# Determine inner angles of twisted polygon

Is there any way to determine inner angle of twisted polygon? (Here's a picture of "normal" and "twisted" polygon http://courses.be.washington.edu/ARCH/481/1.Tapestry%20Reader/1.Data/6.Problems/graphics.invis/fulltwist.gif )

I know how to determine inner angle of polygon if I know its orientation (CW or CCW), however twisted polygon changes orientation after intersection, so if I check angle for CCW orientation, the CW part will have inverse angle values.

I thought about using winding numbers algorithm and see if values are negative or positive, but it is too slow to check that for every angle.

• Did you name the angles correctly in the twisted picture ? (I do not know ... just asking) Apr 11, 2014 at 15:09
• @babou I just found that picture on the internet, because I couldn't upload one. I think that for my problems names aren't important, just values. But yes, if the names should be important, names aren't correct in twisted polygon (C and D should switch names) Apr 11, 2014 at 15:24
• I do not know the area, and do not understand the statement of the problem. But ... would it be the case that, when you cross an edge while following another one, the inside and outside (w.r.t. the edge you follow) switch sides, and the winding number is inversed (multiplied by -1). Well it may be more complicated if the twisted polygon folds onto itself, as you get high winding numbers. But which is the inner angle, then ... sorry ... rambling. Apr 11, 2014 at 16:38
• Can you provide a clearer definition of what a "twisted polygon" is? Is this a standard term? The picture wasn't enough for me to understand.
– D.W.
Apr 12, 2014 at 0:30
• @D.W. I found that term in some algorithms in computational geometry (for example FIST algorithm). It is self-intersecting polygon, but one which doesn't fold into itself. I hope it's clearer now? Apr 15, 2014 at 9:15