How do you calculate the angle between two normals in glsl?

Question

How do you calculate the angle between two normals in glsl? I am trying to add the fresnel effect to the outer edges of an object (combining that effect with phong shading), and I think that the angle is the only thing I am missing. Fragment Shader: varying vec3 N; varying vec3 v; void main(void) { v = vec3(gl_ModelViewMatrix * gl_Vertex); N = normalize(gl_NormalMatrix * gl_Normal); gl_Position = gl_ModelViewProjectionMatrix * gl_Vertex; } Vertex Shader: varying vec3 N; varying vec3 v; void main(void) { vec3 L = normalize(gl_LightSource[0].position.xyz - v); vec3 E = normalize(-v); vec3 R = normalize(-reflect(L,N)); vec4 Iamb = gl_FrontLightProduct[0].ambient vec4 Idiff = gl_FrontLightProduct[0].diffuse * max(dot(N,L), 0.0); vec4 Ispec = gl_FrontLightProduct[0].specular * pow(max(dot(R,E),0.0), gl_FrontMaterial.shininess); vec4 Itot = gl_FrontLightModelProduct.sceneColor + Iamb + Idiff + Ispec; vec3 A = //calculate the angle between the lighting direction and the normal// float F = 0.33 + 0.67*(1-cos(A))*(1-cos(A))*(1-cos(A))*(1-cos(A))*(1-cos(A)); vec4 white = {1.0, 1.0, 1.0, 1.0}; gl_FragColor = F*white + (1.0-F)*Itot; } varying vec3

Answer 1

To find the angle between any two vectors you can take advantage of the dot product, an operation that is readily available in glsl.

For any two vectors v1 and v2, v1 dot v2 = |v1||v2| cos u where u is the angle between the two vectors.

so cos u = (v1 dot v2) / (|v1||v2|)

You can easily find the dot product and the magnitudes of the vectors in glsl. You also have the inverse cosine function available. Just note that your angle will come out in radians.