These measurements on this page (slagcoin) are often cited on SRK and youtube.
but all is incorrect
He did not measure this. All is fabricated on the basis observation JLW and JLF
He probably did not have the means to take precise measurements, they way you've done on your methodology page, but he hasn't claimed to.
In the section about restrictors, he is only describing the relationships among engage, throw, and restrictor shape, and it is all borne out as fact by geometry. Kowal, I greatly respect you for your work, but I think you've also jumped to the conclusion that he is trying to say that all restrictors of the shapes shown measure out to the percentages shown. He does not make this claim. They don't represent any specific stick. They're just an example of what can happen, and in the text below he even describes how changes to the throw and engage in actual designs will change these areas.
It's misleading specifically because it's not accurately represented.
It does not claim to accurately represent any particular stick/restrictor combo. It represents the relationships between engage, throw, and restictor shape, and it does so very accurately.
Your drawings go one step further and illustrate these relationships over several examples of possible changes. There's nothing inconsistent between your drawings and his though, and if you read the text below his drawings on the site he describes verbally the cases you've illustrated.
There is no "relationship" between "engage" and throw. They are separate.
The relationship between engage throw directly determines the proportions of the engage zones.
As engage distance increases, the areas of the cardinal engage zones increase in proportion to the areas of the diagonal engage zones.
As throw distance increases, the areas of the diagonal engage zones increase in proportion to the areas of the cardinal engage zones.
Therefore:
(cardinal engage area)/(diagonal engage area) is directly proportional to (engage distance)/(throw distance)
You basically said this right here:
The image above shows how much impact a change in either restriction size, deadzone size, or both have on the diagonal zones.
restriction size (diameter of circle or width of square) = 2 x throw distance
deadzone size (width of square) = 2 x engage distance
In fact, it's probably safer to assume that a stick properly made to use a round restrictor will have a different build than one where someone took a stick originally designed for square restriction and threw on a round restrictor.
Agreed, and this is not inconsistent with anything I've said.
Actually, it is of great value when you are not at the most extreme position. If there is only a small area in which a diagonal can be engaged, it is much harder to find that area.
While this may look to be the case, based on the diagrams you posted, it isn't often this way in actual practice. Geometry dictates that with a stick where the switches are simple and without levers (not nearly always the case) the shaft must move further to actuate two at the same time. However, regardless of how far the shaft is able to move, the actuation occurs in exactly the same place. If you don't ride the restrictor while playing, the ability to find the diagonal will be exactly the same. If you were able to proceed outward from where restriction occurs, the zone will become larger, but this would necessarily change the shape of the restriction. Ergo, ease of actuation has nothing to do with restriction shape, unless you are riding the restrictor. It's much more beneficial to examine the actual build of the joystick to evaluate for this trait than to focus on the restrictor.
In practice, activation of a diagonal is achieved by placing the stick anywhere in a diagonal engage zone (one of the red areas in your drawings), not by placing the stick at the exact actuation point.
Look at your drawings. The ones on the left are exactly the same as the ones on the right, except that the ones on the left have decreased throw distances, causing the diagonal engage areas to be smaller in proportion to the cardinals.
If you are not riding the restrictor, it will be harder to engage a diagonal because there is a smaller area in which you must place the stick to do so.
If you are riding the restrictor, it will be harder to engage a diagonal because there is a smaller portion of the circumference along which you must place the stick to do so.
A larger area is easier to find than a smaller one. This is true in all cases.
I understand it very well. But I can imagine many folks who don't understand the dynamics of myriad actuator and switch configurations, seeing those diagrams and thinking it's a hard and fast rule. It is definitely not.
The relationship between engage and throw determines the proportions between the cardinal and diagonal engage zones.
A larger engage zone is easier to find than a smaller one.
Balancing the cardinal and diagonal zones is helpful in making them both equally easy to find.
These are hard and fast rules, true in all cases, and borne out by geometric fact.