H(t,s)=\left\{\begin{array}{llll}
z_0+\rho_2e^{i(\varphi+ts\Delta\varphi)}&t \in [0,1] \\
z_0+[\rho_2-(t-1)(\rho_2-\rho_1)]e^{i(\varphi+s\Delta\varphi)}&t \in [1,2] \\
z_0+\rho_1e^{i[\varphi+s\Delta\varphi-(t-2)s\Delta\varphi]}&t \in [2,3] \\
z_0+[\rho_1+(t-3)(\rho_2-\rho_1)]e^{i\varphi}&t \in [3,4] \\
\end{array}\right.