Computer Graphics. Viewing & Projections

Vw &

Ovrvw rr : rss r t -vw trsrt: st st, rr w.r.t. r rqurs r rr (rt syst) rt: 2 trsrt st, rt trsrt t 2D rqurs t r y rt rts ss

Rr P usuy st try trsrt t wr rts t rs t surs trsrt t r rts u rt w.r.t. vw vu sur rv (sr) rstrt ut s

Rr P trsrt t wr rts t rs t surs trsrt t r rts

M-Vw rsrt ut / uts: t ts (u ts t.) u t sts & rtts trsrts 3D r st & rtrs r: w t rr ts s? s s s s

M-Vw rsrt st : trsrt ts t (t) wr rt syst y y x x wr rt syst t x: t t t rt syst

M-Vw rsrt 2 : trsrt rty t r rts: t-t y y x x r rt syst t s ts w -vw trx rrs ss, ts rus t rt syst

M-Vw rsrt

M-Vw rsrt -vw trsrt sts:. trst t r t r t 2. rtt t rt xs 3. ssy s s ts rss s us OGL: xt wr rts! t & r ts rtts y s wr rt syst (.., systs)

Rr P try trsrt t wr rts t rs t surs trsrt t r rts rt

Itrut Csst

Itrut A t [t rt ] s t trst vsu yr [vw vu] t v st, wt x tr [tr rt] st t, rrst y rt wt s rs v sur [t rr]. (Art, 435) Hs Vr Vrs: Prstv 64

Itrut r rt: rt rys r strt s rt sur/vw s r rts strt s r s strt rt sur/ vw tr rt rt rys/ rtrs

Itrut rs r rt: rtr y rt rt () rstv rt: tr rt () rt vw vtr rur t vw : vw r (v) rys rtr rt: rtrs (r r vr r )

Csst Pr r rts r rstv rtr qu -t t xtr t tw-t rt str tr vr tr tr-t s r rts: rtrs r t tr rstv rts: rtrs vr r

Pr t ty rtrs r r rsrt: stt ts t r sr r s r r sss r rts: s tw v rt xs r rt CG: s rr utts str

Pr ty ts: rttur rws (.., us w r y rtr y rur s) vsuts rs:

Pr ty ts: rttur rws (.., us w r y rtr y rur s) vsuts rs: s ts sur t rt

Pr : S Css t rt, s rt, rt rt rtr rts vw s rur t t rt xs r r t t A (2) rt s r -r t t rt xs us rttur

Axtr Pr t -r t t rt xs r s r r, s r t t s ss: str rt: s t rt xs tr rt: s t y tw rt xs trtr rt: t rt xs s rt r xs

Axtr Pr str rts A (2)

Oqu Pr rt rt () s t rur t vw r (v) ttr st rt t wt rtr rts vw usuy rur t rt syst A (2)

Oqu Pr Cvr rt: 45 tw vw Ct rt: 63.4 tw vw (rt(2)), -ts srtr y ½ ts r t rstv rts! M. Hr, FH Hr, (22)

Oqu Pr Cvr rt, α = 3 α = 45 Br/Br (23) Ct rt, α = 3 α = 45 Br/Br (23) A (2)

Prstv

Prstv vwr t t t ty sst y vs ts A (2) 2 3

Prstv Prt: Vs Pts w y vs ts xu?

Prstv Prt: Vs Pts vw rt t rt xs M. Hr, FH Hr, (22)

Prstv rsrt ss r s s usuy t rsrv vs ts st vw wt rst t rt xs tr vs ts vw trsts rt xs, tw y tw xs r trst, y xs s trst

Cr M r

Prstv : Cr M sr y r rs rtrs: st, rtt rtur suttr t t, ty s ( vs. w) t s rsut st rt (4:3, 6:9,.85:, 2.35:, 2.39:) rsut (t rs)

Prstv : Cr M s CG st: t 3D (= ) vw rt: vtr 3D (v) st: vwrt s r utt r r ts (r r ) y COP - x vw r

7 t tury ustrt P Cr

U Purw P Cr

Crr P Hss P Cr

P Cr Cr Osur, Grw Ry Osrvtry

Ls Fr

Mt Bur

Prstv : Cr M rs tw r CG r? st vw w.r.t. COP rtt t ty r ( vs. s) ty rrt s ts (s r) t : vs. xst tys ss rts tur t ts: vs. > xst r s vw vu

Cr M: Rt r: -vw-trsrt: trsrt r rt syst t r rt syst st (wtut rt) tr s wr rt syst s r usuy s r w.r.t. t t r t rt syst ut s rt ts r rss

Cr M: Rt -vw trsrt: rrst s trx us rts tty trx y ut s t t rr ts t s v r s tt s s vs rt r t t r t tr -vw trsrt: rt

Cr M: Rt r st st t r () vw rt r -t t u rt t sy r rt syst wy? utt rur ss r r rt syst us rss ruts w? A (2)

Cut t Prt

Prstv : Mt vw r t x-y-, st COP t r (,, ); vw ut: t (x, y, ) t rt rt t: x, y, y (x, y, ) COP (,, ) (x, y, )

Prstv : Mt rt : rtr qut x' y' x y x' y' x y x / y / y (x, y, ) COP (,, ) (x, y, )

Prstv : Mt srt s rt trx trx us rts ' ' / / y x y x y x y y y x x x / ' / ' NEVER st t st rt t r st t r!!!

Pr : Mt vw t x-y- rtrs r t -xs tus, -vus r rt t us trx ' ' y x y x y x

Otr Pr qu rt ) t( ) s( ) t( ) s( ) s( ) t( ) s( ) t( ) s( P

Otr Pr Cvr rt: = 45º rsrt ts -rt s s²α + s²α = Ct rt: = 63.4º rsrt y 2 ts -rt s s²(α/2)+s²(α/2) = /2 ) s( ) s( P 2 ) s( 2 ) s( P

: Prs vw rustu s yr s x (xsv) ts u s t r sur rv sut: r rss wt vw vus ' ' / / y x y x y x

: C Vw Vus x/y

: C Vw Vus x/y vw vu

: C Vw Vus x/y vw vu r/rt

: C Vw Vus x/y vw vu r/rt r/

: C Vw Vus x/y vw vu x/y r/rt r/

: C Vw Vus x/y vw vu x/y r/rt r/ -

: C Vw Vus x/y vw vu x/y r/rt r/ - sr, trst, s vw vu s y ty trsr: u ts r tuy trsr!

Rr P try trsrt t wr rts t rs t surs trsrt t r rts u rt w.r.t. vw vu sur rv (sr)