## Marschner Shader Part III

This is the last part of the three post regarding the Marschner shader. I will explain how to efficiently make the shader for this model, how to add ambient and diffuse lighting and at the end of the post I will also give source code for generating Marschner lookup textures and a video showing the results I had in CS.

**Lookup Textures**

Because there are too many computations done in *M* and *N* functions to be put in the pixel shader, the best optimization is to use lookup textures, that need to be updated as rarely as possible.

We can easily observe that apart from the constants defined in Table 1 ( page 8 ) from Marschner’s paper, the *M* function only depends on *q* _{ i }and *q* _{r }, and *N *on* q* _{ d }and *f* _{ d}. Although this might seem a good optimization at first, taking into account that all these angles must be computed from inverse trigonometric functions, such as acos and asin, which aren’t fast at all, indexing the lookup textures directly by cos and sin sounds a better idea.

The way in which sinus and cosinus values can be computed for all these angles can be found in GPU Gems 2, Chapter 23:

- sin
*q*_{ i }= (*light*·*Tangent*), - sin
*q*_{ o }= (*eye*·*Tangent*). *lightPerp*=*light*– (*light*·*tangent*) x*tangent*,*eyePerp*=*eye*– (*eye*·*tangent*) x*tangent*.- cos
*f*_{ d }= (*eyePerp*·*lightPerp*) x ((*eyePerp*·*eyePerp*) x (*lightPerp*·*lightPerp*))^{-0.5}

As for the cos *q* _{d} if we observe that *q* _{ d} depends on *q* _{ i } and *q* _{r }then we figure out that we can use a channel from the lookup texture indexed by the sins of these two angles.

The easiest way to build these two textures is to make a lookup texture for *M*, having *M _{R, }*

*M*

_{TT, }*M*and cos

_{TRT}*q*

_{d, }and a lookup texture for

*N.*However, in the original paper

*N*and

_{TT }*N*each have three channels, but they can be reduced to only one channel if we consider the absorption to have one channel as well.

_{TRT }These are the lookup textures obtained with my first implementation of the Marschner project:

**Ambient and diffuse lighting**

The Marschner model only specifies the specular component for lighting, so in order to obtain nice visual effects, both ambient and diffuse lighting were added to this model.

I used the lighting from the Nalu Demo, presented in detail in one of my previous posts:

/* Compute diffuse lighting with phi-dependent component */ float diffuse = sqrt(max(0.0001, 1 - uv1.x * uv1.x)); /* Pass colors */ float4 diffuseColor; diffuseColor.rgb = diffuse * objColor.rgb * DiffuseCol; diffuseColor.a = objColor.a; float3 ambientColor; ambientColor = objColor.rgb * AmbientCol; float3 lighting = (( M.r * N.r + M.g * N.g + M.b * N.b ) / (cos_qd * cos_qd)); lighting += diffuseColor.rgb; OUT.xyz = lighting + diffuseColor.rgb * 0.2 + IN.AmbientColor;

**Source code**

Here you can find the first version of my Marschner C# Project, which generates the lookup textures needed for a shader similar to the one presented in the Nalu Demo post.

There are still some things that can be improved, but I plan to release another version for that, as soon as I get a chance. Until then feel free to improve the project yourself.

These are the two adjustments done to the original model, as described in Marschner:

- The absorption is specify by only one channel.
- Instead of the standard
*N*component, the simplify version was used._{TRT}

You can find more information in the README, INSTALL and LICENSE files from the archive.

**Demo**

Next you can see the effects this shader has on Krystal’s hair. If you want to play with the application yourself checkout the hair branch from CS main repository.

## Marschner in Nalu Demo

Before starting to implement anything I downloaded and installed the Nalu Demo from Nivida, that uses Marschner shader for hair rendering, just to have a closer look at this implementation.

Sadly enough this applications doesn’t provide any source code (except for the hlsl shaders) so I had to do some reverse engineering in order to use this shader as a test shader for hair rendering in CS. I set most of the parameters based on the application and configuration files and I used the lookup textures and computed some angles based on Chapter 23 from GPU Gems 2.

In order to keep things simple I chose to set all the application variables in shaders, but if you’d like to pass the light position for instance to the vertex shader you can just comment the line where I set the value for light position in the vs (`float4 LightPos = float4 (9000, 0, 0, 0);`

).

These are the connectors I used:

struct a2vConnector { float4 objCoord : POSITION; float3 objNormal : NORMAL; float3 Tangent: TEXCOORD0; }; struct v2fConnector { float4 projCoord : POSITION; float3 angles : TEXCOORD1; half4 diffuseColor : COLOR0; half3 ambientColor : COLOR1; };

I only modified the a2vConnector in order to have the Tangent buffer too.

The vertex shader looks like this:

v2fConnector main(a2vConnector a2v, uniform float4x4 modelViewProj : state.matrix.mvp, // Light and eye directions in object space uniform float3 objLightDir, uniform float3 objEyePos, // Reflectance model parameters uniform float DiffuseCol, uniform float AmbientCol, uniform float3 worldPointLight0Pos, uniform float3 PointLightColor, uniform float4x4 ModelViewIT : state.matrix.modelview.invtrans) { v2fConnector v2f; float4 LightPos = float4 (9000, 0, 0, 0); objLightDir = normalize(LightPos.xyz - a2v.objCoord.xyz); objEyePos = ModelViewIT[3].xyz; AmbientCol = 0; DiffuseCol = 0.75; PointLightColor = 1; worldPointLight0Pos = LightPos.xyz; float4 objColor = float4(1,0,0,1); /* Compute the tangent from adjacent vertices */ float3 objTangent = normalize(a2v.Tangent - a2v.objCoord.xyz ); /* Project */ float4 objCoord = a2v.objCoord; float4 projCoord = mul(modelViewProj, objCoord); v2f.projCoord = projCoord; float3 objEyeDir = normalize(objEyePos - objCoord.xyz); /* Compute longitudinal angles */ float2 uv1; uv1.x = dot(objLightDir, objTangent); uv1.y = dot(objEyeDir, objTangent); v2f.angles.xy = 0.5 + 0.5*uv1; /* Compute the azimuthal angle */ float3 lightPerp = objLightDir - uv1.x * objTangent; float3 eyePerp = objEyeDir - uv1.y * objTangent; float cosPhi = dot(eyePerp, lightPerp) * rsqrt(dot(eyePerp, eyePerp) * dot(lightPerp, lightPerp)); v2f.angles.z = 0.5*cosPhi + 0.5; /* Compute diffuse lighting with phi-dependent component */ float diffuse = sqrt(max(0, 1 - uv1.x*uv1.x)); /* Pass colors */ v2f.diffuseColor.rgb = diffuse*objColor.rgb * DiffuseCol; v2f.diffuseColor.a = objColor.a; v2f.ambientColor = objColor.rgb * AmbientCol; // compute point light lighting float3 Delta = worldPointLight0Pos-a2v.objCoord; float3 pointLightDir = normalize(Delta); float NDL = dot(objTangent, pointLightDir); float pointLightDist = sqrt(dot(Delta,Delta)) * (1.0/400.0); float att = min(1,max(0,pointLightDist)); v2f.ambientColor = (1.0-att) * PointLightColor; return v2f; }

The only thing I modified in the vertex shader is using Tangent instead of objNormal to determine the objTangent vector. I also added code to get the objEyePos and objLightDir. Here it is important to take into account that the hair geometry being recreated every frame doesn’t have any World (or Model) matrix (it is the Identity matrix).

Moving on to the pixel/fragment shader:

float4 main(v2fConnector v2f, // Parameters for the hair model uniform half Rcol, uniform half TTcol, // Lookup tables for the hair model (fixed point) uniform sampler2D lookup1fixed, uniform sampler2D lookup2fixed ) : COLOR { Rcol = 1.87639; TTcol = 3.70201; /* Compute the longitudinal reflectance component */ half2 uv1 = v2f.angles.xy; half4 m = h4tex2D(lookup1fixed, uv1); /* Compute the azimuthal reflectance component */ half2 uv2; uv2.x = cos( (asin (2 * v2f.angles.x - 1) - asin (2 * v2f.angles.y - 1) ) / 2 ) * 0.5 + 0.5; //m.w; uv2.y = v2f.angles.z; half4 ntt = h4tex2D(lookup2fixed, uv2); /* Combine longitudinal and azimuthal reflectance */ half3 lighting; lighting = (m.r * ntt.a * Rcol.r).xxx; // Primary highlight lighting = m.b * ntt.rgb * TTcol.r; // Transmittance (using MTRT instead of MTT) lighting += v2f.diffuseColor.rgb; // Diffuse lighting float4 COL; COL.rgb = lighting + v2f.diffuseColor.rgb*0.2 + v2f.ambientColor; //COL.rgb = v2f.ambientColor; COL.a = v2f.diffuseColor.a; return COL; }

For the pixel shader I had to compute the first cosinus angle (see GPU Gems Chapter 23) because the lookup texture I got doesn’t have an alpha channel. So `uv2.x = cos( (asin (2 * v2f.angles.x - 1) - asin (2 * v2f.angles.y - 1) ) / 2 ) * 0.5 + 0.5; //not m.w;`

.

**LE:** There is still a bug regarding the usage of ntt.a (which is invalid) for the primary highlight.

And that’s pretty much it regarding the Nvidia Nalu Marschner shader.

Almost forgot, here are the lookup textures:

Next you can see a comparison between Krystal rendered with Phong, Kajiya and Kay and Marschner. If you have any questions about the Phong shading model (or per pixel lighting) you can look over these pdfs: Basics of GPU-Based Programmig and MathematicsOfPerPixelLighting.