// find the type of a specific vertex in a polygon, either Concave or Convex.
public PolygonType VertexType(int vertexNo)
{
PolygonData triangle;
if (vertexNo == 0)
{
triangle = new PolygonData(new List <PointF> {
PtList[PtList.Count - 2], PtList[0], PtList[1]
}); // the polygon is always closed so the last point is the same as the first
}
else
{
triangle = new PolygonData(new List <PointF> {
PtList[vertexNo - 1], PtList[vertexNo], PtList[vertexNo + 1]
});
}
if (Math.Sign(triangle.Area) == Math.Sign(this.Area))
{
return(PolygonType.Convex);
}
else
{
return(PolygonType.Concave);
}
}
// From Wikipedia:
// One way to triangulate a simple polygon is by using the assertion that any simple polygon
// without holes has at least two so called 'ears'. An ear is a triangle with two sides on the edge
// of the polygon and the other one completely inside it. The algorithm then consists of finding
// such an ear, removing it from the polygon (which results in a new polygon that still meets
// the conditions) and repeating until there is only one triangle left.
// the algorithm here aims for simplicity over performance. there are other, more performant
// algorithms that are much more complex.
// convert a triangle to a list of triangles. each triangle is represented by a PointF array of length 3.
public static List<PointF[]> Triangulate(PolygonData poly) {
List<PointF[]> triangles = new List<PointF[]>(); // accumulate the triangles here
// keep clipping ears off of poly until only one triangle remains
while (poly.PtListOpen.Count > 3) // if only 3 points are left, we have the final triangle
{
int midvertex = FindEar(poly); // find the middle vertex of the next "ear"
triangles.Add(new PointF[] { poly.PtList[midvertex - 1], poly.PtList[midvertex], poly.PtList[midvertex + 1] });
// create a new polygon that clips off the ear; i.e., all vertices but midvertex
List<PointF> newPts = new List<PointF>(poly.PtList);
newPts.RemoveAt(midvertex); // clip off the ear
poly = new PolygonData(newPts); // poly now has one less point
}
// only a single triangle remains, so add it to the triangle list
triangles.Add(poly.PtListOpen.ToArray());
return triangles;
}
// find an ear (always a triangle) of the polygon and return the index of the middle (second) vertex in the ear
public static int FindEar(PolygonData poly) {
for (int i = 0; i < poly.PtList.Count - 2; i++) {
if (poly.VertexType(i + 1) == PolygonType.Convex) {
// get the three points of the triangle we are about to test
PointF a = poly.PtList[i];
PointF b = poly.PtList[i + 1];
PointF c = poly.PtList[i + 2];
bool foundAPointInTheTriangle = false; // see if any of the other points in the polygon are in this triangle
for (int j = 0; j < poly.PtListOpen.Count; j++) // don't check the last point, which is a duplicate of the first
{
if (j != i && j != i + 1 && j != i + 2 && PointInTriangle(poly.PtList[j], a, b, c)) foundAPointInTheTriangle = true;
}
if (!foundAPointInTheTriangle) // the middle point of this triangle is convex and none of the other points in the polygon are in this triangle, so it is an ear
return i + 1; // EXITING HERE!
}
}
throw new ApplicationException("Improperly formed polygon");
}
/// <summary>
/// This method returns a 3D representation of this area
/// </summary>
/// <param name="nodesDict">List of all the nodes on the map</param>
/// <param name="map">bounds of the map</param>
/// <param name="brush">Color of this area</param>
/// <returns>ModelUIElement3D of this area</returns>
public virtual ModelUIElement3D get3DSurface(Dictionary<long, OsmSharp.Osm.Node> nodesDict, Map map, System.Windows.Media.SolidColorBrush brush) {
List<PointF> ptlist = getScaledPointsSurface(nodesDict, map);
// Divide the polygons in triangles, this is code (and these two classes) are from: https://polygontriangulation.codeplex.com/
PolygonData poly = new PolygonData(ptlist);
List<PointF[]> triangles = Triangulation2D.Triangulate(poly);
// Surrounding tags of the mesh
ModelUIElement3D model = new ModelUIElement3D();
GeometryModel3D geometryModel = new GeometryModel3D();
// Mesh and his his properties
MeshGeometry3D mesh = new MeshGeometry3D();
DiffuseMaterial material = new DiffuseMaterial((System.Windows.Media.Brush)brush);
Point3DCollection positions = new Point3DCollection();
Int32Collection indices = new Int32Collection();
// Add points and indices to their collection
foreach (PointF[] points in triangles) {
foreach (PointF point in points) {
positions.Add(new Point3D(point.X, point.Y, height));
}
int count = positions.Count;
indices.Add(count - 3);
indices.Add(count - 2);
indices.Add(count - 1);
}
// Add these collections to the mesh
mesh.Positions = positions;
mesh.TriangleIndices = indices;
// Set the color of front and back of the triangle
geometryModel.Material = material;
geometryModel.BackMaterial = material;
// Add the mesh to the model
geometryModel.Geometry = mesh;
model.Model = geometryModel;
return model;
}
// find the type of a specific vertex in a polygon, either Concave or Convex.
public PolygonType VertexType(int vertexNo) {
PolygonData triangle;
if (vertexNo == 0) {
triangle = new PolygonData(new List<PointF> { PtList[PtList.Count - 2], PtList[0], PtList[1] }); // the polygon is always closed so the last point is the same as the first
} else {
triangle = new PolygonData(new List<PointF> { PtList[vertexNo - 1], PtList[vertexNo], PtList[vertexNo + 1] });
}
if (Math.Sign(triangle.Area) == Math.Sign(this.Area))
return PolygonType.Convex;
else
return PolygonType.Concave;
}