# Lighting affects appearance

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1 Lighting affects appearance 1

2 Source emits photons Light And then some reach the eye/camera. Photons travel in a straight line When they hit an object they: bounce off in a new direction or are absorbed (exceptions later). 2

3 Basic fact: Light is linear Double intensity of sources, double photons reaching eye. Turn on two lights, and photons reaching eye are same as sum of number when each light is on separately. This means we can render lights separately Newton s drawing: (Wandell) 3

4 (Varshney) 4

5 Color is a function (Angelopoulou) Light Intensity Radiance (I): intensity of light emitted per unit of solid angle. l n Irradiance (E): Intensity of light striking surface per unit area. Because of foreshortening, as <l,n> decreases, the same light is spread over more and more area. In this picture, E = I*<n,l> Intensity of light also decreases with square of distance. 5

6 Why is intensity linearly related to cosine theta? Let s just take a 1D example. Imagine a distant point source. All light it emits passes through a circle a distance r from the point, with a length 2pi*r. Now, imagine a small patch of material of length 1. The light striking this patch also strikes a part of the circle. If the patch is very small, the angle between the light ray and the circle is a right angle. So if the patch is length 1, the part of the circle that the patch shadows is cos theta. The total light striking the patch is cos(theta)/2pi*r, which grows linearly with cos(theta). Light Reflection: Mirror r n l r r l 2( l 2( l n) n n) n l 6

7 Light Reflection: Lambertian Amount of light striking surface proportional to cos Angle between light direction and surface. Equal brightness in all directions Albedo is fraction of light reflected. Diffuse objects (chalk, cloth, matte paint). Brightness doesn t depend on viewpoint. Surface normal Light This surface appears to be foreshortened according to cos. So, if light striking a pixel at any angle is the same, the amount of light must increase with cos. That is, more light in direction of surface normal. Surface normal 7

8 nˆ Lambertian + Point Source ˆ ˆ l is direction of light l l l l is intensity of light i max(0, ( l nˆ) i is radiance is albedo is surface normal Note: color depends on surface. With mirror, color only depends on light. Surface normal lˆ Light Lambertian Examples Scene (Oren and Nayar) Lambertian sphere as the light moves. (Steve Seitz) 8

9 Ambient Assume Lambertian surface normal receives equal light from all directions. i a Diffuse lighting, no cast shadows. Ambient (and point) light can be colored Specular surfaces Brightness depends on viewing direction. Specularity is spread out. Mirror, smooth light all bounces same way. 2 (l n ) n Slightly rougher, direction of bounce varies. Diffuse, many bounces ( csnotes/shading/shading.html) 9

10 Empirical model (eg., hack) Phong s model reflected energy falls off as: cos n Phong s model n very big, this is like mirror. As n gets smaller, specularity more spread out. Good model for plastic Specularity color of source. (Forsyth & Ponce) Lambertian + specular Two parameters: how shiny, what kind of shiny. Many objects combine shiny and diffuse material Wood with veneer; glossy paint, plastic, greasy skin. Some fraction of light reflected as diffuse, some as specular. 10

11 Lambertian+Specular+Ambient ( More complex reflectances Physically realistic models Torrance Sparrow models roughness of surfaces and shadowing of microfacets. Specular peak can deviate from mirror direction. Can produce much greater specularity at low incident angles. Fresnel term. Specularity varies with incident angle. Glass only specular as angle approaches 90 degrees. Models built from observation. Measurement for every lighting direction and viewing direction. A function describing this is called a BRDF 4D function (can be reduced to 3D if there is rotational symmetry). 11

12 BRDF BRDF Not Always Appropriate BRDF BSSRDF (Jensen, Marschner, Levoy, Hanrahan) 12

13 Luminescence Surface shifts color of light. Can reflect more light of a color than is present in source. This is why objects can glow in black light. Transparency Some fraction of light passes through material. Varying this fraction for different colors produces colored, transparent objects. 13

14 Refraction sin Snell's Law : sin 1 2 n 2 n 1 c c 1 2 n is index of refraction c is speed of light in medium. Illumination Attenuation Light scatters from particles in the air. Fog or hazy air has more particles, more scattering. 14

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