This book should provide a firm foundation for understanding graphics development. However, there are many subjects that it does not cover which are also important in rendering. Here is a list of topics that you should investigate, with a quick introduction to the basic concepts.

This list is not intended to be a comprehensive tour of all interesting graphical effects. It is simply an introduction to a few concepts that you should spend some time investigating. There may be others not on this list that are worthy of your time.

Vertex Weighting. All of our meshes have had fairly simple linear transformations applied to them (outside of the perspective projection). However, the mesh for a human or human-like character needs to be able to deform based on animations. The transformation for the upper arm and the lower arm are different, but they both affect vertices at the elbow in some way.

The system for dealing with this is called vertex weighting or skinning (note: “skinning”, as a term, has also been applied to mapping a texture on an object. So be aware of that when doing searches). A character is made of a hierarchy of transformations; each transform is called a bone. Vertices are weighted to particular bones. Where it gets interesting is that vertices can have weights to multiple bones. This means that the vertex's final position is determined by a weighted combination of two (or more) transforms.

Vertex shaders generally do this by taking an array of matrices as a uniform block. Each matrix is a bone. Each vertex contains a vec4 which contains up to 4 indices in the bone matrix array, and another vec4 that contains the weight to use with the corresponding bone. The vertex is multiplied by each of the four matrices, and the results are averaged together.

This process is made more complicated by normals and the tangent-space basis necessary for bump mapping. And it is complicated even further by a technique called dual quaternion skinning. This is done primarily to avoid issues with certain bones rotating relative to one another. It prevents vertices from pinching inwards when the wrist bone is rotated 180 degrees from the forearm.

BRDFs. The term Bidirectional Reflectance Distribution Function (BRDF) refers to a special kind of function. It is a function of two directions: the direction towards the incident light and the direction towards the viewer, both of which are specified relative to the surface normal. This last part makes the BRDF independent of the surface normal, as it is an implicit parameter in the equation. The output of the BRDF is the percentage of light from the light source that is reflected along the view direction. Thus, the output of the BRDF is multiples into the incident light intensity to produce the output light intensity.

By all rights, this sounds like a lighting equation. And it is. Indeed, every lighting equation in this book can be expressed in the form of a BRDF. One of the things that make BRDFs as a class of equations interesting is that you can actually take a physical object into a lab, perform a series of tests on it, and produce a BRDF table out of them. This BRDF table, typically expressed as a texture, can then be directly used by a shader to show how a surface in the real world actually behaves under lighting conditions. This can provide much more accurate results than using models as we have done.

Scalable Alpha Testing. We have seen how alpha-test works via discard: a fragment is culled if its alpha is beneath a certain threshold. However, when magnifying a texture providing that alpha, it can create an unfortunate stair-step effect along the border between the culled and unculled part. It is possible to avoid these artifacts, if one preprocesses the texture correctly.

Valve software's Chris Green wrote a paper entitled Improved Alpha-Tested Magnification for Vector Textures and Special Effects. This paper describes a way to take a high-resolution version of the alpha and convert it into a distance field. Since distances interpolate much better in a spatial domain like images, using distance-based culling instead of edge-based culling produces a much smoother result even with a heavily magnified image.

The depth field can also be used to do other effects, like draw outlines around objects or drop shadows. And the best part is that it is a very inexpensive technique to implement. It requires some up-front preprocessing, but what you get in the end is quite powerful and very performance-friendly.

Screen-Space Ambient Occlusion. One of the many difficult processes when doing rasterization-based rendering is dealing with interreflection. That is, light reflected from one object that reflects off of another. We covered this by providing a single ambient light as something of a hack. A useful one, but a hack nonetheless.

Screen-space ambient occlusion (SSAO) is the term given to a hacky modification of this already hacky concept. The idea works like this. If two objects form an interior corner, then the amount of interreflected light for the pixels around that interior corner will be less than the general level of interreflection. This is a generally true statement. What SSAO does is find all of those corners, in screen-space, and decreases the ambient light intensity for them proportionately.

Doing this in screen space requires access to the screen space depth for each pixel. So it combines very nicely with deferred rendering techniques. Indeed, it can simply be folded into the ambient lighting pass of deferred rendering, though getting it to perform reasonably fast is the biggest challenge. But the results can look good enough to be worth the effort.

Light Scattering. When light passes through the atmosphere, it can be absorbed and reflected by the atmosphere itself. After all, this is why the sky is blue: because it absorbs some of the light coming from the sun, tinting the sunlight blue. Clouds are also a form of this: light that hits the water vapor that comprises clouds is reflected around and scattered. Thin clouds appear white because much of the light still makes it through. Thick clouds appear dark because they scatter and absorb so much light that not much passes through them.

All of these are light scattering effects. The most common in real-time scenarios is fog, which meteorologically speaking, is simply a low-lying cloud. Ground fog is commonly approximated in graphics by applying a change to the intensity of the light reflected from a surface towards the viewer. The farther the light travels, the more of it is absorbed and reflected, converting it into the fog's color. So objects that are extremely distant from the viewer would be indistinguishable from the fog itself. The thickness of the fog is based on the distance light has to travel before it becomes just more fog.

Fog can also be volumetric, localized in a specific region in space. This is often done to create the effect of a room full of steam, smoke, or other particulate aerosols. Volumetric fog is much more complex to implement than distance-based fog. This is complicated even more by objects that have to move through the fog region.

Fog system deal with the light reflected from a surface to the viewer. Generalized light scattering systems deal with light from a light source that is scattered through fog. Think about car headlights in a fog: you can see the beam reflecting off of the fog itself. That is an entirely different can of worms and a general implementation is very difficult to pull off. Specific implementations, sometimes called “God rays” for the effect of strong sunlight on dust particles in a dark room, can provide some form of this. But they generally have to be special cased for every occurrence, rather than a generalized technique that can be applied.

Non-Photorealistic Rendering. Talking about non-photorealistic rendering (NPR) as one thing is like talking about non-Elephant biology as one thing. Photorealism may have the majority of the research effort in it, but the depth of non-photorealistic possibilities with modern hardware is extensive.

These techniques often extend beyond mere rendering, from how textures are created and what they store, to exaggerated models, to various other things. Once you leave the comfort of approximately realistic lighting models, all bets are off.

In terms of just the rendering part, the most well-known NPR technique is probably cartoon rendering, also known as cel shading. The idea with realistic lighting is to light a curved object so that it appears curved. With cel shading, the idea is often to light a curved object so that it appears flat. Or at least, so that it approximates one of the many different styles of cel animation, some of which are more flat than others. This generally means that light has only a few intensities: on, perhaps a slightly less on, and off. This creates a sharp highlight edge in the model, which can give the appearance of curvature without a full gradient of intensity.

Coupled with cartoon rendering is some form of outline rendering. This is a bit more difficult to pull off in an aesthetically pleasing way. When an artist is drawing cel animation, they have the ability to fudge things in arbitrary ways to achieve the best result. Computers have to use an algorithm, which is more likely to be a compromise than a perfect solution for every case. What looks good for outlines in one case may not work in another. So testing the various outlining techniques is vital for pulling off a convincing effect.

Other NPR techniques include drawing objects that look like pencil sketches, which require more texture work than rendering system work. Some find ways to make what could have been a photorealistic rendering look like an oil painting of some form, or in some cases, the glossy colors of a comic book. And so on. NPR has as its limits the user's imagination. And the cleverness of the programmer to find a way to make it work, of course.