approximate an ellipse using straight lines of equal length - with closure

Question

I'd like to construct (i.e. graph using a computer program) an ellipse from straight lines of equal length. With closure - i.e. without any gaps in the perimeter. I know that straight lines of equal length will not result in the best approximation but it is a constraint I have to live with. Since a computer program will be doing the calculations iterating to an answer is OK.

I am open to all suggestions, but one approach which comes to mind requires calculation of where end B, of a chord AB, with A placed at coordinates x,y intersects with the perimeter. I. E. if one end of chord AB is at x_a,y_a what are the coordinates of B? So with this approach the algorithm would iterate using ellipses of increasingly smaller perimeters until end B of the last placed chord had the same coordinates as end A of the first chord.

I'm not a mathematician (as you've already figured out) so I apologize if the problem is not explained very well or using the right terminology.

Thanks for any help you can offer. Bob

Answer 1

When I studied for mechanical technician, we used this method:

http://draftingmanuals.tpub.com/14276/css/Parallelogram-Ellipses-119.htm

or

https://www.uwgb.edu/dutchs/MATHALGO/Ellipses.HTM

If you are using a computer programm you can programm all those lines or segments and calculate the points of intersection. And with these points of intersection, obtain the segments that will be part of your ellipse. The more the lines or segments, the more precise your ellipse. This, if I have understood correctly your question.