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Area-Normalized Thematic Views ?: A h Kcahry

Grfiphics and Visualization Tram, CIC-8, MS 5287

keahey @lanl.gov Los Alamab Narional Labomrory; Loa Ahnos, 87545 USA

ABSTRACT This papcr presznrs a now1 [echniquc for dcaling wlth u clu- sic problem ~ a f frequently arises in VirudlzRTion Very cx-

pressive n o n b v mansfomawns can be auroomatically gcn- C Y ’ A ~ ~ ro correcr thcmalic maps so lhar the arc45 of map re- gions are proportional TO rhe rhcmbc variabks assgned tu

curring “visual lies” that Occurs in informtitton visualinman. rhcm. This helps to c1irnmare one of rhe mOST COTnmOnly Oc-

KEYWORDS: v~suxlizauo~~, rhernanc maps, nonlraccrrrnng- n;ficorinn, fbhcp views

Inrroducrlon Thematic vmbles are c u m o n l y used in cmcography to cn- code addraon&l informawn wmin the rpan~l layout ot J

map. Common examples of rhcrnatic variabkr we popula- Don &nsiq, pollunon level and buth rare. Such ‘-~hemes” arc normally encudcd through rhc usc of colof-maps. In this papcr wc will explore rcchniques for wing h i s Thematic m- formarion tu drrzcrly define spaual rransformtlao~is in ordrr to muke rhe vie* mote consistent wirh die rhemauc encad- ings. This idea was prcscnred in [IJ wrhin the conte%t of a foci-based mdgnlficarion s y w m , in &is papcr we will in- rrantwre *e idea murc fully through Ibz use ot u recenily dcvdopcd foci-less sysicm for magnifica~on. Thex area- normalrzcd views can give rrse 10 rather slgWfiCUiT distor- nons, potenuslly making it difficult for rhe vicwcr to recop- r u e familiar fcaiurrs such as stale oalines and orher land- marks. A key i.o rhc usefulness of rhcsc: v ~ e w i s rhc abilicy to srnoolhly inrerpolm bcrween thc rcpdar and normslired views of thc space, allowrng the viewer to lateractively rcd- PC rhe relauoruhip between rhc normal bmiliru view and rhe vlew which more uccur;rrcly rcflcczs [he rhematic conten1

Nmlinear Magnification Fields

Muny approaches hnvt k e n describcd in the Iiwraturc for stretching and distonng spaces ro produce effective visual- izmons. The rcm nonlinear magnificaiwn was inrroduccd in (31 tu dcscribe the eltfrctb corrunon to a11 of these ap- proaches-Thc bale properties of nonlinear mzrgnrficaaon are non-occluding:-plscc rnagnificauun which preserves B view

of rhe global contexK. Leung and Appc~ky [SI first Cstkitb-

li?jhcJ rhe marhrmtrricd relationship between 1D mgnitica- rion and rramformarion funciions for nonlinear rnngmfica- tion, This idca was earendedto higher dimensions in [+, 21, rc- sulrlng in chc non(8mur rnagr@cariu,tJdd A method i s dc- scnbed in [4] rhar computes swrable spatial uiulsformationr basccl on a s p e d c d scalar field of na4grlific3nrion vylues. The scalar mtrgnificarion ticld i s pyricdarly merable to us= end program manipularion, and provides a much m r c expressive c l ss of rrsrtsfunnatioos than IS possible wirh rrdmosal foci- bwvd approaches to nunlinepr magniliriluon such as 11.3).

Thematic Magnification The sddmonul expressivencss of nonlinear magnificarion ticlds is crucial to rhc merhods we prcscnl here; it IS now possible ro cretm Joru-driven m1gmfi~‘urm~s[4], where properwe of rhe d m iuc uwd to direcrly define rhe rnagrwlicanon best s u i c d fur vicwtig rhas &u This capsbiliry as a na1ural march io rhe color-cncoding of rhcrnanc variables in maps. We can easily delinu rouunes which p1ac.c a regular grid ovcr 4 raster imiigc of RCB vihci, md use the ramplea RCB values IO

derirc sur[sble magnificauon levels at each point in the grid, producing a magnificarion mesh #j described in 141. Corn- plex cffecrs can be whreved by encoding differenr infoma- [ion in clrch RCB channel; Ihz cxampks m rhis papcr use the R channcl JO define thc magnificarion vducs, and rhe G channel TO specify logical ”don‘t cure” values for rhsse areas ofthe map whac [he R values arc nor well detincd (e.g. in rhc bodies of water surrounding geogruphic regions)

Elrample 1: Interstate Speed Limits Thc 1ntcrsIate highway rysmn in rhc Unifed Stater COVZTS

errry stttce in rhe uniun, an4 each swc i s able IO definc tke maximum s p d lifflir on thurc: porrions of rhc intersrates that pass [krough ir, Thcrc i s considersblc variuiion in h c rpccd limm chosen. from 55 malcs pzr hour in sitries such u, Con- necticut co cffccrively no speed Iunir in Montma l . so that fur B driver planning to rravel acmss rhc USA, che umc rtquired for a particrrlir route will bG EI function of both rhe geographic distance involved and rhc speed limirs rhar 4 1 be entorccd enwutt . B y encodmg rhe speed Iimir inforniarion for cach swc UP u thernaric variable in a msp of chc USA. we can rhhan sample that map to obtain a sumble magnificauon fjeld. Here we define mignificarion as rhe ~nvcrsz of rhe s p 4 limir, so h a t srares wirh higher speed limrr will shrink w rcflca rhe

‘All rped luim wcrc obwned fro1113 rcc BUD unrlag F N , mh~ QU- h n u r tor Montan4 was rubmanly w lo la0 MPH. rnsrical

Apr-28-98 09:46am From-CIC-ACL

p . :- s?

mncrcusccj rale of ravel. Figure 1 S ~ L J W S thc Theuuric cncod- inp ot sp.pced limits by stare, along with a rrunsforrncd version of the m3p which d c c t s the rheniaric mapnificanun.

Figure 1: State Speed Limits and Normalized Driving View

Example I l r Presidential Election Resulfs Thc prcsidcntial elccuo~i is the Unireed Starer is dccidd by rhe number of electoral vufcs cnch candidare receives Each SIate has 3 given number ot clcctwd vures (based on The EWW popdurion), and all of the electoral votcs for tl single scaw must fx given murely to only one of the cmdrdaws. 11 is commsn prucncc un clccuon day for The news or&mi- zarions u) shoo a map ut rht USA, shading a staw in blue (or dx& gray) if they voted for rhc D c m o c ~ 4 0 ~ candidare, and red (or lighhr pray) if rhey rowd tor rhc Republican can- didate. This gives rise u) 3 classic problem in information visualizacion rhar uccurs when rhc urea used IO visually rep- resent each region is nor conrirtcnt wirh !.he acruaj thematic vanablc of imponanca [6]. Figure 2 shows a tradinonul view

of rhe presidrnual clccbun rcslrlrs from 1996. If this imagc were IO accurarely reflect r h ~ number of clcclornl votes each cttndidatc received we would expect rhe rarro of red (jighi) to bluc (dark) pcrels co be 0.42; wh31 we actually gcF how- ever is a ratio of 1 23, an cmor aS 193% which could leave h e viewer ro mistakenly infcr rhar chc Rcpubhcxn carididare {Dole) won The election insred ut rhc Dcmocratxc candidare (Clmron). The error occurs because large und sparscly pop- ulareu swes such as Alaska and Montunu visually domma~e thc imagc cvcn though they have very few elecrural votcs,

while states with a large number of clcctoral voIes such as New York, Texas and California we not rgprcrrenid with an area-emphasis pruporuonal lo their elecroral conrribunons

Figure 2: Tradibonal View of Eleation Resuirs and Eleclomi votes

To s4uce rturi ITO OF we can construct a map of rhc USA where shading b rucd to represent the number of electaral voces in each state, 3s shown in r h ~ right mugc of Figat 3. We cap theri compwe a magnificarlon based on that Chcmatic content 10 transform rhe normal vie* nf rhe elecuon into onc ihm rnorc accuraicly rcprtscnrs rhe acrual proportion of elec- tord v o m rcccivcd by each cmdid~t.e. The result is shown

5056654939 T-242 P . 0 4 h S F-673

in Figure 3, where [tie rat10 or red (hghr) to blue (dark) pixels is 0.69- Although rhij still represents in error af 64%, Ttus 13 less rhan 1/3 of rhe totd CI

und {he ratio of pixels now Clmron won rhe election.

OT found in the original image, wcuri-ilcly reflects the fact rhat

Figure 3: Normallzed Vie*$ of Elecrion Results and Electoral vows

Concluslons Aiea-normalized thcmauc vicws proviae a practicable merhod for reducing one of rhe m o a egregrous .s~asuul lies" encoun- WCJ in visudizauon, parricularly In rhe usc ufchcmauc maps. Because of rhc posstbilrry mar Y thematic map will rrprc- sent an inherently dcgmerarc bpecificdion having no ~ V W -

ble solurrons~4], rhrs method doas nor guarantee rransforma- ~JOUS giving perfect area in all cases Howcva, it i s possible LO weight rhe iterarive method in a manna =irndw to that us& in 141 w cnsurc that weas ofhightsr error will be corrccwd as much as is possible, rhus guaromtcemg that h e rransformed vicw will 81 lzasr be 311 improvement over thc original.

Acknowledgements I would J&c to [hank members of the Sofroarc PFUJUCUW Rcacrtrch Dcpparrmmr at Bell Labs for initial discussions un rh~s applicsuon of northmar magmfication.

REFERENCES I N d d l &idmOn and 611 S h b i . A POlYfOCd PruJcC-

Ran far swsucal surfaces. Tht- Currographrc JPW~IQI, Is( 1):3641, Junc 1978.

2. T. Alan Kzahey. Norrlrrrrur Magnijicarion PbI, he- m, Department of Compwr Scrence. lndiana Univer- siry, December 1997

3. T Alan Keshey and Edward L. Roberrson. Techelqws for non-linear magnificmrm uawiformacioss In Pro-

ireding3 of the IEEE SyrnposiI*rti DPI b2form;ioo Viscrul- izanon, IEEE Vwultz,ctclon, pages 3 8 4 5 , Ocroba 1996.

4 T. Alan Keahcy and Edwwd L. Robemon. Nonlinear magnifrcarion fields In Pmxe4tngs of rhr lE&E .S~mpu-

rrum ~ r i I&-murion Viwulrzuuw, IEEE Wrualreorwr , Ocrubcr 1997.

5. Y.K. Leung and M.D. Appcrky. A Ftvicw ana tax- onomy of rlisrorrion-oriented presenrarion techniques ACM Tranmcrtorrs ~n COmpcIrn-Hww hzi*ruciloti,

1(7).126160,1394.

6. E R. TI&. Thr b r r ~ l DiApluy of Quufilrrurive. Illforwia- lion. Graphic Prcss, 1983.