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 * redistribute this software in source and binary code form, provided | 
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 * that the following conditions are met: | 
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 * | 
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 * 1. Acknowledgement of the program authors must be made in any | 
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 *    publication of scientific results based in part on use of the | 
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 *    program.  An acceptable form of acknowledgement is citation of | 
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 *    the article in which the program was described (Matthew | 
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 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher | 
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 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented | 
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 *    Parallel Simulation Engine for Molecular Dynamics," | 
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 *    J. Comput. Chem. 26, pp. 252-271 (2005)) | 
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 * | 
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 * 2. Redistributions of source code must retain the above copyright | 
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 * 1. Redistributions of source code must retain the above copyright | 
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 *    notice, this list of conditions and the following disclaimer. | 
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 * | 
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 * 3. Redistributions in binary form must reproduce the above copyright | 
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 * 2. Redistributions in binary form must reproduce the above copyright | 
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 *    notice, this list of conditions and the following disclaimer in the | 
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 *    documentation and/or other materials provided with the | 
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 *    distribution. | 
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 * University of Notre Dame has been advised of the possibility of | 
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 * such damages. | 
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 * | 
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 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your | 
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 * research, please cite the appropriate papers when you publish your | 
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 * work.  Good starting points are: | 
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 *                                                                       | 
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 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).              | 
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 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).           | 
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 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).           | 
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 * [4]  Vardeman & Gezelter, in progress (2009).                         | 
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 * | 
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 * | 
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 *  Triangle.cpp | 
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 * | 
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 *  Purpose: Provide basic triangle object for OOPSE | 
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 *  Purpose: Provide basic triangle object for OpenMD | 
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 * | 
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 *  Created by Charles F. Vardeman II on 29 July 2008. | 
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 *  @author  Charles F. Vardeman II | 
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 *  @version $Id: Triangle.cpp,v 1.2 2008-12-05 16:20:38 chuckv Exp $ | 
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 *  @version $Id: Triangle.cpp,v 1.4 2009-11-25 20:02:01 gezelter Exp $ | 
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 * | 
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 */ | 
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#include "math/Triangle.hpp" | 
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 | 
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using namespace oopse; | 
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using namespace OpenMD; | 
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Triangle::Triangle() : HaveNormal_(false), HaveCentroid_(false),HaveArea_(false), area_(0.0), normal_(V3Zero),  | 
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                       centroid_(V3Zero),facetVelocity_(V3Zero), mass_(0.0), | 
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                       a_(V3Zero),b_(V3Zero),c_(V3Zero){ | 
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Triangle::Triangle() : HaveNormal_(false), HaveCentroid_(false), | 
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                       HaveArea_(false), area_(0.0), normal_(V3Zero),  | 
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                       centroid_(V3Zero), facetVelocity_(V3Zero), mass_(0.0), | 
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                       a_(V3Zero), b_(V3Zero), c_(V3Zero){ | 
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} | 
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void Triangle::addVertices(Vector3d P1, Vector3d P2, Vector3d P3){ | 
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  centroid_ = (vertices_[0] + vertices_[1] + vertices_[2])/3.0; | 
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  return centroid_; | 
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} | 
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Mat3x3d Triangle::computeHydrodynamicTensor(RealType viscosity) { | 
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  Vector3d u0 = -a_; | 
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  Vector3d v0 = centroid_ - vertices_[0]; | 
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  RealType s0 = 0.5*cross(u0,v0).length(); | 
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   | 
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  Vector3d u1 = -c_; | 
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  Vector3d v1 = centroid_ - vertices_[1]; | 
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  RealType s1 = 0.5*cross(u1,v1).length(); | 
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   | 
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  Vector3d u2 = b_; | 
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  Vector3d v2 = centroid_ - vertices_[2]; | 
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  RealType s2 = 0.5*cross(u2,v2).length(); | 
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   | 
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  Mat3x3d H; | 
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  H = hydro_tensor(centroid_,centroid_,vertices_[1],vertices_[0],s0,viscosity)+ | 
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    hydro_tensor(centroid_,centroid_,vertices_[1],vertices_[2],s1,viscosity)+ | 
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    hydro_tensor(centroid_,centroid_,vertices_[2],vertices_[0],s2,viscosity); | 
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 | 
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  return H.inverse(); | 
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} | 
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Mat3x3d Triangle::hydro_tensor( | 
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                               const Vector3d& ri, | 
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                               const Vector3d& rj0, | 
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                               const Vector3d& rj1, | 
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                               const Vector3d& rj2, | 
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                               RealType s, RealType viscosity){ | 
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   | 
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  Vector3d v2 = (rj0 + rj1 + rj2)/3.0;  // sub-centroid | 
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  Vector3d dr = ri - v2;                // real centroid to sub-centroid | 
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  RealType l2 = 1.0/dr.lengthSquare();   | 
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  | 
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  Mat3x3d G; | 
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  G = (SquareMatrix3<RealType>::identity() + outProduct(dr,dr)*l2)*sqrt(l2); | 
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  G *= 0.125/3.14159285358979; | 
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  G *= s/viscosity; | 
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  return G; | 
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} |