Question

say, I have 100 points and want to draw a closedcurve (I’m using C# and graphics), like this:

Graphics g = this.CreateGraphics();
        Pen pen = new Pen(Color.Black, 2);
        Point[] points = new Point[DrawingPoints];
        for (int x = 0; x < DrawingPoints; x++)
        {
            int px = r.Next(0, MaxXSize);
            int py = r.Next(0, MaxYSize);
            Point p = new Point(px, py);
            points[x] = p;
        }
        g.DrawClosedCurve(pen, points);

It is connecting points as they get into points[] and lines cross – you will not get a solid figure with this.

Is there an algorithm that will help me toss the points to get a solid figure? Here’s a picture below (tried as hard as I could hehe) to help visualize what I’m asking for.

Answer 1

Well, in O(n log n) time, you could compute the centroid of the points and sort them in order of angle about that centroid, leaving a star-shaped polygon. That’s efficient but probably messes up the order of your points too much.

I think you’d be happier with the results of a 2-OPT method for TSP (description here). 2-OPT is worst-case exponential but polynomial-time in practice.