Algorithm to arrange the set of points clockwise and make sure that the path connecting the points is closed

Question

I did this problem differently, and after a month, trying to do it myself, I think it is time for fresh eyes to look at it. I am trying to make an image scaling application to re-select 8-bit sprites and turn them into vector images. So far I am working; it takes an image, breaks it into shapes (areas with adjacent pixels of the same color), and then each pixel in the form is replaced by four pixels:

private Point[] expand(int x, int y){
    x *= factor;
    y *= factor;
    return new Point[]{new Point(x+half_factor,y), new Point(x+factor,y+half_factor),
            new Point(x+half_factor, y+factor), new Point(x,y+half_factor)};
}

Each of the four points is placed in a 2D Boolean array:

private void placePoint(int x, int y){
    table[x][y] = !table[x][y];
    extrema(x,y);
}

And the result for one individual form is as follows:

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Answer 1

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