/// <summary>
/// Flips the given triangle edge in the triangulation.
/// Flipping for Delaunay means changing the edge for the adjacent two triangles to the other possibility.
/// </summary>
/// <param name="T"></param>
/// <param name="a_Edge"></param>
private static void Flip(Triangulation T, TriangleEdge a_Edge)
{
var a_Triangle = a_Edge.T;
var a_Twin = a_Edge.Twin.T;
if (a_Triangle == null || a_Twin == null)
{
throw new GeomException("Cannot flip edge if neighbouring triangles don't exist");
}
// retrieve other adjacent edges to edge vertices
// e3 . e1
// / | \
// . | .
// \ | /
// e2 . e0
var e0 = a_Triangle.OtherEdge(a_Edge, a_Edge.Point1);
var e1 = a_Triangle.OtherEdge(a_Edge, a_Edge.Point2);
var e2 = a_Twin.OtherEdge(a_Edge.Twin, a_Edge.Point1);
var e3 = a_Twin.OtherEdge(a_Edge.Twin, a_Edge.Point2);
// create new triangle edges
var euv = new TriangleEdge(e0.Point1, e2.Point2, null, null);
var evu = new TriangleEdge(e2.Point2, e0.Point1, euv, null);
euv.Twin = evu;
// Remove old triangles
T.RemoveTriangle(a_Triangle);
T.RemoveTriangle(a_Twin);
// add new triangles
T.AddTriangle(new Triangle(e0, e2, evu));
T.AddTriangle(new Triangle(e3, e1, euv));
}
public void InValidTriangulationTest()
{
var m_delaunay = new Triangulation();
var t1 = new Triangle(m_topVertex, m_rightVertex, m_botVertex);
var t2 = new Triangle(m_topVertex, m_botVertex, m_leftVertex);
t1.E2.Twin = t2.E0;
t2.E0.Twin = t1.E2;
m_delaunay.AddTriangle(t1);
m_delaunay.AddTriangle(t2);
Assert.IsFalse(Delaunay.IsValid(m_delaunay));
}
public void AddTriangleTest()
{
var tr = new Triangle(v1, v2, v4);
var T2 = new Triangulation();
T2.AddTriangle(tr);
Assert.AreEqual(1, T2.Triangles.Count);
}
public TriangulationTest()
{
v1 = new Vector2(0, 0);
v2 = new Vector2(1, 1);
v3 = new Vector2(2, 0);
v4 = new Vector2(1, -1);
e1 = new TriangleEdge(v1, v2);
e2 = new TriangleEdge(v2, v3);
e3 = new TriangleEdge(v3, v1);
t1 = new Triangle(e1, e2, e3);
e4 = new TriangleEdge(v1, v3);
e5 = new TriangleEdge(v3, v4);
e6 = new TriangleEdge(v4, v1);
t2 = new Triangle(e4, e5, e6);
T = new Triangulation();
T.AddTriangle(t1);
T.AddTriangle(t2);
}
/// <summary>
/// Triangulates the polygon recursively.
/// Finds the leftmost point and creates a triangle with that or splits polygon in two.
/// </summary>
/// <param name="vertices"></param>
/// <returns></returns>
private static Triangulation TriangulateRecursive(List <Vector2> vertices)
{
if (vertices.Count == 3)
{
return(new Triangulation(vertices));
}
var triangulation = new Triangulation();
//Find leftmost vertex
var leftVertex = LeftMost(vertices);
var index = vertices.IndexOf(leftVertex);
var prevVertex = vertices[MathUtil.PositiveMod(index - 1, vertices.Count)];
var nextVertex = vertices[MathUtil.PositiveMod(index + 1, vertices.Count)];
//Create triangle with diagonal
Debug.Assert(leftVertex != prevVertex && leftVertex != nextVertex && prevVertex != nextVertex);
var triangle = new Triangle(prevVertex, leftVertex, nextVertex);
//check for other vertices inside the candidate triangle
var baseline = new Line(prevVertex, nextVertex);
float distance = -1f;
int diagonalIndex = -1;
for (int i = 0; i < vertices.Count; i++)
{
var v = vertices[i];
if (v != leftVertex && v != prevVertex && v != nextVertex &&
triangle.Contains(v))
{
if (baseline.DistanceToPoint(v) > distance)
{
distance = baseline.DistanceToPoint(v);
diagonalIndex = i;
}
}
}
//Do Recursive call
if (diagonalIndex == -1) //didn't change
{
if (!triangle.IsClockwise())
{
// shouldnt happen but in case it does
// reverse triangle
triangle = new Triangle(triangle.P0, triangle.P2, triangle.P1);
}
triangulation.AddTriangle(triangle);
vertices.Remove(leftVertex);
triangulation.AddTriangulation(TriangulateRecursive(vertices));
}
else
{
var minIndex = Mathf.Min(index, diagonalIndex);
var maxIndex = Mathf.Max(index, diagonalIndex);
var poly1List = vertices.Skip(minIndex).Take(maxIndex - minIndex + 1).ToList();
var poly2List = vertices.Skip(maxIndex).Concat(vertices.Take(minIndex + 1)).ToList();
triangulation.AddTriangulation(TriangulateRecursive(poly1List));
triangulation.AddTriangulation(TriangulateRecursive(poly2List));
}
return(triangulation);
}
