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I NDI CE Mes hpol i gonal e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Pol i edr i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Model l azi one3D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Mac c hi neCNC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Comput ergr af i c a3DRender i ng. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1516 3DS,Rhi no,VRay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171819 ZahaHadi d. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Fr ankGehr y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Nor manFos t er . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Makot oSeiWat anabe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Mas s i mi l i anoFuks as . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


MESHPOLI GONALE Unames hpol i gonal eèunac ol l ez i onediv er t i c i ,s pi gol ief ac c ec hedef i ni s c onol af or madiunogget t opol i edr i c onel l ac omput ergr af i c a3Denel l amodel l az i ones ol i da. Lef ac c ec ons i s t onos ol i t ament edit r i angol i ,quadr i l at er iodal t r is empl i c ipol i gonic onv es s i ,dalmoment o c hec i òs empl i f i c ai lr ender i ng,mapos s onoes s er ec ompos t ianc hedapol i gonic onc av ipi ùgener i c i ,opol i gonic onbuc hi . Lemes hs onopr i mi t i v egr af i c hec hec ons ent onodir i s ol v er ec ongr andeef f i c i enz aipr oc edi ment idiv i s ua l i z z az i onedel l ef or memodel l at e:s onos t r i s c edit r i angol io magl i ediquadr i l at er ic onc uir appr es ent i amounpol i edr o qual s i as ioc onc uiappr os s i mi amos uper f i c ic ur v e. L' uni t àbas ediunames hèi lv oxel ,ov v er opi xeldiv ol ume: nel l amodel l az i onegeomet r i c apers uddi v i s i ones paz i al es i s uddi v i dei lv ol umec hec ont i enel ' ogget t oc hes ides i der amodel l ar ei nunagr i gl i at r i di mens i onal edipos i z i oniei nognipos i z i ones idet er mi nal apr es enz aoas s enz adimat er i al e.

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POLI EDRI I nmat emat i c a,ei npar t i c ol ar ei ngeomet r i as ol i daei nt eor i adeigr af i ,unpol i edr oèuns ol i dodel i mi t at odaun numer of i ni t odif ac c epi anepol i gonal i .Comepr i mipol i edr idapr ender ei nc ons i der az i one,perl al or os empl i c i t à, v is onoic ubi ,ipar al l el epi pedi ,l epi r ami dieipr i s mi .Fr aipol i edr ipi ùc ompl es s ioc c upanounr uol oc ent r al ei c i nques ol i dipl at oni c i ,not if i ndal l ' ant i c aGr ec i a. I lt er mi nepol i edr oder i v adalgr ec oπολύε δρον( πολύς ,pol y s=" mol t i "eἔ δρον ,édr on=" f ac c i a" ) .Mol t iogget t imi c r os c opi c inat ur al i( mol ec ol e, pr ot oz oi ,v i r us ,et c . )hannof or meos i mmet r i epol i edr al i .Ic r i s t al l is ipos s onopr es ent ar ei nques t af or maanc heal i v el l omac r os c opi c o.

DEFI NI ZI ONE

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I nmat emat i c anones i s t eunadef i ni z i oneuni v oc adipol i edr o. Unadef i ni z i onemol t ogener al eèl as eguent e: Unpol i edr oèl ' uni onediunnumer of i ni t odipol i goninel l os paz i o,c hes ii nc ont r ano ac oppi es uil or ol at i . I nal t r epar ol e,ognil at odic i as c unodiques t ipol i gonic oi nc i dees at t ament ec oni l l at odiunal t r opol i gono.Neic as ipi ùs t udi at i ,ipol i gonif or manounas uper f i c i ec he del i mi t aunaz onas ol i dadel l os paz i o:i nques t oc as operpol i edr os ii nt endeques t o s ol i do,enons ol oipol i gonic henedel i mi t anol as uper f i c i e.


FACCE Ipol i gonis onol ef ac c edelpol i edr o.Lef ac c epos s onoav er el ef or mepi ùs v ar i at e:pos s onoes s er et ut t ec ongr uent ic omenel c ubo,av er es empr el os t es s onumer odil at is enz aper òes s er ec ongr uent ic omei nunpi ùgener i c opar al l el epi pedo,oppur eav er e numer odil at iv ar i abi l ec omei nunpr i s maounapi r ami de.

L’ Appl es t or es ul l a5t hAv enue L’ at omi um diBr uxel l es S CHELETRO

Ver t i c ies pi gol idiunpol i edr of or manoun gr af o,det t os c hel et r odelpol i edr o.Ades empi o,l os c hel et r odelt et r aedr oèungr af oc ompl et oc on4v er t i c i . Los c hel et r odiunpol i edr oc onv es s oèungr af o pl anar e:i nf at t ièpos s i bi l epr oi et t ar edaun punt oi nt er nodelpol i edr oi lgr af os uunaqual s i as i s f er ac ent r at anelpunt o,equi ndis uc c es s i v ament enelpi anot r ami t eunapr oi ez i one s t er eogr af i c a. I lgr af odiunpol i edr opi ùc ompl es s opuònon es s er epl anar e.

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OPERAZI ONICONIPOLI EDRI Al c uneoper az i oniper met t onodit r as f or mar eunpol i edr oi nunal t r o,odiaf f i anc ar epi ùpol i edr ii nmododar i c opr i r el o s paz i o. TAS S ELLAZI ONE Al c unipol i edr ipos s onoes s er eus at ic omemat t oniperr i empi r el os paz i os enz al as c i ar ebuc hi ,s i mi l ment eaquant oac c ade nel l ear ni e:unat al eoper az i oneèdet t at as s el l az i onedel l os paz i o( opav i ment az i onedel l os paz i o) .Ipol i edr ii nunat as s el l az i ones onoadi ac ent il ungol el or of ac c e.Fr ais ol i dipl at oni c i ,l ' uni c oi ngr adodit as s el l ar el os paz i oèi lc ubo;f r ais ol i diar c hi medei ,v is onoi l dodec aedr or ombi c oel ' ot t aedr ot r onc at o.Ot t aedr iet et r aedr ir egol ar ipos s onoes s er eus at iac oppi e pert as s el l ar el os paz i o. Ot t aedr it r onc at i Cubi

Ot t aedr i t et r aedr i

Dodec aedr ir ombi c i

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Las t r ut t ur aWeai r ePhel an


CUPOLEGEODETI CHE Unac upol ageodet i c aèuns ol i doc onmol t ef ac c e,l ac uif or maèmol t os i mi l eaquel l adiunas f er a( odiunapor z i onediques t a) . Comeneir adi ol ar imos t r at is opr a,nel l ec upol egeodet i c heès pes s of ac i l ev er i f i c ar egl ief f et t idel l ar el az i onediEul er o.

Di s ney Wor l d Mont r eal

Mus eoDal ìa Fi guer es

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MODELLAZI ONE3D

ConModel l azi one3Ds ii ndi c aunpr oc es s o at t oadef i ni r eunaqual s i as if or mat r i di mens i onal ei nunos pazi ovi r t ual egener at as u c omput er ;ques t iogget t i ,c hi amat imodel l i 3Dvengonor eal i zzat iut i l i zzandopar t i c ol ar i pr ogr ammis of t war e,c hi amat imodel l at or i 3D,opi ùi ngener al es of t war e3D.Ques t o t er mi nevi eneut i l i zzat oi nambi t oi nf or mat i c o,es idi s t i nguedaal t r it i pidimodel l azi onet r i di mens i onal e,c omeades empi ol as c ul t ur at r adi zi onal e.

CENNISTORI CI

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Las t or i adel l aComput ergr af i c a3Dènat ur al ment emol t or ec ent e,l os t es s ot er mi nedi gr af i c ac omput er i zzat anas c es ol onel1960. Unadel l epr i mer appr es ent azi onit r i di mens i onal is uc al c ol at or eès t at aquel l adelf amos o " pr i mouomo"o" Boei ngMan"r eal i zzat adaWi l l i am Fet t er ;uni ns i emedil i neec hedes c r i vevanol as agomavi r t ual ediunpi l ot adiaer eo. Apar t i r edal1959,l aGener alMot or s ,i nc ol l abor azi onec onl aI BM,s vi l uppai ls i s t ema " DAC" ,unodeipr i mis i s t emiCADdel l as t or i a;at t r aver s ounapennaot t i c aeunos c her mo s ens i bi l e,gl ioper at or idi s egnavanodel l ec ur vemat emat i c hei nunos pazi ovi r t ual e,c onl e qual idel i mi t avanoipr of i l i ,l es ezi oniel es uper f i c idel l eaut omobi l i . Del l apr i mamet àdegl ianni60'èanc hei li ls i s t emac hi amat o" Adage" ,c ons i der at ada mol t il apr i mawor ks t at i onCADi ndi pendent e. Daquant or i por t at os ievi nc ec hel anas c i t adel l amodel l azi one3Davvennei nambi t oi ndus t r i al e,pr i mar i ament ec omes uppor t oal l apr oget t azi one.Daal l or aic ampidiut i l i zzo del l amodel l azi one3Dedel l agr af i c at r i di mens i onal es is onoenor menent eampl i at i , us c endoi nbuonapar t edal l 'ambi t ot ec ni c o.


LAMODELLAZI ONENELAPRATI CAOPERATI VADALLAGRAFI CA3D

Lamodel l azi one3Dpuòanc hees s er ef i neas ès t es s a,ei nques t oc as oi lmodel l ogener at ononr i c hi edeul t er i or iel abor azi oni ,magener al ment el amodel l azi oner appr es ent ai lpr i mos t epdiunas er i edioper azi onis uc c es s i vec hedet er mi ner annol ' el abor at of i nal e. Ques t opr i mos t ep,nel l as pec i f i c aar eadel l aComput ergr af i c a3D,nonpuòmaimanc ar e,ener appr es ent ai lpr es uppos t odipar t enza.Sipr endaades empi ounc as opar t i c ol ar eabbas t anzac ompl es s o:ar eal i zzazi onediun' " i mmagi nes t at i c af ot or eal i s t i c adiunper s onaggi o3D" . Ques t ac ompor t ais eguent ipas s aggies s enzi al i : Model l azi one3Dpr i mar i a Model l azi one3Ds ec ondar i a Sur f ac i ng( def i ni zi onedeimat er i al idis uper f i c i e) Mappat ur a( def i ni zi onedel l ec oor di nat edipr oi ezi one) Appl i c azi onedel l eText ur e I ns er i ment odel l os c hel et r o Ski nni ngdelmodel l o Def i ni zi onedel l apos t ur adelmodel l o Al l es t i ment os c eni c o[ 6] I l l umi nazi onedel l as c ena Render i ngdel l as c ena Sal vat aggi odel l ' i mmagi nei nunf i l egr af i c o Out putf i nal e( ades .s t ampas uc ar t a) Ounc as or el at i vament epi ùs empl i c e:" Cor poi nal l umi ni odiunmul i nel l o,r eal i zzat oc onmac c hi naut ens i l e" . Model l azi one3Ddel l apar t ei nunmodel l at or eCAD As s embl aggi oever i f i c adel l apar t enelmodel l odiAs s i eme Es por t azi onedelmodel l o3Di nunf or mat omac c hi nac ompat i bi l e Lavor azi onec onmac c hi naut ens i l eCNCdel l ' ogget t o Pul i t ur a,r i f i ni t ur a Anodi zzazi oneel uc i dat ur adel l ' ogget t o As s embl aggi onelpr odot t of i nal e Comes inot al ar eal i zzazi onedelmodel l o3Dèpos t as empr eal l ' i ni zi odel l ac at enaoper at i va,edèl abas edel l es uc c es s i veoper azi oni .

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Lemac c hi neCNC( c omput ernumer i c alc ont r oli ni ngl es e) ,c hef i noagl ianniot t ant aer anous at es ol operl avor azi oniad al t apr ec i s i one,s onooggimol t odi f f us eei mpi egat ei nquas iognic ampodel l amec c ani c a.Lat ec nol ogi adel l emac c hi ne CNChac oper t ounpo't ut t iir amidel l amec c ani c a;l emac c hi neaCNCpi ùc omunis onopr es s epi egat r i c i ,punzonat r i c i , t or ni ,f r es at r i c iemac c hi nedit agl i ol ami er a( l as er ,os s i t agl i o,pl as ma,aget t od' ac qua,ec c . ) .Es s er appr es ent anol ' evol uzi onedel l emac c hi neNC,per c héper met t onoi lc ont r ol l onumer i c odi r et t odaunc omput eres t er no( DNC) .

CAPACI TA’DELLEMACCHI NECNC

Lamaggi orpar t edeic ent r idil avor oc ont r ol l at idac omput ers onodot at idimovi ment over t i c al edelmandr i noi ngr adodi r eal i zzar ei nc i s i oni ,s c ul t ur eel avor azi onidigr andi s s i mapr ec i s i one.Lavor azi onir eal i zzat es uques t emac c hi nepos s ono anc hear r i var eades s er ei ndi s t i ngui bi l iadunoc c hi onones per t i s s i mor i s pet t oaogget t id' ar t er eal i zzat iamano.Seut i l i zzat ec onf r es ec oni c heos f er i c hepos s onoar r i var eac r ear es uper f i c ias s ol ut ament el i s c e,dial t i s s i mapr ec i s i one,i nmodo r api do,aut omat i zzat oeadunc os t oes t r emament ec ont enut o.Lemi gl i or imac c hi neCNCar r i vanoaunapr ec i s i onediun dec i mi l l es i modimi l l i met r o( 100nanomet r i ) . Lemac c hi neCNCpi ùavanzat es onodot at edit es t at eor i ent abi l i( as s ii nc l i nabi l i )i ngr adodir uot ar egi r os c opi c ament e l ungodueas s i( nor mal ment ec hi amat iA,B,CoQ) .Ques t oc ons ent edii nc l i nar el ' ut ens i l er i s pet t oat ut t iipi anidil avor o r endendopos s i bi l er eal i zzar ef i gur emol t oc ompl es s eanc het i poor gani c oedi f f i c i l ment eot t eni bi l iper s i noc onunal avor azi onemanual e,c omeades empi ounac avi t àc onuns i ngol of or omol t os t r et t omas uf f i c i ent eperf arpas s ar el af r es a.Le t es t ei nc l i nabi l iper met t onoanc hediot t i mi zzar el al avor azi onec ons ent endodil avor ar ec onl ' ut ens i l ei nc l i nat or i s pet t oal pi anod' avanzament o,evi t andodiut i l i zzar el apar t edel l ' ut ens i l eavel oc i t àzer o( c ent r odir ot azi onedel l af r es a) .Coni c ont r ol l inumer i c ipi ùr ec ent is ii ni zi anoadi mpl ement ar ef unzi onidil avor azi oneavanzat adel l es uper f i c i ,per met t endodi l avor ar es uper f i c i3DNURBSi nmodonat i vo,s enzabi s ognodipr ogr ammiCAM i nt er medi .Los f r ut t ament oot t i mal edel l e c ar at t er i s t i c hediques t emac c hi nepuòavveni r eat t r aver s oappos i t iac c es s or iperc opi at ur aes t ampioppur evi ac omput er ,at t r aver s ounac at enadipr ogr ammi :pr i mas ic r eac oni lCADunogget t o,c hepoivi enepas s at oalCAM c hes ii nc ar i c a dic r ear ei lpr ogr ammaperl ar eal i zzazi ones uunadat amac c hi na,ei nf i nei lpr ogr ammavi enees egui t odal l amac c hi na c r eandol ' ogget t omat er i al e. Pr at i c ament et ut t el emac c hi neCNCmoder nes ono" ac i r c ui t oc hi us o"( ac at enac hi us aor et r oazi onat o) :ognias s eèdot at o dienc oder( enc oderr ot at i vioppur er i gheot t i c he)c heper met t onoalc ont r ol l odic onos c er ei nognii s t ant el apos i zi one del l at es t adil avor azi oner i s pet t oalpezzo.L' us odir i gheot t i c heper met t ei lr ec uper oc ompl et odeigi oc hidel l at r as mi s s i onemi s ur andodi r et t ament eenonat t r aver s oic i nemat i s mil apos i zi onedel l ' as s eequi ndiunamaggi or epr ec i s i onedi l avor o.

ASSI

Car at t er i s t i c apr i nc i pal ediques t emac c hi neèi lnumer odigr adidil i ber t àdi s poni bi l i ,det t ias s idel l amac c hi na.Perl e f r es es onogener al ment e3,4o5,perit or nis ivada2a4,l epunzonat r i c iel emac c hi nepert agl i ohannogener al ment e2 o3,ment r el epannel l at r i c i( FI NNPOWER,Sal vagni ni . . . )ar r i vanoa24as s i .Lepi egat r i c ipos s onoaver ef i noa11as s ie s onol emac c hi ne" s i ngol e"pi ùc ompl es s e;l emac c hi nes pec i al ic ombi nat eeigr andipor t al idil avor azi onepos s onoar r i var e adaver eanc hedec i nedigr adidil i ber t àoas s idi ver s i .It i pipi ùc omunis ono 2as s i :movi ment os ol os uXeY.Pezzil i mi t at ial avor azi onipi anes enzavar i azi onidipr of ondi t à. 2. 5as s i( dueas s iemezzo) :s it r at t adimac c hi nei ngr adodioper ar es ut ut t iet r egl ias s i ,mas ol t ant oapas s idi s c r et is u unodies s i( gener al ment el ' as s eZ) ,c i oèges t i s c onol ' i nt er pol azi ones ol t ant os udueas s i .Sonooggii lt i popi ùec onomi c o. 4e5as s i :ol t r ealmovi ment os uit r eas s iX, YeZs iaggi ungel ' i nc l i nazi one( edevent ual ment el ar ot azi one)delmandr i noo diunat avol ar ot obas c ul ant es ol i dal ealpi anomac c hi na.Ques t emac c hi nepos s onor eal i zzar e pr at i c ament equal s i as it i podis agomapur c hél af or madel l ec onc avi t ànonvadai ni nt er f er enzac oni lmandr i no.Ques t emac c hi nes onomol t oc os t os e,evengonous at eanc heperl avor azi onis upezzidigr andi s s i medi mens i oni( t ur bi ne,el i c henaval i ,s c oc c hepermot or i ,s t ampi . . . )

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COMPUTERNUMERI CALCONTROL


TI POLOGI EDIMODELLAZI ONE

Daunpunt odivi s t at i pol ogi c o,t ut t al amodel l azi one3D,r i ent r ai nduegr andif ami gl i e,ognunar i guar dant eunbendet er mi nat o gener edimodel l i : LAMODELLAZI ONEORGANI CA-èl at i pi c amodel l azi oneut i l i zzat aperr eal i zzar egl ies s er iumaniol ec r eat ur e,ani mal ioumanoi di . Vi eneus at apert ut t iis ogget t i" nat ur al i " ,c omer oc c e,pi ant e,al ber ieperi lt er r i t or i oi ngener al e,i nques t ic as iimodel l is onot ant o pi ùr i us c i t iquant opi ùs onor i c c hidipar t i c ol ar i .Anc hemol t iogget t idii ndus t r i aldes i gn,c heabbi anof or memor bi deear r ot ondat e, pos s onos er vi r s idiunamodel l azi oneor gani c a. LAMODELLAZI ONEGEOMETRI CA-èi lt i podimodel l azi onemenor ec ent e,vi eneut i l i zzat aperr eal i zzar eogget t it ec ni c iomec c ani c i , oc omunqueperqual s i as ic os ac heabbi aunanat ur aar t i f i c i al e,ec henonr i ent r inel l ac at egor i apr ec edent e.Gener al ment el ac ompl es s i t àdeimodel l ir eal i zzat ic onques t ogener edimodel l azi oneèmol t oi nf er i or e,s es iguar daal l ' as pet t oes t er i or edel l es i ngol e f or me,manons es ic ons i der anoas pet t il egat ial l apr ec i s i oneeal l ac or r i s pondenzadel l epar t i .

TECNI CHEDIMODELLAZI ONE3D

Sipos s onodi vi der ei nt r ec at egor i epr i nc i pal i : 1. Model l azi onePr oc edur al e( aut omat i c aes emi aut omat i c a) 2. Model l azi oneManual e 3. Dadat ipr oveni ent idamodel l ir eal i( s c ans i onet r i di mens i onal e) Cheal or ovol t apos s onoveni r es uddi vi s ei nt r edi s t i nt igener idimodel l azi one: Model l azi oneSol i da-dovel ' ogget t or i s ul t ant eèc ons i der at oc omef or mat odaunvol umepi eno. Model l azi oneVol umet r i c a-det er mi nadel l eent i t àgener ant iunas uper f i c i ei mpl i c i t a. Model l azi onedis uper f i c i-l ' ogget t oi nques t oc as oèdet er mi nat odal l es ues uper f i c ies t er ne. I nal c unimodel l at or iunogget t oèc ons i der at of omat odas uper f i c if i nc héques t es onoaper t e,ment r evi ener i c onos c i ut oc omes ol i do unavol t ac het ut t el es uper f i c is i anos al dat ef r adil or oef or mi nounc or poc hi us o. I ls eguent eel enc oes ami nal edi ver s et ec ni c hediModel l azi oneManual e.Al c unedel l et ec ni c hedes c r i t t e( c omeades .l es uper f i c i pat c h) ,es s endoabbas t anzadat at e,r i s ul t anoes s er es uper at eeobs ol et er i s pet t oat ec ni c hepi ùr ec ent ieavanzat e.Mal gr adoques t o t al uniModel l at or i3D,mant engonoall or oi nt er noal c unidiques t is t r ument ic omeac c es s or iout i l i t à.

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TECNI CHEDIMODELLAZI ONE3D

Sipos s onodi vi der ei nt r ec at egor i epr i nc i pal i : 1.Model l azi onePr oc edur al e( aut omat i c aes emi aut omat i c a) 2.Model l azi oneManual e 3.Dadat ipr oveni ent idamodel l ir eal i( s c ans i onet r i di mens i onal e) Cheal or ovol t apos s onoveni r es uddi vi s ei nt r edi s t i nt igener idimodel l azi one: Model l azi oneSol i da-dovel ' ogget t or i s ul t ant eèc ons i der at oc omef or mat odaunvol umepi eno. Model l azi oneVol umet r i c a-det er mi nadel l eent i t àgener ant iunas uper f i c i ei mpl i c i t a. Model l azi onedis uper f i c i-l ' ogget t oi nques t oc as oèdet er mi nat odal l es ues uper f i c ies t er ne. I nal c unimodel l at or iunogget t oèc ons i der at of omat odas uper f i c if i nc héques t es onoaper t e,ment r evi ener i c onos c i ut oc omes ol i dounavol t ac het ut t el es uper f i c i s i anos al dat ef r adil or oef or mi nounc or poc hi us o. I ls eguent eel enc oes ami nal edi ver s et ec ni c hediModel l azi oneManual e.Al c unedel l et ec ni c hedes c r i t t e( c omeades .l es uper f i c ipat c h) ,es s endoabbas t anzadat at e, r i s ul t anoes s er es uper at eeobs ol et er i s pet t oat ec ni c hepi ùr ec ent ieavanzat e.Mal gr adoques t ot al uniModel l at or i3D,mant engonoall or oi nt er noal c unidiques t i s t r ument ic omeac c es s or iout i l i t à. COSTRUZI ONIDIBASE( s ol i dies uper f i c i ) Pr i mi t i ve-Gener al ment eognipac c het t o3Dc henons ioc c upis ol odir ender i ng,c ont i eneals uoi nt er nouns etpi ùomenonut r i t odipr i mi t i ve,os s i adiogget t ipr edef i ni t i( s ol i dios uper f i c i ) ,di r et t ament ei mpi egabi l i ;dis ol i t ol epr i mi t i ves t andar d,c i oès empr epr es ent i ,s ono:i lpi ano,i lCubo/ Par al l el epi pedo,l aSf er a,i lCi l i ndr o,i lCono/ Pi r ami de,i lTor o,es pes s ol aTei er a. c os t r uzi oneperes t r us i one c os t r uzi oneperr i vol uzi one SUPERFI CIPATCH Lamodel l azi oneperpat c hèunodeis i s t emimenor ec ent iut i l i zzat ii ngr af i c a3D,enelc or s odelt empos ièmol t oevol ut as vi l uppandounas er i edinuovet ec ni c he. Nel l as uaf or mapi ùs empl i c edet er mi nadel l es uper f i c ipar amet r i c hegener at edaquat t r oopi ùc ur veadi ac ent ic hef or mi nounper i met r oc hi us o. Super f i c i ediCoons-det er mi naunapat c hi nt er pol at at r as ol oquat t r oc ur vedibor do,avent iiver t i c ii nc omune,i lpr i moal gor i t modiques t ac l as s edis uper f i c if u s vi l uppat adaSt evenA.Coonsnel 1967. [ 10] Pat c hdiBézi er-èunas uper f i c i epar amet r i c ac ont r ol l abi l el oc al ment emedi ant eunagr i gl i adipunt idic ont r ol l o,c ongi ungendoas s i emepi ùpat c hdiBézi ers iot t engonos uper f i c ipi ùc ompl es s ec hi amat es uper f i c is pl i ne[ 11] ,i nques t oc as oipunt idic ont r ol l os it r ovanoal l 'i nt er s ezi onet r al evar i epat c h. Model l azi oneSpl i ne( s uper f i c i )[ modi f i c a] Lamodel l azi ones pl i neut i l i zzal at ec ni c adelpat c hi ng,pr ec edent ement edes c r i t t a,el ec ur ves pl i ne.Fondament al ment eunmodel l or eal i zzat omedi ant eques t os i s t emaèf or mat odaunagabbi adic ur ves pl i ne,i nt er s ec ant iec ol l egat et r al or o.Gl is pazic ompr es it r at r eoquat t r oc ur ves pl i neuni t eneil or opunt idic ont r ol l o, vengonopoir i empi t idapat c h. [ 12]Tal es i s t emas ipr es t as opr at t ut t oar eal i zzar emodel l ior gani c i . MODELLAZI ONEPERSPLI NEPATCHI NG COSTRUZI ONIAVANZATE( s ol i dies uper f i c i ) Lec os t r uzi oniavanzat eut i l i zzanol os t es s oc onc et t oal l abas edel l ' es t r us i oneedel l ar i vol uzi ones empl i c e,maviaggi ungonodeic ont r ol l imol t opi ùs of i s t i c at i . Es t r us i oneSweep Cos t r uzi oneperLof t Ri vol uzi ones ubi nar i o

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MODELLAZI ONEPOLI GONALE Sit r at t adit ec ni c hebas i l ar inel l ' ambi t odel l agr af i c a3D. Lamodel l azi onepol i gonal eoper as us uper f i c ior gani zzat ei nmagl i epi ùomenodet t agl i at edif ac c epol i gonal i .Ques t es uper f i c ipos s onos ol oappr os s i mar el 'ogget t o f i nal es es i amoi npr es enzadiunbas s ol i vel l odipol i goni( i nques t oc as oc as ol 'ogget t ovi enedet t oLow Pol y) .I nal t r ic as iunmodel l opol i gonal e-amodel l azi oneul t i mat a-puòes s er ef or mat oanc hedaunnumer omol t oel evat odif ac c e. Is eguent is i s t emipr oc edonodaipi ùel ement ar iaipi ùevol ut i : Pers pos t ament odiel ement i-unmodel l opol i gonal eèf or mat oda3el ement ies s enzi al i :f ac c e,l at iever t i c i ;l os pos t ament oar bi t r ar i odiuns i ngol oel ement oodi gr uppidies s i ,det er mi naunamodi f i c adel l ames hdipar t enza.Las el ezi onediunc omponent edel l ames hei ls uos pos t ament o( t r as c i nament o,r ot azi one,r i di mens i onament oet c . ) ,nel l os pazi oèl at ec ni c api ùel ement ar edimodel l azi onepol i gonal e. Dapr i mi t i vedibas e-Unodeis i s t emipi ùs empl i c iedi r et t iperi ni zi ar eamodel l ar eunogget t opol i gonal e,èquel l odipar t i r edaunapr i mi t i vapol i gonal edibas e,e i ni zi ar eamodi f i c ar l as pos t ando,r uot ando,s c al andois uoic omponent i ,f i noaot t ener el af or mavol ut a.Ques t at ec ni c aèmol t os empl i c e,mac ons ent ei ngener edi ot t ener emodel l ipoc oc ompl es s i ,vi nc ol at ic i oèal l ac ompl es s i t à( anc hei nt er mi nididens i t àpol i gonal edel l ames h)del l apr i mi t i vadipar t enza.

Met ododel l ames hpi ana-ol t r eamodi f i c ar eipol i gonidimes hes i s t ent i( ades .del l epr i mi t i ve) ,es i s t el apos s i bi l i t àdic r ear es i ngol ar ment eognipol i gonodel l 'ogget t oedic os t r ui r eipol i goninel l apos i zi onepi ùc omodaperr eal i zzar ei lmodel l of i nal e.Unodeis i s t emididi s egnodi r et t odeipol i gonivi enedet t oMet ododel l a mes hpi ana.Sit r at t ai ns os t anzadic r ear eunagr i gl i adipol i gonipos i zi onat ii npi anoeavent il as t r ut t ur ai lpr of i l oel ac onf or mazi onegener al edel l 'ogget t of i nal e. Pos i zi onat iipol i gonis ulpi ano,s ipas s aadet er mi nar nel at r i di mens i onal i t à:os pos t andoipunt idel l agr i gl i al ungol apr of ondi t àdelmodel l o,oat t r aver s odeis i s t emidies t r us i one.

Met odoat el adir agno-Sit r at t adiunavar i ant edel l apr ec edent et ec ni c a.I nques t oc as onons ic os t ui s c onoepos i zi onanot ut t iipol i gonidibas edelmodel l o,mas i par t edaunas uazona( c ent r al e) ,es ii ni zi anoac r ear eemodel l ar eis i ngol ipol i gonic onuns i s t emaappunt oa" t el adir agno" ,c i oèdal l 'i nt er noepr oc edendomanmanover s ol ezonees t er nedelmodel l o.Èuns i s t emac ompl es s oedi s pendi os oi nt er mi nidit empo,ut i l i zzat os opr at t ut t operi ls uoal t ogr adodipr ec i s i one. PerRi f i ni t ur aPr ogr es s i va-èi ls i s t emapi ùevol ut o,puòc ons i der ar s iunodeipar adi gmidel l aModel l azi one3D.Adot t andounqual s i as imet odoanal i zzat opr ec edent ement es ii ni zi aadef i ni r el af or mai nunamani er amol t os c hemat i c a,per l opi ùappr os s i mandonel amor f ol ogi aef ac endoat t enzi oneat ener ees t r emament ebas s oi l numer oi ni zi al edipol i goni .Dovendoges t i r epoc hipol i gonièpos s i bi l emodi f i c ar emol t oagevol ment el epr opor zi oniei lvol umegener al edel l af or ma.Sol oquandos i ès oddi s f at t idel l 'as pet t ogr ezzodelmodel l os ipuòi ni zi ar e-adot t andogl is pec i f i c is t r ument idiognipac c het t os of t war e-adef i ni r emaggi or ment el af or ma.Èi mpor t ant ec heaognipas s aggi odir i f i ni t ur as ipas s iadef i ni r epr i maivol umimaggi or idelmodel l o,perandar epoiadef i ni r el ezones empr epi ùpi c c ol e,l adef i ni zi one ei lnumer odidet t agl iappor t abi l ièadi s c r ezi onedelgr af i c o3D.I lpr i nc i pi of ondament al edat ener eament eèc he:t ant omi nor eèi lnumer odipol i gonipr es ent inel model l o,t ant omaggi or eèl apos s i bi l i t àdimodi f i c ar nel amor f ol ogi agener al e-t ant omaggi or eèi lnumer odipol i gonit ant omenos ipot r àmodi f i c ar el af or magi à i mpos t at ai npr ec edenza.I npr at i c aognipas s aggi oèi r r ever s i bi l e,t ant opi ùs idef i ni s c onoipar t i c ol ar idel l 'ogget t o,t ant omenos ipot r àmodi f i c ar e( oc or r egger e) i ls uoas pet t ogener al e. [ 18]Aques t opr obl emas ipuòpor r er i medi os al vandoi lmodel l oi nmani er apr ogr es s i va,i nmododaaver eadi s pos i zi onet ut t iipas s aggii nt er medidimodel l azi one,i nc as odier r or es ipuòr i par t i r edalmodel l opr ec edent eami nor edet t agl i o,s ei ls of t war eut i l i zzat of aus odeil ayer ,èpos s i bi l ec ons er var el evar i ever s i onii nl ayers epar at i . PerDi s pl ac ementmap PerSc ul t ur a3D

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SUPERFI CINURBS Lat ec nol ogi aNURBSf ui nt r odot t adal l aBoei ngnel1975,ac r oni modinonuni f or mr at i onalBs pl i ne( BSpl i ner azi onal inonuni f or mi ) , vi eneut i l i zzat ai ngr af i c a3Dperr eal i zzar eunavas t at i pol ogi adimodel l i ;èpar t i c ol ar ment eadat t aar appr es ent ar es uper f i c ior gani c he,ades empi odic r eat ur eeper s onaggi ,eogget t idides i gnc her i c hi edanos uper f i c ic ompl es s eepr ec i s ec omel eaut omobi l i .Les uper f i c iNURBSs onos uper f i c imat emat i c heper f et t ament es mus s at e,nonc ar at t er i zzat edal l at i pi c as f ac c et t at ur adel l es uper f i c ipol i gonal i , s onof ac i l ment emodi f i c abi l iec ont r ol l abi l iat t r aver s opoc hipunt idic ont r ol l o,c hi amat iCV( Cont r olVer t i c es ) . Unas uper f i c i eNURBSpuòes s er egener at aodal l es t es s ec ur veNURBS,at t r aver s ooper azi onidies t r us i one,r i vol uzi one,l of t i ng,pat c hi ng eal t r e,oppur edapr i mi t i vedit i poNURBSc omes f er e,c i l i ndr i ,t or iet c .Les uc c es s i vemodi f i c hediunmodel l oNURBS,di pendonomol t o dagl is t r ument imes s iadi s pos i zi onedalSof t war e3D,mai ngener es ipas s aaedi t ar eipunt idel l as uper f i c i e,oiver t i c iCV,doveènec es s ar i os ipos s onoaggi unger eor i muover ec ur venel l edi r ezi oniUeV,c omes ipos s onoaggi unger eer i muover eiver t i c idic ont r ol l onel l e c ur ve.

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COMPUTERGRAFI CA3D

MODELLI3D

Lac omput ergr af i c a3Dèunr amodel l a gr af i c ac omput er i zzat ac hes ibas a s ul l ' el abor azi onedimodel l ivi r t ual ii n3D dapar t ediunc omput er .Es s avi eneut i l i zzat ai ns i emeal l aani mazi onealc omput ernel l ar eal i zzazi onedii mmagi nivi s ual iperc i nemaot el evi s i one,vi deogi o c hi ,i ngegner i a,us ic ommer c i al ios c i ent i f i c i .I lt er mi nepuòanc hees s er er i f er i t o adi mmagi nipr odot t ec onl os t es s o met odo.

Ogget t it r i di mens i onal is empl i c ipos s onoes s er er appr es ent at ic on equazi onioper ant is uuns i s t emadir i f er i ment oc ar t es i anot r i di mens i onal e:peres empi o,l ' equazi onex² +y² +z² =r ²èper f et t aperuna s f er adir aggi or .Anc hes eequazi onic os ìs empl i c ipos s onos embr ar e l i mi t at i ve,l ' i ns i emedegl iogget t ir eal i zzabi l ivi eneampl i at oc onuna t ec ni c ac hi amat ageomet r i as ol i dac os t r ut t i va( CSG,c ons t r uc t i ve s ol i dgeomet r y) ,l aqual ec ombi naogget t is ol i di( c omec ubi ,s f er e,c i l i ndr i ,ec c . )perf or mar eogget t ipi ùc ompl es s iat t r aver s ol eoper azi onibool eane( uni one,s ot t r azi oneei nt er s ezi one) :unt ubopuòad es empi oes s er er appr es ent at oc omel adi f f er enzat r aduec i l i ndr i avent idi amet r odi f f er ent e. Anc heques t at ec ni c anonr i s ul t aper òs uf f i c i ent eades c r i ver ec on equazi onis empl i c iunagr anquant i t àdiogget t i ,perc uinonèdiut i l i zzoc omune.Permodel l ar es uper f i c ic ur vei nmodoar bi t r ar i os i pos s onous ar el epat c h,ovver ol ' es t ens i onedel l es pl i ne,c heappr os s i manoc ur vec ont i nue,al l et r edi mens i oni .Lepat c hpi ùc omunement eus at es onoi npr at i c abas at es us pl i neNURBS. L' i mpi egodiequazi onimat emat i c hepur ec omeques t er i c hi edel ' ut i l i zzodiunagr anquant i t àdipot enzadic al c ol o,enons onoqui ndi pr at i c heperl eappl i c azi onii nt empor eal ec omevi deogi oc hies i mul azi oni .Unat ec ni c api ùef f i c i ent e,mac heper met t eunmi nor el i vel l odidet t agl i o,permodel l ar eogget t ic ons i s t enelr i l evar es ol o al c unipunt idel l ' ogget t o,s enzai nf or mazi onis ul l ac ur vac ompr es a t r adies s i .I lr i s ul t at oèc hi amat omodel l opol i gonal e.Ques t opr e s ent a" f ac c et t e"pi ut t os t oc hec ur ve,mas onos t at es vi l uppat et ec ni Lagr af i c ac omput er i zzat at r i di mens i onal eèbas i l ar ment el a c hedir ender i ngperovvi ar eaques t aper di t adidat i . s c i enza,l os t udi oei lmet ododipr oi ezi onedel l ar appr es ent azi o- Del l es uper f i c ipol i gonal idiunmodel l os enzai nf or mazi onis ul l ac ur nemat emat i c adiogget t it r i di mens i onal it r ami t eun' i mmagi ne vat ur apos s onoes s er ec omunquer af f i nat epervi aal gor i t mi c ai ns ubi di mens i onal eat t r aver s ol ' us odit ec ni c hec omel apr os pet t i vae per f i c iper f et t ament ec ur ve:ques t at ec ni c aèc hi amat a" s uper f i c idi l ' ombr eggi at ur a( s hadi ng)pers i mul ar el aper c ezi onediques t i s uddi vi s i one" ,per c hél as uper f i c i evi enes uddi vi s ac onunpr oc es s o ogget t idapar t edel l ' oc c hi oumano.Ognis i s t ema3Ddevef or ni r e i t er at i voi npi ùs uper f i c i ,s empr epi ùpi c c ol e,f edel ial l ac ur vai nt er dueel ement i :unmet ododides c r i zi onedels i s t ema3Ds t es s o pol at aec hevannoac ompor r eun' uni c as uper f i c i es empr epi ùl i s c i a. ( " s c ena" ) ,c ompos t odir appr es ent azi onimat emat i c hediogget t i t r i di mens i onal i ,det t i" model l i " ,eunmec c ani s modipr oduzi one diun' i mmagi ne2Ddal l as c ena,det t o" r ender er " .

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CREAZI ONEDELLASCENA Unas c enas ic omponedi" pr i mi t i ve"( model l it r i di mens i onal ic henonpos s onoes s er eul t er i or ment es c ompos t i ) ;i lmodopi ùs empl i c eper or gani zzar l aèquel l odic r ear eunar r aydipr i mi t i ve,maques t omet odononper met t eunades c r i zi onepi ùdet t agl i at adel l as c ena,s empl i c ement e" s pi ega"alr ender erc omedi s egnar el as t es s a.Unat ec ni c api ùavanzat aor gani zzagl iogget t ii nunas t r ut t ur adat iad al ber o( s c enegr aph) ,c heper met t edir aggr uppar el ogi c ament egl iogget t i( ades empi o,s ipuòqui ndir epl i c ar epi ùvol t eunogget t o, avendol omodel l at oat t r aver s opi ùpat c hNURBSr aggr uppat e,al l ' i nt er nodel l as t es s as c ena) . Lepr i mi t i ves onogener al ment edes c r i t t eal l ' i nt er nodelpr opr i os i s t emadir i f er i ment ol oc al e,evengonopos i zi onat es ul l as c enaat t r aver s ooppor t unet r as f or mazi oni .Let r as f or mazi oniaf f i nipi ùi mpi egat e,c omeomot et i a,r ot azi oneet r as l azi one,pos s onoes s er edes c r i t t ei nunos pazi opr oi et t i voc onunamat r i c e4x4:es s es iappl i c anomol t i pl i c andol amat r i c eperi lvet t or eaquat t r oc omponent ic he r appr es ent aognipunt odic ont r ol l odel l ec ur va.Laquar t adi mens i oneèdenomi nat ac oor di nat aomogenea. Adogninododel l os c enegr aphèas s oc i at aunat r as f or mazi one,c hes iappl i c aanc headogninodos ot t opos t o,r i c r eandol ' i nt er azi one f i s i c at r aogget t ir aggr uppat i( c omequel l at r aunuomoei ls uoves t i t o) .Anc hei ns i s t emidimodel l azi oneer ender i ngc henonf annous o dis c enegr aphèc omunquegener al ment epr es ent ei lc onc et t odit r as f or mazi oneappl i c at a" i nver t i c al e" .

RENDERI NG I lr ender i ngèi lpr oc es s odipr oduzi onedel l ' i mmagi nef i nal eapar t i r edalmodel l omat emat i c odels ogget t o( s c ena) .Es i s t onomol t ial gor i t midir ender i ng,mat ut t ii mpl i c anol apr oi ezi onedeimodel l i3Ds uunas uper f i c i e2D. Gl ial gor i t midir ender i ngs idi vi donoi nduec at egor i e:s c anl i ner ender er ser ayt r ac er s .Ipr i mioper anoogget t operogget t o,di s egnandodi r et t ament es us c her moognipol i gonoomi c r opol i gono;es s ir i c hi edonoqui ndic het ut t igl iogget t i( anc hequel l imodel l at ic onc ur ve c ont i nue)s i anos t at is f ac c et t at ii npol i goni .Is ec ondioper anopi xelperpi xel ,t r ac c i andounr aggi ovi s ual ei mmagi nar i odalpunt odi vi s t aal l ' i nt er nodel l as c ena,edet er mi nandoi lc ol or edelpi xeldal l ei nt er s ezi onic ongl iogget t i . Unadel l ef unzi onipr i nc i pal idiunr ender erèl adet er mi nazi onedel l as uper f i c i enas c os t a.I lr ayt r ac i ngs vol gei mpl i c i t ament eques t a f unzi one,det er mi nandoi lc ol or ediunpi xeli nbas eal l ' i nt er s ezi onedelr aggi ovi s ual ec olpr i moogget t o,maperl ' al t r ot i podial gor i t mis er vonot ec ni c hepi ùavanzat eperdet er mi nar equal epol i gonos i ai lpi ùvi c i noalpunt odivi s t a.I lmet odopi ùs empl i c eèquel l odi di s egnar eipol i goniapar t i r edaquel l ipi ùl ont ani ,i nmodoc hequel l ipi ùvi c i nil is ovr as c r i vano;maques t at ec ni c a,det t apai nt er ' sal gor i t hm," al gor i t modelpi t t or e" ,s ir i vel ai nef f i c ac ec onpol i gonis ovr appos t i .Perr i s ol ver eques t opr obl emaf us vi l uppat ol ozbuf f e r i ng,c hei mpi egaunbuf f erperc ons er var el ac oor di nat azr el at i vaadognipi xelel abor at o:s el apr of ondi t àdelpol i gonoc hes t aper es s er eel abor at operi lpi xelèmi nor ediquel l oi nmemor i a,i lpi xelvi ener i s c r i t t o;al t r i ment il ' al gor i t mopas s aalpi xels uc c es s i vo. Un' i mmagi neper f et t ament eni t i da,c onpr of ondi t àdic ampoi nf i ni t anonèaf f at t of ot or eal i s t i c a.L' oc c hi oumanoèabi t uat oal l ei mper f ezi onic omei ll ensf l ar e( i lr i f l es s os ul l al ent e) ,l al i mi t at ezzadel l apr of ondi t àdic ampoei lmot i onbl ur( " ef f et t omovi ment o" )pr es ent inel l ef ot ogr af i eeneif i l m.

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RHI NOCEROS Rhi noc er os ,c omunement ec hi amat oRhi no,èuns of t war eappl i c at i voperl amodel l azi onedis uper f i c is c ul t ur at e( f r eef or m)r eal i zzat o daRober tMc Neel&As s oc i at es ,un' azi endadiSeat t l enel l os t at odiWas hi ngt on,negl iUSA. I nRhi no,t ut t el eent i t àgeomet r i c hes onor appr es ent at emedi ant eNURBS( ac r oni modiNonUni f or m Rat i onalBSpl i nes ) .Mol t os empl i c ement e,l eNURBSs onounar appr es ent azi onemat emat i c amedi ant el aqual eèpos s i bi l edef i ni r eac c ur at ament egeomet r i e2De3Dqual i l i nee,ar c hies uper f i c i eaf or mal i ber a. Rhi novi enenor mal ment eut i l i zzat operi ldes i gni ndus t r i al e,i lRever s eengi neer i ngeperl amodel l azi onedipr ot ot i pi .St or i c ament e nat os upi at t af or maWi nt els ar àdi s poni bi l ec onl apr os s i maver s i oneanc heperl ' ambi ent eAppl eMacOSX.

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3DSTUDI OMAX 3dsMax( c hi amat oanc he3DSt udi oMaxos ol oMax)èunpr ogr ammadigr af i c avet t or i al et r i di mens i onal eeani mazi one,r eal i zzat odal l a di vi s i oneMedi a&Ent er t ai nementdiAut odes k.Er as t at os vi l uppat oc omes uc c es s or edi3DSt udi operDOS,mas upi at t af or maWi n32. I ni zi al ment el adi vi s onediAut odes kr es pons abi l edi3dsMaxs ic hi amavaKi net i x,manel1998i ns egui t oal l aac qui s i zi onediDi s c r eet Logi cdapar t edel l as oc i et àdiSanRaf aelneer edi t òi lnome.Ladi vi s i oneMedi a&Ent er t ai nementdiAut odes koggii nc l udenumer os i al t r ipr odot t iperl agr af i c a3D,c omeades empi oi lpopol ar eMaya,aggi unt oalc at al ogoas egui t odel l ' ac qui s i zi onediAl i as . 3dsMaxèunodeipi ùut i l i zzat is of t war eperc r eazi one3Dpernumer os er agi onit r ac uil epot ent ic apac i t àdiedi t i ngel as uaar c hi t et t ur adipl ugi n.I nf at t ianc hes emol t is t r ument inons onopar t edelpr odot t o,i lpr odot t odi s ponediunagr andes c el t adipl ugi nr eal i zzat ida t er zepar t i . Al c unepr ec edent iver s i onir i c hi edevanounas pec i al ec hi avehar dwar edipr ot ezi onedac opi e( undongl e)c hedovevaes s er ei ns er i t a nel l apor t apar al l el aperpot erut i l i zzar ei lpr ogr amma. 3dsMaxhaunas er i edif unzi onal i t àavanzat e.Fi ndal l aver s i one7. 0s onopr es ent is t r ument idit ext ur eavanzat i ,c omeungener at or ee r ender i zzat or ebui l t i nnor malmap,s t at ii nc l us ipermi gl i or ar el ec apac i t àdipr oget t azi onedivi deogi oc hi .Apar t i r edal l aver s i one 6. 0,ès t at oi nc l us oMent alRay,unpot ent es i s t emadir ender i ng.Dal l aver s i one5. 0,3dsMaxi nc l udes t r ument idii l l umi nazi oneavanzat ac omeRadi os i t yeLi ghtTr ac er ,s i mi l ias t r ument idipr of es s i oal iperi lr ender i ngf ot or eal i s t i c oc omef i nal Render ,Br azi lr / seVr ay. 3dsMaxi nc l udeanc heHavokReac t or :uns of t war eperl ac r eazi onedir eal i s t i c hes i mul azi onidi nami c he( us at eanc hei npar ec c higi oc hi c omeHal f l i f e2,Obl i vi on,MaxPayne2eTr i bes :Vengeanc e) . Is et t emet odibas edimodel l azi ones ono: • Model l azi onec onpr i mi t i ve • NURMS • Sur f ac et ool • NURBS • Model l azi onec onpol i goni • Model l azi onec onmes h • Model l azi onec onpat c h

18


VRAY VRayèunmot or edir ender i ngapagament o,del l abul gar aChaosGr oup,pr es ent epervar ipr ogr ammidigr af i c a3D,t r aiqual it r ovi amoAut odes k3dsMax,Rhi noc er os ,Ci nema4D,Maya,Sof t i mageXSI ,Sket c hUp,Bl ender . FUNZI ONALI TA` Ques t opot ent eedel as t i c omot or edir ender i ngper met t edif ar er ender i ngf ot or eal i s t i c iedi l l us t r at i vigr azi eal l ef unzi onal i t àc hes uppor t a,t r al equal it r ovi amo: GI( ac r oni modiGl obalI l l umi nat i on,edèl ' i l l umi nazi onegl obal e,anc hedet t ai ndi r et t a) DoF( ac r oni modiDept hofFi el d," pr of ondi t àdic ampo"eper met t el ar eal i zzazi onedir enderc onunoopi ùogget t is f oc at i ) Caus t i c he( f enomenof i s i c odiac c umul odil uc er i f l es s aor i f r at t apr oi et t at ai nf or mec ar at t er i s t i c hes ual t r iogget t i ,ades empi ol a f or maac ar di oi dedel l al uc er i f l es s adal l ' i nt er nodiunc i l i ndr ool ef or mei r r egol ar ii nmovi ment os ulf ondodiunapi s c i napr ovoc at e dal l anonuni f or mi t àdel l as uper f i c i eondul at a) Rayt r ac i ng( t ec ni c adii l l umi nazi onec het r ac c i ai lper c or s odiognir aggi odil uc eemes s odal l as or gent el umi nos a) Phot onMappi ng( s i s t emadii l l umi nazi onec hec r eauna" mappa"f ot oniperi l l umi nar el as c ena) Fur( per met t el ac r eazi onedic hi omeepel l i c c e) HDRI( ac r oni modiHi ghDi nami cRangeI magi ng) CARATTERI STI CHE Lat ec ni c adii l l umi nazi onec hi amat aI r r adi anc eMap,èl ac ar at t er i s t i c apr i nc i pal ediques t omot or edir ender i ng,c heper met t el ac r eazi onedi" mappe"dii l l umi nazi onedaappl i c ar eal l es c ene3D,i nmodovel oc eemol t os c al abi l e,pot endoi nt er agi r es ul l aquant i t àdi f ot oni ,s ul l al or odi mens i one,s ul l a" pot enza"del l aGI ,emol t ial t r ipar amet r i .Tut t oques t ol or endet r aimot or idir ender i ngpi ùpopol ar ieut i l i zzat iperqual s i as it i podiappl i c azi one,c omer enderdii nt er ni ,es t er niedi l l us t r azi oni .Ques t omot or edir ender i ngvi enei ns t al l at os empr ec omepl ugi nes ii nt egr amol t obenenelpr ogr ammapr i nc i pal e,f or nendomat er i al ivr ay,l uc ivr ay,edef f et t ivr ay. LAVERSI ONE1. 5 Lanuovaver s i one1. 5i mpl ement aal c unenuovef eat ur esc ome: Mot i onBl urperi lPar t i c l eSys t em SunandSkySys t em ( c heper met t edis i mul ar ei lc ol or edel l al uc eedelc i el odel l as c enas empl i c ement evar i andol apos i zi onedel l aVr ay Sunl i ght ) Ambi entOc c l us i on( unef f et t os i mi l eal l aGImamol t opi ùvel oc edac al c ol ar e,anc hes epi ùi mpr ec i s o) Fas tSSSappr oxi mat i on( SSSèl ' ac r oni modiSubSur f ac eSc at t er i ng,unos haderc heper met t edis i mul ar eimat er i al it r as l uc i di ) Phys i c al l ybas edc amer a( unat el ec amer ac hes i mul agl ief f et t if i s i c ir eal iper met t endol ar egol azi onedel l ' ot t ur at or eedeldi af r amma) .

19


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Nat ai nI r aq,has t udi at omat emat i c aal l aAmer i c anUni ver s i t ydiBei r utpr i madit r as f er i r s iaLondr a pers t udi ar eal l aAr c hi t ec t ur alAs s oc i at i on.Dopoaverc ons egui t oi lt i t ol ohal avor at oc oni ls uoex maes t r o,l ' ar c hi t et t ool andes eRem Kool haasal l ' Of f i c ef orMet r opol i t anAr c hi t ec t ur edi vent ando s oc i anel1977. Nel1994hai ns egnat oal l aGr aduat eSc hoolofDes i gndel l ' Uni ver s i t Ă diHar var d,oc c upandol ac at t edr ac hef udiKenzoTange.Nel1980s t abi l i s c ei ls uos t udi oaLondr a.Dur ant egl i anniot t ant ai ns egnaal l aAr c hi t ec t ur alAs s oc i at i on.


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Fr ankGEHRY Fr ankOwenGehr ynas c eaTor ont o,i nCanadanel1929.Nel1947s it r as f er i s c ec onl af ami gl i aaLos Angel es ,dove,nel1954,s il aur eai nar c hi t et t ur aal l aUni ver s i t yofSout her nCal i f or ni a.Nel l os t es s o annoc ambi ai ls uoc ognomeor i gi nar i o( Gol denber g)i nGehr y.Dal195657f r equent aic or s idis pec i al i zzazi onei npi ani f i c azi oneur bani s t i c at enut ial l aHar var dGr aduat es c hoolofdes i gn,nelMas s ac hus et t s .Tr ai l1957ei l1958l avor apr es s ol os t udi o" Wel t onBec ket&As s oc i at es " ,ment r edal1958al 1961l avor apr es s ol os t udi o" Vi c t orGr uenAs s oc i at es "diLosAngel es .Suc c es s i vament e,nel1961,s i t r as f er i s c eaPar i gic onl as uaf ami gl i a,dovel avor anel l os t udi odiAndr éRemondet .Tor nat oaLos Angel es ,nel1962apr ei ls uos t udi opr of es s i onal ediar c hi t et t ur a" Fr ankO.Gehr yandAs s oc i at es "a Sant aMoni c a.

Guggenhei m Bi l bao I lGuggenhei m diBi l baoèi lpr oget t oc hehapor t at oFr ankGehr yal l apopol ar i t àgr azi eal l es uef or menuoveeal l os pl endor edat odal r i ves t i ment oi nt i t ani o,c heèr i us c i t oac onqui s t ar el ' appr ezzament odiunvas t opubbl i c oedac os t i t ui r eunapr i nc i pal eat t r at t i vaper i lt ur i s moi nt er nazi onal enel l apr ovi nc i abas c a. Lapr oget t azi oneel ar eal i zzazi onediunas t r ut t ur ac os ìc ompl es s aès t at ar es apos s i bi l egr azi eal l ' ut i l i zzodeipi ùmoder nis of t war e dipr oget t azi oneedic al c ol o( i lpr ogr ammaus at oèl os t es s oc hevi eneadoper at oi nFr anc i aperl apr oget t azi onedegl iaer eimi l i t ar i ) . Ol t r eadaverr adi c al ment ec ambi at oi lvol t odel l ac i t t àbas c a,i lMus eoGuggenhei m èi ndi s c ut i bi l ment eunapi et r ami l i ar edel l ' ar c hi t et t ur ac ont empor anea[ s enzaf ont e]edelnuovomododic onc epi r ei lr appor t ot r ac ont eni t or eec ont enut onegl iedi f i c imus eal i [ s enza f ont e] ,di vent andoanc h’ es s ooper ad’ ar t e. Res t aqui ndiunf ar odel l ' ar c hi t et t ur ac ont empor aneai ns er endos iper f et t ament enelc ont es t oambi ent al es eppuri nf or t ec ont r as t oa c aus adelr i ves t i ment o.

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Fos t ernac quenel1935aManc hes t eri n unaf ami gl i adioper ai ,l as c i òl as c uol aa 16annieandòal avor ar enegl iUf f i c idel Tes or odelc omunediManc hes t er .Dopoi l s er vi zi omi l i t ar enel l aRoyalAi rFor c es i i s c r i s s eal l aSc uol adiAr c hi t et t ur aePi ani f i c azi oneUr banadel l ' Uni ver s i t àdiManc hes t erec ons eguìi ldi pl omanel1961. Cont i nuògl is t udial l ' Uni ver s i t àYal e,negl i St at iUni t i .Tor nat oi nI nghi l t er r a,Fos t er f ondònel1965unos t udi o,Team 4,c onRi c har deSueRoger sel amogl i eWendy.Nel 1967Roger sl as c i òTeam 4perl avor ar e c onRenzoPi ano,eFos t erf ondòc onl a mogl i el aFos t erAs s oc i at es ,or anot ac ome Fos t erandPar t ner s .Tr ai l1971ei l1983 c ol l abor òc onBuc kmi ns t erFul l ers udi ver s i pr oget t i ,af f er mandos ial i vel l oi nt er naUAEPavi l i onShanghaiExpo2010 zi onal e. Ipr i mipr oget t idiFos t ers onoc ar at t er i zzat idaunpr onunc i at os t i l ehi ght ec h,es i c onc ent r anos ugl ias pet t it ec nol ogi c ie s t r ut t ur al i ,mai ns egui t ol el i needel l es ue c os t r uzi onis ivannoi npar t eaddol c endoe is uoipr oget t ies pr i monounamoder ni t à pi ùac c et t abi l e.

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Makot oSeiWat anabe Nat oaYokohama,i nGi appone.Has t udi at oar c hi t et t ur aal l aYokohamaNat i onalUni ver s i t yes ièl aur eat o nel1976.Hal avor at os ot t oAr at aI s ozakiaTokyo. Idi s egnidiWat anabes onoc ar at t er i zzat idaunappr oc c i omoder no,c heus anoi lc omput ereal gor i t mimat emat i c ipergener ar eis uois t i l i .Pi Údir ec ent e,hapubbl i c at ounl i br onel2009i nt i t ol at oAl gor i t hmi cDes i gn, c heappr of ondi s c ei ls uomet ododipr oget t azi onedis t r ut t ur ei nf or mat i zzat e.

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Mas s i mi l i anoFUKSAS Nat oi nI t al i amadior i gi nel i t uana,Mas s i mi l i anoFuks ass ièl aur eat oi nar c hi t et t ur aal l ' Uni ver s i t àLaSapi enzadiRomanel1971,magi àdueannipr i maavevaaper t ounos t udi onel l ac api t al e[ s enzaf ont e] ,c uif ar anno s egui t oquel l idiPar i gi( 1989)eVi enna( 1993) .Dal1994al1997,annodel l as uael ezi oneac ons i gl i er ediammi ni s t r azi onedel l ' I ns t i t utFr anç ai sd' Ar c hi t ec t ur e,ès t at omembr odel l ec ommi s s i oniur bani s t i c hediBer l i noe diSal i s bur goevi s i t i ngpr of es s orpr es s ol ' Éc ol eSpéc i al ed' Ar c hi t ec t ur ediPar i gi ,l ' Ac ademyofFi neAr t sdi Vi enna,l aSt aat l i c heAkademi ederBi l dendenKüns t ediSt oc c ar dael aCol umbi aUni ver s i t ydiNew Yor k.[ 1] Sioc c upas opr at t ut t odeipr obl emiur baninel l egr andiar eemet r opol i t aneedhai nc ent r at ol as uapr at i c apr of es s i onal es opr at t ut t os ul l ar eal i zzazi onedioper epubbl i c he.Nel l es uer eal i zzazi oniFuks asc er c as empr edi c r ear eunnes s ot r al ac os t r uzi oneedi lc ont es t oi nc uies s as it r ovaedi ls uomododipr oget t ar es ievol veda unas er i edimodel l ibi di mens i onal it r as f er i t ipoii nt r i di mens i onal eedi nf i ner eal i zzat i . Har i c evut onumer os ipr emii nt er nazi onal it r ac uii lVi t r uvi oI nt er nac i onalal aTr ayec t or i a( 1998) ,i lGr and Pr i xd' Ar c hi t ec t ur e( 1999)el ' Honor ar yFel l ows hi pdel l ' Amer i c anI ns t i t ut eofAr c hi t ec t s( 2002) .Nel2010è s t at oi ns i gni t odel l aLegi ond' onor e.

30


NUOVAFI ERADIMI LANO I lpr oget t odelNUOVOPOLO FI ERI STI COe'c ar at t er i zzat o dalgr andeas s ec ent r al e:l a gr andec oper t ur at r as par ent emodi f i c agl is paziede' c ont i nui t a'divi s i one.I l c ent r os er vi zi ,gl iuf f i c i , l ' ar eac ongr es s ual e,s ono f ul c r odels i s t ema:t r ans i zi onedal l ' " i ngr es s o"d' onor e al l ' as s ec ent r al e.

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