Given a 2D point, is there a function to find the coordinates of the equivalent point transformed as shown in this diagram:
The new point has the same Y value, but the new X value depends on the Y value. The points {0, 1}, {0.5, 1}, and {1, 1} are all transformed to {0.5, 1}.
I don't know the name for this type of transform, so I've temporarily referred to it as a 'gore transform' - gores being related to the interrupted map projections where the location's coordinates are transformed onto tapering flaps. (Y is latitude and X is longitude.) I've spent hours looking with delight at the map projection pages (especially the wonderful Progonos site), but haven't yet located a useful function/formula.