Perspective Projection. Parallel Projection

Transcription

1 CS475/CS675 - Comute Gahics Pojectos Viewing Pojectos Cente of Pojection? Cente of Pojection Object Object Image Pane o Pojection Pane Image Pane o Pojection Pane Othogahic Pojection To View Mutiviews ( o o incia anes) Fo ojection on the ane we get the ojection mati as P Tue sie o shae fo ines Tansfom and then oject using an othogahic ojection such that at mutie adjacent faces ae visibe bette eesentation of a 3D object using view Face aae to ojection ane shows tue shae and sie If U be the mati fomed b stacking u the unit vectos aong the thee aes and T be the aonometic ojection then If U be the mati fomed b stacking u the unit vectos aong the thee aes and T be the aonometic ojection then TU T Side View TU T ' ' Font View ' ' ' ' ' ' The foeshotening atios fo each ojected incia aes ae then given b: f ' ' f ' ' f ' '

2 Deending on the kind of foeshotening the cause we can have thee tes of aonometic ojections Timetic (a foeshotenings ae diffeent) Deending on the kind of foeshotening the cause we can have thee tes of aonometic ojections Deending on the kind of foeshotening the cause we can have thee tes of aonometic ojections Timetic (a foeshotenings ae diffeent) Timetic (a foeshotenings ae diffeent) Dimetic (two foeshotenings ae the same) Dimetic (two foeshotenings ae the same) Isometic (a foeshotenings ae the same) f f f f f f f f f f f f f Assuming we otate b R and R befoe we do the ojection on the ane Now we a this aonometic ojection T to U T P R R sin sin sin sin cos cos sin sin sin sin TU f f f So the foeshotening atios become f sin f f sin Fo Isometic ojections if we sove fo f f f then we get ο θ356 and ±45

3 Obiue Pojection Obiue Pojection Obiue Pojection The ojectos ae aae to each othe but the ae not eendicua to the ane of ojection P ' ' On anes aae to ane of ojection show tue shae and sie P ' P ' ' cos sin P ' o cot P Cente of Pojection Object Image Pane o Pojection Pane Paae ines convege We get non-unifom foeshotening Shae is not eseved We see in esective so esective viewing seems natua and hes in deth ecetion Ea 5th centu The Litte Gaden of Paadise 3th centu Aeo b Giotto is tica 3 o 45 Pojectos convege at a finite cente of ojection When cot / we get Cabinet ojections Lines eendicua to the ojection ane ae foeshotened b haf P Pojectos ο tan When α 45 we get a Cavaie ojection Lines eendicua to the ojection ane ae not foeshotened

4 5th centu The Batist in Foence Fiio Buneeschi 5th centu Fesco of Ho Tinit Masaccio ' c c P' ' ' ' ' c c c P c ' P' ' ' P Fist we a a esective tansfom to a oint X that takes it to X ' X ' P X ' ' c c ' 5th centu Schoo of Athens Rahae c ' '

5 Fist we a a esective tansfom to a oint X that takes it to X ' Now we add ojection on the ane VP Vanishing oint in the diection Set of ines not aae to the ojection ane convege at a vanishing oint To find the vanishing oint aong the diection we a the esective tansfomation to the oint at infinit aong the diection X ' P X X ' P P X ' ' ' If c ' then we get ' c ' ' ' ' c ' Singe oint esective Two oint esective X ' P X ' ' ' ' ' ' ' CoP is at ( / ) VP is at / Cente of ojection (CoP) on ais X ' P X ' P P P ' ' CoP is at / VP is at / Cente of ojection (CoP) on ais ' If / c then we get ' c ie the vanishing oint ies an eua distance on the oosite side of the ojection ane as the cente of ojection Singe oint esective ' ' Two vanishing oints Two CoPs? ' ' Fom htt://gatewahsatwodesscom

6 Thee oint esective Geneation of esective views Geneation of esective views P P P P ' ' ' Thee vanishing oints Thee CoPs? Tansfom and then a singe oint eseective Let us t to tansate a a esective and oject to T P T m n m n m n M C Eshe Ascending and Descending Tansation aong ine Geneation of esective views Geneation of esective views Geneation of esective views Rotate about ais and then a singe oint eseective ojection T P R Rotate about ais and then a singe oint eseective ojection T P R Tansation aong the ais causes change in scaing cos We get a two oint esective

7 Geneation of esective views Geneation of esective views Rotate about ais ais and then a singe oint eseective ojection T P R R sin Pana Pojections Rotate about ais ais and then a singe oint eseective ojection Pesective Paae T P R R sin cos sin sin sin Taonom We get a thee oint esective Othogahic Aonometic Obiue Font To Side Timetic Cavaie Dimetic Cabinet Isometic One Point Two Point Thee Point