Viewing in 3D. Viewing in 3D. Planar Geometric Projections. Taxonomy of Projections. How to specify which part of the 3D world is to be viewed?
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- Dominic Stanley
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1 Viewig i 3D Viewig i 3D How o speci which pa o he 3D wo is o e viewe? 3D viewig voume How o asom 3D wo cooiaes o D ispa cooiae? Pojecios Cocepua viewig pipeie: Xom o ee coos 3D cippig Pojec Xom o viewpo Paa Geomeic Pojecios A pojecio is ome he iesecio o ceai ies (pojecos) wih a pae (he pojecio pae) Pojecos ae ies om he cee o pojecio hough each poi o ojec Cee o pojecio a iii esus i a paae pojecio A iie cee o pojecio esus i a pespecive pojecio Taoom o Pojecios paae muiview aoomeic ohogaphic paa geomeic pojecios oique pespecive poi poi 3 poi 3 isomeic imeic imeic 4
2 Paae Pojecio Ohogaphic Pojecio Pojecos ae ohogoa o pojecio suace, which is pica paae o oe o he cooiae paes: 5 6 Aoomeic Pojecios Aoomeic Pojecios Aow pojecio pae o move eaive o ojec. How ma ages o a cue s coe ae equa? oe: imeic wo: imeic hee: isomeic 7 8
3 Oique Pojecios Pespecive Pojecio Aia eaioship ewee pojecos a pojecio pae. 9 Vaishig Pois N-poi Pespecive Paae ies (o paae o he pojecio pae) o he ojec covege a a sige poi o he pojecio pae (he vaishig poi): vaishig poi oe-poi wo-poi hee-poi
4 3 Ohogaphic Pojecios Diecio o pojecio is oma o he pojecio pae. Tpica, pojec oo oe o he cooiae paes. Fo eampe: Tpica, sevea o hese pojecios (e.g., o, igh, a op/pa views) ae show ogehe 4 Pespecive Pojecio Z Y (,,) (,,) 5 Osevaios The ak o he mai is 3 ( pojecio) Pois o he pojecio pae ae o chage he pespecive pojecio Le s see wha happes o a poi a iii aog he Z ais: This is a vaishig poi 6 Takig a Phoogaph Aage ojecs Posiio a poi he camea Choose a es, se he oom Take a picue Eage a cop o ge a pi
5 Takig a Viua Phoogaph Takig a Viua Phoogaph Aage ojecs App moeig asomaios o ojecs: chage om ojec cooiaes o wo cooiaes Posiio a poi he camea Posiio, poi, a oie he viua camea: eie a asomaio om wo o ee cooiaes Choose a es, se he oom Take a picue Pojec ojecs appig he pespecive asomaio oowe a pespecive ivie. The esu is omaie evice cooiaes. Eage a cop o ge a pi App viewpo asomaio o oai acua wiow cooiaes. Speci a view voume: eie a pespecive asomaio ha asoms ee cooiaes o caoica omaie viewig space (cip cooiaes) 7 8 The OpeGL Viewig Pipeie ojec cooiaes Moeview mai ee cooiaes Pojecio mai cip cooiaes Pespecive ivisio Viewpo Tasomaio omaie evice cooiaes wiow cooiaes Moeview Mai The iiia OpeGL camea is a he oigi, poiig ow he egaive -ais. The moeview mai is composie om simpe 3D asomaios: gloaiei gtasae, groae, gscae gloamai, gmumai Camea ca aso e posiioe he gulooka ouie: gulooka(ee,ee,ee,c,c,c,up,up,up ) 9
6 Pojecio Mai Speciie eiig a view voume (view usum): gfusum(e, igh, oom, op, ea, a) Pojecio Mai Aso ca e speciie gupespecive(ov, aspec, ea, a) aspec w/h ov veica ie o view age (egees) w h ea a ea a Pojecio Mai Deivaio, pa I gfusum eies he oowig pespecive asomaio mai: gfusum eies a geea (possi skewe) viewig pami. We is make his pami io a caoica oe: We is shea he skewe pami, he scae. 3 4
7 5 Sheaig Mai Tasoms he cee o he viewig wiow (o he ea pae) o (,,-), makig he view pami smmeic aou he Z-ais: 6 Scaig Mai Scae he smmeic pami o ceae a 45 egee age ewee each pae a he Z-ais: 7 Deivaio, pa II The caoica pami is he asome io a cue, usig a pespecive asomaio: ) ( 8 Fia... Muipig he asomaios gives us he esie mai:
8 The eec o Z View Fusum Cippig I homogeeous cooiaes a pois isie he view usum sais a o he oowig iequaiies: < w > w w > a < w > w < w > w Lies mus e cippe agais he paes: w w w w w w 9 3 Viewpo Tasomaio Viewpo Tasomaio Deies a pie ecage i he wiow io which he ia image is mappe: gviewpo(,, wih, heigh) (, ) speci he owe e coe o he viewpo: wih (,) heigh 3 Tasoms omaie evice () cooiaes o wiow (w) cooiaes. cooiaes age i [-,] w cooiaes age i [, wih], [,heigh] The esuig asomaio is: wih w ( ) heigh ( ) w 3
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