TURNER WHITTED S RAY-TRACING ALGORITHM: PRACTICE PROGRAMAÇÃO 3D MEIC/IST

Transcription

1 TURNER WHTTED S RAY-TRACNG AGORTHM: PRACTCE PROGRAMAÇÃO 3D MEC/ST

2 Ray Tacig Histoy

3 Ray Tacig Histoy

4 Whitted ay tacig t combies i a sige mode: Hidde suface emova Shadig due to diect iumiatio Shadig due to idiect iumiatio (efectio ad efactio effects due to efective/tasucid objects) Shadow computatio (had shadows)

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6 mage Redeig ight Pixe (RGB) y e Camea umiatio z e eye x e Objects y o x o z o

7 Ray Castig Fo each pixe i the viewpot; shoot a ay; fo each object i the scee compute itesectio ay-object; stoe the cosest itesectio; if thee is a itesectio shade the pixe usig coo, ights, mateias; ese /* ay misses a objects */ shade the pixe with bacgoud coo

8 Ray-Tacig de Tue Whitted Bacwad Ray Tace We tace ight ays fom the eye though a pixe i the viewpot - pimay ays ie we foow ight beams i the evese diectio of the ight popagatio Fid the itesectio with the fist object duig the bacwads tace of the ay The coo of the ay (hece at the equied pixe) is made up of 3 cotibutios: -oca coo due to diect iumiatio (it ca be i shadow) ad ambiet ight ; -coo fom a ay comig fom the efectio diectio efected ay; - coo fom a ay comig fom the efactio diectio tasmitted o efatced ay; Shadow feees, efected ad efacted ays ae caed secoday ays Defie the viewpoit, the view widow ad the viewpot esoutio fo each pixe i the viewpot { compute a ay i Wod space fom the eye towads the pixe; pixe_coo = tace ( scee, eye, pimay ay diectio, 1); }

9 Agoithm s ecusive atue R 2 2 R 1 T1 1 3 T 2 R 3 1 R 1 2 T 1 3 R 2 R 3 T 2

10 Coo tace (Scee scee, Vecto3d oigi, Vecto3d ay diectio, it depth) { itesect ay with a objects ad fid a hit poit (if ay) cosest to the stat of the ay if (!itesectio poit) etu BACKGROUND; ese { coo = object mateia s ambiet coo; compute oma at the hit poit; fo (each souce ight) { = uit ight vecto fom hit poit to ight souce; if ( oma>0) if (!poit i shadow); //tace shadow ay coo += diffuse coo + specua coo; } if (depth >= maxdepth) etu coo; if (efective object) { Ray = cacuate ay i the efected diectio; Coo = tace(scee, poit, Ray diectio, depth+1); educe Coo by the specua efectio coefficiet ad add to coo; } if (tasucid object) { tray = cacuate ay i the efacted diectio; tcoo = tace(scee, poit, tray diectio, depth+1); educe tcoo by the tasmittace coefficiet ad add to coo; } etu coo; }

11 ResY (pixes) height (eft) (ight) The axes i the Camea Fame y e v z e eye x e u Viewig diectio viewig widow-viewpot tasfomatio y e t (top) o x e ResX (pixes) width b (bottom)

12 Camea Positio ad Oietatio eye = viewe at = taget poit i the cete of viewig widow (ea pae i OpeG), up = up diectio view = at - eye y 0 up eye up at x 0 eye fovy at z 0 Wod Coodiates ea fa

13 Camea Fame - x e y e z e (uv) up eye data: eye, at, up z 0 y 0 at view = at - eye x 0 z e 1 eye at up eye eye at z e y 0 at view x 0 z 0

14 Camea Fame - x e y e z e (uv) x e up eye z e x e 1 upz e upz e y 0 at view y e up z 0 x 0 x e eye z e view x e y e y 0 up z e at at eye z 0 x 0 y e z e x e

15 Pimay Rays d aio : p( t) o td y w x w o eye z w d p xy eye

16 h Computig Pimay Rays v ResY-1 y 2 1 Ray at the eft-bottom coe of the uit squae pixe p xy (w/2, h/2) p xy u( x) v( y) x Re sx y Re sy w o ( ) u ( ) v 1 u x v y h (-w/2, -h/2) o x ResX-1 u w p xy o x 1 w xe Re sx h y Re sy y e

17 Ray at the cete of the squae pixe p xy o 1 w x 0.5 Re sx x e h y Re 0.5 sy y e fo uit squae pixes, ie. s=1;

18 Computig Pimay Rays Ray at the eft-bottom coe of the squae pixe d y o ay : p( t) o eye o td x o d f eye at z o d d f z e h y Re sy 1 y 2 e w x Re sx 1 2 x e

19 Computig Pimay Rays fo Pixe aea Viewig Widow: (eft, bottom) ad (ight, top) Viewpot: ResX, ResY x ad y ae positios withi a uit squae pixe x p e xy ad y e u( x) x ae i Wod cood so p e v( y) y e xy is aso i WCS u( x) eft ( ight eft) x x Re sx v( y) d d bottom ( top bottom) f z e u( x) y e u( y) x e y y Re sy

20 Camea Data i C stuct _Camea { /* Camea defiitio*/ Vecto eye, at, up; foat fovy; foat ea,fa; //hithe ad yo paes it ResX,ResY; foat w,h; Vecto xe,ye,ze; //uv fame }; typedef stuct _Camea Camea; Camea* camceate( Vecto eye, Vecto at, Vecto up, doube fovy, doube ea, doube fa, it ResX, it ResY ); Ray camgetpimayray( Camea camea, doube x, doube y );

21 The Camea object itiaizatio: Data iput: fov, ResX, ResY, ea, fa, eye, at, up Give: x, y d f eye at 1 z e eye at Ray i paametic fom : o + td o eye d d h 2d f ta fov 2 f w Re sx Re sy h 1 eye at xe upze upze z e (omaize d; why?) Ray at the eft-bottom coe of the squae pixe h y Re sy 1 2 y e w x Re sx 1 2 y e x e z e x e

22 Shadow Feeees Shadow ay : p( t) p i t s s p i No ight at that poit

23 tesectios computatio Read the sides Geomety tesectios Sef-itesectios pobem due to foatig-poit pecisio (secoday ays ad shadow-feees) Soutio: Sighty offset itesectios Read the atice : Adew Woo et a., t s Reay Not a Redeig Bug, You See, EEE CG&A, Septembe 1996, vo. 21

24 Áea apaete eegia umiosa (umes) A i A 2 umes / m eegia umiosa (umes) ' A A cos i' A cos umes / m 2

25 Refectio Mode fo ambet Sufaces uz icidete uz icidete uz icidete 1. Refete iguamete em todas as dieções 2. Diffuse tesity: iea vaiatio with age cos

26 Diffuse Refectio Compoet 1 cos - /2 0 /2 p i g b g b d dg db cos cos cos

27 Diffuse Refectio Compoet,, [0,1 ] Eq. 1 db dg d b g db b dg g d db b dg g d b g cos cos cos db b dg g d b g

28 Ambiet pus Diffuse: db dg d b g db dg d ab ag a b g

29 Specua Refectio Compoet v Specua aea v =1 =4 =8-1 -0,5 0 0,5 1 g b especua g b s sg sb cos cos cos Eq.2,, [0,1 ]

30 Specua Refectio Compoet sb sg s b g db dg d b g db dg d ab ag a b g v

31 Specua Refectio Compoet uz efetida v p i

32 Specua Refectio Vecto 2 h h h ) ( h

33 Refectio Distibutio v p i Ambiet Diffuse Specua C C amb C uz dif C v uz s

34 Mutipe ight Souces uzes sb sg s b g db dg d b g db dg d ab ag a b g v v v ) 2( uzes sb sg s b g db dg d b g db dg d ab ag a b g ) 2(

35 Shadow Feeees Shadow ay : p( t) p i t s s p i No ight at that poit

36 Mode with mutipe ights ad shadow othewise 1 i shadow if 0 f s uzes sb sg s b g db dg d b g s db dg d ab ag a b g f

37 Refectios fom othe objects efected ay : p( t) p i t v p i Refective suface

38 Tasucid objects Raio efatado : p( t) p t i t 1 v h 1 p i t 2 h 2 Se aw h1 si 2 h 2 si 1

39 Refacted Ray v t ( v ) v v v t i p i v t sii v t si t hi sii h t t 2 cos t 1si t t t 1 v t v t t si t efacted ay : t cos ( ) t p( t) p i t t

40 Advetêcia: Refação ão é simpes!

41 Objectos efetoes e taspaetes edução da taspaêcia edução da efexão ) ( ) ( ) ( ) (1 ) ( ) ( ) ( t b t g t b g uzes sb sg s b g db dg d b g s db dg d ab ag a b g o f

42 Textuas v 1.0 v 1.0 v u u u Textuas 2D = mages ode o domíio é u, v [0,1] [0,1] R 2

43 Sistemas de coodeada de textua a caixa face x=x max v (0,0) u v (1,1) u (0,0) v u y y y y max mi mi (0,0) y u v z z z z max mi mi z x

44 Sistema de coodeadas de textua a esfea x y z si si cos si cos y x z z y x x y 2 2 ta / ta 1 1 v u 1) ( 1) ( w u j h v i i j

45 Sistema de coodeadas de textua o tiâguo v 3 (u 3,v 3 ) v 3 v 1 = v 2 u 1 = u 3 u 2 u 1 (u 1,v 1 ) 2 (u 2,v 2 )

46 Textua o tiâguo e coodeadas baicêticas p 1 v 12 v 23 v 31 2 / ) ( 2 / ) ( 2 / ) ( p p v p p v p p v i i i A A A A 3 A 1 A A A A A T T T T A A A A A A / / / p 2 p 3 it p i v u v u v u v u i i ) (

47 Textua

48 Textuas de ugosidade (bump textues) e Textuas de desocametos (dispacemet mappig) ' (, ) Petuba aeatoiamete as omais dos objetos Petuba aeatoiamete as posições dos potos

49 y=-x y=x Textua ambiete (eviomet maps) z=x (1,1) face dos aios x>y e x>z z x y u y x 2x v (0,0) u z=-x v z x 2x

50 Pocessameto ati-aiasig a dx dy sub-pixes pixe dx, dy = vaiáveis aeatóias ace um aio paa cada sub-pixe Faça uma média dos vaoes obtidos

51 Ati-aiasig pixe pixe pixe (a) oigia (b) uifome (c) jitteed

52 Refiameto Pogesivo amostagem iicia pimeia subdivisão seguda subdivisão subdivisão fia pixes sedo visitados pixes já visitados

53 Radiosidade e Ray Tacig stadad aytacig goba iumiatio Kaus Muee, Stoy Boo Uivesity, Compute Sciece (CSE 564)

54 Todays State of the At - Some Sapshots

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59 RT Acceeatio Moe efficiet computatios Hieachica data stuctues: Kd-Tee, BVH o Gids