How to paint an arbitrary shape with lines?

Question

Programming

How to paint over the shape of an arbitrary area with a continuous line? The optimal algorithm is the one in which the line length is minimal.
As input, the program receives an array of border coordinates (x, y) of an arbitrary area and the line width. Let's allow the minimum exit for borders of area.
A more complicated version: the line, approaching the border of the area, should unfold along the arc of a circle.

Answer 1

The algorithm is serious, I'm afraid no one will implement it for you for free. I would do like:
And yet, the algorithm for the shortest path through all points is a traveling salesman problem , known for its complexity. I'm afraid that it will be quite difficult to optimize something here, this is more a task for research institutes.