Traditional Rendering (Ray Tracing and Radiosity)

Transcription

1 Tradiional Rendering (Ray Tracing and Radiosiy) CS 517 Fall 2002 Compuer Science Cornell Universiy Bidirecional Reflecance (BRDF) λ direcional diffuse specular θ uniform diffuse τ σ

2 BRDF Bidirecional Reflecance Disribuion Funcion Ligh Source Ψ N x Θ Deecor f r ( x, Ψ Θ) = dl( x Θ) de( x Ψ) = dl( x Θ) L( x Ψ)cos( N, Ψ dω x ) Ψ BRDF special case: ideal diffuse Pure Lamberian Energy ρd = Energy Energy ρd = Energy ρ d ou in ou in = 0 ρ 1 L( x Θ)cos( N L( x Ψ)cos( N x d x x, Θ) dω Θ, Ψ) dω L cos( N x, Θ) dωθ Lπ = = L( x Ψ)cos( N, Ψ) dω E = Ψ Ψ f π r ρ f d r ( x,ψ Θ) = π

3 Wha is his course abou Wha does image generaion mean? Physics of ligh How do we generae images? Global illuminaion algorihms Wha do we display o he user? Percepion Copyrigh Program of Compuer Graphics How do we do all of his efficienly? Clusering, alernaive represenaions, image-based rendering ec. Ray Tracing

4 Classic Ray Tracing Inroduced in 1980 by Turner Whied Pre-daes Rendering Equaion! Exising rendering: Phong shading Local illuminaion (specular, diffuse) Insighs Trace rays from eye ino scene Backward ray racing Find visible objecs Shade visible poins Shadows Reflecions Refracions Firs global illuminaion algorihm! Whied 1980: Firs ray raced image

5 Basic Algorihm - View Seup Synheic camera defined by eye poin and view plane in world coordinaes View plane divided ino pixels corresponding o he image dimensions Eye Poin Environmen View Plane Basic Algorihm - View Rays Rays are cas from he eye poin hrough each pixel in he image y Axis x Axis z Axis Eye (x, y) (0, 0)

6 Visibiliy Deerminaion Inersec eye ray wih all objecs in scene Find closes objec Z-buffer was exising algorihm No inersecion? Show background color Basic Algorihm - Shadows Cas ray from he surface poin o each ligh source: shadow rays Inersecion Poin

7 Basic Algorihm - Shadows, con. Shadow ray is blocked = shadow Basic Algorihm Shadow Rays If shadow ray no blocked, calculae radiance based on shading model To Ligh Source Inersecion Poin

8 Basic Algorihm - Reflecions If objec specular, shoo secondary refleced rays Normal Vecor Shading: Reflecions Refleced ray R I θ N θ R I = (I.N) N I = I - (I.N) N T R = I + (-I ) T = 2 (I.N) N - I I I T I R

9 Basic Algorihm - Refracions If objec ransparen, shoo secondary refraced rays Shading: Refracions Compue refraced ray T Index of refracion: η = cvacuum cmaerial Snell s law: sinθi η = sinθ η i η sinθ = η sinθ i i Ray from rare o dense medium I θ i N θ T

10 Toal Inernal Reflecion Consider ray from dense o rare T 0 T 1 T 2 T 3 NI 0 I 1 I 2 I 3 sinθ i η = 1 η i Transmied Ray 2 η i ηi i T = - I + N (N.I) - 1-( ) η η T = -η I + N η cos θi - cosθ = ( N. I) i ηi η = η 1- η η 2 η sin 2 2 ( 1 ( N. I) ) θi I θ i N θ T

11 Image-based Classic Ray Tracing Gahering approach from he ligh sources (direc illuminaion) from he refleced direcion (perfec specular) from he refraced direcion (perfec specular) All oher conribuions are ignored! No he soluion o he rendering equaion Whied RT Shading Model Nlighs n I ( x, y) = ( k ( N. L) + k ( N. H ) ) V + i= 1 d diffuse a Illuminaion a surface equals Ambien +Diffuse +Specular highlighs + Secondary specular reflecions and ransmissions s specular I + k I + s ambien refleced refraced r k i I Equivalen o Blinn-Phong plus conribuions from specularly refleced and ransmied rays

12 High-level algorihm For each pixel (x,y) { eye ray e = ray hrough pixel (x,y) color of pixel (x,y) = Trace (e, scene) } Trace (Ray eyeray, Scene scene) { o = inersec (eyeray, scene) if (o!= null) { Shade (o, p, N, scene, e, ) } else reurn background color } Shade Shade (Objec o, Poin p, Normal N, Scene scene, Ray ray, ) { for each ligh { if (!inersec (shadowray, scene)) color += diffuse+specular // no in shadow } if (o.specular) color += k s Trace (refleced ray) if (o.ransparen) color += k Trace (refraced ray) }

13 Basic Algorihm - Recursion Refleced and/or ransmied recursively spawn more rays Ray ree Deph cuoff Weigh cuoff V S 0 S 1 R T V S 0 S 1 S 0 S 1 R S 0 S 1 S 0 S 1 Whied RT Assumpions Ligh Source: poin ligh source Hard shadows Single shadow ray direcion Maerial: Blinn-Phong model Diffuse wih specular peak Ligh Propagaion Occluding objecs Specular inerreflecions only race rays in mirror reflecion direcion only

14 For eye rays: Ray Inersecion Tes ray agains all objecs Find closes visible objec find inersecion poin and surface normal and compue secondary rays For shadow rays: Check if ray inersecs some objec before he ligh Rays Ray defined as origin O and a direcion D R = O + D Where, O is ray s origin For eye rays, O is he eye posiion For reflecions/refracions, O is he original poin of inersecion D is he direcion For eye rays, D is he direcion hrough pixel (x,y) For reflecions/refracions, D is he refleced/refraced direcion

15 Ray and inersecion poins Ray e = (O, D) where O is he origin, D is he direcion O D p p = O + D = 0: p = O < 0: p lies behind he origin of he ray Inersecion: sphere Assume sphere x 2 + y 2 + z 2 = 1 Poin of inersecion p = O + inersecion D p.x = O.x + inersecion D.x p.y = O.y + inersecion D.y p.z = O.z + inersecion D.z p lies on sphere Solve A 2 inersecion + B inersecion + C = 0 A = 1, B = 2 (O.D), C = (O.O - 1) p D O

16 Inersecion: sphere inersecion = (-B ± S)/(2 A), S = sqr (B*B - 4 AC) 3 possibiliies: S = 0, S < 0, S > 0 Wha do hey mean? 2 soluions: Which roo should be picked? inersecion < 0: Wha does his mean? Normal: (x, y, z) (pre-normalized for sphere) Inersecion of ray wih cube O D p

17 Inersecion: cube Too many cases: consider slabs pairs of parallel planes Inersecion: cube Near = -inf, Far = +inf For each pair of planes for he x,y,z axes { Solve for O[i] + D[i] 1 = Min[i] Solve for O[i] + D[i] 2 = Max[i] Wha if 1 > 2? swap xmin Near = max (1, Near ) Far = min (2, Far ) } if ( Near > Far ) missed box else hi box xmax

18 Wha does his mean? Hi objec Miss objec 2y 2y Near Far 2x 1y Near Far 2x 1y 1x 1x Y slab Oher issues Wha if ray is parallel o a plane (say x)? Check if O.x is beween slabs Find correcly