Last TimeTodayLights In PBRT (Sect 13.1)Point Lights (Sect 13.2)Point Light SceneSpotlightSpotlight SceneTexture Projection LightProjection Light SceneGoniophotometric LightGoniophotometric Light SceneDistant (Directional) Lights (Sect 13.3)Area Lights (Sect 13.4)Area Light Examples (Disks)Infinite Area Lights (aka Env. Maps)Environment MapsUsing Environment MapsNon-Trivial Light Sampling (Sect 15.6)Distant Light SamplingSampling Area Lights (Sect 15.6.3)Sphere Optimization / Cone SamplingSampling Env. MapsSlide 23Improving Env. Map SamplingSlide 25More Env. Map SamplingNext Time02/7/05 © 2005 University of WisconsinLast Time•Kubelka-Munk•Materials•Textures02/7/05 © 2005 University of WisconsinToday•Lights–Read PBR Chapter 13•Direct Lighting02/7/05 © 2005 University of WisconsinLights In PBRT (Sect 13.1)•Lights are the only emitters of power•Required functions:–Constructor takes a light-to-world transform and the number of samples required to determine the light’s contribution–Function to sample a light direction, return the power, and a ray for testing visibility (shadow ray)–An estimate of the total power emitted by the light–Is the light a Dirac delta light (based on a point light source)02/7/05 © 2005 University of WisconsinPoint Lights (Sect 13.2)•Specify transformation, the translation part gives the light’s position in world coordinates, and intensity (W/sr)•Sampling is trivial–Construct ray from point to light’s location, normalize to get direction–Shadow ray goes from pt to light posn–Power is I/r2•Total emitted power is 4I•It’s a delta light•There are several ways to modify the outgoing intensity …02/7/05 © 2005 University of WisconsinPoint Light Scene02/7/05 © 2005 University of WisconsinSpotlight•Point light but with a cone of directions–Define max cone size and where fall-off starts–Axis of the cone is always +z in light’s coordinates–Change it with the light’s transformation•Sampling is trivial, but if the point is outside the cone, no power comes out, and if it’s in the fall-off region, power is reduced•Total power is 2I(1-coshalf)02/7/05 © 2005 University of WisconsinSpotlight Scene02/7/05 © 2005 University of WisconsinTexture Projection Light•Like a spotlight, but region is restricted to a rectangular field of view, and texture map modulates intensity–The texture map is always perpendicular to +z axis–The light loads the map itself, but stores the result in a MipMap•Sampling is easy:–Ray to point light – center of projection–Intensity scaled by texture pixel along ray – just look up texture•Total power assumes average texture value over entire solid angle of projection02/7/05 © 2005 University of WisconsinProjection Light Scene02/7/05 © 2005 University of WisconsinGoniophotometric Light•A goniophotometric diagram describes the outgoing intensity in each direction–Represent diagram as a texture map with spherical texture projection•Sample like a point light but give intensity according to map•Total power assumes average map intensity•Maps are available for many lights02/7/05 © 2005 University of WisconsinGoniophotometric Light Scene02/7/05 © 2005 University of WisconsinDistant (Directional) Lights (Sect 13.3)•Light comes from same direction no matter where you are•How do you sample a ray to the light?–Given surface point•Is it a Dirac delta light? In the same way as a point light? •How much power arrives from this light?02/7/05 © 2005 University of WisconsinArea Lights (Sect 13.4)•Light defined by the area over which it emits–In PBRT, defined by a vector of Shape that emit–So you can make a light out of multiple triangles, for instance•Constant radiance over entire area–But only from “front” (positive normal) side–Function to return this•Total power?•Dirac Delta light?•Sampling …02/7/05 © 2005 University of WisconsinArea Light Examples (Disks)Note: You can see an area light in Physically-Based Renderings02/7/05 © 2005 University of WisconsinInfinite Area Lights (aka Env. Maps)•Assume that the lighting is coming from infinitely far away, but from all directions–L(x,) is independent of which parameter?–This is the Environment Mapping assumption•Given a point to compute incident lighting for, is this a Dirac delta light?02/7/05 © 2005 University of WisconsinEnvironment Maps•Radiance depends on direction, parameterized in spherical coordinates (only upper hemisphere shown below)–Other possibilities – cube maps are common in real-time graphics02/7/05 © 2005 University of WisconsinUsing Environment Maps•Radiance is found by looking up the direction in the map•Total power is approximated by light that arrives at bounding sphere of world•Sampling seems obvious …02/7/05 © 2005 University of WisconsinNon-Trivial Light Sampling (Sect 15.6)•Some lights are not trivial to sample, even given a point for which we want incident radiance–Also some tricks about converting probability measures•We also want to be able to sample a light source outgoing radiance directly–Used in algorithms that start tracing rays from the light•Sect 15.6 has all the details, here just an overview02/7/05 © 2005 University of WisconsinDistant Light Sampling•Recall, distant lights have radiance in a single direction•We need to handle the case when no target point is given•Sample point on the “disk” – projection of world’s bounding sphere normal to the light direction•Return 1/r2 as probability, but there is an implied Dirac Delta term for the directional component02/7/05 © 2005 University of WisconsinSampling Area Lights (Sect 15.6.3)•If given a point, we need to choose a point on the light from which the radiance is emitted–Routines to choose points on Shapes uniformly at random–Have to convert area measure on the light into solid angle measure at the point–Optimization for some cases if point is outside shape•Eg Sphere•If no point is given, we need a direction and a point of origin on the surface02/7/05 © 2005 University of WisconsinSphere Optimization / Cone Sampling•If point is outside sphere, most emitted rays cannot hit it•Sample within the cone of visible points–Same as sampling the outgoing direction from a spotlightmaxr  maxmax221cos121cos)1(cos2p02/7/05 © 2005 University of WisconsinSampling Env.