Finding midpoint of line

JoeHershman

I am setting up something what I want to draw a line to the middle point of another line.  I have gone about a few approaches to finding that Midpoint none of which are returning the proper result.

• Using GetCenter on the bounding envelope, works good with small lines, but for large lines works very poor as the envelope may not even be on the line
• Trying to just grab the middle point (i.e., polyline.Paths[0][polyline.Paths[0].Count/2]).  Better because at least it is always on the line, but with long lines usually not near the center because a curved section will have so many points compared to a straight section.

I am stuck thinking I need to compute the length of the line and find the point closest to the center of that length.  Calling a GeometryService is out of the question because this needs to work quickly, responding to a user event immediately.  I am having fears of high school trigonometry as I think about calculating the length of each individual line segment and adding them all up.  Anyone have a simpler approach that I am missing?

Thanks
-Joe

DominiqueBroux

I am afraid you can't avoid calculating the length of each individual line segment if you want to get the real middle point of a polyline:).

But once the length of a segment is calculated it's just a LINQ matter to aggregate for a multi paths polyline.

Below is an extension class allowing to get the midpoint of a polyline by code like:
var point = polyline.Midpoint();

It's based on the calculation of the length and the calculation of a linear position along the line (M = length/2 being a particular case).

That's a good LINQ exercise 🙂

public static class GeometryExtension {     public static MapPoint MidPoint(this Polyline polyline)     {         var length = polyline.Length();         var m = length / 2.0;         return polyline.LinearPosition(m);     }      // length of a multipath polyline     public static double Length(this Polyline polyline)     {         return polyline.Paths.Sum((Func<PointCollection, double>)Length);     }      // length of one path     private static double Length(this PointCollection points)     {         return points.Zip(points.Skip(1), Length).Sum();     }      // length of a segment     private static double Length(MapPoint point1, MapPoint point2)     {         return Math.Sqrt(Math.Pow(point2.X - point1.X, 2) + Math.Pow(point2.Y - point1.Y, 2));     }      // Get a M position on a multipath polyline     public static MapPoint LinearPosition(this Polyline polyline, double m)     {         PointCollection path1 = polyline.Paths.Where(path => DecrementTotal(path.Length(), ref m))             .DefaultIfEmpty(polyline.Paths.Last()) // for the case where m > polyline length             .First();         return path1.LinearPosition(m);     }      // Get a M position on a polyline     private static MapPoint LinearPosition(this IEnumerable<MapPoint> points, double m)     {         var seg = points.Zip(points.Skip(1), (pt1, pt2) => new Tuple<MapPoint, MapPoint>(pt1, pt2))             .Where(segment => DecrementTotal(Length(segment.Item1, segment.Item2), ref m))             .FirstOrDefault();         return seg == null ? points.Last() : seg.LinearPosition(m);     }      // Get a M position on a segment     private static MapPoint LinearPosition(this Tuple<MapPoint, MapPoint> segment, double m)     {         var ratio = m / Length(segment.Item1, segment.Item2);         return new MapPoint(segment.Item1.X + ratio * (segment.Item2.X - segment.Item1.X), segment.Item1.Y + ratio * (segment.Item2.Y - segment.Item1.Y));     }      private static bool DecrementTotal(double l, ref double cumul)     {         if (l >= cumul)             return true;         cumul -= l;         return false;     } }