Mountain bike handlebars are not normally straight tubes - they're swept backward and upward a few degrees for ergonomic reasons. A typical bar has 8 degrees of backsweep and 5 degrees of upsweep. The first view below is front-on - showing the upsweep, and the second is top-down - showing the backsweep:
The default installation of a handlebar in the stem clamp is with the upsweep parallel to the head angle (angle of the fork). However, riders often roll the bar forwards or backwards in the stem clamp to find the most comfortable position for themselves. Rolling the bar forwards increases the effective upsweep while reducing the backsweep, and rolling it backwards reduces the upsweep while increasing the backsweep.
It occurs to me that this rolling might not be a linear exchange of backsweep for upsweep. For example, rolling a bar with 8 degrees of backsweep and 5 degrees of upsweep, back by one degree, doesn't make it effectively a bar with 9 degrees of backsweep and 4 degrees of upsweep.
Is there a better explanation of what's happening here?
Is there a formula for how rotation affects the two sweeps?