/// <summary>
/// Finds normal vector of a hyper-plane given by vertices.
/// Stores the results to normalData.
/// </summary>
/// <param name="vertices"></param>
/// <param name="normalData"></param>
private void FindNormalVector(VertexWrap[] vertices, double[] normalData)
{
switch (Dimension)
{
case 2: FindNormalVector2D(vertices, normalData); break;
case 3: FindNormalVector3D(vertices, normalData); break;
case 4: FindNormalVector4D(vertices, normalData); break;
default:
{
for (var i = 0; i < Dimension; i++)
{
nDNormalSolveVector[i] = 1.0;
}
for (var i = 0; i < Dimension; i++)
{
var row = jaggedNDMatrix[i];
var pos = vertices[i].Vertex.Position;
for (int j = 0; j < Dimension; j++)
{
row[j] = pos[j];
}
}
StarMath.gaussElimination(Dimension, jaggedNDMatrix, nDNormalSolveVector, normalData);
StarMath.normalizeInPlace(normalData, Dimension);
break;
}
}
}
/// <summary>
/// Computes the volume of the (n=initialPoints.Count)D simplex defined by the
/// pivot and initialPoints.
/// This is computed as the determinant of the matrix | initialPoints[i] - pivot |
/// </summary>
/// <param name="pivot"></param>
/// <param name="initialPoints"></param>
/// <returns></returns>
double GetSimplexVolume(VertexWrap pivot, List <VertexWrap> initialPoints)
{
var dim = initialPoints.Count;
var m = nDMatrix;
for (int i = 0; i < dim; i++)
{
var pts = initialPoints[i];
for (int j = 0; j < dim; j++)
{
m[i, j] = pts.PositionData[j] - pivot.PositionData[j];
}
}
return(Math.Abs(StarMath.determinantDestructive(m, dim)));
}
/// <summary>
/// Creates the Delaunay triangulation of the input data.
/// Be careful with concurrency, because during the computation, the vertex position arrays get resized.
/// </summary>
/// <param name="data"></param>
/// <returns></returns>
public static DelaunayTriangulation <TVertex, TCell> Create(IEnumerable <TVertex> data)
{
if (data == null)
{
throw new ArgumentException("data can't be null.");
}
if (!(data is IList <TVertex>))
{
data = data.ToArray();
}
if (data.Count() == 0)
{
return new DelaunayTriangulation <TVertex, TCell> {
Cells = Enumerable.Empty <TCell>()
}
}
;
int dimension = data.First().Position.Length;
// Resize the arrays and lift the data.
foreach (var p in data)
{
double lenSq = StarMath.norm2(p.Position, dimension, true);
var v = p.Position;
Array.Resize(ref v, dimension + 1);
p.Position = v;
p.Position[dimension] = lenSq;
}
// Find the convex hull
var delaunayFaces = ConvexHullInternal.GetConvexFacesInternal <TVertex, TCell>(data);
// Resize the data back
foreach (var p in data)
{
var v = p.Position;
Array.Resize(ref v, dimension);
p.Position = v;
}
// Remove the "upper" faces
for (var i = delaunayFaces.Count - 1; i >= 0; i--)
{
var candidate = delaunayFaces[i];
if (candidate.Normal[dimension] >= 0)
{
for (int fi = 0; fi < candidate.AdjacentFaces.Length; fi++)
{
var f = candidate.AdjacentFaces[fi];
if (f != null)
{
for (int j = 0; j < f.AdjacentFaces.Length; j++)
{
if (object.ReferenceEquals(f.AdjacentFaces[j], candidate))
{
f.AdjacentFaces[j] = null;
}
}
}
}
var li = delaunayFaces.Count - 1;
delaunayFaces[i] = delaunayFaces[li];
delaunayFaces.RemoveAt(li);
}
}
// Create the "TCell" representation.
int cellCount = delaunayFaces.Count;
var cells = new TCell[cellCount];
for (int i = 0; i < cellCount; i++)
{
var face = delaunayFaces[i];
var vertices = new TVertex[dimension + 1];
for (int j = 0; j <= dimension; j++)
{
vertices[j] = (TVertex)face.Vertices[j].Vertex;
}
cells[i] = new TCell
{
Vertices = vertices,
Adjacency = new TCell[dimension + 1]
};
face.Tag = i;
}
for (int i = 0; i < cellCount; i++)
{
var face = delaunayFaces[i];
var cell = cells[i];
for (int j = 0; j <= dimension; j++)
{
if (face.AdjacentFaces[j] == null)
{
continue;
}
cell.Adjacency[j] = cells[face.AdjacentFaces[j].Tag];
}
}
return(new DelaunayTriangulation <TVertex, TCell> {
Cells = cells
});
}
/// <summary>
/// Finds (dimension + 1) initial points.
/// </summary>
/// <param name="extremes"></param>
/// <returns></returns>
private List <VertexWrap> FindInitialPoints(List <VertexWrap> extremes)
{
List <VertexWrap> initialPoints = new List <VertexWrap>();// { extremes[0], extremes[1] };
VertexWrap first = null, second = null;
double maxDist = 0;
for (int i = 0; i < extremes.Count - 1; i++)
{
var a = extremes[i];
for (int j = i + 1; j < extremes.Count; j++)
{
var b = extremes[j];
var dist = StarMath.norm2(StarMath.subtract(a.PositionData, b.PositionData, Dimension), Dimension, true);
if (dist > maxDist)
{
first = a;
second = b;
maxDist = dist;
}
}
}
initialPoints.Add(first);
initialPoints.Add(second);
for (int i = 2; i <= Dimension; i++)
{
double maximum = 0.0001;
VertexWrap maxPoint = null;
for (int j = 0; j < extremes.Count; j++)
{
var extreme = extremes[j];
if (initialPoints.Contains(extreme))
{
continue;
}
var val = GetSimplexVolume(extreme, initialPoints);
if (val > maximum)
{
maximum = val;
maxPoint = extreme;
}
}
if (maxPoint != null)
{
initialPoints.Add(maxPoint);
}
else
{
int vCount = InputVertices.Count;
for (int j = 0; j < vCount; j++)
{
var point = InputVertices[j];
if (initialPoints.Contains(point))
{
continue;
}
var val = GetSimplexVolume(point, initialPoints);
if (val > maximum)
{
maximum = val;
maxPoint = point;
}
}
if (maxPoint != null)
{
initialPoints.Add(maxPoint);
}
else
{
ThrowSingular();
}
}
}
return(initialPoints);
}
