From 94d3e79a8617f88dc0219cfdeedfa3147833719d Mon Sep 17 00:00:00 2001
From: Adrian Kummerlaender
Date: Mon, 24 Jun 2019 14:43:36 +0200
Subject: Initialize at openlb-1-3

---
 src/geometry/blockGeometryStatistics3D.hh | 1471 +++++++++++++++++++++++++++++
 1 file changed, 1471 insertions(+)
 create mode 100644 src/geometry/blockGeometryStatistics3D.hh

(limited to 'src/geometry/blockGeometryStatistics3D.hh')

diff --git a/src/geometry/blockGeometryStatistics3D.hh b/src/geometry/blockGeometryStatistics3D.hh
new file mode 100644
index 0000000..86ed1ec
--- /dev/null
+++ b/src/geometry/blockGeometryStatistics3D.hh
@@ -0,0 +1,1471 @@
+/*  This file is part of the OpenLB library
+ *
+ *  Copyright (C) 2011, 2014 Mathias J. Krause, Simon Zimny
+ *  E-mail contact: info@openlb.net
+ *  The most recent release of OpenLB can be downloaded at
+ *  <http://www.openlb.net/>
+ *
+ *  This program 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 2
+ *  of the License, or (at your option) any later version.
+ *
+ *  This program 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 this program; if not, write to the Free
+ *  Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+ *  Boston, MA  02110-1301, USA.
+ */
+
+/** \file
+ * Representation of a statistic for a 3D geometry -- generic implementation.
+ */
+
+#ifndef BLOCK_GEOMETRY_STATISTICS_3D_HH
+#define BLOCK_GEOMETRY_STATISTICS_3D_HH
+
+#include <iostream>
+#include <math.h>
+#include <fstream>
+#include <sstream>
+#include <cmath>
+
+#include "geometry/blockGeometry3D.h"
+#include "geometry/blockGeometryStatistics3D.h"
+
+namespace olb {
+
+template<typename T>
+BlockGeometryStatistics3D<T>::BlockGeometryStatistics3D( BlockGeometryStructure3D<T>* blockGeometry)
+  : _blockGeometry(blockGeometry), clout(std::cout,"BlockGeometryStatistics3D")
+{
+  _statisticsUpdateNeeded=true;
+}
+
+
+template<typename T>
+bool& BlockGeometryStatistics3D<T>::getStatisticsStatus()
+{
+  return _statisticsUpdateNeeded;
+}
+
+template<typename T>
+bool const & BlockGeometryStatistics3D<T>::getStatisticsStatus() const
+{
+  return _statisticsUpdateNeeded;
+}
+
+
+template<typename T>
+void BlockGeometryStatistics3D<T>::update(bool verbose)
+{
+
+  if (getStatisticsStatus() ) {
+    _material2n.clear();
+
+    _nX = _blockGeometry->getNx();
+    _nY = _blockGeometry->getNy();
+    _nZ = _blockGeometry->getNz();
+    _h = _blockGeometry->getDeltaR();
+
+    for (int iX = 0; iX < _nX; ++iX) {
+      for (int iY = 0; iY < _nY; ++iY) {
+        for (int iZ = 0; iZ < _nZ; ++iZ) {
+          takeStatistics(iX, iY, iZ);
+        }
+      }
+    }
+
+    _nMaterials=int();
+    std::map<int, int>::iterator iter;
+    for (iter = _material2n.begin(); iter != _material2n.end(); iter++) {
+      _nMaterials++;
+    }
+
+    if (verbose) {
+      clout << "updated" << std::endl;
+    }
+    getStatisticsStatus()=false;
+  }
+}
+
+
+template<typename T>
+int BlockGeometryStatistics3D<T>::getNmaterials()
+{
+  update();
+  return _nMaterials;
+}
+
+template<typename T>
+int BlockGeometryStatistics3D<T>::getNvoxel(int material)
+{
+  update();
+  return _material2n[material];
+}
+
+template<typename T>
+std::map<int, int> BlockGeometryStatistics3D<T>::getMaterial2n()
+{
+  update();
+  return _material2n;
+}
+
+template<typename T>
+int BlockGeometryStatistics3D<T>::getNvoxel()
+{
+  update();
+  int total = 0;
+  std::map<int, int>::iterator iter;
+  for (iter = _material2n.begin(); iter != _material2n.end(); iter++) {
+    if (iter->first!=0) {
+      total+=iter->second;
+    }
+  }
+  return total;
+}
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::getMinLatticeR(int material)
+{
+  update();
+  return _material2min[material];
+}
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::getMaxLatticeR(int material)
+{
+  update();
+  return _material2max[material];
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getMinPhysR(int material)
+{
+  std::vector<T> tmp(3,T());
+  _blockGeometry->getPhysR(&(tmp[0]), &(getMinLatticeR(material)[0]));
+  return tmp;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getMaxPhysR(int material)
+{
+  std::vector<T> tmp(3,T());
+  _blockGeometry->getPhysR(&(tmp[0]), &(getMaxLatticeR(material)[0]));
+  return tmp;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getLatticeExtend(int material)
+{
+  update();
+  std::vector<T> extend;
+  for (int iDim = 0; iDim < 3; iDim++) {
+    extend.push_back(_material2max[material][iDim] - _material2min[material][iDim]);
+  }
+  return extend;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getPhysExtend(int material)
+{
+  update();
+  std::vector<T> extend;
+  for (int iDim = 0; iDim < 3; iDim++) {
+    extend.push_back(getMaxPhysR(material)[iDim] - getMinPhysR(material)[iDim]);
+  }
+  return extend;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getPhysRadius(int material)
+{
+  update();
+  std::vector<T> radius;
+  for (int iDim=0; iDim<3; iDim++) {
+    radius.push_back((getMaxPhysR(material)[iDim] - getMinPhysR(material)[iDim])/2.);
+  }
+  return radius;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::getCenterPhysR(int material)
+{
+  update();
+  std::vector<T> center;
+  for (int iDim=0; iDim<3; iDim++) {
+    center.push_back(getMinPhysR(material)[iDim] + getPhysRadius(material)[iDim]);
+  }
+  return center;
+}
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::getType(int iX, int iY, int iZ, bool anyNormal)
+{
+
+  update();
+  std::vector<int> discreteNormal(4, 0);
+  std::vector<int> discreteNormal2(4, 0);
+  std::vector<int> nullVector(4, 0);
+
+  if (_blockGeometry->getMaterial(iX, iY, iZ) != 1
+      && _blockGeometry->getMaterial(iX, iY, iZ) != 0) {
+
+    //boundary0N and boundary 0P
+    if (_blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = 0;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = 0;
+        }
+      }
+    }
+
+    // boundary1N and boundary1P
+    if (_blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 0;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 0;
+        }
+      }
+    }
+
+    // boundary2N and boundary2P
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ + 1) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ - 1) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 0;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 0;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // externalCornerNNN and externalCornerNPN
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ + 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ + 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ + 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // externalCornerNPP and externalCornerNNP
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ - 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ - 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ - 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 1;
+        }
+
+        else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // externalCornerPPP and externalCornerPNP
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ - 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ - 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+
+          discreteNormal[0] = 1;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 1;
+        }
+
+        else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ - 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // externalCornerPNN and externalCornerPPN
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ + 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ + 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 1;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ + 1) == 1) {
+
+        if (discreteNormal == nullVector) {
+
+          discreteNormal[0] = 1;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = -1;
+        }
+
+        else {
+          discreteNormal2[0] = 1;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // internalCornerPPP and internalCornerPNP
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 1;
+        }
+
+        else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // internalCornerPNN and InternalCornerPPN
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // internalCornerNPP and internalCornerNNP
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) == 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 1;
+        }
+
+        else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // internalCornerNPN and internalCornerNNN
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) == 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+
+          discreteNormal[0] = 2;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = -1;
+        }
+
+        else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 2;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 2;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // externalEdge0PN and externalEdge0NN
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ + 1) != 1) {
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // externalEdge0NP and externalEdge0PP
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ - 1) != 1) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 0;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 0;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // externalEdge1NN and externalEdge1NP
+    if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = -1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = -1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = -1;
+        }
+      }
+    }
+
+    // externalEdge1PN and externalEdge1PP
+    if (_blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0) {
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = 1;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 0;
+          discreteNormal[3] = 1;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 0;
+          discreteNormal2[3] = 1;
+        }
+      }
+    }
+
+    // externalEdge2NN and externalEdge2PN
+    if (_blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 0;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = -1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = -1;
+          discreteNormal2[3] = 0;
+        }
+      }
+    }
+
+    // externalEdge2PP and externalEdge2NP
+    if (_blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) == 1) {
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = 1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = 1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 0;
+        }
+      }
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) == 1) {
+
+        if (discreteNormal == nullVector) {
+          discreteNormal[0] = 3;
+          discreteNormal[1] = -1;
+          discreteNormal[2] = 1;
+          discreteNormal[3] = 0;
+        } else {
+          discreteNormal2[0] = 3;
+          discreteNormal2[1] = -1;
+          discreteNormal2[2] = 1;
+          discreteNormal2[3] = 0;
+        }
+      }
+    }
+
+    // internalEdge0NN and internalEdge0PN
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) == 1) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 0;
+        discreteNormal[2] = -1;
+        discreteNormal[3] = -1;
+      }
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 0;
+        discreteNormal[2] = 1;
+        discreteNormal[3] = -1;
+      }
+    }
+
+    // internalEdge0NP and internalEdge0PP
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) == 1) {
+
+      if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 0;
+        discreteNormal[2] = -1;
+        discreteNormal[3] = 1;
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 0;
+        discreteNormal[2] = 1;
+        discreteNormal[3] = 1;
+      }
+    }
+
+    // internalEdge1PP and internalEdge 1NP
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX + 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 1;
+        discreteNormal[2] = 0;
+        discreteNormal[3] = 1;
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 1;
+        discreteNormal[2] = 0;
+        discreteNormal[3] = -1;
+      }
+    }
+
+    // internalEdge1PN and internalEdge1NN
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 1
+        && _blockGeometry->getMaterial(iX - 1, iY, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ - 1) == 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ + 1) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ + 1) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = -1;
+        discreteNormal[2] = 0;
+        discreteNormal[3] = 1;
+      }
+
+      if (_blockGeometry->getMaterial(iX, iY, iZ + 1) == 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY + 1, iZ - 1) != 0
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 1
+          && _blockGeometry->getMaterial(iX, iY - 1, iZ - 1) != 0) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = -1;
+        discreteNormal[2] = 0;
+        discreteNormal[3] = -1;
+      }
+    }
+
+    // internalEdge2PP and internalEdge2NP
+    if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY + 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY - 1, iZ) == 1) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 1;
+        discreteNormal[2] = 1;
+        discreteNormal[3] = 0;
+      }
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1
+          && _blockGeometry->getMaterial(iX + 1, iY - 1, iZ) == 1) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = -1;
+        discreteNormal[2] = 1;
+        discreteNormal[3] = 0;
+      }
+    }
+
+    // internalEdge2PN and internalEdge2NN
+    if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ - 1) != 0
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 1
+        && _blockGeometry->getMaterial(iX, iY, iZ + 1) != 0
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 1
+        && _blockGeometry->getMaterial(iX, iY - 1, iZ) != 0) {
+
+      if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1
+          && _blockGeometry->getMaterial(iX - 1, iY + 1, iZ) == 1) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = 1;
+        discreteNormal[2] = -1;
+        discreteNormal[3] = 0;
+      }
+
+      if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1
+          && _blockGeometry->getMaterial(iX + 1, iY + 1, iZ) == 1) {
+
+        discreteNormal[0] = 4;
+        discreteNormal[1] = -1;
+        discreteNormal[2] = -1;
+        discreteNormal[3] = 0;
+      }
+    }
+
+    // special boundary conditions
+    if (discreteNormal2 != nullVector && anyNormal == false) {
+      discreteNormal = checkExtraBoundary(discreteNormal, discreteNormal2);
+    }
+  }
+
+  if (discreteNormal[1] == 0 && discreteNormal[2] == 0 && discreteNormal[3] == 0) {
+    clout<<"WARNING: no discreteNormal is found"<<std::endl;
+  } else if (_blockGeometry->getMaterial(iX-discreteNormal[1], iY-discreteNormal[2], iZ-discreteNormal[3]) != 1) {
+#ifdef OLB_DEBUG
+    clout<<"WARNING: discreteNormal is not pointing outside the fluid. Use option: anyNormal"<<std::endl;
+#endif
+  }
+
+  return discreteNormal;
+}
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::computeNormal(int iX, int iY, int iZ)
+{
+  update();
+  std::vector<int> normal (3,int(0));
+
+  if (iX != 0) {
+    if (_blockGeometry->getMaterial(iX - 1, iY, iZ) == 1) {
+      normal[0] = -1;
+    }
+  }
+  if (iX != _nX - 1) {
+    if (_blockGeometry->getMaterial(iX + 1, iY, iZ) == 1) {
+      normal[0] = 1;
+    }
+  }
+  if (iY != 0) {
+    if (_blockGeometry->getMaterial(iX, iY - 1, iZ) == 1) {
+      normal[1] = -1;
+    }
+  }
+  if (iY != _nY - 1) {
+    if (_blockGeometry->getMaterial(iX, iY + 1, iZ) == 1) {
+      normal[1] = 1;
+    }
+  }
+  if (iZ != 0) {
+    if (_blockGeometry->getMaterial(iX, iY, iZ - 1) == 1) {
+      normal[2] = -1;
+    }
+  }
+  if (iZ != _nZ - 1) {
+    if (_blockGeometry->getMaterial(iX, iY, iZ + 1) == 1) {
+      normal[2] = 1;
+    }
+  }
+  return normal;
+}
+
+template<typename T>
+std::vector<T> BlockGeometryStatistics3D<T>::computeNormal(int material)
+{
+
+  update();
+  std::vector<T> normal (3,int(0));
+  std::vector<int> minC = getMinLatticeR(material);
+  std::vector<int> maxC = getMaxLatticeR(material);
+  for (int iX = minC[0]; iX<=maxC[0]; iX++) {
+    for (int iY = minC[1]; iY<=maxC[1]; iY++) {
+      for (int iZ = minC[2]; iZ<=maxC[2]; iZ++) {
+        if (_blockGeometry->getMaterial(iX,iY,iZ) == material) {
+          normal[0]+=computeNormal(iX,iY,iZ)[0];
+          normal[1]+=computeNormal(iX,iY,iZ)[1];
+          normal[2]+=computeNormal(iX,iY,iZ)[2];
+        }
+      }
+    }
+  }
+  T norm = sqrt(normal[0]*normal[0]+normal[1]*normal[1]+normal[2]*normal[2]);
+  if (norm>0.) {
+    normal[0]/=norm;
+    normal[1]/=norm;
+    normal[2]/=norm;
+  }
+  return normal;
+}
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::computeDiscreteNormal(int material, T maxNorm)
+{
+
+  update();
+  std::vector<T> normal = computeNormal(material);
+  std::vector<int> discreteNormal(3,int(0));
+
+  T smallestAngle = T(0);
+  for (int iX = -1; iX<=1; iX++) {
+    for (int iY = -1; iY<=1; iY++) {
+      for (int iZ = -1; iZ<=1; iZ++) {
+        T norm = sqrt(iX*iX+iY*iY+iZ*iZ);
+        if (norm>0.&& norm<maxNorm) {
+          T angle = (iX*normal[0] + iY*normal[1] + iZ*normal[2])/norm;
+          if (angle>=smallestAngle) {
+            smallestAngle=angle;
+            discreteNormal[0] = iX;
+            discreteNormal[1] = iY;
+            discreteNormal[2] = iZ;
+          }
+        }
+      }
+    }
+  }
+  return discreteNormal;
+}
+
+
+template<typename T>
+bool BlockGeometryStatistics3D<T>::check(int material, int iX, int iY,
+    int iZ, unsigned offsetX, unsigned offsetY, unsigned offsetZ)
+{
+  update();
+  bool found = true;
+  for (int iOffsetX = -offsetX; iOffsetX <= (int) offsetX; ++iOffsetX) {
+    for (int iOffsetY = -offsetY; iOffsetY <= (int) offsetY; ++iOffsetY) {
+      for (int iOffsetZ = -offsetZ; iOffsetZ <= (int) offsetZ; ++iOffsetZ) {
+        if (_blockGeometry->getMaterial(iX + iOffsetX, iY + iOffsetY,
+                                        iZ + iOffsetZ) != material) {
+          found = false;
+        }
+      }
+    }
+  }
+  return found;
+}
+
+template<typename T>
+bool BlockGeometryStatistics3D<T>::find(int material, unsigned offsetX,
+                                        unsigned offsetY, unsigned offsetZ, int& foundX, int& foundY,
+                                        int& foundZ)
+{
+  update();
+  bool found = false;
+  for (foundX = 0; foundX < _nX; foundX++) {
+    for (foundY = 0; foundY < _nY; foundY++) {
+      for (foundZ = 0; foundZ < _nZ; foundZ++) {
+        found = check(material, foundX, foundY, foundZ, offsetX,
+                      offsetY, offsetZ);
+        if (found) {
+          return found;
+        }
+      }
+    }
+  }
+  return found;
+}
+
+
+template<typename T>
+void BlockGeometryStatistics3D<T>::print()
+{
+
+  update();
+  std::map<int, int>::iterator iter;
+  for (iter = _material2n.begin(); iter != _material2n.end(); iter++) {
+    clout << "materialNumber=" << iter->first
+          << "; count=" << iter->second
+          << "; minLatticeR=(" << _material2min[iter->first][0] <<","<< _material2min[iter->first][1] <<","<< _material2min[iter->first][2] <<")"
+          << "; maxLatticeR=(" << _material2max[iter->first][0] <<","<< _material2max[iter->first][1] <<","<< _material2max[iter->first][2] <<")"
+          << std::endl;
+  }
+}
+
+
+template<typename T>
+void BlockGeometryStatistics3D<T>::takeStatistics(int iX, int iY, int iZ)
+{
+
+  int type = _blockGeometry->getMaterial(iX, iY, iZ);
+  if (_material2n.count(type) == 0) {
+    _material2n[type] = 1;
+    std::vector<int> minCo;
+    std::vector<int> maxCo;
+    minCo.push_back(iX);
+    minCo.push_back(iY);
+    minCo.push_back(iZ);
+    _material2min[type] = minCo;
+    maxCo.push_back(iX);
+    maxCo.push_back(iY);
+    maxCo.push_back(iZ);
+    _material2max[type] = maxCo;
+
+  } else {
+    _material2n[type]++;
+    if (iX < _material2min[type][0]) {
+      _material2min[type][0] = iX;
+    }
+    if (iY < _material2min[type][1]) {
+      _material2min[type][1] = iY;
+    }
+    if (iZ < _material2min[type][2]) {
+      _material2min[type][2] = iZ;
+    }
+    if (iX > _material2max[type][0]) {
+      _material2max[type][0] = iX;
+    }
+    if (iY > _material2max[type][1]) {
+      _material2max[type][1] = iY;
+    }
+    if (iZ > _material2max[type][2]) {
+      _material2max[type][2] = iZ;
+    }
+  }
+}
+
+// This function compares two discrete normals (discreteNormal, discreteNormal2) in case of a duplicate assignment of boundary types.
+// The goal of this function is to combine these special boundaryVoxels to an existing one (in this case boundary or externalEdge) according to
+// the x-, y- and z-values of their discrete normals.
+// In the following the algorithm is declared only for the x value, but it is also valid for the y and z values.
+//
+// for x1 = x2, the new value of x is x1 (1)
+// for x1*x2 = -1, the new value of x is 0 (2)
+// for x1*x2 = 0, the new value is 0   (3)
+//
+// It may be possible that all three values equal 0. To avoid that the values are tested again (x²+y²+z²==0) and the loosest assumption (3) is
+// redefined to.
+//
+// If x,y and z == 0 --> find those x,y or z which are 0 because of (3) and redefine them to the value !=0
+//
+// Additionally the calculated entries are multiplied with (-1) to get the right existing boundary.
+
+template<typename T>
+std::vector<int> BlockGeometryStatistics3D<T>::checkExtraBoundary(
+  std::vector<int> discreteNormal, std::vector<int> discreteNormal2)
+{
+
+  update();
+  std::vector<int> Data(6, 0);
+
+  for (int i = 1; i < 4; i++) {
+    if (discreteNormal[i] == discreteNormal2[i]) {
+      Data[i - 1] = discreteNormal[i];
+      Data[i + 2] = 1;
+    } else if (discreteNormal[i] * discreteNormal2[i] == -1) {
+      Data[i - 1] = 0;
+      Data[i + 2] = 2;
+    } else if (discreteNormal[i] * discreteNormal2[i] == 0) {
+      Data[i - 1] = 0;
+      Data[i + 2] = 3;
+    }
+  }
+
+  std::vector<int> newDiscreteNormal(4, 0);
+
+  for (int i = 1; i < 4; i++) {
+    newDiscreteNormal[i] = Data[i - 1];
+  }
+
+  if (Data[0] * Data[0] + Data[1] * Data[1] + Data[2] * Data[2] == 0) {
+    for (int i = 1; i < 4; i++) {
+      if (Data[i + 2] == 3) {
+        if (discreteNormal[i] == 0) {
+          newDiscreteNormal[i] = (-1) * discreteNormal2[i];
+        } else {
+          newDiscreteNormal[i] = (-1) * discreteNormal[i];
+        }
+      }
+    }
+  }
+
+  if (newDiscreteNormal[1] * newDiscreteNormal[1] + newDiscreteNormal[2]
+      * newDiscreteNormal[2] + newDiscreteNormal[3]
+      * newDiscreteNormal[3] == 1) {
+    newDiscreteNormal[0] = 0;
+  } else {
+    newDiscreteNormal[0] = 3;
+  }
+  return newDiscreteNormal;
+}
+
+
+} // namespace olb
+
+#endif
-- 
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