound.
Mesh:2.29mm Mesh:1.96mm Mesh:1.64mm
Mesh:1.14mm Mesh:0.65mm
Figure 22
Figure 21

15. Differentsettingsinthe ribbonbarallow auserto choose the type of a stressor displacement.
Figure showsthe total translationforgivenloads. Save buttonwill save the resultsdisplaysettingsso
that theycan be laterviewedagain.
Convergence
By makingthe meshdenseranddenser the resultshouldconverge tothe actual number.Depending
on what accuracy of answer is required a suitable mesh can be chosen. The best approach to the
problem is to plot the resulting values from the studyagainst the mesh size used. In some cases the
SE systemallowtouse onlya small size mesh,because otherwise the problemcannotbe solved.
In some casesthe convergence cannotbe observedatall andthe reasonfor that may be singularity.
Singularity
The singularityproblem shouldbe consideredwhen the loadsare distributed.If there isapointload
onlythenthe problemcanbe solvedwithasingle element.Usingthe maximumpossiblemeshfor
everyproblemshouldbe avoidedsincethe denseristhe meshthe longeritwill take forCAD
software tosolve simultaneousequations.
Figure 23

16. Optimization
For some devices it is required to find the optimum size/shape to maximise performance, minimize
weight etc. Reasonable assumptions shouldbe made prior to starting optimisation to avoid costly
investigations whichmayleadtounrealisticresults.
In CAE the problemisstatedina followingmanner [5]:
Minimize:S,where S=fn(a,b,c…)
Subjectto:a<x; b>x; c<y; d=>z etc.
The functionS isknownas the objective orevaluationfunctionanda,b,care variableswhichmaybe
subjecttoa numberof constraints.
Set of potential solutions represent a mountainous surface where SE software tries some “x” as an
initial guess.Itthenchecksall valuesalongthe pathtothe maximum“x”selectedbyauserandshows
the best result which should satisfy the task the user has given [5]. The number of values along
describedpathis the numberof iterationswhichusershouldinput – the biggeritis the longeritwill
take to run the optimization (ittakes3minfor 5 iterationsinthe example presentedlater);however,
the resultwill be more accurate.
Consider an example with a Spindle
(Figure 24), where S is a mass and the
thickness of the shaft is limited
between two values. The number of
iterations was taken as 5 and the set
up limitationscan be found from the
Figure. The Torque and a linear force
were applied to the Spindle. SE show
the message that “Optimization
convergedbecause the latestchanges
in design fall within the convergence
criteria”andprovidesauserwithExcel
table with the results (Figure 25)– the
lastresultisthenthe optimum.
Figure 24

17. Figure 25
Curves and Surfaces
Curves
Inmanycasesthe devicecanhave complexshapes,suchashandlesof thesteeringwheelanddifferent
approachestodrawcurveshave beencreatedoverthe years. Traditionallythe curvesare drawnusing
the splines. A userdefinesthe pointswhichare theninterpolatedwithacurve fittingalgorithm:given
n+1 pointsthe curve of nth
degree isneededtodescribe itsshape [].
Highdegree curvesare often [6]:
 “Squiggly”(Figure 26)
 Difficulttocontrol at local regions
 Hard (expensive) tocompute –plottingcurvesinvolvesthe solutionof potentiallylarge sets
of simultaneousequations.
Figure 26
There are twomethodswhichuse interpolationsplines:

18.  Langrangianmethod:Findingaparametricequationwhichdescribesacurve passingthrough
the pointssetby a user
 Hermite method:Thisrequiressettingatleasttwocontrol pointsandtangentof the curve at
thispoints.
However,inCAEanothermethodcalledApproximationsplinesisused. The methodof drawing
curvesinCAD isverysimilarto Bezier’smethod.Beziercurves interpolatethe endpoints,but
approximate the intermediate points. Beziercurvesare describedusing‘blendingfunctions’which
create smoothcurvesbetweenthe control points. The equationof aBeziercurve is [6]:
where
Beziermethodimpliesthat there are fixedcontrol pointsP0P1 P2 and soon. Consideranexample
with3 control pointsasshowninthe leftside of Figure 27-28. There are linesdrawnbetweenthese
points(splines) andone more line whichconnectsthese two.Overaset periodof time the the left
endof the purple line musttravel fromP0to P1, at the same time the right endof the same purple
line musttravel fromP1 to P2. The red dot(the endof the curve) inthe same set periodof time
musttravel fromone endof the purple line toanotherandthus ‘draw’a curve.For more complex
curvesthere mustbe more control pointsbutthe approach staysthe same.
𝑆( 𝑡) = ∑ 𝐵𝑖,𝑑 (𝑡)𝒑𝑖
𝑑
𝑖=0
𝐵𝑖,𝑑 = ( 𝑑
𝑖
) 𝑡 𝑖
(1 − 𝑡)
𝑑−𝑖
Figure 27 [8]

19. The red curve can be describedbythese equations [6]:
The basisfunctionS isthena set of functionsandnota polynomial.
In CAE the curvesare drawnusingB-Spline curve whichare verysimilartoBezier.The majorover
Bezieristhatwe achieve continuityinpiecewise curvesbysharingcontrol pointsinthe formulation.
The numberof pointssharedisdependentonthe degree of continuityrequired.Thismeansthat
local changesto the curve are possible [6].
B-spline curve equationlooksvery similartoBezier[6]:
where pi representsthe n-1control points.The degree of polynomial segmentsis(k-1).Bi,k are the
normalisedB-spline blendingfunctions.B-Spline functionsare howeverdefinedbyarepeating
formulai.e.usingCox-De Boorformulation [6]:
S = P
0
’’ = (1-t)
2
P
0
+ 2(1-t)t P
1
+ t
2
P
2
P
0
’ = (1-t)P
0
+ tP
1
P
1
’ = (1-t)P
1
+ tP
2
P
0
’’ = (1-t)P
0
’ + tP
1
’
𝑺( 𝑡) = ∑ 𝐵𝑖,𝑘(𝑡)𝒑𝑖
𝑛
𝑖=0
𝑖𝑓 𝑡𝑖 ≤ 𝑡 ≤ 𝑡𝑖+1 𝑡ℎ𝑒𝑛 𝐵𝑖,1(𝑡) = 1 𝑒𝑙𝑠𝑒 𝐵𝑖,1(𝑡) = 0
Figure 28 [8]

20. Thismeansthat B-Splinesessentiallyrepresentasetof curve segmentswhichoverlapeachother.
Hence any lengthof spline canbe completedof segmentswhichoverlapandshare control points
P0,P1,P2 etc.
A knotvectormust be definedtocontrol the extentof the overlap,the positions of the joins
betweensegmentsandtheircontinuity.Knotvectorissimplyalistof ‘n+k+1’ valuessothat for‘n+1’
control pointsthe curve is describedby‘n+1’blendingfunctionsandkisthe numberof intervals.
The continuityforsuchcurve will be thenCk-2
[6].
A rational functioncanbe definedasthe ratioof two polynomialsandwe cantherefore define a
rational spline functionsforanytype of spline.Incase of B-Spline the rational isdefinedas [6]:
However,apartfromcontrol points,degree of the polynomial andaknotvector itis alsoneededto
define the weightingfactorwi.
The major propertyof Rational Splinesistocreate circlesandellipses whichhave exact
representationsratherthanthe approximate versionsthatnon-rational polynomialsproduce.
Continuity
If two curvesare connectedusingthe Connectcommand,thenitdoesnotmeanbydefaultthatthe
total curve will be continuous.Inordertomake themcontinuousthe Tangenttool inSE can be used:
Figure 29
It has several options:
Tangent:Createscontinuitybetweenthe twocurves,the geometricderivativesatthe endsof these
twocurvesare thenequal butparametricare not.This tool was more activelyusedinthe designof
the steeringwheelsince itdoesnotleadtothe strong change of the shape of the curve
𝐵𝑖,𝑘( 𝑡) =
𝑡 − 𝑡𝑖
𝑡𝑖+𝑘−1
𝐵𝑖,𝑘−1( 𝑡) +
𝑡𝑖+𝑘 − 𝑡
𝑡𝑖+𝑘 − 𝑡𝑖+1
𝐵𝑖+1,𝑘−1(𝑡)
𝑷( 𝑡) =
∑ 𝑤𝑖 𝒑𝒊 𝐵𝑖,𝑘(𝑡)𝑛
𝑖=0
∑ 𝑤𝑖 𝐵𝑖,𝑘(𝑡)𝑛
𝑖=0

21. Figure 30
Figure 31
Tangent+Equal Curvature:Createscontinuitybetweenthe twocurvessothat bothgeometricand
parametricderivativesare equal. Thistool canbe useful if the transitionfromone curve toanother
mustbe verysmooth.
Surfaces
Mathematical descriptionof surfacesisbasedonthe same methodsasthose whichare usedto
describe curves. If eachpointona Beziercurve wasmovedalonga secondBeziercurve at some
angle to the firsta BezierSurface patchwouldbe tracedout. Similarlytothe curve the surface
approximatesall of the pointsexceptthe edge pointswhichare interpolated.
B-Spline Surface Patchesare preferredinCAEoverBezierforthe same reasonsasfor the curves.
Since Rational Splinesare more suitable forcreatingcirclesandellipses,the Rational Parametric
Surfacesare usedfor modellingcylindersandspheres.
A fewexamplesof creatingSurfacesinSE whichwere usedindesigningaSteeringWheel:
Lofting:SE automaticallyspansbetweentwolinesalongthe curve 4 times,andthenfillsthe space
withmaterial.

22. LoftedCut:The same approachis usedhere.Spaniscreatedbetweenacurve anda line and
betweentwocurves andthe material isthenremoved.
Figure 33
Rounding:Useful forremovingsharpedges,addsamaterial butinsteadof equationforthe curve
the equationforthe circle isused – SE sweepsthe line along the arcof desiredradius.
Figure 34
Helix:Veryuseful forcreatingsprings.The inputsare veryconvenient:axisof revolution,cross-
sectional area,numberof pitchesandtheirdensity.
Figure 32

23. Figure35
Direct Modelling
In contrastto ordered or ParametricmodellingDirectmodellingdoesnotconsistof buildingsteps,
where if one stepismodifiedthe SEsoftware runsthroughthroughall stepstoupdate the part.
Directmodellingimpliesdirectinteractingwithpartgeometryinordertogenerate oreditshapes.It
can alsobe calledsynchronoussince the modellingstepsdonotdependoneachotherand existin
parallel sothatif one commandiseditedthe definitionof otherstaysthe same.Incontrast, in
ParametricModellingthe usermustsetuprelationsof interest:ausermust structure the history
tree insuch a way that the model canbe editedinthe waythatmightbe desiredatsome future
time andclearlythiscan be a difficultandsometimesimpossibletask [7].The orderof historytree in
ParametricModelling thentriestorepresentthe designintent.
In SE environmentyoucanswitchfromOrderedto Synchronousmodelling:
Figure 36

24. The command ribbonwill thenchange slightlyandyouwill seeFace Relate commandsinadditionto
other.There will alsobe 2 sketchingtoolboxes –one for2D and one for3D sketching. A usercan
change the DesignIntent,remove or addrelationsitwantstosee:
Figure 37
Figure 38
Figure 39
Figure 40
To sum up,the advantagesof DirectModellingare [7]:
 RapidEditingof a range of shapes
 Editingnon-nativeCADfiles
 Preparinggeneral geometryforFEA
The weaknessesof itare:
 It isbad at some complex geometrieswhere designintentiscodedinthe historytree
 Historybasedmodelsworkbestoncommandswhere multiple stepsare dominant,eg
sweeps
Consideranexample of aSpindle designwithsynchronoustechnology. Withsynchronoustechnology
toolsbecome easiertouse.InFigure 41 the extrusionismade justbyselectingwhatside of aspindle
must be extruded. In Figure 42 the Cutout was made faster, since the sketch can be drawn without
changingthe viewto 2D. In Figure 43 the dimensionscanbe easilyputin3D and modified.However,
inSynchronousmodellingyoucannotEditFormulaforthe dimensioni.e.settingthe relationbetween

25. dimensionsisimpossible.However,simple relate toolsare kept,so two dimensionscanbe set to be
equal (Figure 44).
Figure 42
Figure 41
Figure 43

26. Parametric modelling was preferred over Direct because it allows more control by setting the
parameters. It is also more convenient to show all SE tools using parametric modelling (such as Part
Families). However Synchronous Technologyhas the potential to change the entire CAD industry
because the newparadigmisnotonlypotentiallyfasterbutitalsoopensupthe use of CADto a much
widerapplicationarea[7].
Standard Parts
SolidEdge togetherwithasoftwarehasalibrary(afolder –Figure 45) withsome standardpartswhich
are readyto use,sothata userdoesnotneedtospendtime onsupportingpartssuchasscrews,bolts,
bearings, etc. This folder is called Training and consists of 6 folders and a big set of parts. Folders
include: actuator clamp, Four Bar, Sheet Metal, simulation (simulations for some parts), Try it (this
folderconsistsof not-so-ordinaryparts) andWiringHarness.The restof the folderisa bignumberof
(generally) connectingelements,suchasbolts,screws,housings,washersetc.
Figure 45
For the designof a SteeringWheel the standardpartScrew1was usedtoattach the micro-
controller.
For particular design and specific dimensions, the part from Part Library can be modified using the
Part Families. New dimensions can be set up and unwanted features can be suppressed. However
there are some parts made withsynchronoustechnologyandtheyshouldbe modifiedbyclickingon
the lines,curves,anglesetc.,whichdimensionsshouldbe changed.
Besides SE libraries parts/assembliescan also be found online, f.e. on GrabCad or Traceparts. These
are the environmentswhere engineerscanshare and discusstheirmodels.The modelsuploadedare
generallymade usingdifferentsoftwares:ProEngineer,AutoCad,SolidWorks,SolidEdge etchowever
using STEP format to save these files will allow a user to open the model in any environment
independentlyof where itwasmade.
Figure 44

27. For this designGrabCad was usedto findappropriate micro-controllerand a displayfor the Steering
Wheel. Their assemblieswere turned into parts to avoid complicatedSteering Wheel Assemblyand
savingall parts of subassemblies(savingspace).
Figure 46
Rendering and Animation
SE allows a user to create Animations. These may have different purposes: Marketing, Web site,
Internal,Customerattraction.SEoffersdifferenttypesof Animations:
 FIE
 Kinematics
 Flythrough
 Explodedview
The approachon how to create an explodedview anditsanimationandthe animationof flythrough
was describedinAssemblies. The FIE Animationcanbe made by runningthe FIE analysis – there is a
button‘Animate’,whiththe helpof whichyoucansee how the part deflectsandbyclickingthe ‘Save
Movie’ button (top right) you can save the animation as a movie and view later. Solid Edge savesall
moviesasa VLC mediafile.
Figure 47

28. These animationscan be very useful inindustrypresentations – theyare clear and make it faster for
colleaguesandcustomerstounderstandhow the device works/deflects/looks.
(The videoswill be uploaded)
Drafting
References
[1] F. Mill,“ParametricDesign,”Universityof Edinburgh,Edinburgh,2016.
[2] F. Mill,“Introductiontoparametricdesign,”Universityof Edinburgh,Edinburgh,2016.
[3] F. Mill,“Assemblies,”Universityof Edinburgh,Edinburgh,2016.
[4] F. Mill,“FIE,”Universityof Edinburgh,Edinburgh,2016.
[5] F. Mill,“Optimization,”Universityof Edinburgh,Edinburgh,2016.
[6] F. Mill,“IntroductiontoCurve GeometryforCAD,”Universityof Edinburgh,Edinburgh,2016.
[7] F. Mill,“DirectModelling,”Universityof Edinburgh,Edinburgh,2016.
[8] [Online].Available:http://www.jasondavies.com/animated-bezier/.