Fall 2014 CSCI 420: Computer Graphics 5.1 Lighting and Shading Hao Li http://cs420.hao-li.com 1
Debunking Lunar Landing Conspiracies � with Global Illumination � https://www.youtube.com/watch?v=O9y_AVYMEUs 2
Single Light Source for Global Illumination � https://www.youtube.com/watch?v=O9y_AVYMEUs 3
Lighting 4
Outline • Global and Local Illumination • Normal Vectors • Light Sources • Phong Illumination Model 5
Global Illumination • Ray tracing • Radiosity • Photon Mapping Tobias R. Metoc • Follow light rays through a scene • Accurate, but expensive (off-line) 6
Raytracing Example Martin Moeck, Siemens Lighting 7
Radiosity Example Restaurant Interior. Guillermo Leal, Evolucion Visual 8
Local Illumination camera • Approximate model • Local interaction between light source light, surface, viewer • Phong model (this lecture): n fast, supported in OpenGL • GPU shaders • Pixar Renderman (offline) 9
Local Illumination • Approximate model camera • Local interaction between light, surface, viewer light source • Color determined only based on v l surface normal, relative camera n position and relative light position • What effects does this ignore? 10
Outline • Global and Local Illumination • Normal Vectors • Light Sources • Phong Illumination Model 11
Normal Vectors • Must calculate and specify the normal vector - Even in OpenGL! • Two examples: plane and sphere 12
Normals of a Plane, Method I • Method I: given by ax + by + cz + d = 0 • Let be a known point on the plane p 0 • Let be an arbitrary point on the plane p • Recall: if and only if orthogonal to u · v = 0 u v n · ( p − p 0 ) = n · p − n · p 0 = 0 • . c ] T n 0 = [ a b • Consequently n = n 0 • Normalize to | n 0 | 13
Normals of a Plane, Method II • Method II: plane given by p 0 , p 1 , p 2 • Points must not be collinear • Recall: orthogonal to and u × v v u n 0 = ( p 1 − p 0 ) × ( p 2 − p 0 ) • . • Order of cross product determines orientation • Normalize to n = n 0 | n 0 | 14
Normals of Sphere f ( x, y, z ) = x 2 + y 2 + z 2 − 1 = 0 • Implicit Equation • Vector form: f ( p ) = p · p − 1 = 0 • Normal given by gradient vector � � � | n 0 | = 2 p n 0 2 = p • Normalize 15
Reflected Vector • Perfect reflection: angle of incident equals angle of reflection • Also: , , and lie in the same plane l n r • Assume , guarantee | r | = 1 | l | = | n | = 1 l · n = cos( θ ) = n · r r = α l + β n Solution : α = − 1 and β = 2( l · n ) r = 2( l · n ) n − l 16
Outline • Global and Local Illumination • Normal Vectors • Light Sources • Phong Illumination Model 17
Light Sources and Material Properties • Appearance depends on - Light sources, their locations and properties - Material (surface) properties: � � � � � - Viewer position 18
Types of Light Sources • Ambient light: no identifiable source or direction • Point source: given only by point • Distant light: given only by direction • Spotlight: from source in direction - Cut-off angle defines a cone of light - Attenuation function (brighter in center) 19
Point Source • Given by a point p 0 • Light emitted equally in all directions • Intensity decreases with square of distance 20
Limitations of Point Sources • Shading and shadows inaccurate • Example: penumbra (partial “soft” shadow) • Similar problems with highlights • Compensate with attenuation 1 q = distance | p − p 0 | � a + bq + cq 2 a, b, c constants • Softens lighting • Better with ray tracing • Better with radiosity 21
Distant Light Source • Given by a direction vector • Simplifies some calculations • In OpenGL: ⇥ x 1 ⇤ T - Point source y z ⇥ x 0 ⇤ T - Distant source y z 22
Spotlight • Most complex light source in OpenGL • Light still emanates from point • Cut-off by cone determined by angle θ 23
Global Ambient Light • Independent of light source • Lights entire scene • Computationally inexpensive • Simply add to every pixel on [ G R G B ] G G every object • Not very interesting on its own A cheap hack to make the scene brighter 24
Outline • Global and Local Illumination • Normal Vectors • Light Sources • Phong Illumination Model 25
Phong Lighting 26
Phong Illumination Overview • Calculate color for arbitrary point on surface • Compromise between realism and efficiency • Local computation (no visibility calculations) • Basic inputs are material properties and : l, n, v = unit vector to light source l = surface normal n = unit vector to viewer v = reflection of at l p r (determined by and ) l n 27
Phong Illumination Overview [ G R G B ] 1. Start with global ambient light G G 2. Add contributions from each light source 3. Clamp the final result to [0, 1] • Calculate each color channel (R,G,B) separately • Light source contributions decomposed into - Ambient reflection - Diffuse reflection - Specular reflection • Based on ambient, diffuse, and specular lighting and material properties 28
Ambient Reflection � I a = k a L a • Intensity of ambient light is uniform at every point • Ambient reflection coefficient k a (material), 0 ≤ k a ≤ 1 • May be different for every surface and r,g,b • Determines reflected fraction of ambient light • L a = ambient component of light source (can be set to different value for each light source) • Note: L a is not a physically meaningful quantity 29
Diffuse Reflection • Diffuse reflector scatters light • Assume equally all direction • Called Lambertian surface • Diffuse reflection coefficient k d (material), 0 ≤ k d ≤ 1 • Angle of incoming light is important 30
Lambert’s Law • Intensity depends on angle of incoming light. 31
Diffuse Light Intensity Depends On Angle Of Incoming Light • Recall = unit vector to light l = unit surface normal n = angle to normal θ cos( θ ) = l · n • . n • . I d = k d L d ( l · n ) θ l • With attenuation: = distance to light source, q = diffuse component of light L d 32
Specular Reflection • Specular reflection coefficient k s (material), 0 ≤ k s ≤ 1 • Shiny surfaces have high specular coefficient • Used to model specular highlights • Does not give mirror effect (need other techniques) specular reflection specular highlights 33
Specular Reflection • Recall = unit vector to camera v = unit reflected vector r φ = angle between and v r n • . cos( φ ) = v · r v φ l • . I s = k s L s (cos φ ) α r • is specular component of light L s • is shininess coefficient α • Can add distance term as well 34
Shininess Coefficient α = 1 • . I s = k s L s (cos φ ) α (cos φ ) α • is the shininess α coefficient φ Higher gives α narrower curves Source: Univ. of Calgary low α high α 35
Summary of Phong Model • Light components for each color: - Ambient ( ), diffuse ( ), specular ( ) L a L d L s • Material coefficients for each color: - Ambient ( ), diffuse ( ), specular ( ) k a k d k s • Distance q for surface point from light source = unit vector to light = reflected about l l r n = surface normal = vector to viewer n v 36
Summary of Phong Model 37
BRDF • Bidirectional Reflection Distribution Function • Must measure for real materials • Isotropic vs. anisotropic • Mathematically complex • Programmable pixel shading Lighting properties of a human face were captured and face re-rendered; Institute for Creative Technologies 38
Summary • Global and Local Illumination • Normal Vectors • Light Sources • Phong Illumination Model 39
http://cs420.hao-li.com Thanks! 40
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