Critique my lighting model.

I was working on a custom lighting model a while ago, for use with GLSL shaders and whatnot. I haven't posted anything about it here yet, and I'd like to get some feedback on it before I start making real use of it (using it in applications and such).

I've got an explaination of the model, and a link to the image of the formula here. It's not exactly a professional article or anything, but i'm not a professional :). There are also plenty of holes in my knowledge of the math for this stuff too (I really need highschool to be done with so I can move on to these more interesting things), so there's also a good chance I sound like an idiot to those of you who know this stuff well.

Thanks!

erm, 'i' goes from 0 to infinity but isn't used anywhere in the formula.. your integrating a constant? ;)

Well the lighting model doesn't look all that much different from the standard algorithms.

The model I'm using is this:

Code:

float4 PS(float3 Light : TEXCOORD0,float3 Norm : TEXCOORD1, float3 View : TEXCOORD2,float2 TerrainUV : TEXCOORD3, float2 DetailUV : TEXCOORD4,float4 Ext : COLOR1) : COLOR { //Normalize all vectors - //First line is same as m_pDevice->SetRenderState(D3DRS_NORMALIZENORMALS,true) float3 Normal=normalize(Norm); float3 LightDir=normalize(Light); float3 ViewDir=normalize(View); //Diffuse float Diff=saturate(dot(Normal,LightDir)); //Reflection vector (pure phong) float3 Reflect=normalize(2*Diff*Normal-LightDir); //Specular float Specular=pow(saturate(dot(Reflect,ViewDir)),fGlossiness); //Base Texel color float4 TerrainColor=tex2D(Terrain,TerrainUV); //Detail color float4 DetailColor=tex2D(Detail,DetailUV); //Modulate terrain with detail float4 MixColor=(TerrainColor*DetailColor); //Constant ambient float4 Ambient={0.2,0.2,0.2,1.0}; //Final formula for all light in scene float4 GlobalLight=(Ambient)+ (vDIC * Diff) + (vSpecIC * Specular); //Final mix return GlobalLight+MixColor; }

My formula is just the standard lighting equation. I'm not so sure the formula needs altered any to achieve great lighting effects as it has been tried and tested many thousands of times.

For atmospheric scattering you can check out my thread concerning this very topic. There is a group on www.gamedev.net making an engine called Infinity which looks amazing. They use the shader for scattering as well which is how they are achieving such awesome screenshots.

EDIT:
Materials are just a handy way to stick diffuse color and power, specular color and power (glossiness), emissivity color and power, and ambient color and power into a common structure. And what is Cook? Cook-Torrance?

Quote:

For example, the Lambertian lighting model makes use of a specular componant for the light itself. This would indicate that the light is emitting a specular color, when in reality, the specular color is the result of the diffuse light color being reflected off the destination surface material. Put more simply, the specular color componant is actually produced through some combination of the surface color and the light color. The diffuse material componant has also been removed. Rather than multiplying the light diffuse by a solid material color, the diffuse light contribution is multiplied by the texture color (assuming the lighting model is being run at the fragment level).

The material and light ambient componants have been left in the equation, to allow for the (cheap) simulation of atmospheric light scattering.

Let me critique here.

Quote:

For example, the Lambertian lighting model makes use of a specular componant for the light itself. This would indicate that the light is emitting a specular color, when in reality, the specular color is the result of the diffuse light color being reflected off the destination surface material.

There is nothing stated here that is different from the standard lighting equation. Color comes from reflection of a certain wavelength of light. The specular component is simulating what wavelength of light the material reflects at the specular level. It must be different from the diffuse at times because we cannot accurately 'real-time' integrate atmospheric scattering, wavelength changes, etc, at every point along the ray from source to destination and finally to infra-red. The specular component is not a simulation of 'emitting' anything. The specular component is saying that this object reflects this wavelength of specular light. Again we separate them because diffuse alone cannot do specular so we combine the two formulas with differing color values to arrive at the final color.

Quote:

The diffuse material componant has also been removed. Rather than multiplying the light diffuse by a solid material color, the diffuse light contribution is multiplied by the texture color (assuming the lighting model is being run at the fragment level).

This is no different than the standard model. When textures are involved you have more colors being thrown into the mix. If you add them you get very bright pixels and this is not an accurate simulation of what happens to light. When you modulate them (multiply) this is a very good approximation of what happens to wavelengths of light when they are mixed. If we could just simulate lighting with no textures then modulation would not be needed. However this makes for a boring setup. Textures actually must act as a 'material' that also reflects light. But note that a red texel is going to reflect a diff wavelength of light than a blue texel. Simulating this at the texel level would be ...well....slow. So we account for the entire texture by using modulation, which is not 100% accurate, but it's good enough.

Quote:

The material and light ambient componants have been left in the equation, to allow for the (cheap) simulation of atmospheric light scattering.

This has nothing to do with simulating atmospheric light scattering and in no way represent what happens. The closest formula that simulates light scattering at constant atmospheric density is the standard fog formula. However, the fog formula fails to take into account the angle of the sun or light source, the emmissive power of the sun, the atmosphere density, the size of the particles in the atmosphere, the wavelength(s) of light those particles reflect, the amount of light that is removed from the atmosphere by rays being reflected off particles back into space, the relative cloud cover which is going to reflect more back into space (out-scattering), the amount of light added by reflection (in-scattering), and optical depth.

Here are facts about light and atmospheric scattering taking from a master's thesis on the subject. Quote taken from Real-Time Rendering of Atmospheric Scattering Effects for Flight Simulators by Ralf Stokholm Nielsen.

The blue color of the sky is caused by the wavelength dependency of
Rayleigh scattering that favorites the shorter blue wavelength.
When the optical depth approaches infinity, the inscattered color approaches
the color of sunlight. This is why the horizon is white during
the day and red/orange during sunset and sunrise.
Atmospheric scattering is divided into Mie and Rayleigh scattering,
governing the scattering of particles(aerosols) and molecules respectively.
Rayleigh scattering, with equal scattering in the forward and backward
directions, is a subset of the far more complicated Mie scattering.
The Mie scattering phase function can be approximated, using the
Henyey-Greenstein phase function.

The standard fog formula is:

Lo=original color
Cfog=fog color
f(s) - color is a function of distance
L(s)=Lo*(1-f(s))+Cfog*f(s)

Atmospheric scattering is this:

L(s,theta) - final color is a function of distance and angle
Lo=original color
Fext=coefficient represent extinction of light
Lin(s,theta) = in-scattering is a function of distance and angle - computed using Rayleigh and Mie scattering as an approximation of the Henyey-Greenstein phase function.
L(s,theta)=Lo*Fext(s)+Lin(s,theta)

Note the differences. The range fog and even exponential fog formulas fail to account for many real-time atmospheric variables. Also the standard fog formulas attempt to simulate radiant flux, radiosity, and irradiance using pure RGB to RGB values. The actual scattering formula accounts for these and outputs values as radiance values which are then converted to RGB values using wavelength conversion formulas.

Standard lighting formulas for ambient, diffuse, and specular.

X - denotes component-wise multiply --> FinalColor=(A1*A2,R1*R2,G1*G2,B1*B2)

Ambient
C_amb = final ambient color
G_amb = global ambient color
M_amb = material ambient color

C_amb=G_amb X M_amb

Diffuse
C_diff = final diffuse color
N = surface normal
L = light vector
S_diff = diffuse color of light source
M_diff = diffuse color of material

C_diff=(N dot L)S_diff X M_diff

Specular phong
C_spec = final specular color
v = vector to viewer
r = reflected light vector (reflecting light vector about surface normal)
m_gls = glossiness factor
S_spec = specular color of light source
M_spec = specular color of material

C_spec=((v dot r)^m_gls)S_spec X M_spec

Specular Blinn phong
n = surface normal
h = halfway vector

C_spec=((n dot h)^m_gls)S_spec X M_spec

Final equation

C_lit=C_spec+C_diff+C_amb

Expanded
C_lit=i(max(n dot h,0)^m_gls)S_spec X M_spec + max(n dot l,0)S_diff X M_diff) +G+amb X M_amb

Taken from 3D Math Primer for Graphics and Game Development by Fletcher Dunn and Ian Parberry.

Quote:

Originally Posted by Bubba

There is nothing stated here that is different from the standard lighting equation. Color comes from reflection of a certain wavelength of light. The specular component is simulating what wavelength of light the material reflects at the specular level. It must be different from the diffuse at times because we cannot accurately 'real-time' integrate atmospheric scattering, wavelength changes, etc, at every point along the ray from source to destination and finally to infra-red. The specular component is not a simulation of 'emitting' anything. The specular component is saying that this object reflects this wavelength of specular light. Again we separate them because diffuse alone cannot do specular so we combine the two formulas with differing color values to arrive at the final color.

But the standard model allows for a specular componant for the light, and a specular compontant for the material, which are integrtated into the equation to acheive this simulation, which to me, seems a little innacurate. What i'm suggesting is that the specular componant should only be calculated based on/from the diffuse color. Rather then set these two specular colors, just calculate one, which inherits the diffuse properties...or something :).

Quote:

Originally Posted by Bubba

This is no different than the standard model. When textures are involved you have more colors...

No, it isn't. That would more apply to the shader program (in GLSL, replacing gl_FrontMaterial.diffuse with texture2D()). I should have been more specific in what I was trying to say.

Quote:

Originally Posted by Bubba

This has nothing to do with simulating atmospheric light scattering and in no way represent what happens....

Again, I probably didn't explain properly. I confused actual atmosphereic light scattering with ambient light (hence, the ambient light term :rolleyes:).

Quote:

Originally Posted by Perspective

erm, 'i' goes from 0 to infinity but isn't used anywhere in the formula.. your integrating a constant?

Now I'm even more confused about integrals. I know I need to integrate something here, since I know the final light color is a function of time (or something, I don't really know), and because I saw another lighting paper do it :p. Does i represent time, the current pixel, or am I way off?

EDIT:

Quote:

Originally Posted by Bubba

And what is Cook? Cook-Torrance?

Cook is my last name.

Thanks again.

Typically 'i' is the light index for 'n' lights and you sum (or integrate) over all lights to get the final colour value for that pixel.