public HalfEdge(Vertex a_Vertex)
{
// Using new here prevents reference equality. Is it really necessary to copy?
m_Origin = new Vertex(a_Vertex.X, a_Vertex.Y, a_Vertex.Ownership);
Triangle = null;
Twin = null;
Next = null;
Prev = null;
}
public virtual bool AddVertex(Vertex a_Vertex)
{
Triangle triangle = FindTriangle(a_Vertex);
if (triangle == null)
{ return false; }
AddVertex(triangle, a_Vertex);
return true;
}
protected void AddVertex(Triangle a_Triangle, Vertex a_Vertex)
{
m_Vertices.Add(a_Vertex);
m_Triangles.Remove(a_Triangle);
HalfEdge h1 = a_Triangle.HalfEdge;
HalfEdge h2 = h1.Next;
HalfEdge h3 = h2.Next;
HalfEdge h4 = new HalfEdge(h1.Origin);
HalfEdge h5 = new HalfEdge(h2.Origin);
HalfEdge h6 = new HalfEdge(h3.Origin);
HalfEdge h7 = new HalfEdge(a_Vertex);
HalfEdge h8 = new HalfEdge(a_Vertex);
HalfEdge h9 = new HalfEdge(a_Vertex);
m_HalfEdges.AddRange(new List<HalfEdge>() { h4, h5, h6, h7, h8, h9 });
h4.Twin = h7;
h7.Twin = h4;
h5.Twin = h8;
h8.Twin = h5;
h6.Twin = h9;
h9.Twin = h6;
// Set all next
h1.Next = h5;
h5.Prev = h1;
h5.Next = h7;
h7.Prev = h5;
h7.Next = h1;
h1.Prev = h7;
h2.Next = h6;
h6.Prev = h2;
h6.Next = h8;
h8.Prev = h6;
h8.Next = h2;
h2.Prev = h8;
h3.Next = h4;
h4.Prev = h3;
h4.Next = h9;
h9.Prev = h4;
h9.Next = h3;
h3.Prev = h9;
m_Triangles.Add(new Triangle(h1));
m_Triangles.Add(new Triangle(h2));
m_Triangles.Add(new Triangle(h3));
}
public override bool AddVertex(Vertex a_Vertex)
{
Triangle triangle = FindTriangle(a_Vertex);
if (triangle == null)
{ return false; }
AddVertex(triangle, a_Vertex);
// Find halfedges of triangle
HalfEdge h1 = triangle.HalfEdge;
HalfEdge h2 = triangle.HalfEdge.Next.Twin.Next;
HalfEdge h3 = triangle.HalfEdge.Next.Twin.Next.Next.Twin.Next;
// Flip if needed
LegalizeEdge(a_Vertex, h1, h1.Triangle);
LegalizeEdge(a_Vertex, h2, h2.Triangle);
LegalizeEdge(a_Vertex, h3, h3.Triangle);
return true;
}
private void LegalizeEdge(Vertex a_Vertex, HalfEdge a_HalfEdge, Triangle a_Triangle)
{
if (a_Vertex == null || a_HalfEdge == null || a_Triangle == null)
{
Debug.LogError("Invalid call to LegalizeEdge");
return;
}
Vertex v1, v2, v3;
try
{
// Points to test
v1 = a_HalfEdge.Twin.Next.Next.Origin;
v2 = a_HalfEdge.Next.Twin.Next.Next.Origin;
v3 = a_HalfEdge.Next.Next.Twin.Next.Next.Origin;
}
catch (NullReferenceException)
{
Debug.LogError("Null pointers in call to LegalizeEdge");
return;
}
if (v1 == null || v2 == null || v3 == null)
{
Debug.LogError("Invalid halfedge in call to LegalizeEdge");
return;
}
if (a_Triangle.InsideCircumcenter(v1) || a_Triangle.InsideCircumcenter(v2) || a_Triangle.InsideCircumcenter(v3))
{
HalfEdge h1 = a_HalfEdge.Twin.Next.Twin;
HalfEdge h2 = a_HalfEdge.Twin.Prev.Twin;
Flip(a_HalfEdge);
LegalizeEdge(a_Vertex, h1.Twin, h1.Twin.Triangle);
LegalizeEdge(a_Vertex, h2.Twin, h2.Twin.Triangle);
}
}
public void Create()
{
Vertex v1 = new Vertex(-500000, -500000);
Vertex v2 = new Vertex(500000, 500000);
Vertex v3 = new Vertex(-500000, 500000);
Vertex v4 = new Vertex(500000, -500000);
m_Vertices.AddRange(new List<Vertex>() { v1, v2, v3, v4 });
HalfEdge h1 = new HalfEdge(v1);
HalfEdge h2 = new HalfEdge(v2);
HalfEdge h3 = new HalfEdge(v3);
m_HalfEdges.AddRange(new List<HalfEdge>() { h1, h2, h3 });
h1.Next = h2;
h2.Next = h3;
h3.Next = h1;
h2.Prev = h1;
h3.Prev = h2;
h1.Prev = h3;
HalfEdge h4 = new HalfEdge(v2);
HalfEdge h5 = new HalfEdge(v1);
HalfEdge h6 = new HalfEdge(v4);
m_HalfEdges.AddRange(new List<HalfEdge>() { h4, h5, h6 });
h4.Twin = h1;
h1.Twin = h4;
h4.Next = h5;
h5.Next = h6;
h6.Next = h4;
h5.Prev = h4;
h6.Prev = h5;
h4.Prev = h6;
HalfEdge h7 = new HalfEdge(v1);
HalfEdge h8 = new HalfEdge(v2);
HalfEdge h9 = new HalfEdge(v3);
HalfEdge h10 = new HalfEdge(v4);
m_HalfEdges.AddRange(new List<HalfEdge>() { h7, h8, h9, h10 });
h10.Next = h7;
h7.Prev = h10;
h8.Next = h10;
h10.Prev = h8;
h9.Next = h8;
h8.Prev = h9;
h7.Next = h9;
h9.Prev = h7;
h3.Twin = h7;
h7.Twin = h3;
h8.Twin = h6;
h6.Twin = h8;
h2.Twin = h9;
h9.Twin = h2;
h10.Twin = h5;
h5.Twin = h10;
m_Triangles.Add(new Triangle(h1));
m_Triangles.Add(new Triangle(h4));
}
protected Triangle FindTriangle(Vertex a_Vertex)
{
foreach (Triangle triangle in m_Triangles)
{
if (triangle.Inside(a_Vertex))
{
return triangle;
}
}
return null;
}
public static float SquaredDistance(Vertex v1, Vertex v2)
{
return Mathf.Pow (v1.X - v2.X, 2) + Mathf.Pow (v1.Y - v2.Y, 2);
}
public static float Slope(Vertex v1, Vertex v2)
{
float value = (v2.Y - v1.Y) / (v2.X - v1.X);
return value;
}
public static Vertex Midpoint(Vertex v1, Vertex v2)
{
float mx = (v1.X + v2.X) / 2;
float my = (v1.Y + v2.Y) / 2;
return new Vertex(mx, my);
}
public static float Distance(Vertex v1, Vertex v2)
{
return Mathf.Sqrt(SquaredDistance(v1, v2));
}
private Vertex CalculateCircumcenterT(Vertex a_VertexA, Vertex a_VertexB, Vertex a_VertexC)
{
// determine midpoints (average of x & y coordinates)
Vertex midAB = Utility.Midpoint(a_VertexA, a_VertexB);
Vertex midBC = Utility.Midpoint(a_VertexB, a_VertexC);
// determine slope
// we need the negative reciprocal of the slope to get the slope of the perpendicular bisector
float slopeAB = -1 / Utility.Slope(a_VertexA, a_VertexB);
float slopeBC = -1 / Utility.Slope(a_VertexB, a_VertexC);
// y = mx + b
// solve for b
float bAB = midAB.Y - slopeAB * midAB.X;
float bBC = midBC.Y - slopeBC * midBC.X;
// solve for x & y
// x = (b1 - b2) / (m2 - m1)
float x = (bAB - bBC) / (slopeBC - slopeAB);
return new Vertex (x, (slopeAB * x) + bAB);
}
public bool InsideCircumcenter(Vertex a_Vertex)
{
return (Circumcenter.DeltaSquaredXY (a_Vertex) < CircumcenterRangeSquared);
}
public bool Inside(Vertex a_Vertex)
{
int i, j = m_Vertices.Length - 1;
bool oddNodes = false;
for (i = 0; i < m_Vertices.Length; i++)
{
if ((m_Vertices[i].Y < a_Vertex.Y &&
m_Vertices[j].Y >= a_Vertex.Y ||
m_Vertices[j].Y < a_Vertex.Y &&
m_Vertices[i].Y >= a_Vertex.Y)
&& (m_Vertices[i].X <= a_Vertex.X || m_Vertices[j].X <= a_Vertex.X))
{
oddNodes ^= (m_Vertices[i].X +
(a_Vertex.Y - m_Vertices[i].Y) /
(m_Vertices[j].Y - m_Vertices[i].Y) *
(m_Vertices[j].X - m_Vertices[i].X)
) < a_Vertex.X;
}
j = i;
}
return oddNodes;
}
public float DeltaSquaredXY(Vertex t)
{
float dx = (X - t.X);
float dy = (Y - t.Y);
return (dx * dx) + (dy * dy);
}