/// <summary>
/// Delta distance squared between this and other vertex t
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public float DeltaSquared(Vertex t)
{
float dx = (X - t.X);
float dy = (Y - t.Y);
float dz = (Z - t.Z);
return (dx * dx) + (dy * dy) + (dz * dz);
}
/// <summary>
/// Insert.
/// </summary>
/// <param name="v"></param>
/// <param name="old"></param>
protected void Insert(Vertex v, Triangle old)
{
// Avoid duplicates, if this facet contains v as a vertex,
// just return.
if ((old.A.X == v.X) && (old.A.Y == v.Y)) return;
if ((old.B.X == v.X) && (old.B.Y == v.Y)) return;
if ((old.C.X == v.X) && (old.C.Y == v.Y)) return;
m_points.Add(v);
// Split old into 3 triangles,
// Because old is counter clockwise, when duplicated,
// ab, bc, ca is counter clockwise.
// By changing one point and keeping to the commutation,
// they remain counter clockwise.
Triangle ab = new Triangle(old); // contains old ab, v is new C.
Triangle bc = new Triangle(old); // contains old bc, v is new A.
Triangle ca = new Triangle(old); // contains old ca, v is new B.
ab.C = v;
bc.A = v;
ca.B = v;
// This also makes assigning the sides easy.
ab.BC = bc;
ab.CA = ca;
bc.AB = ab;
bc.CA = ca;
ca.AB = ab;
ca.BC = bc;
// The existing trianges that share an edge with old,
// now share an edge with one of the three new triangles.
// Repair the existing.
// One way of looking at it:
// for (int j = 0; j < 3; j++)
// {
// if ((ab.AB != null) && (ab.AB.Edge(j) == old)) ab.AB.SetEdge(j, ab);
// if ((bc.BC != null) && (bc.BC.Edge(j) == old)) bc.BC.SetEdge(j, bc);
// if ((ca.CA != null) && (ca.CA.Edge(j) == old)) ca.CA.SetEdge(j, ca);
// }
// This is faster, null check is once per edge, and default logic
// reduces the compares by one. Instead of 3*3*2 comparisons = 18,
// Worst case is 3*3 = 9, Average is 2+3+3=8.
Triangle[] ta = { ab.AB, bc.BC, ca.CA };
Triangle[] tb = { ab, bc, ca };
for (int j = 0; j < 3; j++)
{
if (ta[j] == null) continue;
if (ta[j].Edge(0) == old)
{
ta[j].SetEdge(0, tb[j]);
continue;
}
if (ta[j].Edge(1) == old)
{
ta[j].SetEdge(1, tb[j]);
continue;
}
ta[j].SetEdge(2, tb[j]);
}
// Add the new, remove the old.
Facets.Add(ab);
Facets.Add(bc);
Facets.Add(ca);
Facets.Remove(old);
// Check for 1st order flipping.
// Triangle ab has neighbor ab.AB.
// Depth of up to recursion deep.
// Remember that due to commutators, same.same is outward,
// same.different is inward.
flipIfNeeded(ab, ab.AB, Recursion);
flipIfNeeded(bc, bc.BC, Recursion);
flipIfNeeded(ca, ca.CA, Recursion);
return;
}
/// <summary>
/// Setup.
/// </summary>
/// <param name="bounds"></param>
public void Setup(Rect bounds)
{
Triangle.ResetIndex();
Facets.Clear();
Points.Clear();
Bounds = bounds;
Vertex tl = new Vertex(Bounds.xMin, Bounds.yMin, 0);
Vertex tr = new Vertex(Bounds.xMax, Bounds.yMin, 0);
Vertex bl = new Vertex(Bounds.xMin, Bounds.yMax, 0);
Vertex br = new Vertex(Bounds.xMax, Bounds.yMax, 0);
Triangle t1 = new Triangle();
Triangle t2 = new Triangle();
t1.A = bl;
t1.B = tr;
t1.C = tl;
t2.A = bl;
t2.B = br;
t2.C = tr;
t1.AB = t2;
t2.CA = t1;
Facets.Add(t1);
Facets.Add(t2);
}
/// <summary>
/// Append point.
/// </summary>
/// <param name="v"></param>
public void Append(Vertex v)
{
// Find a triangle containing v.
for (int i = 0; i < Facets.Count; i++)
{
if (Facets[i].Contains(v))
{
Insert(v, Facets[i]);
}
}
}
/// <summary>
/// The distance between this and t.
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public float Distance(Vertex t)
{
return (float)System.Math.Sqrt(DeltaSquared(t));
}
/// <summary>
/// Delta distance squared between this and other vertex t
/// </summary>
/// <param name="t"></param>
/// <returns></returns>
public float DeltaSquaredXY(Vertex t)
{
float dx = (X - t.X);
float dy = (Y - t.Y);
return (dx * dx) + (dy * dy);
}