Local Illumination The Phong model is a local illumination model shaded color depends purely on local surface configuration surface normal viewing direction light direction diffuse specular and ambient reflectances Other surfaces have no effect n r they don t block light no shadows L they don t illuminate the surface v consider glMaterial GL EMISSION just causes that surface to glow doesn t effect other surfaces I I L kd cos I L ks cos n I a ka I L kd n L I L ks r v n I a ka But in reality surfaces interact a great deal Towards Global Illumination Illumination of one object depends on others other objects can block light shadows may reflect image of other objects reflection other objects may illuminate this object emissive surfaces Ray tracing already models some of these interactions shadows specular reflections specular transmission refraction and with distributed sampling we extended this to soft shadows glossy reflections These are only some of the possible phenomena 1 Direct Ray Tracing vs Global Illumination Direct lighting only Global Illumination images from Henrik Wann Jensen and Per Christensen Efficient Simulation of Light Transport in Scenes With Participating Media Using Photon Maps SIGGRAPH 98 Color Bleeding A hallmark of global illumination floor is illuminated by walls the floor itself is gray red blue bleed onto floor Why is this light hitting walls is white the wall is red or blue thus it reflects mostly red light absorbs other wavelengths this red light illuminates floor the floor is gray reflects wavelengths equally thus it reflects red light previous image with 90 color saturation increase 2 Caustics Objects can focus light onto other surfaces these effects are called caustics specular reflection transmission of light onto a diffuse surface These are important for realistic scenes typically very striking components of overall illumination images by Henrik Wann Jensen http graphics stanford edu henrik images caustics html Participating Media In general real world objects aren t situated in a vacuum they are surrounded by air smoke smog fog haze mist all of which interact with light call these participating media participate in light transport There are two primary effects attenuation media absorbs some of the light passing through it scattering scatters reflects light in different directions some scatters towards eye that s why we see the media 3 Indirect Illumination Not all surfaces are directly lit by lights the world is rife with indirect light often preferred for lighting a room Consider torchiere style lamps light is pointed at ceiling opaque basket beneath light is the floor in shadow no image from Cornell Program of Computer Graphics http www graphics cornell edu online research Two Views of Global Illumination Every surface is a light source illuminating all the others at each surface some light is arriving from all directions some of it is reflected back of the surface distributed over some set of outgoing directions solving this is tricky each surface depends on all the others assuming everything is diffuse makes it tractable Must trace all possible paths of light from sources to eye backward ray tracing explores a very limited subset and it s difficult to extend consider caustics how to shoot rays at a prism to guarantee that they hit a light forward ray tracing could work but could be very expensive most workable ray based methods combine these two bi directional path tracing photon maps Metropolis and they are far beyond the scope of this course 4 Global Illumination Algorithm Radiosity View a surface element as illuminating all other surfaces but we assume that all surfaces are perfectly diffuse in other words they reflect light equally in all directions this actually makes the problem tractable In radiosity we simulate physically correct transport of light assuming we use physical material models there will actually be conservation of energy and such Thus the goal is true photorealism before we were interested in whether images looked good now we can consider whether they are measurably good Physical Image vs Radiosity Simulation Which image is the photograph and which is the simulation 5 Radiosity Terminology We ll assume that the world is divided into polygonal patches subdividing the world into discrete elements is necessary radiosity algorithms are finite element methods The algorithm will compute a radiosity for every patch energy per unit area leaving a patch per unit time same as power per unit area Watts meter2 leaving patch This is a function of irradiance the power per unit area incident on the patch And the reflectance of the surface the fraction of incoming light which is reflected by the surface diffuse assumption means that this is a constant The Radiosity Equation Radiosity method revolves around solving a single equation incoming power from patch j B dA Ei dAi 1i23i 123 outgoing power emitted power i reflectance F ji form factor from j i The form factor is the proportion of the total power leaving patch j that is received by patch i 6474 8 B j F ji dA j Bi total radiosity of patch i Ei radiosity emitted by patch i dAi area of patch i all surfaces in the world 6 Solving the Radiosity Equation This is really the main part of the radiosity method incoming power from patch j B dA Ei dAi 1i23i 123 outgoing power emitted power i reflectance 6474 8 B j F ji dA j How do we solve this recursive integral equation next time we ll look at some simple methods 7