source: branches/HeuristicLab.Analysis.AlgorithmBehavior/HeuristicLab.Analysis.AlgorithmBehavior.Analyzers/3.3/ConvexHullMeasures.cs @ 10198

#region License Information
/* HeuristicLab
 * Copyright (C) 2002-2013 Heuristic and Evolutionary Algorithms Laboratory (HEAL)
 *
 * This file is part of HeuristicLab.
 *
 * HeuristicLab is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * HeuristicLab is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HeuristicLab. If not, see <http://www.gnu.org/licenses/>.
 */
#endregion

using System;
using System.Collections.Generic;
using System.Linq;
using MIConvexHull;

namespace HeuristicLab.Analysis.AlgorithmBehavior.Analyzers {
  public static class ConvexHullMeasures {
    //Calculates the volumne of a d-simplex
    private static double CalculateSimplexVolume(List<double[]> simplex) {
      double[,] diffs = new double[simplex.Count, simplex.Count];

      for (int i = 0; i < simplex.Count; i++) {
        for (int j = 0; j < simplex.Count; j++) {
          diffs[i, j] = simplex[i].EuclideanDistance(simplex[j]);
        }
      }

      double det = alglib.rmatrixdet(diffs);
      double result = det / simplex[0].Count().Fact();

      return result;
    }

    //calculate center for boundary triangulation (slowwwww.....)
    private static double[] CalculateInnerPoint(List<double[]> hyperHull) {
      double[] result = new double[hyperHull[0].Count()];

      for (int i = 0; i < hyperHull[0].Count(); i++) {
        result[i] = (hyperHull.Max(x => x[i]) + hyperHull.Min(x => x[i])) / 2.0;
      }

      return result;
    }

    //calculates the volume of a convex d-polytope
    //decomposition based on boundary triangulation
    public static double CalculateVolume(List<double[]> convexHull) {
      double[] innerPoint = CalculateInnerPoint(convexHull);
      double volume = 0.0;

      for (int i = 0; i < convexHull.Count - 1; i += 2) {
        List<double[]> simplex = new List<double[]>();
        simplex.Add(innerPoint);
        simplex.Add(convexHull[i]);
        simplex.Add(convexHull[i + 1]);
        volume += CalculateSimplexVolume(simplex);
      }
      return volume;
    }

    public static double CalculateVolumeNew(List<double[]> convexHull) {
      double volume = 0.0;

      int dim = convexHull.First().Length;
      if (dim > convexHull.Count)
        throw new ArgumentException("Nr. of points for volume calculation must be greater than dimension", "convexHull");

      var triangulation = Triangulation.CreateDelaunay(ConvertToVertex(convexHull));
      var simplices = ConvertFromTriangulation(triangulation);
      foreach (var simplex in simplices) {
        volume += CalculateSimplexVolume(simplex.ToList());
      }

      return volume;
    }

    private static List<double[][]> ConvertFromTriangulation(ITriangulation<DefaultVertex, DefaultTriangulationCell<DefaultVertex>> triangulation) {
      List<double[][]> results = new List<double[][]>();

      foreach (var cell in triangulation.Cells) {
        results.Add(cell.Vertices.Select(x => x.Position).ToArray());
      }

      return results;
    }

    private static List<DefaultVertex> ConvertToVertex(List<double[]> data) {
      List<DefaultVertex> result = new List<DefaultVertex>();
      for (int i = 0; i < data.Count(); i++) {
        double[] d = data[i];
        DefaultVertex vertex = new DefaultVertex();
        vertex.Position = d;
        result.Add(vertex);
      }
      return result;
    }
  }
}