Confused intersection of polygon and vertical lines

As shown in, I have a polygon in this shape, which needs to be split with a vertical line. At present, according to the order of the polygon P1, P2, P3, P4 and the vertical line respectively to find the four intersections of T1-T4, and according to P1, T1, P2, T2, P3, T3, P4, t4 records. Of course, this polygon can be more complex, but now we need to consider the Charts shown in the figure to be representative. What method can be used to obtain the split of the three polygon, respectively, P1-T1-T4, T1-P2-T2-T3-P4-T4, T2-P3-T3