I get the irregular shapes by following the gaps that make up the manufacture.
I just hate cutting tufts, and when you do, that's when I get a noticable join. So the style of the carpet will often dicatate the shape of the repair I do.
It's not really taht hard. You still use your paper pencil trrick to find the right direction, you still have two long run cuts that I always do first. Check the 'width' and away you go.
Now you do the first angle cut, laying it over the cut out making sure you have excess all round. When it's sitting nice, cut it's opposite side so you have 2 directions completely cut.
Then follow the same idea for the final two sides.
When I'm cutting these angle cuts, I always lay it on top of the cut out, line up a row/gap and run my awl all the way through and check the other side. Maybe even mark with pen in the side of the backing so you know before you cut, that it'll end up right.
The cut just becomes a formality then.
We had a term in the joinery shop years ago that I love. "one mark, one cut, one fit". Simply, mark it out, do your cut, and then trim as necessary.
Once you get donig this sort of stuff a lot and gain your confidence, you'll rarely need to trim much. We also had another saying, cut it twice and it's still too short!!
Essentially, if you stuff up, generally it's quicker and better to just make a new start rather than trying to save something that is going to make to work twice as hard and still not get the best results.
John