Nested_Rotated

Nested rotated polygons

A scheme example of use of the tool [User-Defined\N-fold Scheme-Socket _ _ ]:
Given the polygon p = ABCD ... , the point F and the angle w = GHI.
From F we draw orthogonals to the sides of the polygon and then define lines which make angles w
with these orthogonals. Then we find the intersection-points of these lines with the polygon.
This defines a new polygon p' = JKL... . We repeat the same procedure and create 10 polygons iscribed one into the other. The whole scheme depends (masters) on the initial polygon p, the angle w and the point G. The basic property of the polygons is that as the angle w changes, their angles remain constant.
On the picture below we define the intersection-point not of the side of the polygon, but of its extension-line (which afterwards is hidden). Only then the angles are calculated correctly, as w varies.

Catch I and modify the angle. Watch how the nested polygons change.

http://users.math.uoc.gr/~pamfilos/