Last TimeTodayRaytracing (PBR Sect. 1.2)RaytracingRecursive Ray TracingRaytracing Implementation (PBR Sect. 1.3)PBRT main() functionPBRT Render() functionPBRT Integrator() functionsMeasuring Light (PBR Chap. 5)Light and ColorWhiteHelium Neon LaserNormal DaylightTungsten LightbulbPBRT and Spectra (PBR Sect. 5.1)Radiometric Quantities (PBR Sect. 5.2)Radiant FluxIrradianceIrradiance to FluxMeasuring AngleIntensityRadianceIncident and Exitant RadianceIrradiance from Radiance (PBR Sect. 5.3)01/21/05 © 2005 University of WisconsinLast Time•Course introduction•A simple physically-based rendering example01/21/05 © 2005 University of WisconsinToday•Raytracing–Chapter 1 of the PBR•Radiometry – measuring light–Chapter 5 of PBR•Chapter 2-4 of PBR are about geometric issues01/21/05 © 2005 University of WisconsinRaytracing (PBR Sect. 1.2)•Cast rays out from the eye, through each pixel, and determine what the rays hit–Builds the image pixel by pixel, one at a time•Cast additional rays from the hit point to determine the pixel color•Rays test visibility – what do I see from this point in this direction?–Ray casting is widely used in graphics to test visibility01/21/05 © 2005 University of WisconsinRaytracingShadow raysReflection rayTransmitted ray01/21/05 © 2005 University of WisconsinRecursive Ray Tracing•When a reflected or refracted ray hits a surface, repeat the 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)–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•The result is a ray tree01/21/05 © 2005 University of WisconsinRaytracing Implementation (PBR Sect. 1.3)•Raytracing breaks down into several tasks:–Constructing the rays to cast–Intersecting rays with geometry–Determining the “color” of the thing you see–PBRT breaks these tasks into several steps, because it makes the system very general•Intersection testing is “geometry” and we won’t talk about it–Chapters 3 and 4 of the book–You have to read it to understand how to use the provided code, but ignore how it’s implemented01/21/05 © 2005 University of WisconsinPBRT main() function•Loads the scene•Initializes things•Renders the scene•Cleans up01/21/05 © 2005 University of WisconsinPBRT Render() function•Basic raytracer interpretation:–Sampler chooses which pixel–Camera constructs the ray through that pixel–Integrator determines the color coming back along the ray–Film records that pixel•Loop, getting all the pixels from sampler•Then tell Film to save file01/21/05 © 2005 University of WisconsinPBRT Integrator() functions•Integrators do most of the interesting work–Although there is plenty of interesting stuff for us in Sampler and Camera and Film•Basic Raytracing Integrator:–Determine what is hit–Get the reflectance function there–Find the incoming light and push through the reflectance function–Use the reflectance function to get reflection/transmission directions–Recurse on those directions01/21/05 © 2005 University of WisconsinMeasuring Light (PBR Chap. 5)•To go much further, we need to talk about measuring properties of light•We will consider only the particle nature of light–No diffraction or interference effects, no polarization•At any place, at any moment, you can measure the “flow” of light through that point in a given direction–The plenoptic function describes the light in a region: (x,,,t)–The plenoptic function over a region defines the light field in that region–We will return to this for image based rendering01/21/05 © 2005 University of WisconsinLight and Color•The wavelength, , of light determines its “color”–Frequency, , is related: •Describe light by a spectrum–“Intensity” of light at each wavelength–A graph of “intensity” vs. wavelength•We care about wavelengths in the visible spectrum: between the infra-red (700nm) and the ultra-violet (400nm)101/21/05 © 2005 University of WisconsinWhite•Note that color and intensity are technically two different things•However, in common usage we use color to refer to both–White = grey = black in terms of color•We will be precise in this part of the course, and only use the words in their physical sense# PhotonsWavelength (nm)400 500 600 700WhiteLess Intense White (grey)01/21/05 © 2005 University of WisconsinHelium Neon Laser•Lasers emit light at a single wavelength, hence they appear colored in a very “pure” way# PhotonsWavelength (nm)400 500 600 70001/21/05 © 2005 University of WisconsinNormal Daylight# PhotonsWavelength (nm)400 500 600 700•Note the hump at short wavelengths - the sky is blue•Other bumps came from solar emission spectra and atmospheric adsorption01/21/05 © 2005 University of WisconsinTungsten Lightbulb•Most light sources are not anywhere near white•It is a major research effort to develop light sources with particular properties# PhotonsWavelength (nm)400 500 600 70001/21/05 © 2005 University of WisconsinPBRT and Spectra (PBR Sect. 5.1)•Represent spectra using 3 piecewise constant basis function–RGB, basically–You won’t get good rainbows with the default•You could change it–You would have to change some reflectance function implementations–You would have to recompile everything•To standardize the writing of images, conversions to XYZ color space are required–If you don’t know what XYZ color space is, read the notes from CS559 last semester (lectures 2 and 3)01/21/05 © 2005 University of WisconsinRadiometric Quantities (PBR Sect. 5.2)•Quantities that measure the amount of light•They differ mostly not in what they measure, but in what you measure it over–Flux: Total in some domain–Irradiance: Per unit area–Intensity: Per unit angle–Radiance: Per unit angle per unit projected area•Basically, all the latter are differential quantities that have no meaning until you integrate them over some domain–Like you have to integrate speed to get distance traveled01/21/05 © 2005 University of WisconsinRadiant Flux•Total amount of energy passing through a surface or region of space per unit time–Typically denoted by  (Phi)–Also called power –Measured in watts (W) or joules/second (J/s)•These are metric quantities (rather