Given a surface normal, find rotation for 3D Plane

Question

So I have a 3D Plane described by 2 Vectors:

P : a point which lies on the Plane
N : the surface normal for the Plane

And i ha

Answer 1

Not sure what method you are using to render, but borrowing from OpenSceneGraph's matrix:

void Matrix_implementation::makeLookAt(const Vec3d& eye,const Vec3d& center,const Vec3d& up)
{
    Vec3d f(center-eye);
    f.normalize();
    Vec3d s(f^up);
    s.normalize();
    Vec3d u(s^f);
    u.normalize();

    set(
        s[0],     u[0],     -f[0],     0.0,
        s[1],     u[1],     -f[1],     0.0,
        s[2],     u[2],     -f[2],     0.0,
        0.0,     0.0,     0.0,      1.0);

    preMultTranslate(-eye);
}

inline void Matrixd::preMultTranslate( const Vec3d& v )
{
    for (unsigned i = 0; i < 3; ++i)
    {
        double tmp = v[i];
        if (tmp == 0)
            continue;
        _mat[3][0] += tmp*_mat[i][0];
        _mat[3][1] += tmp*_mat[i][1];
        _mat[3][2] += tmp*_mat[i][2];
        _mat[3][3] += tmp*_mat[i][3];
    }
}

Hopefully this will give you an idea for your implementation. I'm not very good with quaternions which might have a simpler solution, but this method works well for me.