Normal texture

[Xi_Yang]

I need some help about how to correctly transform the normals from texture coordinate to object (or viewer) coordinate.

For instance, I have a fragment shader like this:

// the interpolated normal provided by vertex shader
in vec3 obj_normal;

// the normal mapping sampler
uniform sampler2D sp_bump;

// the "default" normal value from the texture
const vec3 unit_z = vec3(0,0,1);

void main() {
    // get the normal from texture
    vec3 tex_normal = texture(sp_bump,gl_TexCoord[0].st).rgb;
    tex_normal = normalize(normal_tex*2-vec3(1,1,1));
    
    // normal transform
    vec3 axis = cross(unit_z,obj_normal);
    float cosine = dot(unit_z,obj_normal);
    float sine = length(axis);

    // I guarantee this matrix was correctly generated, as
    // I've tested it both using matrix and using quaternion
    mat3 normal_trans = some_way_that_give_the_matrix();
    
    // now, produce the normal to use later
    // it should has: obj_normal = normal_trans*unit_z;
    // so it should also has this:
    vec3 use_normal = normal_trans * tex_normal;
}

However, my transform is not working correctly, especially when the obj_normal is nearly towards camera. What’s the problem inside there?

Thanks!