POLYGON CRUX.zip

I have always loved the simplicity of Bezier curves - so much so that I invented geometric modeling kernel (algorithm) which is based on rational, quadratic Bezier curves. I am not surprised that Rhino SubD kernel is also based on the Bezier curves. Examples of geometric modeling kernels: NURBS surfaces, polygon meshes, T-splines, subdivision surfaces.

POLYGON CRUX.zip

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If our polygon is not regular, we can find $A_i-1$, $A_i$, and $A_i+1$, such that $A_i$ is not the midpoint of the arc between $A_i-1$ and $A_i+1$. Notice that when we move $A_i$ to the midpoint of this arc, the area of the polygon becomes bigger, since the area of $\triangle A_i-1 A_i A_i+1$ increases. Ergo, the maximal polygon is the polygon for which $A_i$ is the midpoint of arc $A_i-1A_i+1$ for all $i$.

I'm looking for a script that will square the corners of polygons that are near 90 degrees but not exactly. Near could be dealt with via a variable, for example within 5 degrees of 90 (85 - 95 degrees).

In your original code, Lines #157-162 appear to be building (or trying to build) a polygon from a single point, which isn't valid. Also, when looking at your polygon.json file, there appear to be numerous polygons, but your code seems to be treating all the points are a single set of points instead of groups of points. 041b061a72