The operational problem may be steps or any other consideration which requires you to make one or more height/distance points along track.
Presuming that you are looking at a constant ROD/ROC, there will be a range of values which is feasible for your particular aircraft. If the gradient required is beyond the capability of your aircraft, then you will need to orbit for part of the climb/descent to get around that problem. If you end up flying airlines, you will find this problem to be a common requirement as ATC does its aircraft separation juggling act.
In earlier days, we just did the sums in our heads as mental arithmetic - these days, the FMC/FMS kits will do the work for you, if you want to go that way. One of the difficulties, these days, is that many pilots have a real problem using the FMC/FMS as a mental crutch.
A sideline problem is where the aircraft performance outstrips the IVSI’s range. For example, on the B727, it was very common to have the IVSI pegged on the stop during a descent. In this case, the pilot has to run continuous calculations on the way down, looking at altimeter changes either in a time or distance interval, depending on just what you were trying to achieve. Some civil aircraft can come down quite quickly - the IAI Westwind is a good example.
It gets more interesting in the fast jet community. I had a mate relate a tale from his F/A 18 days – given an unrestricted climb to a high level, ATC required that he advise leaving each 1000 foot level. Sitting the aircraft on its tail, his transmission was along the lines of “left 1000 2000 3000 4000 .. " finishing at TOC. As he observed, the ATC-er concerned learned a simple lesson regarding fast jet performance on that occasion.
The easiest way to map values to the CTA/CTR profile is to start with a known spot - either where you need to start or finish the climb/descent and then work out the gradient (ft/nm) from that point to each of the step vertices in turn. This should cover any real world situation you might encounter.
From the resulting gradients, it becomes evident which one is limiting. That's the step which you need to watch like a hawk all the way up or down. On occasion, you may have multiple steps which give very similar gradients and you need to monitor more than one.
If that doesn’t give you enough information, say so and I’ll run up some graphics to amplify the comments.
