1

Let's consider there is a polygon with near orthogonal edges that is in the range of (70, 89)° or (91, 110)°. We know the sum of angles in a polygon is multiple of 180°.

The question is how to convert a polygon with customized shape to a minimum polygon with right angles.

As a very simple case, let's consider the example below: enter image description here

What we want to achieve is, the polygon below: enter image description here

The number of edges can be more. The example above is just a simple example.

Majid Azimi
  • 907
  • 1
  • 11
  • 29
  • Not an answer but a suggestion: fix the midpoints of each edge, select the orientation of one of the edges, then start by creating new edges perpendicular to the selected edge that go through the midpoint of the next edge. Continue this process for all edges. This will give a solution that meets the criteria, but it may not be optimal, in the sense of minimizing change from the original polygon. – RaffleBuffle Apr 27 '21 at 21:27
  • 1
    **What have you tried?** What do you mean by "minimum polygon?" I can imagine fitting a polygon with right angles inside the original polygon, finding a polygon with the same area as the original but right angles at the vertices, maintaining some of the vertex angle bisectors, etc. The red picture doesn't provide enough specifics about what you want to achieve and/or what measure is important (e.g. area difference between original and modified polygon, relative "stability" of vertex locations, etc.). Please show some work and post a question. Where are you stuck? – Rethunk Apr 30 '21 at 01:35

0 Answers0