How to "unroll" curve AND distort geometry with it


This is a tricky one. I am trying to unroll a curve while simultaneously “distorting” geometry with it; it is basically a cartogram exercise. I have done the part of “unrolling” the curve (see image, the curve getting unrolled is the cyan color line, the unrolled result is the red color line). The issue is I cannot figure out a logic of distorting the other geometry (countries) with respect to the transformed curve. In other words, the distance to the borders in relation to the curve should be maintained after it’s transformation, thus causing the cartogram representation.

I tried making an x and y curve normal to certain points along the cyan curve and then using those distances to rebuild the border geometry for the red curve, but it doesn’t seem right.

I don’t know if this is clear enough, but any suggestions are welcomed (if any). I appreciate any help and wish this were easier to explain!


Hello - use the Flow command - flow your map curves from the cyan to the red line. Any luck?


This was the result