The books by McCluney (1994) and Malacara (2002) discuss blackbody emitters and the standard illuminants in detail. Wilkie and Weidlich (2011) noted that common practice in rendering has been to use the blackbody distribution of Equation (12.1) to model light emission for rendering, while Kirchoff’s law, Equation (12.4), would be more accurate. They also point out that as objects become hot, their BRDFs often change, which makes Kirchoff’s law more difficult to adopt, especially in that models that account for the effect of temperature variation on BRDFs generally aren’t available.
Warn (1983) developed early models of light sources with nonisotropic emission distributions, including the spotlight model used in this chapter. Verbeck and Greenberg (1984) also described a number of techniques for modeling light sources that are now classic parts of the light modeling toolbox. Barzel (1997) described a highly parameterized model for light sources, including many controls for controlling rate of falloff, the area of space that is illuminated, and so on. Bjorke (2001) described a number of additional controls for controlling illumination for artistic effect. (Many parts of the Barzel and Bjorke approaches are not physically based, however.)
The goniometric light source approximation is widely used to model area light sources in the field of illumination engineering. The rule of thumb there is that once a reference point is five times an area light source’s radius away from it, a point light approximation has sufficient accuracy for most applications. File format standards have been developed for encoding goniophotometric diagrams for these applications (Illuminating Engineering Society of North America 2002). Many lighting fixture manufacturers provide data in these formats on their Web sites.
Ashdown (1993) proposed a more sophisticated light source model than goniometric diagrams; he measured the directional distribution of emitted radiance at a large number of points around a light source and described how to use the resulting 4D table to compute the received radiance distribution at other points. Another generalization of goniometric lights was suggested by Heidrich et al. (1998), who represented light sources as a 4D exitant lightfield—essentially a function of both position and direction—and showed how to use this representation for rendering. Additional work in this area was done by Goesele et al. (2003), who further investigated issues in measuring light sources, and Mas et al. (2008), who introduced a more space-efficient representation and improved rendering efficiency.
Real-world light sources are often fairly complex, including carefully designed systems of mirrors and lenses to shape the distribution of light emitted by the light source. (Consider, for example, the headlights on a car, where it’s important to evenly illuminate the surface of the road, without shining too much light in the eyes of approaching drivers.) As we’ll see in Chapter 16, all of this specular reflection and transmission is challenging for light transport algorithms. It can therefore be worthwhile to do some precomputation to create a representation of light sources’ final emission distributions after all of this scattering that is then used as the light source model for rendering. To this end, Kniep et al. (2009) suggest tracing the paths of photons leaving the light’s filament until they hit a bounding surface around the light. They then record the position and direction of outgoing photons and use this information when computing illumination at points in the scene. Velázquez-Armendáriz et al. (2015) showed how to compute a set of point lights with directionally varying emission distributions to model emitted radiance from complex light sources. They then approximated the radiance distribution in the light interior using spherical harmonics.
Blinn and Newell (1976) first introduced the idea of environment maps and their use for simulating illumination, although they only considered illumination of specular objects. Greene (1986) further refined these ideas, considering antialiasing and different representations for environment maps. Nishita and Nakamae (1986) developed algorithms for efficiently rendering objects illuminated by hemispherical skylights and generated some of the first images that showed off that distinctive lighting effect. Miller and Hoffman (1984) were the first to consider using arbitrary environment maps to illuminate objects with diffuse and glossy BRDFs. Debevec (1998) later extended this work and investigated issues related to capturing images of real environments.
Representing illumination from the sun and sky is a particularly important application of infinite light sources; the “Further Reading” section in Chapter 15 includes a number of references related to simulating skylight scattering. Directly measuring illumination from the sky is also an effective way to find accurate skylight illumination; see Kider et al. (2014) for details of a system they built to do this. (A companion Web site has a large amount of measured skylight data available for download.)
pbrt’s infinite area light source models incident radiance from the light as purely a function of direction. Especially for indoor scenes, this assumption can be fairly inaccurate; position matters as well. Unger et al. (2003) captured the incident radiance as a function of direction at many different locations in a real-world scene and used this representation for rendering. Unger et al. (2008) improved on this work and showed how to decimate the samples to reduce storage requirements without introducing too much error.
As discussed in Chapter 3, one way to reduce the time spent tracing shadow rays is to have methods like Shape::IntersectP() and Primitive::IntersectP() that just check for any occlusion along a ray without bothering to compute the geometric information at the intersection point. Other approaches for optimizing ray tracing for shadow rays include the shadow cache, where each light stores a pointer to the last primitive that occluded a shadow ray to the light. That primitive is checked first to see if it occludes subsequent shadow rays before the ray is passed to the acceleration structure (Haines and Greenberg 1986). Pearce (1991) pointed out that the shadow cache doesn’t work well if the scene has finely tessellated geometry; it may be better to cache the BVH node that held the last occluder, for instance. (The shadow cache can similarly be defeated when multiple levels of reflection and refraction are present or when Monte Carlo ray-tracing techniques are used.) Hart, Dutré, and Greenberg (1999) developed a generalization of the shadow cache, which tracks which objects block light from particular light sources and clips their geometry against the light source geometry so that shadow rays don’t need to be traced toward the parts of the light that are certain to be occluded.
A related technique, described by Haines and Greenberg (1986), is the light buffer for point light sources, where the light discretizes the directions around it and determines which objects are visible along each set of directions (and are thus potential occluding objects for shadow rays). Another effective optimization is shaft culling, which takes advantage of coherence among groups of rays traced in a similar set of directions (e.g., shadow rays from a single point to points on an area light source). With shaft culling, a shaft that bounds a collection of rays is computed and then the objects in the scene that penetrate the shaft are found. For all of the rays in the shaft, it is only necessary to check for intersections with those objects that intersect the shaft, and the expense of ray intersection acceleration structure traversal for each of the rays is avoided (Haines and Wallace 1994).
Woo and Amanatides (1990) classified which lights are visible, not visible, and partially visible in different parts of the scene and stored this information in a voxel-based 3D data structure, using this information to save shadow ray tests. Fernandez, Bala, and Greenberg (2002) developed a similar approach based on spatial decomposition that stores references to important blockers in each voxel and also builds up this information on demand for applications like walkthroughs.
For complex models, simplified versions of their geometry can be used for shadow ray intersections. For example, the simplification envelopes described by Cohen et al. (1996) can create a simplified mesh that bounds a given mesh from both the inside and the outside. If a ray misses the mesh that bounds a complex model from the outside or intersects the mesh that bounds it from the inside, then no further shadow processing is necessary. Only the uncertain remaining cases need to be intersected against the full geometry. A related technique is described by Lukaszewski (2001), who uses the Minkowski sum to effectively expand primitives (or bounds of primitives) in the scene so that intersecting one ray against one of these primitives can determine if any of a collection of rays might have intersected the actual primitives.
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