Perhaps I can help here...
Most times I (as a block maker) use straight line measurements. For example, an oval hat sent to me would be measured as how wide and long the oval is underneath with a straight ruler, and its height done the same. That is because to start with I am looking at it as what size block of wood I need to prepare.
measuring a hat as 'up and over' that is, from ones side base up and over the top and back down the other side is useful for planning out your material but less so for the blockmaker.
eg, a dome crown will be described as its circumference, perhaps its length and width at times and maybe 13cm high. But measure it up and over front to back it becomes 44cm long sort of thing
so generally speaking, measure with a flat ruler. The block maker will ask for up and over if needed.
headsized blocks are measured in circumference cm or inches. Side to side and front to back if needed to work out the type of oval. Flange brim blocks are made a size or two larger then the crown and blocks that make a hat with a brim that folds back inside the hat are made larger too as the folding back inside reduces the size.
If you would like to email me directly i can draw some examples to illustrate it better. email@example.com
I do hope this is of help!