How can I parametrize path (1) and (2) in this picture?
If the part of path (1) between point $c$ and point $b$ is : $x(R_1,\phi)=R_1\cos\phi$ and $y(R_1,\phi)=R_1sin\phi$ for $R_1\in[c,b], \phi\in[0,2\pi]$
How can this curve connect the part between $a$ and $c$?
Part of path (2) between point $a$ and $d$: $x(R_2,\phi)=R_2\cos\phi$ and $y(R_2,\phi)=R_2\sin\phi$ for $R_2\in[a,d], \phi\in[0,2\pi]$
Same here, how can this curve connect the path between $d$ and $b$?