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Points switch places when an ellipse is intersected with a line
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I would like to keep their names constant, is that possible?
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I think yes, it's possible.
But:
No connection to i.imgur.com.
Please send a ggb file as attachment to your post.
sorry was wrong, see later again...
I had to refresh my skills for perspective drawing.
Now I hope it's OK:

I think your principle is wrong and it's bether to determine A_{10} by starting with L+(0,a) (is equal A) and using F_3, S_3, VP4 and VP3
It is possible to create a list for all points with the same verticaleS_3
If you need one of the points you can use: Element(ListS_3,<index>) or ListS_3(<index>) but this syntax not in all cases.
ListS_3 can be improved. Even if there is no construction point on the edge (L, VP4) or (L, VP3), the next higher point can only be constructed by specifying the point in the plane, the height and the corner points VP4, VP3 and L.
F_3 as parameter has been omitted and is implicitly constructed inside in the above expression (.... Intersect(Line(S_3, VP3), Line(VP4, L)).....)
The expression for A_{10} can also be used in a list for all points vertically above S_3.
Analog, with ListR_8, also for the points above R_8 (center).
Analog, with ListG_3, also for the points above G_3 (start step).
In these three lists also the point with the height=0 is contained. This simplifies the construction of the stair steps by using only the points from these lists even for the lowest step (see t1 and q1).
This form is very helpful (if of interest) for any following extensions (create ALL points above the circle).
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