#### Light Emission Descriptions

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 multiple parameters for controlling rate of falloff, the area of space that is illuminated, and so on. Bjorke (2001) described a number of additional techniques for shaping illumination for artistic effect. (Many parts of the Barzel and Bjorke approaches are not physically based, however.)

The goniophotometric 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 websites.

Ashdown (1993) proposed a more sophisticated light
source model than goniophotometric; 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) and Mas et al. (2008), who
introduced a more space-efficient representation and improved rendering
efficiency.

Peters (2021a) has developed efficient techniques for sampling lights defined by lines (i.e., infinitesimally thin cylinders) and shown how to sample the product of lighting and the BRDF using linearly transformed cosines (Heitz et al. 2016a).

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 is important to evenly illuminate the surface of the road without shining too much light in the eyes of approaching drivers.) All the corresponding 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) proposed tracing the paths of photons leaving the light’s filament until they hit a bounding surface around the light. They then recorded the position and direction of outgoing photons and used 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. More recently, Zhu et al. (2021) applied a neural representation to complex lights, encoding lights’ radiance distributions and view-dependent sampling distributions and opacities in neural networks.

#### Illumination from Environment Maps

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 14 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 built to do this.

`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. Lu
et al. (2015) developed techniques for efficiently importance
sampling these light sources.

The use of the `allowIncompletePDF` parameter to avoid generating
low-probability samples from infinite light sources in the presence of
multiple importance sampling is an application of MIS compensation, which
was developed by Karlík et al. (2019).

Subr and Arvo (2007b) developed an efficient technique for sampling environment map light sources that not only accounts for the term from the scattering equation but also only generates samples in the hemisphere around the surface normal. More recently, Conty Estevez and Lecocq (2018) introduced a technique for sampling according to the product of the BSDF and the environment map based on discretizing the environment map into coarse grids of pixels, conservatively evaluating the maximum of the BSDF over the corresponding sets of directions, and then choosing a region of the environment map according to the product of BSDF and pixel values. Given a selected grid cell, conventional environment map sampling is applied. (See also the “Further Reading” section in Chapter 13 for further references to light and BSDF product sampling algorithms.)

When environment maps are used for illuminating indoor scenes, many
incident directions may be blocked by the building structure. Bitterli
et al. (2015) developed the environment map
rectification approach to this problem that we have implemented in the
`PortalImageInfiniteLight`.
One shortcoming of Bitterli et al.’s approach is that the image must be
rectified for each plane in which there is a portal. Ogaki
(2020) addresses this issue by building a BVH over the
portals using Conty Estevez and Kulla’s light BVH
(2018) and then decomposing portals into triangles to
sample a specific direction according to the environment map.

Sampling-based approaches can also be used to account for environment map visibility. Bashford-Rogers et al. (2013) developed a two-pass algorithm where a first pass from the camera finds directions that reach the environment map; this information is used to create sampling distributions for use in a second rendering pass. Atanasov et al. (2018) also applied a two-pass algorithm to the task, furthermore discretizing regions of the scene in order to account for different parts of the environment map being visible in different regions of the scene.

#### Optimizing Visibility Testing

As discussed in Chapter 6, 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.

Another approach for optimizing ray tracing for shadow rays is 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 does not 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 et
al. (1999) developed a generalization of the shadow cache that
tracks which objects block light from particular light sources and clips
their geometry against the light-source geometry so that shadow rays do not
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). A related 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 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 the 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 during rendering. A related approach to reducing the cost of shadow rays is visibility caching, where the point-to-point visibility function’s value is cached for clusters of points on surfaces in the scene (Clarberg and Akenine-Möller 2008b; Popov et al. 2013).

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.

The expense of tracing shadow rays to light sources can be significant; a number of techniques have been developed to improve the efficiency of this part of the rendering computation. Billen et al. (2013) tested only a random subset of potential occluders for intersections; a compensation term ensured that the result was unbiased. Following work showed how to use simplified geometry for some shadow tests while still computing the correct result overall (Billen et al. 2014).

#### Many-Light Sampling

A number of approaches have been developed to efficiently render scenes with hundreds or thousands of light sources. Early work on this problem was done by Ward (1991) and Shirley et al. (1996).

Wald et al. (2003) suggested rendering an image with path tracing and a very low sampling rate (e.g., one path per pixel), recording information about which of the light sources made some contribution to the image. This information is then used to set probabilities for sampling each light. Donikian et al. (2006) adaptively found PDFs for sampling lights through an iterative process of taking a number of light samples, noting which ones were effective, and reusing this information at nearby pixels. The “lightcuts” algorithm, described in the “Further Reading” section of Chapter 13, also addresses this problem.

Tokuyoshi and Harada (2016) organized lights in trees of
bounding spheres and stochastically culled them when shading. Conty Estevez
and Kulla (2018) organized lights in BVHs and introduced
effective approaches for building light BVHs and sampling lights stored in
them. `pbrt`’s `BVHLightSampler` is directly based on their approach.
(The *Iray* renderer uses a BVH in a similar fashion for light
sampling (Keller et al. 2017).) Conty Estevez and Kulla’s approach was
subsequently improved by Liu et al. (2019b), who incorporated
the BSDF in the sampling weight computations.

Incorporating light visibility into the sampling process can substantially improve the results. Vévoda et al. (2018) clustered lights and tracked visibility to them, applying Bayesian regression to learn how to effectively sample lights. Guo et al. (2020) cached information about voxel-to-voxel visibility in a discretization of the scene, which can either be used for Russian roulette or for light importance sampling. Bitterli et al. (2020) showed how to apply spatial and temporal resampling of light samples that include visibility in order to achieve high-quality results with few shadow rays per pixel.

The “bit trail” technique used to encode the path from the root to each
light at the leaves of `pbrt`’s `BVHLightSampler` is due to Laine
(2010).

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