{% g_i(t) = 0 \;\; for \;\; t < T _{i-1} %}

{% g_i(t) = (t - T_{i-1})^3 / 6(T_i - T_{i-1}) \;\; for \;\; T_{i-1} \leq t < T_i %}

{% g_i(t) = \frac{(T_i - T_{i-1})^2}{6} + \frac{(T_i - T_{i-1})(t-T_i)}{2} + \frac{(t-T_i)^2}{2} - \frac{(t-T_i)^3}{6(T_{T_{i+1} - T_i})} \;\; for \;\; T_{i} \leq t < T_{i+1} %}

{% g_i(t) = (T_{i+1} - T_{i-1}) (\frac{2T_{i+1} - T_i - T_{i-1}}{6} + \frac{t-T_{i+1}}{2}) \;\; for \;\; t \geq T_{i+1} %}

{% g_i(t) = t \;\; for \;\; i=s %}