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GYTE – BİL763 – Human- Computer Interaction TERM PAPER PRESENTATION. Fitts ’ Law and Expanding Targets : Experimental Studies and Designs for User Interfaces Authors : Michael J. McGuffin , Ravin Balakrishnan. Student Name : Orkun AKİLE Student Id : 131041028. INTRODUCTION.

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Student name orkun ak le student id 131041028

GYTE – BİL763 – Human-ComputerInteraction


Fitts’ LawandExpandingTargets : ExperimentalStudiesandDesignsfor User InterfacesAuthors : Michael J. McGuffin, RavinBalakrishnan

Student Name : Orkun AKİLE

StudentId : 131041028


  • Recentlythere has beenrenewedinterest in techniquesforfacilitatingtheselection of userinterfacewidgetsorother on-screentargetswith a pointingdevice.

  • One of them is widgetsthatexpandorgrow in responsetotheuser’sfocus of attention.

  • Applications of expandingwidgets can be found in popular operatingsystemssuch as Apple MacOSwheretheicons in thedesktoptoolbarexpandwhenthemousecursor is overthem.

  • Mainly, therearetwocomplementaryadvantagestousingexpandingwidgets.

  • First, widgetsthataresmallwhen not in useconsumelessscreenspace, meaningoptimizeduse of screenspace.

  • Second, whatever a widget’sinitial size, increasingthewidget’s size whentheuserpoints at it maymakethewidgeteasiertoselect, decreaseselection time.

  • FromFitts’ law, a targetwith a smallerfixed size requiremore time toselect. But it is unclear how performance is affected in expandingtargetscase.

  • Therearealsosecondaryissuestoconsiderwhendesigninginterfaceswithmultipleexpandingtargets.

  • Interfacemustcontinuallydeterminewhich of themanytargetstoexpandandwhen.

  • Also, closelyspacedtargetsmayoverlaporotherwiseinterferewitheachotherduringexpansion. Inthiscaseshouldocclusion be allowedorshouldsometargets be displaced.

  • What is thebestperformanceto be expected?


Fitts’ Law

A : Amplitude of themotion

W : Width of thetargetmeasuredalongtheaxis of motion

K : K is a constantwhosevalue is proposedto be 0, ½ or1

ID : Thelogarithm is referredto as index of difficulty.

a, b : Constants a and b varywithfactorssuch as pointingdevice, musclesusedforinput, control-displayratio (C:D). Todetermine a and b typically an experiment is performed. Fitting a straightlinetothemeasureMT valuesyields a and b as theinterceptandslope of theline.

  • Fitts’ lawenables us characterizingperformance of inputdevicesgiven an ID value.

Lower-Level Models of Motor Control

  • Examination of kinematic data forindividualtargetacquisitionsrevelthatthemovement of theuser is often not a single, smoothmotion but rather is composed of a sequence of oneormoresubmovements. Thefirstsubmovement is typicallylargeandfastcoveringmost of thedistancetothetarget. Thismay be followedbysubsequentsmallerandsmallermovementsthatcorrectforanyundershootorovershoot of theinitialmovement.

  • SomemodelstoexplainFitts’ law: deterministiciterative-corrections model, stochasticoptimized-submovement model

Experiment with isolated expanding targets

  • Main hypothesisforexpandingtargets is thatwhencorrectivesubmovementsarenecessary. Targetacquisition time should be depended on the final target size not theinitial.

    Instruments: A workstationrunning Linux, with a 21-inch, 1280x1024 colordisplay. A puck on 12x18 inchdigitizing tablet wasused as inputdevice.


Discretetargetselectiontask is studiedwherethetarget’swidthexpandsdynamicallyafterthestart of movement.

  • Participants had tomovecursor on a small start boxanddwelltherefor 1 second. Thenthey had tomovethecursor as quicklyandaccuratelypossible.

  • One-dimensionalmovement is necessary.

  • Timingbeganwhentargetwasappearedandendedwhentarget is successfullyselected.

  • User clicksdidn’thaveto be successful but recordedforfurtheranalysis.

Pilot study
Pilot Study

  • A pilot study is conductedtodetermineifthedirection of researchwaspromisingandalsoto test whichexperimentalconditionswouldhavesignificanteffects.

  • Staticandexpandingtargetsareused.

  • Spatialexpansion vs. fading-in expansion

  • Three differentvalues p of expansionpoints : 0.25, 0.50, 0.75

  • Resultsshowedthatthemovementtimesforexpandingconditionsweresignificantlysmallerthanstaticcondition. If p is 0.75 resultsare as good as others. Expansion strategydoesn’tmakedifference.

Full study
Full Study

Participants : Twelvevounteers(9 male, 3 female) between 20 and 35 years.


  • Two main conditions: staticandexpanding.

  • P = 0.9

  • Expansion duration : 100 ms

  • 4 targetwidths W = 0.5, 1, 2, and 4 units (1unit=16 pixels)

  • Thirteen A-W combinations : (8,0.5; 8,1; 16,0.5; 16,1; 16,2;

  • 32,0.5; 32,1; 32,2; 32,4; 64,0.5; 64,1; 64,2; 64,4 in units of 16 pixels) with fivelevels of task difficulty (ID), ranging from 3.17 to 7.01 bits.

  • 12 participants

    × 2 conditionsperparticipant

    × 5 blockspercondition

    × 13 A, W combinations per block

    × 5 trials per A, W combination

    = 7800 trials in total

Hypotheses :

  • H1) Theexpandingconditionwillresult in fastermovementtimesthanthestaticcondition.

  • H2) Performance in bothconditionscan be accountedforFitts’ law.

  • H3) Performance in theexpandingcondition is dependentlargely on thetarget’s final size not theinitialone.

  • H4) Performance in expandingcondition can be predictedbased on theFitts’ lawequationgenerated in thebasestaticcondition.


  • Theoverallmovementtimeswere 1.335 secondsforstaticconditionand 1.178 secondsfortheexpandingconditions. Theseresultsclearlyindicatethatexpandingtargets can result in improvedperformance, confirminghypotesis 1.

  • Given a, b constantsusedto fit the data in thestaticcondition, a lowerbound on movement time in theexpandingcondition can be estimated.

  • Theboundplotted in figureappearsto be closetothe data measuredfortheexpandingconditionwhich is a sign of supportforhypothesis H3 and H4.

  • Another set of t-test wasapplied. Inthis test, forstatictargets, forexpandingtargets is selected. Resultsforthispairsarecompared. Accordingtohypothesis, ifusersgainthefullbenefit of expandingtargets, it is expectedthatthetimesforexpandingtargetsto not be significantlyslowerthanthetimesforstatictargets. Tablesummarizestheresults.

  • Theseresultsindicatethat, for, theuserseemstohavebenefittedfullyfromtargetexpansion. Significantdifferencefor= 3.17 can be explainedbythefactthatlower ID valuestendtorequirefewercorrectivesubmovementsthuslessbenefit is expected.

  • Hypothesis 4 is not strictlyconfirmedbythe data. It is thusproposedthatthelowerbound as a usefulestimate of performancewithexpandingtargets.

Summary of findings
Summary of Findings

Resultsindicate that

1 -performance is significantly enhanced by expandingtargets even when expansion occurs after 90% of the distance towards thetarget has been traversed,

2 - the task of acquiring an isolated expanding targetcan be accurately modeled by Fitts’ law,

3 -for sufficiently high ID values,performance is approximately as good as, or better than, the best that couldbe expected, given our rationale for the lower bound on movement time. Thislast point means that users benefited fully from expansion for sufficiently highID, suggesting that the final expanded target size is much more important fordetermining performance than the initial target size.

Multiple expanding targets basic observations

  • It is usefultodistinguishbetween motor spaceandvisualspace.

  • Motor space is the set of allpssiblepositions of thepointingdeviceorthephysicalspacethattheuser’slimbmovesthrough.

  • Visual space is wherevisualfeedback is displayed.

  • In a systemwith a fixed C:D ratio, there is a fixedlinearmappingfromtheinputdevice’sposition in motor spacetothecursor in visualspace.

  • Thedistinctionbetween motor andvisualspace is importantif, forexample, targets in visualspacemoveorchange size in responsetocursormotionorifthecursorjumpsdiscontinuouslytonewpositions.

  • (A) has thedisadvantagethatthespacefreedup, which is betweenthebuttons, theusercannotclick on such data becausemovingthecursorover it causesthenearestwidgettoexpandandoccludethe data.

  • (B) has thedisadvantage of lackingexpansion in motor space, meaningthattargetsareprobablynoeasiertoselectthannonexpandingtargetswould be. Expansion mayhelpwithbrowsingandrecognition of buttons.

  • (C) has thecombinedadvantages of allowingfordensercontrolsthatarealsonohardertoselectwithoutthedisadvantages of (A) and (B)

Untiled expanding targets

  • Experimentalresultsindicatethatwithuntiledtargets, simplyexpandingwidgetsthatarenearthecuresorshouldsignificantlyfacilitateselection. No sophisticatedprediction is necessaryandbecauseexpansionneedonlyoccur in proximitytothecursor, theuser is lesslikelyto be distractedbymultipleexpandingtargets on screen.

  • Thespacingbetweenbuttonswouldallow data behindthewidgetto be visible. Becausethere is a staticmappingfrom motor spacetobuttons, thespacecoveredbytheexpandedwidgetscannot be usedtoclick on the mesh.

    An Example:

Tiled expanding targets without motor expansion
TiledExpandingTargetsWithout Motor Expansion

  • Inthissection, tiledexpandingtargetswhereexpansiondependsonly on thecurrentcursorposition. Althoughthispreventstrueexpansion in motor space, suchexpandingwidgetsstillhaveusefulapplications.

  • The main advantage of expansion is in providingenhancedvisualinformationor in showingmore data associatedwithtargets.

  • Forsimplicity, onlyone-dimensionalarraysorstrips of widgetsareconsidered. Inthese, targetsaretiledalongthehorizontaldimension, there is noreasonthattargetscannot be expanded in motor spaceverticallywhenapproachingaboveorbelow.

Macos x dock imitation
MacOS X DockImitation

  • Whenapproaching a targetfromside, theexpansionandcontraction of neighboringiconscreatessignificantsidewaysmotion. Shiftingtargetspositionawaymakesacquisition of targetmoredifficult.

Overlapping buttons

  • Toavoidexcessivesidewaysshifting of buttons, authorsdesigned a prototypethatallowslimitedoverlapbetweenneighboringbuttons.

  • First, thelayout is generatedsuchthatnobutton is occludedmorethan a givenpercentage, themaxocclusionfactorthat can be tunedtoadjustbehaviour.

  • Second, buttonsthatareoccludedarealwaysexpanded at leastenoughsothattheirvisiblearea is equaltotheiroriginalunoccludedarea. Thisensures a roughlowerbound on how difficulttheyaretosee at anygiven time.


Although the tiled expanding targets just considered arenot expanded in motor space (at least, not along the tiled dimension), the visualexpansion of targets can be used to display more data or more detailed previewsassociated with targets, while still allowing targetsto be efficiently packed into a small screen space when not in use. Furthermore,if targets are only tiled along one dimension, they can be expanded in motorspace along the other dimension to aid selection along that direction.Figures 9 and 10 illustrate two designs that are equivalent in terms of motorspace but that differ critically in the feedback given in visual space.

Considerations for visual feedback reveal a tension between allowing occlusionof neighbors, which can interfere with the visibility of a desired target, versusshifting of neighbors, which creates moving targets during sideways cursormotion. We feel the design in Figure 10 is a good hybrid in that it allows for anadjustable trade-off between these two effects and might be further improvedusingtransparency.

Tiled expanding targets with motor expansion
TiledExpandingTargetswith Motor Expansion

A model of expected benefit
A Model Of ExpectedBenefit


Thisapproachofferspotentiallygreatestadvantages but has not yet beendemonstratedto be workableand is not readyto be applied in realinterfacedesignwork. Accordingto a mathematical model which is set up in thispaperindicatesthat a nerreduction in selection time withtiledexpandingtargetsmay be possible. However, in practice, thebenefitmay be negligiblysmall.