Strategies in finding a rectilinear polygon within a polygon in GIS

What is a Rectilinear polygon?

Use case for a Rectilinear polygon

Rules for the algorithm

Greedy Algorithm

Strategies

Moving along the top line until it forms a right-angle
Moving along the left joint line can also make it right-angle
Form a right angle using dependent, dependee and the angle to make dependent a rectilinear angle (90°/270°). Extend the line until it touches the next polygon line.
In cases it does not touch the next polygon line, move the point to the right angle triangle instead.

Results

Looks correct.
Looks legit.
Seems correct
Looks correct
Not the largest rectilinear possible. There is gap on the right that can be extended.
This looks almost like a rectilinear but 1 corner does not meet criteria.
This is incorrect. 3 points were skipped to obtain this.

Conclusion

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