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How AC works

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Stairs with irregular cut lines

Innhold
It is not as trivial as it sounds to identify "area below 1.90" under a stair. An important concept here is the "cut line" which is the common line between projected area (footprint) below 1.90 and projected area (footprint) above 1.90. For the simplest case this is a straight line. However, if the stair geometry is more complex the cut line will also be more complex. The reason for this could be as simple as a stir built as two beams bearing the foundation for the steps:
For the simplest case this is a straight line. However, if the stair geometry is more complex the cut line will also be more complex:

Figur 5 - Approximating the cut line
This approximation will probably only work if railings, fences etc is not taken into account. Until further notice, it is believed to be possible to filter these out by type.
If the stair includes railings and/or it is an open stair, the footprint becomes more complex:

Figur 6 - open stair with railings
The footprint of stair below 1.90 is lower left in figure. In this case it even contains "holes"; if these introduce problems it should be possibly to apply an algorithm to remove holes. Imposing the footprint for entire stair introduces several possibilities for points C1 and C2 and start/(en d of "cut line":

Figur 7 - footprints for symmetrical stair
As long as at least one of the C points can be found the previous algorithm should work. To ensure symmetry we can run algorithm twice, in CW and CCW directions, and pick first point found in both cases.
If it turns out to be problematic finding C points, we could apply an algorithm for making polygon convex on the stair-below-90 footprint:

Figure 8 – Apply convex footprint enclosing line
If the stair is "asymmetric" around its midpoint line, for example included railings but on only one side, the approach will not work the same way:

Figure 9 – Asymmetrical case
The line between identified points C1-1 and C2-1 are no longer a proper "cut line". TODO: Currently, a simple solution for this case is not identified. We must rely on stairs not including railings, or being symmetrical, and use C1C2 as cut line.
To enable polygon edit, and simplify the further calculation (60-cm rule), we should always perform this "cut line approximation" step.
When the "cut line" is approximated as a straight line the "60 cm rule" is rather easy to implement:

Figur 12 - Adding 60cm compensation
An acceptable and simple approximation is to create a rectangle with the cut line E1E2 as one of the sides, a parallel F1F1 as opposite side, the two other sides being 60cm in length.
There is one exception, for small curved/spiral staircases, where the compensation polygon will be a triangle version of the above: E1E2F1.

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