Sample C# code implementing medial axis transform of a polygon using Voronoi diagram. In order to compile this code, download and reference NetTopologySuite, an open source spatial analysis library.

gistfile1.cs

using System;
using System.Collections.Generic;
using GeoAPI.Geometries;
using NetTopologySuite.Geometries;
using NetTopologySuite.IO;
using NetTopologySuite.Densify;
using NetTopologySuite.Triangulate;

namespace Skeleton
{
  class MainClass
  {
    public static void Main (string[] args)
    {
      IGeometryFactory gfactory = GeometryFactory.Fixed;
      WKTReader greader = new WKTReader (gfactory);
      //Create a new polygon instance
      IGeometry polygon = greader.Read ("POLYGON((0 0, 0 10, 20 10, 20 20, 25 20, 25 10, 40 10, 40 0, 0 0))");
      //Densify polygon and store vertices in point array
      IGeometry densification = Densifier.Densify (polygon, 1);
      IGeometry[] points = new IGeometry[densification.NumPoints - 1];
      for (int i = 0; i <= points.GetUpperBound (0); i++) {
        points[i] = gfactory.CreatePoint (densification.Coordinates[i]);
      }
      //Create a new point collection
      IGeometryCollection pointsCollection = gfactory.CreateGeometryCollection (points);
      //Build Voronoi diagram from point collection
      VoronoiDiagramBuilder voronoiBuilder = new VoronoiDiagramBuilder ();
      voronoiBuilder.SetSites (pointsCollection.Coordinates);
      IGeometryCollection diagram = voronoiBuilder.GetDiagram (gfactory);
      //Intersect Voronoi diagram with target polygon to get crust
      IGeometry crust = diagram.Intersection (polygon);
      //Create an empty geometry collection for the skeleton 
      IList<IGeometry> skeleton = new List<IGeometry> ();
      //Populate skeleton from edges in crust
      for (int i = 0; i < crust.NumGeometries; i++) {
        IGeometry g = crust.GetGeometryN (i);
        for (int j = 1; j < g.Coordinates.Length; j++) {
          //For each polygon in crust get each edge 
          IGeometry edge = gfactory.CreateLineString (new Coordinate[] {g.Coordinates[j-1], g.Coordinates[j]});
          if (!edge.Touches (polygon.Boundary) && edge.Within (polygon)) {
            skeleton.Add (edge); //If this edge does not touch polygon perimeter add to skeleton
          }
        }
      }
    }
  }
}

when i change the polygon to (0 0, 20 0, 20 10, 10 4,5 30, 0 10, 0 0), it has a error. The "densification.NumPoints" is zero.

Using the skeleton I want to find the longest continuous edge. I want to do this to find the bearing of such edge and determine the orientation of the polygon in general. Any ideas for better ways to find the orientation of the polygon?

Using the skeleton I want to find the longest continuous edge. I want to do this to find the bearing of such edge and determine the orientation of the polygon in general. Any ideas for better ways to find the orientation of the polygon?

maybe try moments of inertia/ellipsoid of inertia/principal axes?