protected Triangle CalculateSupertriangle()
{
// Create a supertriangle which is substantially bigger than the convex plane spanned by the point set
// to solve the convexity issue (problem of concave structures occuring in hull).
// https://www.codeguru.com/cpp/cpp/algorithms/general/article.php/c8901/Delaunay-Triangles.htm
(Point min, Point max) = CalculateBoundaryBox();
if (BuildDiagonstics)
{
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Line, DiagColor.Red, min, new Point(min.X, max.Y), new Point(max.X, max.Y), new Point(max.X, max.Y), new Point(max.X, min.Y), min));
}
// Create supertriangle
var dMax = Math.Max(max.X - min.X, max.Y - min.Y);
var xMid = (max.X + min.X) / 2;
var yMid = (max.Y + min.Y) / 2;
return(new Triangle(
new Point(xMid - 20 * dMax, yMid - dMax),
new Point(xMid, yMid + 20 * dMax),
new Point(xMid + 20 * dMax, yMid - dMax)
));
}
protected (Point, Triangle) CalculateOriginSeedTriangle(out int idx1, out int idx2, out int idx3)
{
idx1 = -1;
idx2 = -1;
idx3 = -1;
// Calculate origin point
(Point min, Point max) = CalculateBoundaryBox();
var origin = new Point((min.X + max.X) / 2, (min.Y + max.Y) / 2);
// Find first seed point closest to origin
{
var minDist = double.MaxValue;
for (var i = 0; i < Points.Length; i++)
{
var dist = GeoMath.EuclideanDistance2(Points[i], origin);
if (dist < minDist)
{
idx1 = i;
minDist = dist;
}
}
}
// Find point closest to seed point
{
var minDist = double.MaxValue;
for (var i = 0; i < Points.Length; i++)
{
if (i == idx1)
{
continue;
}
var dist = GeoMath.EuclideanDistance2(Points[i], Points[idx1]);
if (dist < minDist)
{
idx2 = i;
minDist = dist;
}
}
}
// Find point which creates the smallest circumcircle
{
var minCircRadius2 = double.MaxValue;
for (var i = 0; i < Points.Length; i++)
{
if (i == idx1 || i == idx2)
{
continue;
}
var circRadius2 = GeoMath.Circumradius2(Points[idx1], Points[idx2], Points[i]);
if (circRadius2 < minCircRadius2)
{
idx3 = i;
minCircRadius2 = circRadius2;
}
}
if (idx3 == -1)
{
idx1 = -1;
idx2 = -1;
return(new Point(), Triangle.Zero); // No Delaunay triangulation exists
}
}
// Make sure seed triangle points are oriented counter-clockwise
if (GeoMath.TriangleAreaDeterminant(Points[idx1], Points[idx2], Points[idx3]) > 0)
{
var tmp = idx2;
idx2 = idx3;
idx3 = tmp;
}
// Update origin to represent midpoint of seed triangle
origin = GeoMath.CalculateMidpoint(Points[idx1], Points[idx2], Points[idx3]);
var seed = new Triangle(Points[idx1], Points[idx2], Points[idx3]);
if (BuildDiagonstics)
{
// Add boundary box and seed point/triangle to diagnostics
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Line, DiagColor.Red, seed.GetEdgeA().Start, seed.GetEdgeA().End));
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Line, DiagColor.Red, seed.GetEdgeB().Start, seed.GetEdgeB().End));
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Line, DiagColor.Red, seed.GetEdgeC().Start, seed.GetEdgeC().End));
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Line, DiagColor.Red, min, new Point(min.X, max.Y), new Point(max.X, max.Y), new Point(max.X, max.Y), new Point(max.X, min.Y), min));
DiagnosticGeometry.Add(new DiagnosticGeometry(DiagGeometryType.Vertex, DiagColor.Red, origin));
}
return(origin, seed);
}