Let’s say we have an 8-sided-spline with two vertical and two horizontal sides, i.e., it doesn’t stand on a corner.
If that spline covers an area of 200 by 200 cm, then a quarter of it would cover 100 by 100cm. This quarter is of interest.
With the size of a hundred by hundred, cm or % are equal.
We also know that all sides are equal in length before cutting it into the quarter, which means the vertical and horizontal line is now half.
So we can just set this up, measure the distance in y, for example, and take the distance between total size and the first point. There you have the number you are after for the offset.
Reading along might feel too much at first, but it will be as simple as opening a door with a key once you see it.
In math, it takes a little bit longer. We are going back to the full 8 sided one. We know that the sides are equal. We also know that a side rotated 45 degrees will have a horizontal or vertical projection of sqrt(2)/2 compared to the full length.
Pythagoras (a*a)+(b*b)= (c*c)
Since the two shorter sides are equal 2* (a*a)= (c*c)
If c is considered one: 2*a*a=1*1
or a = sqrt(0.5)
Since we have two of those and only one vertical
(2*0.707…)+ one = 2.414…
So if we divide 100 by 2.414, we get half of the vertical (or horizontal), and this number 1- the short side is the offset. Since this is a symmetrical shape, we don’t have to divide all numbers by two, as the ratio is the key. 58.579… is the number we can use directly in this case. So we are back to the quarter, which is all we care about for the bevel.
Please have a look at the practical example.
All the best
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