Algorithm for finding a point in an irregular polygon

Question

Imagagine I have a polygon like the following:

Irregular Polygon

I am looking for a C# algorithm with whom I can find a point (could be the middlepoint or also a random point) inside any polygon.

For finding the center of mass I used the following algorithm:

private Point3d GetPolyLineCentroid(DBObject pObject, double pImageWidth, double pImageHeight)
        {
            Point2d[] pointArray = GetPointArrayOfRoomPolygon(pObject);

            double centroidX = 0.0;
            double centroidY = 0.0;
            double signedArea = 0.0;
            double x0 = 0.0; // Current vertex X
            double y0 = 0.0; // Current vertex Y
            double x1 = 0.0; // Next vertex X
            double y1 = 0.0; // Next vertex Y
            double a = 0.0;  // Partial signed area

            int i = 0;
            for (i = 0; i < pointArray.Length - 1; ++i)
            {
                x0 = pointArray[i].X;
                y0 = pointArray[i].Y;
                x1 = pointArray[i + 1].X;
                y1 = pointArray[i + 1].Y;
                a = x0 * y1 - x1 * y0;
                signedArea += a;
                centroidX += (x0 + x1) * a;
                centroidY += (y0 + y1) * a;
            }

            x0 = pointArray[i].X;
            y0 = pointArray[i].Y;
            x1 = pointArray[0].X;
            y1 = pointArray[0].Y;
            a = x0 * y1 - x1 * y0;
            signedArea += a;
            centroidX += (x0 + x1) * a;
            centroidY += (y0 + y1) * a;

            signedArea *= 0.5;
            centroidX /= (6.0 * signedArea);
            centroidY /= (6.0 * signedArea);

            Point3d centroid = new Point3d(centroidX, centroidY, 0);

            return centroid;
        }

This works good with polygones like this:

L-Polygon

But if my polygon has the form of a C or something like that this algorithmn does not work because the center off mass is outside the polygon.

Does anyone has an idea how to get always points inside any polygon?

FYI, having the centre of mass outside of a polygon is perfectly correct and OK so the algorithm is probably working fine. (though maybe not for the context of your application?) — Chris Sinclair
– Chris Sinclair, Commented Jan 3, 2013 at 11:46
stackoverflow.com/questions/11716268/point-in-polygon-algorithm — Mudassir Hasan
– Mudassir Hasan, Commented Jan 3, 2013 at 11:48
Divide the polygon into triangles using a polygon triangulation algorithm, and then use barycentric coordinates with arbitrary values that total 1.0 to derive points inside the triangles. — Rotem
– Rotem, Commented Jan 3, 2013 at 11:52
"always getting a point inside a polygon" is not possible. But you can choose a point and test whether it's inside or outside using the odd-edge-intercepts method. You can choose the barycenters of the triangles generated by three consecutive vertices; at least two of them will be inside the polygon. — LSerni
– LSerni, Commented Jan 3, 2013 at 11:56

Rotem · Accepted Answer · 2013-01-03 12:13:20Z

9

You can use polygon triangulation to break your polygon apart into triangles.

One such algorithm is demonstrated using c# in this CodeProject article.

Once you have triangles, finding arbitrary points that lie within the triangle is easy. Any barycentric coordinate with a sum of 1.0 multiplied by the vertices of the triangle will give you a point inside the triangle.

The center can be derived using the barycentric coordinate [0.333333, 0.333333, 0.333333] :

float centerX = A.x * 0.333333 + B.x * 0.333333 + C.x * 0.3333333;
float centerY = A.y * 0.333333 + B.y * 0.333333 + C.y * 0.3333333;

or more simply:

float centerX = (A.x + B.x + C.x) / 3f;
float centerY = (A.y + B.y + C.y) / 3f;

answered Jan 3, 2013 at 12:13

Rotem

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2 Comments

LSerni Over a year ago

+1 for the triangularization :-). The OP may also want to look at libraries such as Clipper (angusj.com/delphi/clipper.php).

Thomas Ahle Over a year ago

Or easier: Just look at any three consecutive pairs; Half the time they'll be 'turning in' and their centroid will be in the polygon. The other half of the time they'll be 'turning out' and you just go to the next triple. Computing the 'turning' can be done just using the cross product.

Vipin Sharma · Accepted Answer · 2014-09-06 10:10:32Z

0

Use This:

private Point getCentroid(pointArray)
{
   double centroidX = 0.0;
   double centroidY = 0.0;

   for (int i = 0; i < pointArray.Length; i++)
   {
          centroidX += pointArray[i].X;
          centroidY += pointArray[i].Y;`
   }
   centroidX /= pointArray.Length;
   centroidY /= pointArray.Length;

   return(new Point(centroidX ,centroidY));
}

this code is just to find Center of Mass of Polygon. To check whether a point is inside or outside polygon check this link http://bbs.dartmouth.edu/~fangq/MATH/download/source/Determining%20if%20a%20point%20lies%20on%20the%20interior%20of%20a%20polygon.htm

edited Sep 6, 2014 at 10:10

answered Sep 4, 2014 at 11:36

Vipin Sharma

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1 Comment

S.L. Barth is on codidact.com Over a year ago

That will give the center point, but it is not guaranteed to be inside the polygon.

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