I am trying to implement the Ashikhmin-Shirley model using these formulas:

enter image description here

This is the GLSL 1.2 fragment shader code:

uniform vec4 materialAmbient, materialDiffuse, materialSpecular;
uniform float materialShininess;
uniform vec4 lightAmbient, lightDiffuse, lightSpecular, lightPosition;

varying vec3 P,N;

float pi= 3.1415926535;

vec4 Fd(float NdotV, float NdotL) {
    vec4 fd= (28.0 * materialDiffuse * lightDiffuse) / (23.0 * pi) * (1.0 - materialSpecular * lightSpecular);
    fd*= 1.0 - pow(1.0-NdotV/2.0,5.0);
    fd*= 1.0 - pow(1.0-NdotL/2.0, 5.0);
    return fd;

vec4 Fr(float u, vec4 specular) {
    return specular + (1.0-specular) * pow(1.0 - u, 5.0);

// f= phi
vec4 Fs(float VdotH, float NdotH, float NdotL, float NdotV, float et, float eb, float f) {
    vec4 fs= Fr(VdotH, materialSpecular * lightSpecular);
    fs*= sqrt((et+1.0) * (eb+1.0)) / (8.0 * pi);
    fs*=  pow(NdotH, et*pow(cos(f),2.0) + eb*pow(sin(f),2.0)) / (VdotH * max(NdotL, NdotV));
    return fs;

void main(void) {
    vec3 L= normalize(vec3(lightPosition) - P);
    vec3 V= cameraPosition;
    vec3 H= normalize(L+V);
    float NdotL= max(dot(N,L),0.0);
    float NdotV= max(dot(N,V),0.0);
    float NdotH= max(dot(N,H),0.0);
    float VdotH= max(dot(V,H),0.0);
    gl_FragColor= Fd(NdotV, NdotL) + Fs(VdotH, NdotH, NdotL, NdotV, 128.0,128.0,1.0);

I already checked and it seems like all the uniforms and varying are passed in the right way, I pass P and N from the vertex shader. The variables are:

  1. Light direction: L;
  2. Surface normal: N;
  3. Camera direction: V;
  4. Half vector: H;
  5. Fragment position: P.

The uniforms I pass are:

  1. light{Specular | Diffuse | Ambient} : 0xffffff (converted to a rgba vector of course);
  2. materialAmbient: 0x543807 ;
  3. materialDiffuse: 0xc6901d;
  4. materialSpecular: 0xfdefce;
  5. materialShininess: 27.8974.

This is the result I get:

enter image description here

Which seems very strange to me, I've seen other images of Ashkhmin-Shirley implementations on the web, and they aren't similar. This is an example:

enter image description here

I want one like this !! Maybe I am using wrong values of phi and other values? Or there's something wrong in the formula?

  • 1
    \$\begingroup\$ can you provide a simpler shape in your test image, like a sphere or teapot? as it's hard to judge from this. \$\endgroup\$
    – concept3d
    Commented Nov 25, 2013 at 14:23
  • 1
    \$\begingroup\$ sorry I'm feeling too lazy to look your code over, but here is my tested implementation in use in my engine: szifler.com/gdsegj/ashikhmin_shirley.glsl \$\endgroup\$
    – MickLH
    Commented Nov 25, 2013 at 14:41
  • \$\begingroup\$ @concept3d Ok, I replaced the image, there's a teapot now. \$\endgroup\$ Commented Nov 25, 2013 at 14:43
  • \$\begingroup\$ it gives you vec2(diffuse, specular), multiply by your diffuse texture sample and light color... add the specular before or after depending on if your renderer supports separate specular color \$\endgroup\$
    – MickLH
    Commented Nov 25, 2013 at 14:48
  • 5
    \$\begingroup\$ also it looks like you are using "flat" normals instead of "smooth" ones, you most likely want to research normal smoothing and pre-calculate this in your models vertices to get rid of the square artifacts no matter what lighting model you use \$\endgroup\$
    – MickLH
    Commented Nov 25, 2013 at 14:50

1 Answer 1

vec4 Fr(float u, vec4 specular) {
    return specular + (1.0-specular) * pow(1.0 - u, 5.0);

what's the specular in this function ? I think you specular is wrong,you can change

float Fr(float u) {
    float f = 0.125;  
    float fresnelCoe = f + (1 - f)*pow(1 - u, 5);

f is a constant, different object has difference number


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