9 June 2008 - 14:41Global Relief Mapping Technique

In which direction is the development of relief mapping techniques heading?

Techniques for visualizing surfaces of highly detailed geometry without exploiting the bandwidth to the stress limits by passing a huge amount of primitives down the graphics pipe have been a research topic for quite a while. Currently, techniques such as bump mapping, parallax mapping, and parallax occlusion mapping seem to be the standard techniques that are present in every pipeline of a 3D engine on the market today. Among newer detailed surface techniques we find a large group of relief mapping techniques:

- Per-Pixel Displacement Mapping with Distance Function (GPU GEMS 2)
- Interval Mapping
- Cone Step Mapping
- Relaxed cone step mapping For Relief Mapping (GPU GEMS 3).

All these techniques are based on fixed point iteration schemes (sometimes called ray tracing), which are solved numerically in order to find the actually displacement/offset of the texture coordinates for each pixel. Such approaches are of course much more accurate than the approximations techniques bump mapping and parallax mapping. The advantage of viewing the problem as a fixed point problem is that the problem can be mapped directly onto the pixel shader, which is intuitive and easy!

However, I think techniques which consider the problem more globally will occur in the future. A global approach will solve for all pixels at once and then use the solution to render. I am of course working on such an approach, which most likely will be called inverse mapping. The technique has some relation to my previous post “The Inverse Function Theorem”. The meaning with this post was however to discuss some of the advantages/disadvantages of global approaches versus the fixed point schemes (I will denote the fixed point schemes local schemes from now on), and write about the idea of using mapping techniques for skybox rendering. First a list of some significant advantages and disadvantages:

Advantages: coherent solution, no artifacts, no iteration in pixel shaders, better solutions of deep surfaces, more general computing minded, only needs to be recomputed when the viewpoint changes.
Disadvantages: same time complexity, no culling.

Obtaining a global coherent solution will not contain artifacts as seen in for example the local approach cone step mapping, where solutions sort of blend around the edge of ridges on the surface. The solving technique will differ much from the fixed point techniques and does not match the fix graphical pipeline as well as the these, however GPU’s are beginning to support better languages for general purposes (I am especially referring to CUDA), which the first robust implementation most likely will be targeted towards. One disadvantage is the lack of culling. It is hard to do know which pixels that should be culling since the solution is obtained independent of what is going on in the color buffer, where as the local approaches are performed directly into the color buffer and culling is therefore easy.

I have done some simple CPU and shader implementations which executes fine! I have included a sample picture and a movie of a parabolic cylinder surface, which are rendered using my technique. The white dot shows the position of a point light. Animation Clip (17MB)

The time complexity of the global technique seems to be very similar to the local approaches - but it provides much better quality of the rendering. Furthermore, it should be noted that both local and global techniques lack the support of multiple depth maps, which is a research problem for itself. Allowing multiple depth maps enables the possibility of the surface to fold in the depth direction.

Using a global mapping technique for skyboxes

Everyone that has tried to play an ordinary open scenario FPS game have noticed that the levels of the game are cut off at some point in space. Standing at this cut off boundary one can often see what is called the skybox. My favorite example of a skybox can be found in Half Life 2 Episode 2 (see picture), where the background is not a simple static background, but contains dynamical elements which helps making it a part of the whole scenario. Another good example is the skyboxes used in the game Riddick EFBB – which the Swedish developers Starbreeze actually acquired out of house, but never the less it is some real nice artwork.

Now, imagine having a technique that could present as much geometry you would like at the far distances of the scenario. This technique could be the global mapping technique! It will be able to handle such things and will provide backgrounds of same quality as the rest of the scene! This means that city scenes could render houses of the same quality in the far distances and open spaces with a lot of vegetation could be rendered at the same quality in the far distances. Imagine such techniques in games like: Assassins Creed, Alan Wake, Far Cry 2, GTA IV, the city seen in the Half Life screen, Hitman, The Witcher, to name a few. Of course, the technique that I have discussed have some immediate technical problems, such as the resolution of surface details (normal map, depth maps), the requirement of multiple depth maps, and some difficulties with dynamic environments. But seen in the light of the skybox and LOD techniques (seen in far cry) that are the standards today – this idea would certainly be a step forward!