Lighting and Shading
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1 ighting an Shaing 4 th ~ 5 th Week, 29 Why We Nee Shaing Suppoe we buil a moel of a phere uing many polygon an color it with glcolor We get omething like But we want Why oe the image of a real phere look like?
2 Shaing Determining a color for each fille pixel ight-material interaction caue each point to have a ifferent color or hae Nee to conier ight ource Material propertie ocation of viewer Surface orientation ight-material nteraction ight that trike an object i partially aborbe an partially cattere (reflecte) The amount reflecte etermine the color an bi brightne of fthe object Ex) re urface uner white light The reflecte light i cattere in a manner that epen on the moothne an orientation of the urface
3 ight Source General light ource are ifficult to work with becaue we mut integrate light coming from all point on the urface Simple mathematical ti moel: Point light Ditant light (irectional light) Spotlight Ambient light Point ight Source Emitting light equally in all irection p : the location of a point light ource r ( p ) ) ( p ) = g ( p ) b ( p ) Attenuation Proportional to the invere quare itance ( p, p ) = ( p ) 1 p p p ( p, p ) ( p ) = k 1 + k c l + 2 k q 2
4 Ditant ight Source Parallel irection of light nfinite itance away from the urface ocation irection p = x x y z 1 p = x x y z Spotlight Source Characterize by a narrow range of angle through which light i emitte p : apex of a cone l : irection of pointing θ : angle to etermine with Ditribution ib ti of light Concentrating in the center coφφ = ll ight intenity rop off co e φ = ( l ) e
5 Uniform lighting Ambient ight Source Same amount of light everywhere in cene Contribution of many ource an reflecting urface Phong Reflection Moel A imple moel that can compute rapily Three component (light-material interaction) Ambient Diffue Specular Uing four vector n: normal v: to the viewer or COP l: to light ource r: perfect reflector
6 Ambient Reflection Same at every point on the urface Ambient reflection coefficient k Amount reflecte ( k ), k 1 a = ar ag ab ar ag ab Some i aborbe b an ome i reflecte Three component (re, green, blue) Ambient reflection term in renering equation = k Can be any of the iniviual light ource Can be a global ambient term a a a Diffue Reflection ight cattere equally in all irection Perfectly iffue urface So rough that there i no preferre angle of reflection ambert law Amount of light reflecte i proportional to vertical component of incoming light Reflecte light cou cou = l n Diffue reflection term ( ) = k l n ncorporating a itance term k = ( l n) k + k + k c l q 2
7 Specular Reflection Smooth urface how pecular highlight Specular reflection term = k α ( r v) α: hinine coefficient α infinite : mirror 1 < α < 2 : metal 5< α < 1 : platic α co φ Specular Highlight 9 φ 9 Computation of Reflection ight ource Each light ource ha eparate ambient, iffue, an pecular term + eparate re, green, blue component = nine coefficient,,,,,,,, ( ) ag ab Material propertie ar r g b Matching light ource propertie Nine coefficient: r g b ( k ) ar ag ab Shinine coefficient: α r g b r g b
8 Aing up the Component For each light ource an each color component, the Phong moel can be written Mot urface are neither ieal iffuer nor perfectly pecular = a = k a + a + + k α ( l n) + k ( r v) ncluing the itance term 1 = k aa + 2 kc + kl + kq α ( k ( l n) + k ( r v) ) Computation of Vector Normal vector n = eal reflector ( p p ) ( p ) 1 2 p Angle of incience == angle of reflection r = l + 2 l n n l Halfway vector l 2 ( ( ) ) 2( l n) n l = l + v h = l + v θ + ψ = θ ψ + Half-angle: ( ) φ 2ψ = φ α β = k ( r v ) = k ( n h ) Phong Moel Blinn Moel p 1 n p 2 p
9 Utah Teapot with Different Material Propertie Polygonal Shaing Shaing calculation are one for each vertex Vertex color become vertex hae Polygonal Meh n OpenG, vertex hae are interpolate acro the polygon by efault glshaemoel(g_smooth); f we ue glshaemoel(g_fat); the color at the firt vertex will etermine the hae of the whole polygon
10 Flat Shaing (1) Contant haing polygon have a ingle normal Flat polygon n: contant Ditant light ource l: contant Ditant t viewer v: contant One haing calculation l for each polygon Conier moel of phere Flat Shaing (2) Diappointing for a mooth urface ateral inhibition Human viual ytem ha a remarkable enitivity Mach ban Herman Gri Perceive the increae in brightne along the ege Step chart Flat haing of polygonal meh Perceive an actual intenitie at an ege
11 Smooth Shaing (1) Gourau haing we can et a new normal at each vertex One haing calculation l for each vertex Bilinear interpolation of color Defining vertex normal a the average of the normal aroun a meh vertex n = n n n2 + n3 + n4 1 + n2 + n3 n4 Note ilhouette ege Smooth Shaing (2) Even the moothne introuce by Gourau haing may not prevent the appearance of Mach ban f a polygonal meh i too coare to capture illumination effect in polygon interior? io Flat Shaing Smooth Shaing
12 Phong Shaing nterpolating normal acro each polygon intea of interpolating vertex intenitie One haing calculation l for each pixel off-line Computing vertex normal at each point n n ( α ) = ( 1 α ) n A + α n B ( α, β ) = ( 1 β ) n C + β n D Normal on an ege nterpolation of normal Gourau v. Phong Shaing Gourau haing Fin average normal at each vertex (vertex normal) Apply moifie Phong moel at each vertex nterpolate vertex hae acro each polygon Phong haing Fin vertex normal nterpolate vertex normal acro ege nterpolate ege normal acro polygon Apply moifie Phong moel at each fragment
13 Color Plate 2: Wireframe Color Plate 3: Flat Shaing
14 Color Plate 4: Smooth Shaing Color Plate 1: Bump Mapping
15 Color Plate 7: Environmental Mapping
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