The question was asked about different ways to scale your trim rings. I don't always do it but this is how I do it - when I do it.

First, the theory: I use the cue's diameter at the trim ring locations to determine the proportions. For example, in the picture below, I show the different diameters at the joint, both ends of the wrap and above the buttcap.

In the interests of keeping costs down, although 4 different sizes are called for, the same size

The picture below shows the calculations for each location for reference.

The calculations are pretty simple.

First, determine the ratio between the different trim locations and the size you want at the joint. For example, the diameter at the "A" joint trim is 1.024". If you divide this by .855", the diameter of the joint trim, you get a scale factor of 1.199.

Second, multiply the joint segment width of .125" by the scale factor of 1.199 and you get .150". This will be the width of the "A" joint trim segment.

Do this at each trim location to get accurately proportioned segment sizes. The calculations below each segment in the picture simply show the ratio between the segment size & the space between the segments. As expected, the ratio of .601/.602 is the same for each location, proving that they have the same proportions.

The thickness of each trim ring can be determined the same way.

Below is a cue in which the chain links are perfectly proportioned at each end of the cocobolo handle.