Lighting and Shading. Outline. Raytracing Example. Global Illumination. Local Illumination. Radiosity Example
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1 CSCI 480 Computer Graphics Lecture 9 Lightig ad Shadig Light Sources Phog Illumiatio Model Normal Vectors [Agel Ch ] February 13, 2013 Jerej Barbic Uiversity of Souther Califoria Global Illumiatio Raytracig Example Ray tracig Radiosity Photo Mappig Follow light rays through a scee Tobias R. Metoc Accurate, but expesive (off-lie) Marti Moeck, Siemes Lightig 3 4 Radiosity Example Local Illumiatio light source Approximate model camera Local iteractio betwee light, surface, viewer Phog model (this lecture): fast, supported i OpeGL GPU shaders Restaurat Iterior. Guillermo Leal, Evolucio Visual Pixar Rederma (offlie) 5 6 1
2 Local Illumiatio light source Approximate model Local iteractio betwee light, surface, viewer l v camera Color determied oly based o surface ormal, relative camera positio ad relative light positio What effects does this igore? 7 8 Normal Vectors Must calculate ad specify the ormal vector Eve i OpeGL! Two examples: plae ad sphere Normals of a Plae, Method I Method I: give by ax + by + cz + d = 0 Let p 0 be a kow poit o the plae Let p be a arbitrary poit o the plae Recall: u v = 0 if ad oly if u orthogoal to v (p p 0 ) = p p 0 = 0 Cosequetly 0 = [a b c] T Normalize to = 0 / Normals of a Plae, Method II Method II: plae give by p 0, p 1, p 2 Poits must ot be colliear Recall: u x v orthogoal to u ad v Normals of Sphere Implicit Equatio f(x, y, z) = x 2 + y 2 + z 2 1 = 0 Vector form: f(p) = p p 1 = 0 Normal give by gradiet vector 0 = (p 1 p 0 ) x (p 2 p 0 ) Order of cross product determies orietatio Normalize to = 0 / 0 Normalize 0 / 0 = 2p/2 = p
3 Reflected Vector Perfect reflectio: agle of icidet equals agle of reflectio Also: l,, ad r lie i the same plae Assume l = = 1, guaratee r = 1 l = cos(θ) = r r = α l + β Solutio: α = -1 ad β = 2 (l ) r = 2 (l ) - l Light Sources ad Material Properties Appearace depeds o Light sources, their locatios ad properties Material (surface) properties: Types of Light Sources Ambiet light: o idetifiable source or directio Poit source: give oly by poit Distat light: give oly by directio Viewer positio Spotlight: from source i directio Cut-off agle defies a coe of light Atteuatio fuctio (brighter i ceter) Poit Source Give by a poit p 0 Light emitted equally i all directios Itesity decreases with square of distace Limitatios of Poit Sources Shadig ad shadows iaccurate Example: peumbra (partial soft shadow) Similar problems with highlights Compesate with atteuatio Softes lightig Better with ray tracig Better with radiosity q = distace p p 0 a, b, c costats
4 Distat Light Source Give by a directio vector Simplifies some calculatios I OpeGL: Poit source [x y z 1] T Distat source [x y z 0] T Spotlight Most complex light source i OpeGL Light still emaates from poit Cut-off by coe determied by agle θ θ Global Ambiet Light Idepedet of light source Lights etire scee Computatioally iexpesive Simply add [G R G G G B ] to every pixel o every object Not very iterestig o its ow. A cheap hack to make the scee brighter Phog Illumiatio Model Calculate color for arbitrary poit o surface Compromise betwee realism ad efficiecy Local computatio (o visibility calculatios) Basic iputs are material properties ad l,, v: l = uit vector to light source = surface ormal v = uit vector to viewer r = reflectio of l at p (determied by l ad ) Phog Illumiatio Overview 1. Start with global ambiet light [G R G G G B ] 2. Add cotributios from each light source 3. Clamp the fial result to [0, 1] Calculate each color chael (R,G,B) separately Light source cotributios decomposed ito Ambiet reflectio Diffuse reflectio Specular reflectio Based o ambiet, diffuse, ad specular lightig ad material properties
5 Ambiet Reflectio I a = k a L a Itesity of ambiet light is uiform at every poit Ambiet reflectio coefficiet k a, 0 k a 1 May be differet for every surface ad r,g,b Determies reflected fractio of ambiet light L a = ambiet compoet of light source (ca be set to differet value for each light source) Note: L a is ot a physically meaigful quatity Diffuse Reflectio Diffuse reflector scatters light Assume equally all directio Called Lambertia surface Diffuse reflectio coefficiet k d, 0 k d 1 Agle of icomig light is importat Lambert s Law Itesity depeds o agle of icomig light. Diffuse Light Itesity Depeds O Agle Of Icomig Light Recall l = uit vector to light = uit surface ormal θ = agle to ormal cos θ = l l θ I d = k d L d (l ) 27 With atteuatio: q = distace to light source, L d = diffuse compoet of light 28 Specular Reflectio Specular Reflectio Specular reflectio coefficiet k s, 0 k s 1 Shiy surfaces have high specular coefficiet Used to model specular highlights Does ot give mirror effect (eed other techiques) Recall v = uit vector to camera r = uit reflected vector φ = agle betwee v ad r cos φ = v r l v φ r I s = k s L s (cos φ) α specular reflectio specular highlights L s is specular compoet of light α is shiiess coefficiet Ca add distace term as well
6 Shiiess Coefficiet I s = k s L s (cos φ) α α is the shiiess coefficiet (cos φ) α α = 1 Higher α φ gives arrower curves Summary of Phog Model Light compoets for each color: Ambiet (L a ), diffuse (L d ), specular (L s ) Material coefficiets for each color: Ambiet (k a ), diffuse (k d ), specular (k s ) Distace q for surface poit from light source Source: Uiv. of Calgary l = uit vector to light = surface ormal r = l reflected about v = vector to viewer low α high α BRDF Summary Bidirectioal Reflectio Distributio Fuctio Must measure for real materials Isotropic vs. aisotropic Mathematically complex Programmable pixel shadig Lightig properties of a huma face were captured ad face re-redered; Istitute for Creative Techologies
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