How to not converge or diverge from the runway when there aren't checkpoints?
I'd like to add something to Ron's answer.  Use of geographic checkpoints is used a lot in initial training but it can become a debilitating crutch that leaves you in the lurch as soon as you go to another airport.  I teach in gliders where getting the circuit right is fairly critical the first time, there being only one chance to land.

The really important checkpoint or turnpoint is the turn from downwind to base.  Learn to recognize the presentation of the runway when at a 45 degree aspect to it, which is normally the proper turn point for downwind-to-base unless you are extending or shortening your downwind for a specific reason.  I always weaned my glider students from dependence on geographic points as soon as possible, and certainly before solo.

You are at 45 degrees to the runway when the extended line of the lengthwise edge and an extended line of the threshold are "even" relative to the horizon.   This can be pretty tricky to discern at first but over time you'll learn to recognize this just by the appearance from your vantage point, and you will no longer care about ground landmarks.