Envision a "dashed line" with linear sections and curved sections.
In some domains x, the slope is constant. In others, it's linearly reducing as f(x).
In some domains, the ratio of "dashed line" to "blank" (where f(x) is "null" or "empty set" or "undefined"...or just drawn with a white pen on white paper instead of black pen) is fixed. In others, the ratio reduces linearly as f(x).
In all domains, the total y value of a "dash" and a "blank" is fixed.
The transitions between domains are defined by certain x value waypoints.
Output needed: (x,y) coordinates of each start point of a "dash" and each end point of a "dash."
Preferred format: Excel, x-column, y-column
Do some error checking using a method you prefer.
Options: when the slope is changing, you may allow it to change during a dash, OR you may fix it during the dash. Whatever is easier for your chosen algorithm. The difference in the end coordinates of that dash between the two approaches is almost zero, so it is acceptable either way.