Is it possible to calculate the TBN matrix in the fragment shader?

Question

Just from model position, model normal and texture uv?

Answer 1

Yes. There an article about this by Chris­t­ian Schüler:
http://www.thetenthplanet.de/archives/1180
It's a followup to a book article (ShaderX 5) which did exactly what you need. I've used it myself.

Here is the part that you need: (p : world-space position, N : world-space normal)

mat3 cotangent_frame( vec3 N, vec3 p, vec2 uv )
{
    // get edge vectors of the pixel triangle
    vec3 dp1 = dFdx( p );
    vec3 dp2 = dFdy( p );
    vec2 duv1 = dFdx( uv );
    vec2 duv2 = dFdy( uv );

    // solve the linear system
    vec3 dp2perp = cross( dp2, N );
    vec3 dp1perp = cross( N, dp1 );
    vec3 T = dp2perp * duv1.x + dp1perp * duv2.x;
    vec3 B = dp2perp * duv1.y + dp1perp * duv2.y;

    // construct a scale-invariant frame 
    float invmax = inversesqrt( max( dot(T,T), dot(B,B) ) );
    return mat3( T * invmax, B * invmax, N );
}