Question: Origin of French Curves and Approximating a Conic Rotation

Hello,

I am brand new, just joined in order to thank a member (gmm) for a publicly searchable MaplePrimes post I discovered in researching the origin of french curves. I linked to gmm's post in a blog post I wrote about the application of conic sections in the drafting of sewing patterns. I tried to send gmm an email and discovered the 10 vote reputation threshold, so I'm writing this post with three objectives in mind:

1) to hopefully catch gmm's attention to the fact I wish to acknowledge that fascinating post on the origin of french curves,

2) to ask whether Maple can be used to generate a 2D representation of the new cone edge shape created when the angle of its intersection with a plane changes, and

3) to hopefully get feedback on whether my mathematical description of the application of conic sections in drafting sewing patterns is correct.

Re: #3, I have some background in computer graphics from working 1990 - 2003 closely with, first as a technical writer then as a software engineer the last 5 years, the vector graphics group at Adobe, but my BA is in English, not Computer Science or Math, although I've taken several Computer Science courses, a course in Physics, three semesters of Calculus, one semester of Linear Algebra, and I've extensively studied Bézier curves on my own. The mathematical description I wrote in this post:

http://www.stylemadebyhand.com/2013/02/05/god-is-in-the-details/

is based on my best understanding of what is going on, but I'd be ever so grateful if someone could confirm that I am correct. My husband Martin is a Phd physicist with several graduate courses in Mathematics (to qualify for teaching mathematics at the college level) and he reviewed the post, but his memory of parametric curves is a little fuzzy. He thinks I'm right but he can't absolutely confirm that I am.

If Maple an be used to obtain the shape described above, it will be enormously useful to us as sewists venturing into the apparel industry (offering drafted menswear patterns for home sewing), because the success of our tiny niche business will depend on helping sewists become more proficient at making pattern adjustments, and the shape change I am speaking of is a common adjustment. Specifically, it is the change you need to make to the sleeve cap when you modify the shape of an armhole (armscye). Changing the armhole changes the angle of the plane, so the sleeve cone top edge needs to change as well in order to intersect the body plane at the new angle. Right now most of the sewists on the planet (including me) are mystified by how to do this. Advanced sewists either fiddle with the French Curve in 2D or figure it out making muslin adjustments in 3D on a live or dummy fit model.

Martin tells me Mathematica can do what I am talking about. We have the student version but have not tried this yet. As an academic, Martin can get the student version of anything so if Maple can do what we want I would rather get Maple so I will have a legitimate reason to stay connected with this community and possibly learn of other Maple features that might be useful for pattern drafting. We're using an AutoCad clone to actually draft the patterns, but it cannot make the sort of shape adjustment needed to rotate a sleeve. I'm assuming we can digitize the shape of the armhole to get exact coordinates for extracting the conic section equation for Maple/Mathematica.

Thank you very much for your kind consideration and I look forward to your replies!