MIT Ray Tracing Ray Tracing

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MIT 6.837 - Ray Tacng Ray Tacng MIT EECS 6.837 Fédo Duand and Bab Cule Some sldes couesy of Leonad McMllan MIT EECS 6.

837, Cule and Duand 2 Admnsave Cool assgnmen 1 esuls Assgnmen 2 Due omoow a 11:59pm Assgnmen 3 Onlne hs evenng Due Wednesday Ocobe 1 emmav seanek

1 MIT Ray Tacng Ray Tacng MIT EECS Fédo Duand and Bab Cule Some sldes couesy of Leonad McMllan MIT EECS 6.837, Cule and Duand 1 MIT EECS 6.837, Cule and Duand 2 Admnsave Cool assgnmen 1 esuls Assgnmen 2 Due omoow a 11:59pm Assgnmen 3 Onlne hs evenng Due Wednesday Ocobe 1 emmav seanek dym ko MIT EECS 6.837, Cule and Duand 3 MIT EECS 6.837, Cule and Duand 4 Revew of las week? Revew of las week Lnea, affne and pojecve ansfoms Homogeneous coodnaes Max noaon Tansfomaon composon s no commuave Ohonomal bass change MIT EECS 6.837, Cule and Duand 5 MIT EECS 6.837, Cule and Duand 6

Revew of las week Tansfomaon fo ay acng Tansfomng he ay Fo he decon, lnea pa of he ansfom only

837, Cule and Duand 7 Fun wh ansfomaons: Relavy Specal elavy: Loenz ansfomaon 4 veco (, x, y, z) 4

coloado.edu/~ajsh/s/s.shml γv 0 0 x 0 y 1 z MIT EECS 6.

70c Dgesson Today: Ray Tacng Image by Tune Whed 0.90c 0.99c See also hp://www.cs.mu.oz.

837, Cule and Duand 10 Ovevew of oday Shadows Reflecon Refacon Ray Casng (a.k.a. Ray Shoong) Fo evey pxel (x,y) Consuc a ay fom he eye colo[x,y]=casray(ay) Complexy?

2 Revew of las week Tansfomaon fo ay acng Tansfomng he ay Fo he decon, lnea pa of he ansfom only Tansfomng o no omal ansfomaon n WST = n OS (M -1 ) Consucve Sold Geomey (CSG) n WS v WS MIT EECS 6.837, Cule and Duand 7 Fun wh ansfomaons: Relavy Specal elavy: Loenz ansfomaon 4 veco (, x, y, z) 4 h coodnae can be c o Loenz ansfomaon depends on objec speed v ' γ x' γv = y' 0 z' 0 hp://casa.coloado.edu/~ajsh/s/s.shml γv 0 0 x 0 y 1 z MIT EECS 6.837, Cule and Duand 8 γ Dgesson Relavy Tansfom ay by Loenz ansfomaon 0.65c 0.70c Dgesson Today: Ray Tacng Image by Tune Whed 0.90c 0.99c See also hp:// MIT EECS 6.837, Cule and Duand 9 MIT EECS 6.837, Cule and Duand 10 Ovevew of oday Shadows Reflecon Refacon Ray Casng (a.k.a. Ray Shoong) Fo evey pxel (x,y) Consuc a ay fom he eye colo[x,y]=casray(ay) Complexy? O(n * m) n: numbe of objecs, m: numbe of pxels Recusve Ray Tacng MIT EECS 6.837, Cule and Duand 11 MIT EECS 6.837, Cule and Duand 12

Ray Casng wh dffuse shadng Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gecolo(); Fo evey lgh L col=col+h->gecolol()*l->gecolo* L->geD()->Do3( h->geomal() ); Reun

L->geColo()); Reun col; MIT EECS 6.837, Cule and Duand 13 MIT EECS 6.837, Cule and Duand 14 Quesons? Image compued usng he RADIACE sysem by Geg Wad How can we add shadows?

837, Cule and Duand 15 MIT EECS 6.837, Cule and Duand 16 Shadows Shadows poblem?

3 Ray Casng wh dffuse shadng Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gecolo(); Fo evey lgh L col=col+h->gecolol()*l->gecolo* L->geD()->Do3( h->geomal() ); Reun col; Encapsulang shadng Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); Reun col; MIT EECS 6.837, Cule and Duand 13 MIT EECS 6.837, Cule and Duand 14 Quesons? Image compued usng he RADIACE sysem by Geg Wad How can we add shadows? Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); Reun col; MIT EECS 6.837, Cule and Duand 15 MIT EECS 6.837, Cule and Duand 16 Shadows Shadows poblem? Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L Ray ay2(hpon, L->geD()); H h2(l->geds(),,) Fo evey objec ob ob->nesec(ay2, h2, 0); If (h->get> L->geDs()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); Reun col; Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L Ray ay2(hpon, L->geD()); H h2(l->geds(),,) Fo evey objec ob ob->nesec(ay2, h2, 0); If (h->get> L->geDs()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); Reun col; MIT EECS 6.837, Cule and Duand 17 MIT EECS 6.837, Cule and Duand 18

Avodng self shadowng Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L Ray ay2(hpon, L->geD()); H h2(l->geds(),,) Fo evey objec ob

4 Avodng self shadowng Colo casray(ay) H h(); Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L Ray ay2(hpon, L->geD()); H h2(l->geds(),,) Fo evey objec ob ob->nesec(ay2, h2, epslon); If (h->get> L->geDs()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); Reun col; Shadow opmzaon Shadow ays ae specal How can we acceleae ou code? MIT EECS 6.837, Cule and Duand 19 MIT EECS 6.837, Cule and Duand 20 Shadow opmzaon We only wan o know whehe hee s an nesecon, no whch one s closes Specal oune Objec3D::nesecShadowRay() Sops a fs nesecon Shadow ay casng hsoy Due o Appel [1968] Fs shadow mehod n gaphcs o eally used unl he 80s MIT EECS 6.837, Cule and Duand 21 MIT EECS 6.837, Cule and Duand 22 Quesons? Image Henk Wann Jensen Ovevew of oday Shadows Reflecon Refacon Recusve Ray Tacng MIT EECS 6.837, Cule and Duand 23 MIT EECS 6.837, Cule and Duand 24

Mo Reflecon Compue mo conbuon Cas ay In decon symmec w nomal Mulply by eflecon coeffcen (colo) Mo Reflecon Cas ay In decon symmec w nomal Don foge o add epslon o he ay Whou epslon MIT EECS 6.

5 Mo Reflecon Compue mo conbuon Cas ay In decon symmec w nomal Mulply by eflecon coeffcen (colo) Mo Reflecon Cas ay In decon symmec w nomal Don foge o add epslon o he ay Whou epslon MIT EECS 6.837, Cule and Duand 25 Wh epslon MIT EECS 6.837, Cule and Duand 26 Reflecon Reflecon angle = vew angle Reflecon Reflecon angle = vew angle R = V 2( V ) V θ V θ R R V θ V θ R R V V V MIT EECS 6.837, Cule and Duand 27 MIT EECS 6.837, Cule and Duand 28 Amoun of Reflecon Tadonal (hacky) ay acng Consan coeffcen efleconcolo Componen pe componen mulplcaon Amoun of Reflecon Moe ealsc: Fesnel eflecon em Moe eflecon a gazng angle Schlck s appoxmaon: R(θ)=R 0 +(1-R 0 )(1-cos θ) 5 V θ V θ R R V θ V θ R R MIT EECS 6.837, Cule and Duand 29 meal Delecc (glass) MIT EECS 6.837, Cule and Duand 30

Fesnel eflecance demo Lafoune e al., Sggaph 1997 Quesons? Image by Henk Wann Jensen MIT EECS 6.

837, Cule and Duand 32 Ovevew of oday Shadows Reflecon Tanspaency Compue ansmed conbuon Cas ay

6 Fesnel eflecance demo Lafoune e al., Sggaph 1997 Quesons? Image by Henk Wann Jensen MIT EECS 6.837, Cule and Duand 31 MIT EECS 6.837, Cule and Duand 32 Ovevew of oday Shadows Reflecon Tanspaency Compue ansmed conbuon Cas ay In efaced decon Mulply by anspaency coeffcen (colo) Refacon Recusve Ray Tacng MIT EECS 6.837, Cule and Duand 33 MIT EECS 6.837, Cule and Duand 34 Qualave efacon Refacon Fom Colo and Lgh n aue by Lynch and Lvngson Snell-Descaes Law θ cos θ θ oe ha I s he negave of he ncomng ay MIT EECS 6.837, Cule and Duand 35 MIT EECS 6.837, Cule and Duand 36

Refacon Refacon Snell-Descaes Law sn θ = = sn θ θ cos θ sn θ Snell-Descaes Law = = sn θ = sn θ ( cos θ Iˆ) = sn θ θ cos θ θ oe ha I s he negave of he ncomng ay θ oe ha I s he negave of he ncomng ay

7 Refacon Refacon Snell-Descaes Law sn θ = = sn θ θ cos θ sn θ Snell-Descaes Law = = sn θ = sn θ ( cos θ Iˆ) = sn θ θ cos θ θ oe ha I s he negave of he ncomng ay θ oe ha I s he negave of he ncomng ay MIT EECS 6.837, Cule and Duand 37 MIT EECS 6.837, Cule and Duand 38 Refacon sn θ Snell-Descaes Law = = sn θ = sn θ ( cos θ Iˆ) = sn θ sn θ = ( ˆ cos θ Iˆ) sn θ = ( cos θ ) Iˆ θ cos θ θ oe ha I s he negave of he ncomng ay Refacon sn θ Snell-Descaes Law = = sn θ = sn θ ( cos θ Iˆ) = sn θ sn θ = ( ˆ cos θ Iˆ) sn θ = ( cos θ ) Iˆ cos θ = Iˆ cos θ = 2 1 sn θ = sn θ = θ cos θ θ oe ha I s he negave of he ncomng ay 2 ˆ 2 1 (1 ( Iˆ) ) MIT EECS 6.837, Cule and Duand 39 MIT EECS 6.837, Cule and Duand 40 Refacon sn θ Snell-Descaes Law = = sn θ = sn θ ( cos θ Iˆ) = sn θ sn θ = ( cos θ Iˆ) sn θ = ( cos θ ) Iˆ cos θ = Iˆ cos θ = T = ( Iˆ) 2 1 sn θ = sn θ = ˆ 2 1 (1 ( Iˆ) 2 2 ˆ 2 1 (1 ( Iˆ) ) ) Iˆ Toal nenal eflecon when he squae oo s magnay MIT EECS 6.837, Cule and Duand 41 θ cos θ θ oe ha I s he negave of he ncomng ay Don foge o nomalze Toal nenal eflecon Fom Colo and Lgh n aue by Lynch and Lvngsone MIT EECS 6.837, Cule and Duand 42

poblem Wavelengh Runnng s fase han swmmng Wae

s expemen Usually gnoed n gaphcs Run Peson n

837, Cule and Duand 45 Pnk Floyd, The Dak Sde of

837, Cule and Duand 46 Ranbow Ranbow Fom Colo

Refacon depends on wavelengh Ranbow s caused by

aound 42 degees Dgesson Fom Colo and Lgh n aue

8 Cool efacon demo Engh, D., Maschne, S. and Fedkw, R., Cool efacon demo Engh, D., Maschne, S. and Fedkw, R., MIT EECS 6.837, Cule and Duand 43 MIT EECS 6.837, Cule and Duand 44 Refacon and he lfeguad poblem Wavelengh Runnng s fase han swmmng Wae Beach Lfeguad Refacon s wavelengh-dependen ewon s expemen Usually gnoed n gaphcs Run Peson n ouble Swm Dgesson MIT EECS 6.837, Cule and Duand 45 Pnk Floyd, The Dak Sde of he Moon Pon,, 1725, Allegoy o ewon MIT EECS 6.837, Cule and Duand 46 Ranbow Ranbow Fom Colo and Lgh n aue by Lynch and Lvngsone Dgesson Refacon depends on wavelengh Ranbow s caused by efacon+nenal eflecon+efacon Maxmum fo angle aound 42 degees Dgesson Fom Colo and Lgh n aue by Lynch and Lvngsone MIT EECS 6.837, Cule and Duand 47 MIT EECS 6.837, Cule and Duand 48

9 Quesons? Ovevew of oday Shadows Reflecon Refacon Recusve Ray Tacng MIT EECS 6.837, Cule and Duand 49 MIT EECS 6.837, Cule and Duand 50 Recap: Ray Tacng aceray Inesec all objecs Amben shadng Fo evey lgh Shadow ay shadng If mo Tace efleced ay If anspaen Tace ansmed ay MIT EECS 6.837, Cule and Duand 51 Recap: Ray Tacng Colo aceray(ay) Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L If ( no casshadowray( h->gepon(), L->geD()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); If (h->gemaeal()->smo()) Ray aymo (h->gepon(), gemod(ay->gedecon(), h->geomal()); Col=col+h->geMaeal->geMoColo() *aceray(aymo, h2); If (h->gemaeal()->stanspaen() Ray aytansmed(h->gepon(), gerefacd(ay, h->geomal(), cuenrefaconindex, h->maeal->gerefaconindex()); Col=col+h->geMaeal->geTansmedColo() *aceray(aytansmed, h3); Reun col; MIT EECS 6.837, Cule and Duand 52 Does end? Colo aceray(ay) Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L If ( no casshadowray( h->gepon(), L->geD()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); If (h->gemaeal()->smo()) Ray aymo (h->gepon(), gemod(ay->gedecon(), h->geomal()); Col=col+h->geMaeal->geMoColo() *aceray(aymo, h2); If (h->gemaeal()->stanspaen() Ray aytansmed(h->gepon(), gerefacd(ay, h->geomal(), cuenrefaconindex, h->maeal->gerefaconindex()); Col=col+h->geMaeal->geTansmedColo() *aceray(aytansmed, h3); Reun col; MIT EECS 6.837, Cule and Duand 53 Avodng nfne ecuson Soppng cea: Recuson deph Sop afe a numbe of bounces Ray conbuon Sop f anspaency/ansmed aenuaon becomes oo small Usually do boh Colo aceray(ay) Fo evey objec ob ob->nesec(ay, h, mn); Colo col=amben*h->gemaeal()->gedffuse(); Fo evey lgh L If ( no casshadowray( h->gepon(), L->geD()) col=col+h->gemaeal()->shade (ay, h, L->geD(), L->geColo()); If (h->gemaeal()->smo()) Ray aymo (h->gepon(), gemod(ay->gedecon(), h->geomal()); Col=col+h->geMaeal->geMoColo() *aceray(aymo); If (h->gemaeal()->stanspaen() Ray aytansmed(h->gepon(), gerefacd(ay, h->geomal(), cuenrefaconindex, h->maeal- >gerefaconindex()); Col=col+h->geMaeal->geTansmedColo() *aceray(aytansmed); Reun col; MIT EECS 6.837, Cule and Duand 54

Recuson fo eflecon The Ray Tee R 2 T 3 Eye 2 T 1 R 3 R 1 3 L 1 L 2 1 L 3 L 1 R 1 T 1 0 ecuson 1 ecuson 2 ecusons L 2 L 3

837, Cule and Duand 56 Kewl vsualzaon Ben Galck s SGI demo flyay On an Ahena SGI O2: add 6.837 cd /m/6.837/demos/flyay/daa.

837, Cule and Duand 58 Ray Tacng Hsoy Ray Casng: Appel, 1968 CSG and quadcs: Goldsen & agel 1971 Recusve ay acng: Whed, 1980

10 Recuson fo eflecon The Ray Tee R 2 T 3 Eye 2 T 1 R 3 R 1 3 L 1 L 2 1 L 3 L 1 R 1 T 1 0 ecuson 1 ecuson 2 ecusons L 2 L 3 suface nomal Eye R efleced ay R 2 R 3 T 3 L shadow ay T ansmed (efaced) ay MIT EECS 6.837, Cule and Duand 55 MIT EECS 6.837, Cule and Duand 56 Kewl vsualzaon Ben Galck s SGI demo flyay On an Ahena SGI O2: add cd /m/6.837/demos/flyay/daa../flyay Real-me ay acng Seve Pake e al. (U. of Uah) MIT EECS 6.837, Cule and Duand 57 MIT EECS 6.837, Cule and Duand 58 Ray Tacng Hsoy Ray Casng: Appel, 1968 CSG and quadcs: Goldsen & agel 1971 Recusve ay acng: Whed, 1980 Does Ray Tacng smulae physcs? Phoons go fom he lgh o he eye, no he ohe way Wha we do s backwad ay acng MIT EECS 6.837, Cule and Duand 59 MIT EECS 6.837, Cule and Duand 60

Fowad ay acng Sa fom he lgh souce Bu low pobably o each he eye Wha can we do abou?

shadows of anspaen objecs Des: opaque Sll dy: mulply by anspaency colo Bu hen no efacon Anmaon by Henk Wann Jensen Usng advanced efacon echnque (efacon fo

11 Fowad ay acng Sa fom he lgh souce Bu low pobably o each he eye Wha can we do abou? Fowad ay acng Sa fom he lgh souce Bu low pobably o each he eye Wha can we do abou? Always send a ay o he eye Sll no effcen MIT EECS 6.837, Cule and Duand 61 MIT EECS 6.837, Cule and Duand 62 Does Ray Tacng smulae physcs? Coec anspaen shadow Ray Tacng s full of dy cks e.g. shadows of anspaen objecs Des: opaque Sll dy: mulply by anspaency colo Bu hen no efacon Anmaon by Henk Wann Jensen Usng advanced efacon echnque (efacon fo llumnaon s usually no handled ha well) Dgesson MIT EECS 6.837, Cule and Duand 63 MIT EECS 6.837, Cule and Duand 64 The Rendeng equaon Clean mahemacal famewok fo lghanspo smulaon We ll see ha n ovembe A each pon, ougong lgh n one decon s he negal of ncomng lgh n all decons mulpled by eflecance popey Thusday Reflecance popees, shadng and BRDF Gues lecue by Wojcech Mausk MIT EECS 6.837, Cule and Duand 65 MIT EECS 6.837, Cule and Duand 66

Lecture 5. Plane Wave Reflection and Transmission

Lecture 5. Plane Wave Reflection and Transmission Lecue 5 Plane Wave Reflecon and Tansmsson Incden wave: 1z E ( z) xˆ E (0) e 1 H ( z) yˆ E (0) e 1 Nomal Incdence (Revew) z 1 (,, ) E H S y (,, ) 1 1 1 Refleced wave: 1z E ( z) xˆ E E (0) e S H 1 1z H (