Global Illumination Why Global Illumination • Last lecture – Basic rendering concepts – Primitive-based rendering • Today: – Global illumination – Ray Tracing, and Radiosity (Light-based rendering) 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan What’s Global Illumination Pros/Cons and Applications • Global illumination algorithms used in computer graphics • Advantages are those which, when determining the light falling on a – Accurately predict the appearance of real world surface, take into account not only the light which has taken – Generate correct and better images a path directly from a light source (direct illumination), but • Disadvantages also light which has undergone reflection from other – Too complex to solve analytically surfaces in the world (indirect illumination). – Expensive to get numerical solution From Wikipedia, the free encyclopedia • Applications – Movie….. 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 1 Global Illumination Equation Global Illumination Equation • Reflection Equation • The total light leaving a point is given by the sum of two major terms: – Exitance from the point – Incoming light from other sources reflected at the point Incoming light Light Sum BRDF leaving Incoming light reflected at the point Light Exitance Sum BRDF Incoming leaving light • Energy Balance Equation Incoming light reflected at the point Shadow rays Primary ray 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Photorealistic Rendering Computing Light Transport • Photorealistic Rendering requires solving the equation! • Light sources emit light – Not possible in the general case with today’s technology • Surface reflect or absorb light • Light transport is the problem of figuring out where the • We want to know how much light ? light’s power goes reaches the image plane, and what color it is – Depends on the geometric arrangement and the surface properties • First, we need to describe lights and how surfaces reflect lights. 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 2 Light Sources Reflectance Modeling • Sources emit light: • Reflectance modeling is concerned with the way in which – Point Light light reflects off surfaces – Spot Light • Physical quantity is BRDF: Bidirectional Reflectance – Area Light Distribution Function – Distant Area Light – A function of a point on the surface, an incoming light direction, and (sky, environment map) an outgoing light direction – Tells you how much of the light that comes in from one direction goes out in another direction – General BRDFs are difficult to work with, so simplifications are made From Matt Pharr et al., “Physically Based Rendering ” 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Simple BRDFs Classifying Rendering Algorithms • Diffuse surfaces (Lambertian): • One way to classify rendering algorithms is according to the – Uniformly reflect all the light they receive type of light interactions they capture – A reasonable approximation for matte paints, soot, carpet • For example: The OpenGL lighting model captures: • Perfectly specular surfaces: – Direct light to surface to eye light transport – Reflect incoming light only in the mirror direction – Diffuse and rough specular surface reflectance • Rough specular surfaces: – It actually doesn’t do light to surface transport correctly, because it – Reflect incoming light around the mirror direction doesn’t do shadows • Diffuse + Specular: • We would like a way of describing interactions: light paths – A diffuse component and a specular component • Fresnel surfaces: – Reflect some and transmit some depending on incoming direction 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 3 Describing Light Paths Simple Light Path Examples • Describe light paths according to where they come from, where they go • LE to, and what they do along the way S or D – The light goes straight from the source to the • Assume only two types of surface interactions: S or D viewer – Pure diffuse, D S or D • LDE – Pure specular, S – The light goes from the light to a diffuse surface • Assume all paths of interest: that the viewer can see – Start at a light source, L Light Eye – End at the eye, E • LSE • Use regular expressions on the letters D, S, L and E to describe light – The light is reflected off a mirror into the viewer’s paths eyes – Valid paths are L(D|S)*E • L(S|D)E – Light, followed by either diffuse or specular, zero or more times, ending at – The light is reflected off either a diffuse surface or the eye a specular surface toward the viewer 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan More Complex Light Paths More Complex Light Paths • Find the following: LE LDDE – LE – LDE – LSE – LDDE LSDE – LDSE – LSDE LSE Radiosity Cornell box, LDSE due to Henrik wann Jensen, http://www.gk.dtu.dk/ LDE ~hwj, rendered with ray tracer 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 4 The OpenGL Model Raytracing • The “standard” graphics lighting model captures only • Cast rays out from the eye, through each pixel, and determine what they L(D|S)E hit first – Builds the image pixel by pixel, one at a time • It is missing: • Cast additional rays from the hit point to determine the pixel color – Light taking more than one diffuse bounce: LD*E – Shadow rays toward each light. If they hit something, then the object is • Should produce an effect called color bleeding, among other things shadowed from that light, otherwise use “standard” model for the light • Approximated, by ambient light – Reflection rays for mirror surfaces, to see what should be reflected in the – Light refracted through curved glass mirror • Consider the refraction as a “mirror” bounce: LDSE – Transmission rays to see what can be seen through transparent objects – Light bouncing off a mirror to illuminate a diffuse surface: LS+D+E – Sum all the contributions to get the pixel color – Many others 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Raytracing Recursive Ray Tracing • When a reflected or refracted ray hits a surface, repeat the Shadow rays whole process from that point – Send out more shadow rays – Send out new reflected ray (if required) – Send out a new refracted ray (if required) Reflection ray – Generally, reduce the weight of each additional ray when computing the contributions to surface color – Stop when the contribution from a ray is too small to notice • What light paths does recursive ray tracing capture? Transmitted ray 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 5 Ray Tree B Eye A L1 A L1 L2 C B L2 L2 C L1 L2 L1 PCKTWTCH by Kevin Odhner, POV-Ray 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Kettle, Mike Miller, POV- Ray 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 6 Which paths are missing in Raytracing? Missing Paths • Raytracing cannot do: – LS*D+E: Light bouncing off a shiny surface like a mirror and illuminating a diffuse surface – LDD+E: Light bouncing off one diffuse surface to illuminate others • Basic problem: The raytracer doesn’t know where to send rays out of the diffuse surface to capture the incoming light 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Light Caching Caustics • Cast rays from the light sources out into the scene: shoot – When a ray hits a diffuse surface, accumulate some light there – Surfaces record the amount of light that hits them • Store the light in texture maps • Store the light in quadtrees • Store the light in photon maps • Cast rays from the eye out into the scene: gather – When a ray hits a diffuse surface, look up the amount of light that Standard raytracer: Bi-directional More rays in the Diffuse table and blue ball, raytracer light pass hit it in the light-ray phase mirrors left, right and back, • What paths does it capture? transparent red ball Note the LS*DS*E paths • What sort of visual effects do you see? From Alan Watt, “3D Computer Graphics” 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 7 Refraction caustic Refraction caustics Henrik wann Jensen, Henrik wann Jensen, http://www.gk.dtu.dk/~hwj http://www.gk.dtu.dk/~hwj 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan Still Missing… Radiosity Example • LD*E paths – Diffuse-diffuse transport • Color bleeding is extreme in this example – Formulated and solved with radiosity methods • Textures are applied after – Color bleeding solving for illumination From Alan Watt, “3D Computer Graphics” 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 11/17/2005 (c) 2005 University of Wisconsin Shaohua Fan 8 Radiosity Assumptions Radiosity Meshing • All surfaces are perfectly diffuse • Each patch is colored with its – Means that is doesn’t matter which way light hits or leaves a surface illumination • Illumination is