mat3 cotangentFrame(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(0.00000000000000001, max(dot(T, T), dot(B, B))));
    return mat3( T * invmax, B * invmax, N );
}