**Contents**

## Light Transport

In a typical scene, light is likely to bounce off of the surface of many objects before it reaches the eye. As explained in the previous chapter, the direction in which light is reflected depends on the material type (is it diffuse, specular, etc.), thus light paths are determined by all the successive materials light rays interact with on their way to the eye.

Imagine a light ray emitted from a light source, reflected off of a diffuse surface, then a mirror surface, then a diffuse surface again and then reaching the eye. If we label, the light L, the diffuse surface D, the specular surface S (a mirror reflection can be seen as an ideal specular reflection, one in which the roughness of the surface is 0) and the eye E, the light path in this particular example is LDSDE. Of course you can imagine all sort of possible combinations and even that this path is an infinitely long string of Ds and Ss. The one thing that all these rays would have in common, is a L at the start and an E at the end. The shortest possible light path is LE. This happens if you look directly at a light source. Rays emitted by the light reaches the eye directly (without bouncing off of surface at all). If light rays bounce off the surface only once, which using the light path notation could be expressed as either LSE or LDE, then we have a case of direct lighting (direct specular or direct diffuse). Direct specular is what you have when the sun is reflected off of a water surface for instance. If you look at the reflection of a mountain in the lake, you are more likely to have a LDSE path (assuming the mountain is a diffuse surface), etc., which is a case of indirect ligthing.

Researcher Paul Heckbert introduced the concept of labelling paths that way in paper published in 1990 and entitled "Adaptive Radiosity Textures for Bidirectional Ray Tracing". It is not uncommon to use regular expressions to describe light paths in a compact way. For example any combination of refection off the surface of a diffuse or specular surface can be written as: L(D|S)*E. In Regex (the abbreviation for regular expression), (a|b)* denotes the set of all strings with no symbols other than "a" and "b", including the empty string: {ɛ, "a", "b", "aa", "ab", "ba", "bb", "aaa", ...}.

At this point, you may think, "this is all good, but how does that relate to rendering?". As mentioned several times already in this lesson and the previous one, in the real world, light goes from light sources to the eye. But only a fraction of the rays emitted by light sources actually reach the eye. Therefore, rather than simulation light path from the source to the eye, a more efficient approach is to start from the eye, and walk back to the source.

This is what we typically do in ray tracing. We trace a ray from the eye (we generally call the **eye ray**, **primary ray** or **camera ray**) and check whether this ray intersects any geometry in the scene. If it does (let's call P, the point where the ray intersects the surface), we then need to do two things: compute how much light arrives at P from light sources (direct lighting), and how much light arrives a P indirectly, as a result of light being reflected by other surfaces in the scene (indirect lighting).

- To compute the direct contribution of a light to the illumination of P, we trace a ray from P to the source. If this ray intersects another object on its way to the light, then P is in the shadow of this light (which is why we sometimes call these rays
**shadow rays**). This is illustrated in figure 2. - Indirect lighting comes from other objects in the scene reflecting light towards P, whether as a result of these objects reflecting light from a light source or a a result of these objects reflecting light which is itself bouncing off of the surface of other objects in the scene. In ray tracing, indirect illumination is computed by spawning new rays, called
**secondary rays**from P into the scene (figure 3). Let's explain in more details how and why this works.

If these secondary rays intersects other objects or surfaces in the scene, then it is reasonable to assume, that light travels along these rays from the surfaces they intersect to P. We know that the amount of light reflected by a surface depends on the amount of light arriving on the surface as well as the viewing direction. Thus to know how much light is reflected towards P along any of these secondary rays, we need to:

- Compute the amount of light arriving at the point of intersection between the secondary ray and the surface.
- Measure how much of that light is actually reflected by that surface to P, using the secondary ray direction as our viewing direction.

Computing how much light arrives at a point of intersection between a secondary ray and a surface, is no different than computing how much light arrives at P. Computing how much light is actually reflected in the ray direction towards P, depends on the surface property, and is generally done in what we call a **shader**. We will talk about shaders in the next chapter.

**Monte Carlo**before and particularly

**Monte Carlo ray tracing**, that's what this technique is all about. Shooting a few rays to approximate the exact amount of light arriving on a point. The downside is that the result is only an approximation. The bright side, is that we get a result for a problem which is otherwise not tractable (e.i. it is impossible to compute exactly within any amount of reasonable finite time).

Computing indirect illumination is a **recursive** process. Secondary rays are generated from P, which in turns generate new intersection point, from which other secondary rays are generated and so on. We can count the number of times light is reflected from surfaces from the light source until it reaches P. One bounce indirect illumination is for light bouncing off the surface of objects only once before it gets to P. Two bounces is for light bouncing off twice, three bounces, three times, etc.

The number of time light bounces off the surface of objects can be infinite (imagine a situation for example in which a camera is inside a box illuminated by a light on the ceiling? rays would keep bouncing off the walls for ever). To avoid this situation, we generally stop spawning secondary rays rays after a certain number of bounces (typically 1, 2, or 3). Note though that as a result of setting a limit to the number of bounces, P is likely to look darker than it actually should (since any fraction of the total amount of light emitted by a light source that took more bounces than the limit to arrive at P, will be ignored). If we set the limit to two bounces for instance, then we ignore the contribution all the other bounces above (third, fourth, etc.). However luckily enough, each time light bounces off of the surface of an object, it loses a little bit of its energy. Which means that as the number of bounces increases, the contribution of these bounces to the indirect illumination of a point decreases. Thus, there is a point after which you might consider that, computing one more bounce makes such a little difference to the image, that it doesn't justify the amount of time it actually takes to simulating it.

This long explanation is to show you, that the principle of actually computing the amount of light impinging upon P whether directly or indirectly is simple, especially if we use the ray tracing approach. The only sacrifice to physical accuracy we made so far, is to put a cap on the maximum number of bounces we compute, which is necessary to insure than the simulation will not run for ever. In computer graphics, this algorithm is known as **unidirectional path tracing** (it belongs to a larger category of light transport algorithms known as path tracing). This is simplest and most basic of all **light transport models** based on ray tracing (it is also goes by the name of classic ray tracing of Whitted style ray tracing) . It's called unidirectional, because it only goes in one direction, from the eye to the light source. The part "path tracing" is pretty straightforward: it's all about tracing light paths through the scene.

This method was originally proposed by **Appel** in 1986 ("Some Techniques for Shading Machine Rendering of Solids") and later developed by **Whitted** (An improved illumination model for shaded display - 1979).

Other techniques than ray tracing can be used to compute global illumination. Note though that ray tracing seems to be the most adequate way of simulating the way light spreads out in the real world. But things are not that simple. With unidirectional path tracing for example, some light paths are more complicated to compute efficiently than others. This is particularly true of light paths involving specular surfaces illuminating diffuse surfaces (or any type of surfaces for that matter) indirectly. Let's take an example.

As you can see in the image above, in this particular situation, light emitted by the source at the top of the image, is refracted through a (transparent) glass ball which by the effect of refraction, concentrates all light rays towards a singular point on the plane underneath. This is what we call a caustic. Note that actually no direct light arrives at P from the light source directly (P is in the 'shadow' of the sphere). It all comes indirectly through the sphere by the mean of refraction and transmission. While it may seems more natural in this particular situation to trace light from the light source to the eye, considering that we decided to trace light rays the other way around, let's see what we get.

When it will come to compute how much light arrives at P indirectly, if we assume that the surface at P is diffuse, then we will spawn a bunch of rays in random directions to check which surfaces in the scene redirect light towards P. But by doing so, we will totally fail accounting for the fact that actually all light comes from the bottom surface of the sphere. So obviously we could maybe solve this problem by spawning all rays from P towards the sphere, but since our approach assumes we have no prior knowledge of how light travels from the light source to every single point in the scene, that's not something we can actually do (we have actually no prior knowledge that a light is above the sphere and no reason to assume that this light is the light that contributes to the illumination of P via transmission and refraction). All we can do, is spawn rays in random directions as we do with all other surfaces, which is how unidirectional path tracing works. One of these rays might actually hit the sphere and get traced back to the light source (but we don't even have a guarantee that even a single ray will hit the sphere since their directions are chosen randomly), however this might only be one ray over maybe 10 or 20 or 100 we cast into the scene, thus we might actually miserably fail in this particular case to compute how much light arrives at P indirectly.

Using Heckbert light path's naming convention, we can say that path of the kind LS+DE are generally hard to simulate in computer graphics using the basic approach of tracing back the path of light rays from the eye to the source (or unidirectional path tracing). In Regex, the + sign account for any sequences that matches the element preceding the sign one or more times. For example, ab+c matches "abc", "abbc", "abbbc", and so on, but not "ac". What this means in our case, is that situations in which light is reflected off of the surface of one or more specular surfaces before it reaches a diffuse surface and then the eye (as in the example of the glass sphere), are actually hard to simulate using unidirectional path tracing.

What do we do then? This is where the art of light transport comes into play.

Obviously, while being simple and thus very appealing for this reason, a naive implementation of tracing light path back to the eye is not efficient in some cases. It seems to work well when the scene is only made of diffuse surfaces, but is problematic when the scene contains a mix of diffuse and specular surfaces (which is more often the case than not). So what do we do? Well, we do the same thing as we usually do when we have a problem. We search for a solution. And in this particular case, this leads to looking for developing strategies (or algorithm) that would work well to simulate all sort of possible scenarios. We want a strategy in which LS+DE paths can be simulated as efficiently as LD+E paths. And since our default strategy doesn't work well in this case, we need to come up with news ones. This lead obviously to developing new **light transport algorithms** as better solution to unidirectional path tracing to solve the light transport problem. More formally light transport algorithms are strategies (implemented in the form of algorithms) that attempt to propose a solution to the problem we just presented: solving efficiently ALL possible light paths, or more generally light transport.

Light transport algorithms are not that many, but still, quite a few exist. And don't be mislead. Nothing in the rules of coming up with the greatest light transport algorithm of all times, tells you that you have to use ray tracing to solve the problem. You have the choice of the weapon. In fact, many solution uses what we call an hybrid or multi-passes approach. **Photon mapping** is an example of such algorithm. They require the pre-computation of some lighting information stored in specific data structures (a photon map or a point cloud generally for example), before actually rendering the final image. Difficult light paths are resolved more efficiently by taking advantage of the information stored in these structures. Remember that we said in the glass sphere example that we had no prior knowledge of the existence of the light above the sphere? Well, photon maps in away is way of looking at the scene before it gets rendered and trying to precisely get some prior knowledge of where light "photons" go before rendering the final image. It is based on that idea.

While being quite popular some years ago, these algorithms though are based on a multi-passes approach. In other words, you need to generate some extra data before you can actually render your final image. This is great, if it helps to render images you couldn't render otherwise, but multi-passes rendering is a pain to manage, requires a lot of extra work, requires generally to store extra data on disk, and the process of actually rendering the image doesn't start before all the pre-computation steps are complete (thus you need to wait for a while before you can actually see something). As we said, for a long time they were popular because they made it possible to render things such as caustics which would have been too long to render with pure ray tracing, and that therefore, we generally ignored all together. Thus having a technique to simulate them (no matter how painful it is to setup) is better than nothing. However, of course, a unified approach is better: one in which the multi-pass is not required, and one which integrates smoothly to your existing framework. For example if you use ray tracing (as your framework), wouldn't it be great to come up an algorithm that only uses ray tracing, and never have to pre-compute anything. Well, it does exist.

Several algorithms have been developed around ray tracing and ray tracing only. Extending the concept of unidirectional path tracing, which we talked about above, we can use another algorithm known as bi-directional path tracing. It is based on the relatively simple idea, that for every ray you spawn from the eye into the scene, you can also spawn a ray from a light source into the scene, and then try to connect their respective paths through various strategies. An entire section of Scratchapixel is devoted to light transport and we will review in this section, some of the most important light transport algorithms, such as unidirectional path tracing, bi-directional path tracing, metropolis light transport, instant radiosity, photon mapping, radiosity caching, etc.

## In Summary

Probably one of the most common myths in computer graphics, is that ray tracing is both the ultimate and only way to solve global illumination. While it may be the ultimate way in the sense that it offers a much more natural way of thinking of the way light travels in the real world, it also has its limitations, as we showed in this introduction, and it is certainly not the only way. You can broadly distinguish between two sort of light transport algorithms:

- Those which are not using ray tracing such as photon or shadow mapping, radiosity etc.
- Those which are using ray tracing and ray tracing only.

As long as the algorithm efficiently captures light paths which are difficult to capture with the traditional unidirectional path tracing algorithm, modern implementation do tend to favour light transport method solely based on ray tracing, simply because ray tracing is a more natural way to think about light propagation in a scene, and offers a unified approach to computing global illumination (one in which using auxiliary structures or systems to store light information is not necessary). Note though that while such algorithms do tend to be the norm these days in off-line rendering, real-time rendering system are still very much based on the former approach (they are generally not designed to use ray tracing, and still rely on this things such as shadow maps or light fields to compute direct and indirect illumination).