## Water drop 3b – Physically based wet surfaces

Version : 1.3 – Living blog – First version was 15 avril 2013

This is the third post of a series about simulating rain and its effect on the world in game. As it is a pretty big post, I split it in two parts A and B:

Water drop 1 – Observe rainy world
Water drop 2a – Dynamic rain and its effects
Water drop 2b – Dynamic rain and its effects
Water drop 3a – Physically based wet surfaces
Water drop 3b – Physically based wet surfaces
Water drop 4a – Reflecting wet world
Water drop 4b – Reflecting wet world

Directly following the part A let’s continue with other rain effects:

## Approximation for game

We have begun this post by studying the influence of water on lighting for wet surfaces. Then we have seen two real time implementations with analytic light for both optical phenomena which were inherited directly from the observation. They have some drawbacks, they miss an image based lighting implementation and their cost for in-game usage still a problem for XBOX360/PS3 game. In computer graphic there is a different path available to simulate optical phenomena other than changing the lighting model. We could simply create/edit/capture both wet and dry surfaces BRDF parameters (diffuse, specular, specular power…) with the same lighting model. This is not really a “simulation” as we know the final wet state of the surface but we are now able to render wet surfaces and to dynamically wet our game world. Simply interpolating between dry and  wet BRDF parameters without changing the lighting model do the effect. Nevertheless this approach is stuck to the subsurface scattering events inside the wet material and its top, i.e the diffuse and specular of the wet surface itself. It will not allow to simulate the dual layering lighting we have study in part A when there is a thin layer of water on the top of the wet surface. I will discuss this point later.

The benefit is the simplicity of the process and we still compatible with any kind of lights: image based lighting and analytic. The drawback of requiring a dry and a wet set of BRDF parameters by surfaces is the time to author and store them. The wet lighting model approach required more instructions whereas this one require only few extra instructions (but this still two textures fetch for the blending). However in game development, doubling the storage in memory/disc space and the number of textures to author is prohibited. Hopefully we now know that’s we can express both wet and dry surfaces with the same lighting model, so maybe we can find a way to tweak the dry BRDF parameters to get an approximation of the wet’s one and thus avoid the inconvenient of storing and authoring new textures.

Almost all games I know chose to follow this  BRDF parameters’ tweaking path : Stalker [12], Uncharted 2/3 (on the main character), Assassin’s creed 3 [13], Crysis 2/3, Metal Gear Solid V [15] etc… This is not surprising as the method seems simple and it fit very well with a deferred shading renderer: You can tweak dry BRDF parameters in the G-buffer without complicating the lighting systems. However the wet BRDF parameters generated by these games are either coarse or wrong approximation (in a physical sense, I am agree that’s visually the look can be Ok). Most use the same eye-calibrated factors to attenuate diffuse and boost specular (old fashion) on every wet surfaces of the scene regardless of material properties (roughness/smoothness, porosity, metalic/dielectric…). Assassin’s creed 3 even does an additional wrong step by changing the strength of the factor based on the type of rain. Remember from part A that under any type of rains a porous surface can be water saturated. This only depends on  water precipitation volume and exposition time. A bit differently Tomb Raider : A survivor is born [14] use “dark light” to attenuate the light receive by the diffuse part of the wetted surfaces, the specular part is modified as other games. As they use lights to produce rain with a light prepass renderer, I think they intent to make up the missing of a diffuse parameter in the small G-Buffer with this method. Which again apply wrongly the same modification factors on all dry surfaces.

One of the purposes of the remainder of this section is to improve the BRDF wet parameters generation from the dry one. I want to highlight the benefit of PBR for this parameters generation. I will begin by talking about the tweaking of the diffuse (or subsurface scattering part) and the specular parameters for porous dielectric material then for other kind of materials. I will end with the effect of the thin layer of water which can accumulate above surfaces and the case of thick accumulated water like puddles.

Porous dielectric material

Disclaimer all color values I will talk about are in RGB linear space, not sRGB space. All graph show here are available in a Mathematica file at the end of this section.

We aim to found a factor which can be applied on a dry diffuse parameter to get a wet diffuse parameter and equivalent for the glossiness parameter. I will begin by an overview of previous works, they are all focus on rough dielectric material.

For asphalt in driving simulator, Nakamae et al [2] use a factor between 0.1 and 0.3 to attenuate the diffuse albedo and a factor of 5 to 10 to boost the specular (not PBR). As many other, they perform an empirical calibration for this coefficient without taking into account the properties of the surfaces.

[3] and [16] details the two optical theories that’s we see in this post (part A)  which aim to explain the darkening of the albedo. We will call the model of [3] LD and the model of [16] TBM. I would advice that’s the albedo mention in this paper don’t match the diffuse albedo definition we use in computer graphic (i.e the diffuse color of a perfect lambertian surface), it contain some specular reflection. Both papers purpose a relationship between wet and dry albedo. They explain that’s the highest differences between wet and dry albedo occurs for surface in the middle range of dry albedo. Dark surfaces will tend to absorb more light on first contact with the surface, the contribution of internal reflections will be less important  decreasing the effect of wetting. Bright surfaces will tend to reflect much more light than is absorbed by internal reflection also decreasing the effect of wetting. In both case the relationship between dry and wet albedo depends only on the  index of refraction (IOR) of the surface, the IOR of the water and the dry albedo. The following graph is the wet albedo function of the dry albedo from the optical phenomena of [3] for an IOR of 1.5 for surface (common value for rough dielectric surface) and 1.33 for water. The red line is the dry albedo for comparison:

I found more readable to transform this graph to the fraction of wet / dry albedo function of albedo. This means the factor to apply to dry albedo to retrieve wet albedo:

A good comment about these graphs is done in [6]:

They further show that the wet albedo is a non-linear function of dry albedo, with low albedos reduced more by wetting than high albedos. A consequence of this result (not explicitly stated in their paper) is that wet surface color is more saturated than dry surface color, because the wetting further exaggerates the differences in albedo for different wavelengths.
Source [6]

## Water drop 3a – Physically based wet surfaces

Version : 1.3 – Living blog – First version was 19 March 2013

This is the third post of a series about simulating rain and its effect on the world in game. As it is a pretty big post, I split it in two parts A and B:

Water drop 1 – Observe rainy world
Water drop 2a – Dynamic rain and its effects
Water drop 2b – Dynamic rain and its effects
Water drop 3a – Physically based wet surfaces
Water drop 3b – Physically based wet surfaces
Water drop 4a – Reflecting wet world
Water drop 4b – Reflecting wet world

Physically based rendering (PBR) is now common in game (See Adopting a physically based shading model to know more about it). When I introduce PBR in my company few years ago we were actually working on rain. At this time we were questioning about how our new lighting model should behave to simulate wet surfaces. With classic game lighting model, the way everybody chose was to darken the diffuse term and boost the specular term (Here I refer to the classic specular use as RGB color to multiply with the lighting). The wet diffuse/specular factors being eye calibrate. I wanted to go further than simply adapt this behavior to PBR and this required to better understand the interaction between water and materials. This post is a mix of the result of old and recent researches. I chose to provide up to date information including experimental (not complete) work because the subject is complex and talking about it is useful. This might be of interest for future research. The post describe how water influence materials and provide ways to simulate wet surfaces with physically based lighting model.  I suppose here that’s the reader know the basics of reflected/refracted lights with Snell’s law and index of refraction (IOR).

## Wet surfaces – Theory

People are able to distinguish between a wet and a dry surface by sight. The observation post show many pictures to illustrate this point. The main visual cue people retain is that wet surfaces look darker, more specular and exhibit subtle changes in saturation and hue when wet:

This behavior is commonly observed for natural or human made rough material/porous materials (brick, clay, plaster, concrete, asphalt, wood, rust, cardboard, stone…), powdered materials (sand, dirt, soil…), absorbent materials (paper, cotton, fabrics…) or organic materials (fur, hair…). However this is not always the case, smooth materials (glass, marble, plastic, metal, painted surface, polished surface…) don’t change. For example, there is a big difference between a dry rough stone and a wet rough stone but a very small difference between highly polished wet stone and highly polished dry stone.
In the following discussion, wet surfaces refer mostly to rough and diffuse materials quenched in water and having a very thin water layer on their surfaces.

Why rough wet surfaces are darker when wet ? Because they reflect less light.
There is two optical phenomena imply in this decrease of light reflection and they are details in [3] and [4]. A rough material has small air gaps or pores which will be filling by water when wetting process begin. When pores are filled, there is  “water saturation”, water propagates onto the material as a thin layer.

Let’s first see the impact of the thin layer of water. The rough surface leads to a diffuse reflection (Lambertian surface).  Some of the light reflected from the surface will be reflected back to the surface by the water-air interface due to total internal reflection. Total internal reflection occur when moving from a denser medium into a less dense one (i.e., n1 > n2), above an incidence angle known as the critical angle (See [1] for more detail). For water-air interface, this is $\theta_c=arcsin(\frac{n_{air}}{n_{water}})=arcsin(\frac{1.0}{1.33})=48.75^{\circ}$

Source [1]

This reflected light from the surface is then subject to another round of absorption by the surface before it is reflected again. This light’s back and forth result in darkening of the surface.

Source [2]

Now take a look at the water filling in the pore inside the rough material. There is a concentration of water beneath the surface. The water which replace the air have an index of refraction higher than that of air (1.33 against 1.0) which is closer to index of refraction of most rough dielectric material (1.5). Consequence, following the Snell’s law, light entering in material will be less refracted due to the reduced index of refraction difference: The scattering of light under the surface is more directional in the forward direction. The increase scattering events before the light leave the surface increases the amount of light absorbed and thus reduce the light reflection.

Source[5]

The darkening of the material is also accompanied by a subtle change in saturation and hue. In [11] the spectral reflectance (i.e the “RGB” representation of real world color, the visible range of the spectrum is around 400nm blue to 780 nm red) of a dry and wet stone has been measured to highlight these characteristics. Analyze show that’s there is a significant reduction in reflectance across the whole range of the visible spectrum when the surface gets wet. Which confirm the darkening of the surface. It also show that’s the surface color becomes more saturated because of this reduction.

Source [11].

## Water drop 1 – Observe rainy world

Version : 1.2 – Living blog – First version was 10 December 2012

This post is the first of a series about simulating dynamic rain and its effect on the world. All in the context of games:

Water drop 1 – Observe rainy world
Water drop 2a – Dynamic rain and its effects
Water drop 2b – Dynamic rain and its effects
Water drop 3a – Physically based wet surfaces
Water drop 3b – Physically based wet surfaces
Water drop 4a – Reflecting wet world
Water drop 4b – Reflecting wet world

In several games today there are dynamic weather effects. The most popular weather effect is rain. Rain has sadly often no effect on the gameplay but it has on the visual. Rain in real life has a lot of impact on the appearance of the world. The goal of this series is to describe technique, both technical and artistic, to be able to render a world rainy mood. By wet world, I mean not only world under rain, but also world after it stop raining. Let’s begin this series by an observation of the real-life wet world. As always, any feedbacks or comments are welcome.

## Real wet world

The first thing I have done when I started to study this topic for my game “Remember Me” is to make a lot of references. All pictures are programmer’s photography with low camera :). I should advice that’s I focus on moderate rain in urban environment not rain forest or other heavy rain. Let’s share some result (click for high res version).

The first thing everybody notice when it’s raining in the night is the long stretched highlight reflection of the bright light sources:

But this is not restricted to the night (and even not restricted to wet surface, it is only more visible with wet surfaces):

Highlight reflection vary with the roughness of the underlying surface:

The highlights get dimmer when the surface is rougher (This is energy conservation):

Highlights size depends on view angle. The anisotropic reflection seems to follow a Blinn-Phong behavior (Also Blinn-Phong model don’t allow to strech so much):