Locate "not parametrizable" boundary

Let’s suppose I have a 2D mesh and that the border \partial \Omega of this mesh is obtained by piecing together easily parametrizable \Gamma_{P} and not so easily parametrizable curves \Gamma_{N}, such that \partial \Omega = \Gamma_{P} \cup \Gamma_{N}

For example, let’s suppose I have that:
\Omega \subset [0,1] \times [0,1]
\Gamma_{P} = \{ (0,y) \subset \Omega \} \cup \{ (x,0) \subset \Omega \}
(i.e. two segment with one coordinate equal to 0)
and finally
\Gamma_{N} = \{ (x,y) \subset \Omega, ordered collection of coordinates s.t. \partial \Omega = \Gamma_{P} \cup \Gamma_{N} is a closed curve \}

How could I then locate \Gamma_{N} to impose boundary conditions?