A Stanford Research International Sr. Computer Scientist friend of ours kindly reviewed the last several blog posts and came up with what we believe is a far more elegant solution. We can’t wait to try it out but need to do more work to figure out how to get our numbers to fit his equations. If we can get everything to work his will be a much easier solution to work with in terms of quickly coming up with a sleeve cap shape that is correct for any 3D armhole.
Our friend also corrected some problems with what I wrote previously and his new solution made me revisit/revise some of my other thinking, so here’s a list of corrections, as I understand them. I’ll update the previous posts to point to this one for corrections.
- The pear shape of the armhole constructed in 3D on my dress form is not the correct shape of the armhole. It should be an ellipse similar to the elliptical shape of the armhole in 2D pictured above. What’s happening in 3D on the dress form is that as the soft fabric intersects with the surfaces of the dress form (adjusted to match my dimensions as best as possible) the ellipse is distorted to look more like a pear.
- It’s okay though that the 3D armhole looks like a pear because if I understand our friend correctly, we don’t really need to walk around the sewn armhole seam and collect (x, y) points (44 of them!), we just need to exactly describe the plane of intersection, a far easier and more accurate measurement to get from the 3D constructed armhole on the dress form.
- The vary form rule, otherwise known as a French Curve, does not behave like a quadratic Bézier curve. Paraphrasing what my SRI friend said, French Curves are typically parts of Euler spirals (curves with monotonically increasing curvature), whereas Bézier curves have continuous derivatives up to a certain degree. Béziers properties are not guaranteed by connecting segments drawn with a French Curve. So if you’re redrawing an armhole using a French Curve be aware that it is possible to draw a shape that isn’t a conic section even though it should be one.
- The ideal sleeve cap matching the above pictured armhole won’t look exactly like our plot below because the plot represents a 2D flattening of the pear shape, not an ellipse. However, I do believe the plot is telling me something about the sleeve cap I actually want to sew. Just as my body distorted the perfect armhole ellipse to look like a pear, my body will distort the perfect sleeve cap to look more like the plot below. I think this happens because the surface of my broad, round back pulls mightily at that back armhole seam. So once I am able to compute the supposedly ideal sleeve cap for the ideal armhole ellipse, I will still probably want to add more fabric to the back seam area to account for my broad, round back. There may be some comprising involved, e.g., taking more from the front to add to the back to keep the seam length the same. We’ll see.