Update: Yay! We noodled on this some more and think we've eliminated the tedious step #9. After step #8, hold up a transparent plastic coordinate system so it aligns with the body plane at the armhole and so that the origin (0,0) aligns with the center armhole. Note the (x,y) coordinates of control points along the edge of the bodice armhole. Use the Pythagorean theorm distance formula for Euclidean three-space to calculate the distances between the 3D sleeve cuff (x,y,z) point and all of the (x,y) armhole control points and write these lengths down, in order from front to back (including the important shoulder point). Then do step #10.

Not everyone has a transparent plastic coordinate system but you can use a ruler to the (x,y) armhole control points. That's what we'll have to do for now because we don't have one. Let's see, we might hold up a piece of vellum we can see through and mark the armhole origin (0,0) and control points, then lay it down on a table and do the measuring with a ruler to get the (x,y) points.

Update: Yay! We noodled on this some more and think we've eliminated the tedious step #9. After step #8, hold up a transparent plastic coordinate system so it aligns with the body plane at the armhole and so that the origin (0,0) aligns with the center armhole. Note the (x,y) coordinates of control points along the edge of the bodice armhole. Use the Pythagorean theorm distance formula for Euclidean three-space to calculate the distances between the 3D sleeve cuff (x,y,z) point and all of the (x,y) armhole control points and write these lengths down, in order from front to back (including the important shoulder point). Then do step #10.

Not everyone has a transparent plastic coordinate system but you can use a ruler to the (x,y) armhole control points. That's what we'll have to do for now because we don't have one. Let's see, we might hold up a piece of vellum we can see through and mark the armhole origin (0,0) and control points, then lay it down on a table and do the measuring with a ruler to get the (x,y) points.

Correction: Martin just reminded me that he told me Mathematica will NOT be able to produce the shape we want (he was talking about a different modeling idea) because there is an infinite number of surface intersections that would reflect that same shape in 2D.

So it sounds like there is really no way to accurately approximate the new position of the sleeve without constructing it and eyeballing where it needs to go, or fiddling with a French Curve to approximate the new shape in 2D. So sad!

What we really need is a 3d representation of the sleeve intersecting a plane that we can mainpulate in 3d to the correct position, then reflect the 2d armscye and the 2d sleeve edge. I am guessing if there is software that can do this, we can't afford it.

#1 and #3 still apply.

Thanks again!