I am working with a GIS problem using a single input of a polygon shapefile. 
Consider an irregular polygon. I want to draw vertical lines across the extent of the polygon at equal spacing. 
How I intend to proceed is:

Identify the bounding box (done using PyShp)
Draw vertical Lines parallel to the left edge of the bounding box at equal spacing (How?)
Clip the lines to the extent of the polygon (How, without using ArcPy?)

Note: They are required to be only vertical, and not a graticule. Also, I do not intend to use ArcPy, and intend to perform the coding completing in Python (2.7) as this segment of code needs to go into a tool generated from PyQt.
Find the points/vertices that describe the line at the left edge - (x1, y1), (x2, y2)
Add a constant to the x values - (x1+k, y1), (x2+k, y2)
Find the y values on the polygon at the new x values - (x1+k, y3), (x2+k, y4)
Draw the line between those two points.
Vertical lines in a polygon shapefile