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Southwest Gaming ExpoWorkshop on Network and Systems Support for Games (NetGames 2009)ICIDS 2009 Interactive StorytellingGlobal Game Jam
Rendering Water as a Post-process Effect
IntroductionWater plays an important role in all terrain renderers used in modern games and visualizations to present outdoor areas. This is because it improves general image quality in an extent bigger than any other technique and makes it more photorealistic. Alas, even though it tends to look better and better with every game released it is still far from being realistic.Besides, deferred shading gains popularity every month. Many newer games and engines make use of it, eg. Starcraft 2 and Tabula Rasa. Though deferred shading is typically used to limit lighting-related operations from O(objects_number * lights_number) to O(objects_number) I will prove that it can be helpful in many more algorithms. In this article I will describe a technique of realistic and flexible water rendering by using bump mapping in the post-process stage just after deferred shading. The presented technique fits into the concept of deferred shading pretty nicely, i.e. it helps to avoid additional geometry rendering. A description on deferred shading can be found in [1], [2] and [3]. It is possible to implement this technique using forward rendering but in this case it seems less natural and may require additional work. The presented algorithm eliminates the majority of the flaws of typical techniques used for water rendering such as hard edges or unrealistic colour extinction. I will talk shortly about common drawbacks in the section “Traditional approaches to water rendering”. Theory behind waterThe theory behind water is very complex and not fully understood. It will suffice to say that there is no adequate formal model describing it so far. Survey conducted by Guillot [4] proved that none of the 46 models he analyzed is valid when compared to reality.Existing models are also a way too complex and computationally expensive to be used for real time applications, especially games. A game should not spend most of its CPU or GPU processing time just to update and render realistic water. So a completely different solution has to be found. In my opinion the theory of water for real time applications can be divided into two categories:
Reflection and refractionA light ray going through the water surface gets reflected and refracted, causing specular, caustics and light shafts to appear. Light shafts and caustics play an important role in underwater scenes, however for an observer standing above the water surface they do not improve the quality of water that much.A key to describing reflection and refraction is the Fresnel term. The Fresnel equation tells us how much light is reflected and refracted when it crosses a border between different media (in this case water and air). We have to make an assumption that light goes through two materials only as the term shown later does not apply in a more general case. Besides, both of them have to be homogeneous and one of them has to have a higher density. "Air – water” pair falls well into this assumption. However "air - window glass” does not as it consists of three materials (air – glass – air). Graphically it is depicted as follows:
For any given angle of light a and refraction coefficients describing both materials A and B, namely nA and nB, we use following notation:
The Fresnel term could then be defined as follows:
However this equation is too complex to be computed on GPU per-pixel. Therefore, a frequently used approximation is given below:
This function is very similar to the one described previously so the loss of quality is really insignificant. R(0) is constant and therefore it should be computed only once and then passed to the pixel shader. Index of refraction IOR = 1,33333 Colour extinctionOne of the most important aspects of proper water rendering are colour extinction as light goes deeper and deeper and also light scattering. However, rarely does anyone pay attention to that, although these are the two phenomena which cause water to have the colour we see. This colour is called the “apparent one” and can be totally different from so-called true water colour. To find this true colour, one has to filter out all the particles and organic material from water. It is done in laboratories and for us is not usable. One thing to note is that true water colour is bluish (not completely transparent as it was believed some time ago). We will use this information later on.For each component of the light spectrum, speed of extinction is different. This is due to different wavelengths of the components. The visible range of light is exceptional in that attenuation fades slowly compared to infra-red or ultraviolet. For them, absorption rate is so high they fade away entirely at a maximum depth of a few centimetres. In the table underneath, average depths at which light components die out are presented. The table is valid only for very clean waters. In the case of muddy ones like lakes or rivers it has to be modified:
We make an assumption that extinction is linear with depth. In general this is not true as water is not homogeneous at its whole depth. Many waters consist of tiers of different temperatures and density which makes them different mediums. However, to simulate water in a convincing way it is not necessary to take this into account. Besides, extinction speed ratio and water colour are also influenced by chemical composition of the water area bottom, level of siltation, existence of organic materials (like algae or plankton) and even sky colour! An important conclusion from this deliberation is that the further from the equator the water is the more green its colour becomes.
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for water is equal:
