/*CWBoon 2015 */
#ifdef YADE_POTENTIAL_BLOCKS
//Polyhedral blocks formulated as in Boon et al (2012) using an inner potential particle (Houlsby, 2009) to calculate the contact normal.
#include "PotentialBlock.hpp"

namespace yade { // Cannot have #include directive inside.

YADE_PLUGIN((PotentialBlock));

PotentialBlock::~PotentialBlock() { }


void PotentialBlock::addPlaneStruct() { planeStruct.push_back(Planes()); }
//void PotentialBlock::addVertexStruct()   { vertexStruct.push_back(Vertices()); }
//void PotentialBlock::addEdgeStruct()     { edgeStruct.push_back(Edges());      }

//TODO: We need a check to merge duplicate faces during initialisation, so that when we write the plane coefficients a,b,c,d in the shape class, we don't allow duplicate combinations. This means that the planeNo will change, and we need to ensure it is updated everywhere, after we remove the duplicate faces


void PotentialBlock::postLoad(PotentialBlock&)
{
	if (vertices.empty() and (not a.empty())) { // i.e. if the particle is not initialised

		int planeNo = a.size();

		/* Normalize the coefficients of the planes defining the particle faces */
		Vector3r planeNormVec;
		for (int i = 0; i < planeNo; i++) {
			planeNormVec = Vector3r(a[i], b[i], c[i]);
			if (math::abs(planeNormVec.norm() - 1.0) > 1e-3) { /* Normalize only if the normal vectors are not normalized already */
				d[i] += r; // We need to add "r" and subtract it after normalisation takes place. The d[i] values represent the distances of the planes to the local origin only when the normal vectors (a[i],b[i],c[i] are normalised)
				a[i] /= planeNormVec.norm();
				b[i] /= planeNormVec.norm();
				c[i] /= planeNormVec.norm();
				d[i] /= planeNormVec.norm();
				d[i] -= r;
			}
		}

		/* Check that the defined planes have the same number of coefficients */
		if (b.size() != a.size() or c.size() != a.size() or d.size() != a.size()) {
			std::cout << "The planes do not have the same number of coefficients. Check the input geometry!" << endl;
		}

		/* Make sure r is positive */
		assert(r > 0.0);

		/* Make sure the d[i] values given by the user are positive (i.e. the normal vectors of the faces point outwards)
		   In Python we set d equal to d-r, so here, d reflects these reduced values, which can be negative for two reasons:
		   1. The normal vectors of one or more planes were initially oriented inwards (i.e. min(d)<0 and min(d)+r<0)
		   2. The chosen radius r is larger than the distance of one or more planes to the local origin (i.e. min(d)<=0 and min(d)+r>=0) -> This check is done after centering the particle to its centroid, later on
		*/
		auto dMin = *std::min_element(d.begin(), d.end());
		if (dMin < 0 and dMin + r < 0) { // i.e. when r is not the problem, but the normal vector of at least one plane is oriented inwards
			for (int i = 0; i < planeNo; i++) {
				if (d[i] < 0 and d[i] + r < 0) {
					d[i] += 2 * r;
					a[i] *= -1;
					b[i] *= -1;
					c[i] *= -1;
					d[i] *= -1;
				}
			}
		}

		/* Add a structure containing the vertices associated with each plane*/
		for (int i = 0; i < planeNo; i++) {
			addPlaneStruct();
		}

		// Calculate vertices
		calculateVertices();

		/* Calculate R as half the distance of the farthest vertices, if user hasn't set a positive value for R. */
		/* A reminder that R in the Potential Blocks is meant to represent a reference length, used to calculate the initial bisection search employed to identify points on the particle surfaces. Here, R does not affect the curvature of the faces, like in the Potetial Particles code. The faces of a Potential Block are always flat. */
		/* Although half the distance of the farthest vertices is in no case the circumradius, we just need a value around this order of magnitude for the bisection search code to run smoothly */
		if (R == 0.0 and (not vertices.empty())) {
			Real maxDistance = 0.0, Distance;
			for (unsigned int i = 0; i < vertices.size() - 1; i++) {
				for (unsigned int j = i + 1; i < vertices.size(); i++) {
					Distance = (vertices[i] - vertices[j]).norm();
					if (Distance > maxDistance) { maxDistance = Distance; }
				}
			}
			if (maxDistance > 0.0) { R = maxDistance / 2.; }
			calculateVertices(); //Recalculate vertices after calculating R to improve the check for duplicate vertices
			if (R == 0) { std::cout << "R must be positive. Incorrect automatic calculation from the vertices." << endl; }
		}
		assert(R > 0.0);

		// Calculate geometric properties: volume, centroid, inertia, principal orientation (inertia is calculated after the particle is centered to its centroid)
		Vector3r centr = Vector3r::Zero();
		Real     Ixx, Iyy, Izz, Ixy, Ixz, Iyz;

		calculateInertia(centr, Ixx, Iyy, Izz, Ixy, Ixz, Iyz); //Calculate volume & centroid

		// An attempt to eliminate rounding errors from the calculation of vertices/volume/inertia
		if (math::abs(centr.x()) / R < 1e-6) { centr.x() = 0; }
		if (math::abs(centr.y()) / R < 1e-6) { centr.y() = 0; }
		if (math::abs(centr.z()) / R < 1e-6) { centr.z() = 0; }

		// If the particle is not centered to its centroid, center (translate) the face equations around the centroid and recalculate vertices, volume & inertia
		if (centr.norm() / R > 1e-6) {
			for (int i = 0; i < planeNo; i++) {
				d[i] = -(a[i] * centr.x() + b[i] * centr.y() + c[i] * centr.z() - d[i]);
				//			if (d[i]<0) { a[i] *= -1; b[i] *= -1; c[i] *= -1; d[i] *= -1; }
			}
			position = centr;
			calculateVertices();                                   // Recalculate vertices for the centered particle faces
			calculateInertia(centr, Ixx, Iyy, Izz, Ixy, Ixz, Iyz); // Calculate inertia for the centered particle
		}

		/* Reduce r if it results to negative d values, to ensure the existence of an inner potential particle */
		dMin = *std::min_element(d.begin(), d.end());
		if (dMin <= 0 and dMin + r >= 0) {
			std::for_each(d.begin(), d.end(), [this](Real& dTemp) { dTemp += r; });
			r = 0.5 * (dMin + r);
			std::cout << "Reduced r to half the smallest d value (r=" << r << ") so that min(d)>0." << endl;
			std::for_each(d.begin(), d.end(), [this](Real& dTemp) { dTemp -= r; });
		}

		/* ------------------------------------------------------------------------------------------------------------------------------ */
		if (math::abs(Ixy) + math::abs(Ixz) + math::abs(Iyz) < 1e-15) {
			inertia = Vector3r(Ixx, Iyy, Izz);
		} else { //rotate the planes to the principal axes if they are not already rotated
			// calculate eigenvectors of I
			Matrix3r inertia_tensor(Matrix3r::Zero());
			inertia_tensor << Ixx, -Ixy, -Ixz, -Ixy, Iyy, -Iyz, -Ixz, -Iyz, Izz;
			Matrix3r I_rot(Matrix3r::Zero()), I_new(Matrix3r::Zero());
			matrixEigenDecomposition(inertia_tensor, I_rot, I_new);

			// Here I use the same convension for the positive direction of the principal orientations as for Polyhedra @vsangelidakis
			// I_rot = eigenvectors of inertia_tensors in columns
			// I_new = eigenvalues on diagonal
			// set positive direction of vectors - otherwise reloading does not work
			Matrix3r sign(Matrix3r::Zero());
			Real     max_v_signed = I_rot(0, 0);
			Real     max_v        = std::abs(I_rot(0, 0));
			if (max_v < std::abs(I_rot(1, 0))) {
				max_v_signed = I_rot(1, 0);
				max_v        = std::abs(I_rot(1, 0));
			}
			if (max_v < std::abs(I_rot(2, 0))) {
				max_v_signed = I_rot(2, 0);
				max_v        = std::abs(I_rot(2, 0));
			}
			sign(0, 0)   = max_v_signed / max_v;
			max_v_signed = I_rot(0, 1);
			max_v        = std::abs(I_rot(0, 1));
			if (max_v < std::abs(I_rot(1, 1))) {
				max_v_signed = I_rot(1, 1);
				max_v        = std::abs(I_rot(1, 1));
			}
			if (max_v < std::abs(I_rot(2, 1))) {
				max_v_signed = I_rot(2, 1);
				max_v        = std::abs(I_rot(2, 1));
			}
			sign(1, 1) = max_v_signed / max_v;
			sign(2, 2) = 1.;
			I_rot      = I_rot * sign;
			// force the eigenvectors to be right-hand oriented
			Vector3r third = (I_rot.col(0)).cross(I_rot.col(1));
			I_rot(0, 2)    = third[0];
			I_rot(1, 2)    = third[1];
			I_rot(2, 2)    = third[2];

			inertia     = Vector3r(I_new(0, 0), I_new(1, 1), I_new(2, 2));
			orientation = Quaternionr(I_rot);
			//rotate the particle so that x - is maximal inertia axis and z - is minimal inertia axis
			//orientation.normalize();  //not needed

			for (int i = 0; i < (int)vertices.size(); i++) {
				vertices[i] = orientation.conjugate() * vertices[i];
			}

			Vector3r plane4;
			for (unsigned int i = 0; i < a.size(); i++) {
				plane4 = orientation.conjugate() * Vector3r(a[i], b[i], c[i]);
				a[i]   = plane4.x();
				b[i]   = plane4.y();
				c[i]   = plane4.z();
			}
		}

		for (unsigned int j = 0; j < a.size(); j++) {
			connectivity.push_back(planeStruct[j].vertexID);
		}
	}
}


Real PotentialBlock::getDet(const MatrixXr A) const
{
	/* if positive, counter clockwise, 2nd point makes a larger angle */
	/* if negative, clockwise, 3rd point makes a larger angle */
	int  rowNo      = A.rows();
	Real firstTerm  = 0.0;
	Real secondTerm = 0.0;
	for (int i = 0; i < rowNo - 1; i++) {
		firstTerm += A(i, 0) * A(i + 1, 1);
		secondTerm += A(i, 1) * A(i + 1, 0);
	}
	return firstTerm - secondTerm;
}


Real PotentialBlock::getSignedArea(const Vector3r pt1, const Vector3r pt2, const Vector3r pt3) const
{
	/* if positive, counter clockwise, 2nd point makes a larger angle */
	/* if negative, clockwise, 3rd point makes a larger angle */
	MatrixXr triangle(4, 2);
	triangle(0, 0)   = pt1.x();
	triangle(0, 1)   = pt1.y(); // triangle(0,2) = pt1.z();
	triangle(1, 0)   = pt2.x();
	triangle(1, 1)   = pt2.y(); // triangle(1,2) = pt2.z();
	triangle(2, 0)   = pt3.x();
	triangle(2, 1)   = pt3.y(); // triangle(2,2) = pt3.z();
	triangle(3, 0)   = pt1.x();
	triangle(3, 1)   = pt1.y(); // triangle(3,2) = pt1.z();
	Real determinant = getDet(triangle);
	return determinant; //triangle.determinant();
}

Real PotentialBlock::getVolume()
{
	if (volume < 0) // that would be the case if calculateInertia has not executed yet and volume is still at its -1 default value
		LOG_ERROR("PotentialBlock::getVolume() will return a negative value, probably calculateInertia could not execute yet");
	return volume;
}

void PotentialBlock::calculateVertices()
{
	std::vector<Real> D(3);
	std::vector<Real> Ax(9);
	Matrix3r          Aplanes;
	Real              Distance;
	int               vertCount = 0;
	Real              minDistance;
	int               planeNo = a.size();

	Vector3r plane1, plane2, plane3;
	Real     d1, d2, d3, detAplanes;

	std::vector<int> ipiv(3);
	int              bColNo;
	int              info, three; //FIXME: bColNo, three could be defined as "const int", instead of "int"
	bool             inside;
	Vector3r         vertex;
	Real             plane;
	int              vertexID;

	int closestVertex = 0;
	vertices.clear();

	for (int i = 0; i < planeNo; i++) {
		planeStruct[i].vertexID.clear();
	} //Empty the planeStruct every time calculateVertices is ran

	for (int i = 0; i < planeNo - 2; i++) {
		for (int j = i + 1; j < planeNo - 1; j++) {
			for (int kk = j + 1; kk < planeNo; kk++) {
				plane1 = Vector3r(a[i], b[i], c[i]);
				plane2 = Vector3r(a[j], b[j], c[j]);
				plane3 = Vector3r(a[kk], b[kk], c[kk]);

				d1 = d[i] + r;
				d2 = d[j] + r;
				d3 = d[kk] + r;

				D[0]          = d1;
				D[1]          = d2;
				D[2]          = d3;
				Ax[0]         = plane1.x();
				Ax[3]         = plane1.y();
				Ax[6]         = plane1.z();
				Aplanes(0, 0) = Ax[0];
				Aplanes(0, 1) = Ax[3];
				Aplanes(0, 2) = Ax[6];
				Ax[1]         = plane2.x();
				Ax[4]         = plane2.y();
				Ax[7]         = plane2.z();
				Aplanes(1, 0) = Ax[1];
				Aplanes(1, 1) = Ax[4];
				Aplanes(1, 2) = Ax[7];
				Ax[2]         = plane3.x();
				Ax[5]         = plane3.y();
				Ax[8]         = plane3.z();
				Aplanes(2, 0) = Ax[2];
				Aplanes(2, 1) = Ax[5];
				Aplanes(2, 2) = Ax[8];

				detAplanes = Aplanes.determinant();

				if (fabs(detAplanes) > pow(10, -15)) { //if (parallel == false) {

					bColNo = 1;
					info   = 0; /* LU */
					three  = 3;
					dgesv_(&three, &bColNo, Ax.data(), &three, ipiv.data(), D.data(), &three, &info);

					if (info != 0) {
						//std::cout<<"linear algebra error"<<endl;
					} else {
						inside = true;
						vertex = Vector3r(D[0], D[1], D[2]);

						for (int m = 0; m < planeNo; m++) {
							plane = a[m] * vertex.x() + b[m] * vertex.y() + c[m] * vertex.z() - d[m] - r;
							if (plane > pow(10, -3)) { inside = false; }
						}
						if (inside == true) {
							/* Check for duplicate vertices: New vertices cannot be too close to existing ones */
							if (vertCount == 0) { // Allow the first vertex to be written always
								vertices.push_back(vertex);
								vertCount++;

								vertexID = vertices.size() - 1;
								planeStruct[i].vertexID.push_back(vertexID);
								planeStruct[j].vertexID.push_back(vertexID);
								planeStruct[kk].vertexID.push_back(vertexID);
							} else {
								minDistance = 1.0e15;
								for (int n = 0; n < vertCount; n++) {
									Distance = (vertex - vertices[n]).norm();
									if (Distance < minDistance) {
										minDistance   = Distance;
										closestVertex = n;
									}
								}

								if (minDistance > (R > 0.0 ? R * 1.0e-3 : 1.0e-6)) {
									vertices.push_back(vertex);
									vertCount++;

									vertexID = vertices.size() - 1;
									planeStruct[i].vertexID.push_back(vertexID); // If not duplicate, save new ID
									planeStruct[j].vertexID.push_back(vertexID);
									planeStruct[kk].vertexID.push_back(vertexID);
								} else {
									planeStruct[i].vertexID.push_back(closestVertex); // If duplicate save ID of duplicate
									planeStruct[j].vertexID.push_back(closestVertex);
									planeStruct[kk].vertexID.push_back(closestVertex);
								}
							}

/* Structs associating: Vertices-Edges-Planes: Could become useful in the future */
#if 0
							/* vertexStruct */
							vertexID = vertices.size()-1;
//							addVertexStruct();
//							int vertexID = vertexStruct.size()-1;
//							vertexStruct[vertexID].planeID.push_back(i);   /* Note that the planeIDs are arranged from small to large! */
//							vertexStruct[vertexID].planeID.push_back(j);   /* planeIDs are arranged in the same sequence as [a,b,c] and d */
//							vertexStruct[vertexID].planeID.push_back(kk);   /* vertices store information on planeIDs */


							/* edgeStruct */
							int vertexNo = vertices.size(); int edgeCount=0;
							for (int i=0; i<vertexNo; i++ ){
								for (int j=0; j<vertexNo; j++){
									if(i==j){continue;}
									int v1a = vertexStruct[i].planeID[0];
									int v2a = vertexStruct[i].planeID[1];
									int v3a = vertexStruct[i].planeID[2];
									int v1b = vertexStruct[j].planeID[0];
									int v2b = vertexStruct[j].planeID[1];
									int v3b = vertexStruct[j].planeID[2];

									if(  (v1a != v1b && v2a == v2b && v3a == v3b) || (v1a == v1b && v2a != v2b && v3a == v3b) || (v1a == v1b && v2a == v2b && v3a != v3b)  ){
										Real length = ( vertices[i] - vertices[j] ).norm();
										if(length<pow(10,-3) ){ continue; }
										addEdgeStruct();
										edgeStruct[edgeCount].vertexID.push_back(i); /* edges store information on vertexIDs */
										edgeStruct[edgeCount].vertexID.push_back(j);
										vertexStruct[i].edgeID.push_back(edgeCount); /* vertices store information on edgeIDs */
										vertexStruct[j].edgeID.push_back(edgeCount);
										edgeCount++;
									}
								}
							}

							/* planeStruct */
							vertexID = vertices.size()-1;
							planeStruct[i].vertexID.push_back(vertexID);   /* planes store information on vertexIDs */
							planeStruct[j].vertexID.push_back(vertexID);
							planeStruct[kk].vertexID.push_back(vertexID);
#endif
						}
					}
				}
			}
		}
	}

	//Remove duplicate vertices from each planeStruct[j] and record the IDs of planes with less than 3 vertices (these planes are redundant)
	//This is done to guard the code against non-manifold geometrical inputs
	std::vector<int> pWLTTV; //planes With Less Than Three Vertices
	for (int j = 0; j < planeNo; j++) {
		std::stable_sort(planeStruct[j].vertexID.begin(), planeStruct[j].vertexID.end());
		planeStruct[j].vertexID.erase(std::unique(planeStruct[j].vertexID.begin(), planeStruct[j].vertexID.end()), planeStruct[j].vertexID.end());
		if (planeStruct[j].vertexID.size() < 3) { pWLTTV.push_back(j); }
	}

	//Sort the IDs of the planes to be removed in descending order, in order to start removing from last to first, using the reverse iterators: rbegin(), rend()
	std::stable_sort(pWLTTV.rbegin(), pWLTTV.rend());
	int pWLTTVSize = pWLTTV.size();

	for (int j = 0; j < pWLTTVSize; j++) {
		a.erase(a.begin() + pWLTTV[j]);
		b.erase(b.begin() + pWLTTV[j]);
		c.erase(c.begin() + pWLTTV[j]);
		d.erase(d.begin() + pWLTTV[j]);

		if (not phi_b.empty()) { phi_b.erase(phi_b.begin() + pWLTTV[j]); }
		if (not phi_r.empty()) { phi_r.erase(phi_r.begin() + pWLTTV[j]); }
		if (not cohesion.empty()) { cohesion.erase(cohesion.begin() + pWLTTV[j]); }
		if (not tension.empty()) { tension.erase(tension.begin() + pWLTTV[j]); }
		if (not jointType.empty()) { jointType.erase(jointType.begin() + pWLTTV[j]); }

		planeStruct.erase(planeStruct.begin() + pWLTTV[j]);
	}

	//Here we repeat this check, after the redundant faces are removed, just in case
	if (b.size() != a.size() or c.size() != a.size() or d.size() != a.size()) {
		std::cout << "The planes do not have the same number of coefficients. Check the input geometry!" << endl;
	}
}


void PotentialBlock::calculateInertia(Vector3r& centroid, Real& Ixx, Real& Iyy, Real& Izz, Real& Ixy, Real& Ixz, Real& Iyz)
{
	Vector3r              pointInside(0, 0, 0), vertex, planeNormal, oriNormal(0, 0, 1), crossProd, rotatedCoord;
	Vector3r              pt1, pt2, pt3, baseOnPolygon, oriBaseOnPolygon, centroidPyramid, centroidTetra, tempVert1, tempVert2, tempVert3, tempVert4;
	Real                  totalVolume = 0.0, /*plane,*/ det, area, height, vol, areaPyramid, volumePyramid, heightTetra, tempArea, areaTri, tetraVol;
	Real                  detJ, x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4;
	Quaternionr           Qp;
	unsigned int          h, kk, m, counter;
	int                   lastEntry;
	MatrixXr              B(4, 2), vertexOnPlane;
	std::vector<Vector3r> verticesOnPlane, oriVerticesOnPlane, orderedVerticesOnPlane, oriOrderedVerticesOnPlane; //vector<int> oriOrderedVerticesOnplaneID;

	centroid = Vector3r::Zero();
	Ixx      = 0.0;
	Iyy      = 0.0;
	Izz      = 0.0;
	Ixy      = 0.0;
	Ixz      = 0.0;
	Iyz      = 0.0;

	for (unsigned int j = 0; j < a.size(); j++) {
		if (not verticesOnPlane.empty()) {
			verticesOnPlane.clear();
			oriVerticesOnPlane.clear();
		}
		for (unsigned int i = 0; i < planeStruct[j].vertexID.size(); i++) { //iterate through the vertices of each face
			vertex      = vertices[planeStruct[j].vertexID[i]];         /*local coordinates*/
			planeNormal = Vector3r(a[j], b[j], c[j]);
			crossProd   = oriNormal.cross(planeNormal);
			Qp.w()      = 1.0 + oriNormal.dot(planeNormal);
			Qp.x()      = crossProd.x();
			Qp.y()      = crossProd.y();
			Qp.z()      = crossProd.z();
			Qp.normalize();
			if (crossProd.norm() < pow(10, -7)) { Qp = Quaternionr::Identity(); }
			rotatedCoord = Qp.conjugate() * vertex;

			verticesOnPlane.push_back(rotatedCoord);
			oriVerticesOnPlane.push_back(vertex);
		}

		if (verticesOnPlane.empty()) { continue; }
		//		if(verticesOnPlane.size()<3) {continue;} //Only calculate volume/inertia for faces with three or more vertices
		if (verticesOnPlane.size() < 3) { std::cout << "Face: " << j << " has less than 3 vertices! Check particle geometry" << endl; }

		/* REORDER VERTICES counterclockwise positive*/
		h   = 0;
		kk  = 1;
		m   = 2;
		pt1 = verticesOnPlane[h];
		pt2 = verticesOnPlane[kk];
		pt3 = verticesOnPlane[m];
		orderedVerticesOnPlane.push_back(pt1);
		oriOrderedVerticesOnPlane.push_back(oriVerticesOnPlane[0]);
		counter = 1;

		while (counter < verticesOnPlane.size()) {
			while (m < verticesOnPlane.size()) {
				pt1 = verticesOnPlane[h];
				pt2 = verticesOnPlane[kk];
				pt3 = verticesOnPlane[m];
				if (getSignedArea(pt1, pt2, pt3) < 0.0) {
					/* clockwise means 3rd point is better than 2nd */
					kk  = m; /*3rd point becomes 2nd point */
					pt2 = verticesOnPlane[kk];

				} /* else counterclockwise is good.  We need to find and see whether there is a point(3rd point) better than the 2nd point */
				/* advance m */
				m = m + 1;
				while (m == h || m == kk) {
					m = m + 1;
				}
			}
			//std::cout<<"h: "<<h<<", kk :"<<kk<<", m: "<<m<<endl;
			orderedVerticesOnPlane.push_back(pt2);
			oriOrderedVerticesOnPlane.push_back(oriVerticesOnPlane[kk]);

			h = kk;
			/* advance kk */
			kk = 0;
			while (kk == h) {
				kk = kk + 1;
			}
			/* advance m */
			m = 0;
			while (m == h || m == kk) {
				m = m + 1;
			}
			counter++;
		}

		planeStruct[j].vertexID.clear();
		for (unsigned int i = 0; i < oriOrderedVerticesOnPlane.size(); i++) {
			for (unsigned int n = 0; n < vertices.size(); n++) {
				if (vertices[n][0] == oriOrderedVerticesOnPlane[i][0] and vertices[n][1] == oriOrderedVerticesOnPlane[i][1]
				    and vertices[n][2] == oriOrderedVerticesOnPlane[i][2]) {
					planeStruct[j].vertexID.push_back(n);
				}
			}
		}

		vertexOnPlane    = MatrixXr(orderedVerticesOnPlane.size() + 1, 2);
		baseOnPolygon    = Vector3r(0, 0, 0);
		oriBaseOnPolygon = Vector3r(0, 0, 0);

		for (unsigned int i = 0; i < orderedVerticesOnPlane.size(); i++) {
			vertexOnPlane(i, 0) = orderedVerticesOnPlane[i].x();
			vertexOnPlane(i, 1) = orderedVerticesOnPlane[i].y(); //vertexOnPlane(i,2)=orderedVerticesOnPlane[i].z();
			//std::cout<<"vertexOnPlane0: "<<vertexOnPlane(i,0)<<", vertexOnPlane1: "<<vertexOnPlane(i,1)<<endl;
			baseOnPolygon += orderedVerticesOnPlane[i];
			oriBaseOnPolygon += oriOrderedVerticesOnPlane[i];
		}

		baseOnPolygon               = baseOnPolygon / static_cast<Real>(orderedVerticesOnPlane.size());
		oriBaseOnPolygon            = oriBaseOnPolygon / static_cast<Real>(oriOrderedVerticesOnPlane.size());
		lastEntry                   = orderedVerticesOnPlane.size();
		vertexOnPlane(lastEntry, 0) = orderedVerticesOnPlane[0].x();
		vertexOnPlane(lastEntry, 1) = orderedVerticesOnPlane[0].y(); //vertexOnPlane(lastEntry,2)=orderedVerticesOnPlane[0].z();
		//std::cout<<"vertexOnPlane0: "<<vertexOnPlane(lastEntry,0)<<", vertexOnPlane1: "<<vertexOnPlane(lastEntry,1)<<endl;

		det    = getDet(vertexOnPlane);
		area   = 0.5 * det; //(vertexOnPlane.determinant());
		height = -1.0 * (a[j] * pointInside.x() + b[j] * pointInside.y() + c[j] * pointInside.z() - d[j] - r);
		vol    = 1.0 / 3.0 * area * height;
		totalVolume += vol;
		//std::cout<<"orderedVerticesOnPlane.size(): "<<orderedVerticesOnPlane.size()<<", volume: "<<volume<<", area: "<<area<<", height: "<<height<<endl;

		areaPyramid     = 0.0;
		centroidPyramid = Vector3r(0, 0, 0);
		volumePyramid   = 0.0;
		heightTetra     = 0.0;

		for (int i = 0; i < vertexOnPlane.rows() - 1; i++) {
			B(0, 0)  = vertexOnPlane(i, 0);
			B(0, 1)  = vertexOnPlane(i, 1);
			B(1, 0)  = vertexOnPlane(i + 1, 0);
			B(1, 1)  = vertexOnPlane(i + 1, 1);
			B(2, 0)  = baseOnPolygon.x();
			B(2, 1)  = baseOnPolygon.y();
			B(3, 0)  = vertexOnPlane(i, 0);
			B(3, 1)  = vertexOnPlane(i, 1);
			tempArea = getDet(B);
			areaTri  = 0.5 * tempArea;
			areaPyramid += areaTri;
			heightTetra = fabs(orderedVerticesOnPlane[i].z());
			tetraVol    = 1.0 / 3.0 * areaTri * heightTetra;
			volumePyramid += tetraVol;

			// tempVert1,2,3,4: vertices of the tetrahedron
			tempVert1 = oriOrderedVerticesOnPlane[i];
			tempVert3 = oriBaseOnPolygon;
			tempVert4 = pointInside;

			if (i == vertexOnPlane.rows() - 2) {
				tempVert2 = oriOrderedVerticesOnPlane[0];
			} else {
				tempVert2 = oriOrderedVerticesOnPlane[i + 1];
			}

			centroidTetra = 0.25 * (tempVert1 + tempVert2 + tempVert3 + tempVert4);
			centroidPyramid += (tetraVol * centroidTetra);

			// Calculation of the inertia tensor for each tetrahedron.
			// See article F. Tonon, "Explicit Exact Formulas for the 3-D Tetrahedron Inertia Tensor in Terms of its Vertex Coordinates", http://www.scipub.org/fulltext/jms2/jms2118-11.pdf
			// Tonon's formulae work for any coordinate system, so here we calculate the inertia of each tetrahedron directly to the local centroid of the particle, avoiding Steiner.
			x1 = tempVert1.x();
			y1 = tempVert1.y();
			z1 = tempVert1.z();
			x2 = tempVert2.x();
			y2 = tempVert2.y();
			z2 = tempVert2.z();
			x3 = tempVert3.x();
			y3 = tempVert3.y();
			z3 = tempVert3.z();
			x4 = tempVert4.x();
			y4 = tempVert4.y();
			z4 = tempVert4.z();


			detJ = (x2 - x1) * (y3 - y1) * (z4 - z1) + (x3 - x1) * (y4 - y1) * (z2 - z1) + (x4 - x1) * (y2 - y1) * (z3 - z1)
			        - (x2 - x1) * (y4 - y1) * (z3 - z1) - (x3 - x1) * (y2 - y1) * (z4 - z1) - (x4 - x1) * (y3 - y1) * (z2 - z1);
			detJ = math::abs(detJ);

			Ixx += detJ
			        * (y1 * y1 + y1 * y2 + y2 * y2 + y1 * y3 + y2 * y3 + y3 * y3 + y1 * y4 + y2 * y4 + y3 * y4 + y4 * y4 + z1 * z1 + z1 * z2
			           + z2 * z2 + z1 * z3 + z2 * z3 + z3 * z3 + z1 * z4 + z2 * z4 + z3 * z4 + z4 * z4)
			        / 60.;

			Iyy += detJ
			        * (x1 * x1 + x1 * x2 + x2 * x2 + x1 * x3 + x2 * x3 + x3 * x3 + x1 * x4 + x2 * x4 + x3 * x4 + x4 * x4 + z1 * z1 + z1 * z2
			           + z2 * z2 + z1 * z3 + z2 * z3 + z3 * z3 + z1 * z4 + z2 * z4 + z3 * z4 + z4 * z4)
			        / 60.;

			Izz += detJ
			        * (x1 * x1 + x1 * x2 + x2 * x2 + x1 * x3 + x2 * x3 + x3 * x3 + x1 * x4 + x2 * x4 + x3 * x4 + x4 * x4 + y1 * y1 + y1 * y2
			           + y2 * y2 + y1 * y3 + y2 * y3 + y3 * y3 + y1 * y4 + y2 * y4 + y3 * y4 + y4 * y4)
			        / 60.;

			// a' in the article etc.
			Iyz += detJ
			        * (2 * y1 * z1 + y2 * z1 + y3 * z1 + y4 * z1 + y1 * z2 + 2 * y2 * z2 + y3 * z2 + y4 * z2 + y1 * z3 + y2 * z3 + 2 * y3 * z3
			           + y4 * z3 + y1 * z4 + y2 * z4 + y3 * z4 + 2 * y4 * z4)
			        / 120.;

			Ixz += detJ
			        * (2 * x1 * z1 + x2 * z1 + x3 * z1 + x4 * z1 + x1 * z2 + 2 * x2 * z2 + x3 * z2 + x4 * z2 + x1 * z3 + x2 * z3 + 2 * x3 * z3
			           + x4 * z3 + x1 * z4 + x2 * z4 + x3 * z4 + 2 * x4 * z4)
			        / 120.;

			Ixy += detJ
			        * (2 * x1 * y1 + x2 * y1 + x3 * y1 + x4 * y1 + x1 * y2 + 2 * x2 * y2 + x3 * y2 + x4 * y2 + x1 * y3 + x2 * y3 + 2 * x3 * y3
			           + x4 * y3 + x1 * y4 + x2 * y4 + x3 * y4 + 2 * x4 * y4)
			        / 120.;
		}
		centroid += centroidPyramid;
		orderedVerticesOnPlane.clear();
		oriOrderedVerticesOnPlane.clear();
	}
	centroid = centroid / totalVolume;
	volume   = totalVolume;
	verticesOnPlane.clear();
	oriVerticesOnPlane.clear();
}

} // namespace yade

#endif // YADE_POTENTIAL_BLOCKS
