C++ MESH类代码示例

std::pair<double,double> probe( const MESH& mesh, const DISP& displacement,
                                const PRESS& pressure )
{
    // pick an element
    const std::size_t numElements = std::distance( mesh.elementsBegin(), mesh.elementsEnd() );
    const std::size_t elemNum = (numElements +
                                 static_cast<std::size_t>(std::sqrt(numElements)) ) / 2;

    // geometry
    const typename MESH::Element* geomEp = mesh.elementPtr( elemNum );
    const typename base::Vector<MESH::Element::dim>::Type xi =
        base::constantVector<MESH::Element::dim>( 0. );

    const typename base::Geometry<typename MESH::Element>::result_type x =
        base::Geometry<typename MESH::Element>()( geomEp, xi );

    // displacement
    const typename DISP::Element* dispEp = displacement.elementPtr( elemNum );
    const typename base::Vector<DISP::DegreeOfFreedom::size>::Type uh =
        base::post::evaluateField( geomEp, dispEp, xi );
    
    // pressure
    const typename PRESS::Element* pressEp = pressure.elementPtr( elemNum );
    const typename base::Vector<PRESS::DegreeOfFreedom::size>::Type ph =
        base::post::evaluateField( geomEp, pressEp, xi );

    return std::make_pair( uh[1], ph[0] );
}

 void operator()(MESH& m, double t) {
   (void) t;
   double distance;  
   double r;
   Point directionVector;
   Point pos;
   Point c;
   Point R;
   Point velocity;
   Node node1;
   Node node2;
   
   for(auto it=m.node_begin(); it != m.node_end(); ++ it)
   {
       
       node1 = (*it);
       c = node1.position();
       r = 0.0;
       
       // iterate through connected edges and set r equal to  
       // the length of the shortest connected edge
       for(auto edge_it = node1.edge_begin(); edge_it != node1.edge_end(); ++edge_it)
       {
           if (r == 0.0 || (*edge_it).length() < r)
               r = (*edge_it).length();
       }
       
       // now iterate through all of the other nodes and see if any of
       // them are within distance r
       for(auto it2=m.node_begin(); it2 != m.node_end(); ++it2)
       {
           node2 = (*it2);
           pos = node2.position();
           distance = norm(pos-c);
           if (distance < r && node1 != node2)
           {
               // SET POSITION TO NEAREST POINT ON SURFACE OF SPHERE
               
               // get the direction vector from the center to our node 
               directionVector = pos-c;
               //normalize that vector
               directionVector = directionVector/norm(directionVector);
                   
               // set pos to the direction vector time the sphere's radius
               // which should get us to the point on the sphere closest
               // to the node's current position
               pos = c+directionVector*(r);
               node2.set_position(pos);
                   
               // SET THE COMPONENT OF VELOCITY THAT IS NORMAL TO THE 
               // SPHERE'S SURFACE TO ZERO
               R = (pos-c)/norm(pos-c);
               velocity = node2.value().velocity;
               node2.value().velocity = velocity - inner_prod(velocity,R)*R;
           }
       }
   }
 }

Point get_center(MESH& m)
{
  Point center = Point(0,0,0);
  for(auto it=m.node_begin(); it != m.node_end(); ++ it)
    center += (*it).position();
  center /= m.num_nodes();

  return center;
}

double hyperbolic_step(MESH& m, FLUX& f, double t, double dt, Point ball_loc, int water_tris) {
  for (auto tri_it = m.triangle_begin(); (*tri_it).index() != water_tris; ++tri_it) {
    QVar sum = QVar(0,0,0);

    /* Defines the force of the floating objects by checking its submerged 
    *  cross section of the ball intersects with the centers of adjacent triangles 
    */
    floatObj obj = floatObj();
    if (norm((*tri_it).center()-Point(ball_loc.x, ball_loc.y, 0)) < ball_loc.z)
      obj = floatObj(total_mass*grav, M_PI*ball_loc.z*ball_loc.z, density);

    Point norm_vec = (*tri_it).normal((*tri_it).node1(), (*tri_it).node2());
    // Calcuate flux using adjacent triangle's Q
    if ((*tri_it).adj_triangle((*tri_it).node1(), (*tri_it).node2()).is_valid())
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		(*tri_it).adj_triangle((*tri_it).node1(), (*tri_it).node2()).value().q_bar, obj);
    // Boundary conditions
    else
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		QVar((*tri_it).value().q_bar.h, 0, 0), obj);

    norm_vec = (*tri_it).normal((*tri_it).node2(), (*tri_it).node3());
    // Calcuate flux using adjacent triangle's Q
    if ((*tri_it).adj_triangle((*tri_it).node2(), (*tri_it).node3()).is_valid()) 
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		(*tri_it).adj_triangle((*tri_it).node2(), (*tri_it).node3()).value().q_bar, obj); 
    // Boundary conditions
    else 
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		QVar((*tri_it).value().q_bar.h, 0, 0), obj);

    norm_vec = (*tri_it).normal((*tri_it).node3(), (*tri_it).node1());
    // Calcuate flux using adjacent triangle's Q
    if ((*tri_it).adj_triangle((*tri_it).node3(), (*tri_it).node1()).is_valid())
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		(*tri_it).adj_triangle((*tri_it).node3(), (*tri_it).node1()).value().q_bar, obj); 
    // Boundary conditions
    else
      sum += f(norm_vec.x, norm_vec.y, dt, (*tri_it).value().q_bar, 
      		QVar((*tri_it).value().q_bar.h, 0, 0), obj);

    (*tri_it).value().q_bar2 = ((*tri_it).value().S * dt/(*tri_it).area()) + (*tri_it).value().q_bar - 
                               (sum * dt/(*tri_it).area());
	}

  /* In order to use original (as opposed to update) q_bar values in the equation above, we have to update
   * q_bar values for all triangles after the q_bar values have been calculated.
   * Updates the Source term
   */
  for (auto tri_it = m.triangle_begin(); (*tri_it).index() != water_tris; ++tri_it){
    (*tri_it).value().S = (*tri_it).value().S/(*tri_it).value().q_bar.h*(*tri_it).value().q_bar2.h;
    (*tri_it).value().q_bar = (*tri_it).value().q_bar2;
  }

  return t + dt;
}

double get_volume(MESH& m) {
  double volume = 0.0;
  for(auto it = m.triangle_begin(); it != m.triangle_end(); ++it){
    auto tri = (*it);
    Point normal = get_normal_surface(tri);
    double area = tri.area();
    volume += normal.z * area * (tri.node(0).position().z + tri.node(1).position().z + tri.node(2).position().z) / 3.0;
  }
  return volume;
}

double hyperbolic_step(MESH& m, FLUX& f, double t, double dt) {
  // HW4B: YOUR CODE HERE
  // Step the finite volume model in time by dt.

  // Pseudocode:
  // Compute all fluxes. (before updating any triangle Q_bars)
  // For each triangle, update Q_bar using the fluxes as in Equation 8.
  //  NOTE: Much like symp_euler_step, this may require TWO for-loops
  
  // Implement Equation 7 from your pseudocode here.

  for(auto i = m.edge_begin(); i != m.edge_end(); ++i){
    if ((*i).triangle1().index() != (unsigned) -1 && (*i).triangle2().index() != (unsigned) -1 ){
      MeshType::Triangle trik = (*i).triangle1();
      MeshType::Triangle trim = (*i).triangle2();
      unsigned int edge_k = 0;
      unsigned int edge_m = 0;
      //which edge (*i) is in trik and trim
      while(trik.node(edge_k).index()== (*i).node1().index() 
        || trik.node(edge_k).index()== (*i).node2().index() )
        ++edge_k;
      while(trim.node(edge_m).index()== (*i).node1().index() 
        || trim.node(edge_m).index()== (*i).node2().index() )
        ++edge_m;
      QVar flux = f(trik.normal(edge_k).x, trik.normal(edge_k).y, dt, trik.value().Q, trim.value().Q);
      trik.value().F[edge_k] = flux;
      trim.value().F[edge_m] = -flux;
    }
    else{
      MeshType::Triangle trik;
      if ((*i).triangle1().index() != (unsigned) -1)
        trik = (*i).triangle1();
      else
        trik = (*i).triangle2();
      unsigned int edge_k = 0;
      while(trik.node(edge_k).index()== (*i).node1().index() 
        || trik.node(edge_k).index()== (*i).node2().index() )
        ++edge_k;
      QVar flux = f(trik.normal(edge_k).x, trik.normal(edge_k).y, dt, trik.value().Q, QVar(trik.value().Q.h, 0, 0));
      trik.value().F[edge_k] = flux;
    }
  }

  for(auto i = m.triangle_begin(); i != m.triangle_end(); ++i){
    QVar sum = QVar(0, 0, 0);
    for (int j = 0; j < 3; ++j){
      sum += (*i).value().F[j];
    }
    (*i).value().Q = (*i).value().Q-dt/(*i).area()*sum;
  }
  
  return t + dt;
};

  Point operator()(MESH& m, NODE n, double t) {
    (void) t;
    Point pressure_force = Point(0.0, 0.0, 0.0);

    for(auto it=m.adj_triangle_begin(n.uid()); it != m.adj_triangle_end(n.uid()); ++ it) {
      auto tri = (*it);
      Point normal = get_normal_surface(tri);
      double area = tri.area();
      pressure_force += normal * area * pressure;

    }
    return pressure_force; 
  }  

void post_process(MESH& m) {
  // HW4B: Post-processing step
  // Translate the triangle-averaged values to node-averaged values
  // Implement Equation 9 from your pseudocode here
  for (auto it = m.node_begin(); it != m.node_end(); ++it){
    double sumarea=0;
    QVar sumQ = QVar(0, 0, 0);
    for(auto j = m.triangle_begin(*it); j != m.triangle_end(*it); ++j){
      sumarea += (*j).area();
      sumQ += (*j).value().Q * (*j).area();
    }
    (*it).value().Q = sumQ/sumarea;
  }
}

Point post_process(MESH& m, FORCE force, CONSTRAINT& c, double t, double dt, uint water_nodes) {
  static double ball_bottom = std::numeric_limits<double>::max();
  double water_dis = std::numeric_limits<double>::max();
  double dh = 0;
  static double submerged_height = 0;
  Point bottom_loc;
  Point water_loc;

  for (auto n_it = m.node_begin(); n_it != m.node_end(); ++n_it) {
    // handles the shallow water
  	if ((*n_it).index() < water_nodes) {
	    double sum_area = 0;
	    QVar value = QVar(0,0,0);

	    for (auto tri_it = m.adj_triangle_begin((*n_it).uid()); tri_it != m.adj_triangle_end((*n_it).uid()); ++tri_it) {
	      value += (*tri_it).value().q_bar * (*tri_it).area();
	      sum_area += (*tri_it).area();
	    }

	    (*n_it).value().q = value * 1.0/(sum_area);
	  }
    // handles the ball
    else {
      (*n_it).set_position((*n_it).position() + (*n_it).value().velocity*dt);
      dh = (*n_it).value().q.h - (*n_it).position().z;
      (*n_it).value().q.h = (*n_it).position().z;
      (*n_it).value().velocity += force(m,(*n_it),t)*dt/(*n_it).value().mass;
      if ((*n_it).value().q.h < ball_bottom) {
        ball_bottom = (*n_it).position().z;
        bottom_loc = (*n_it).position();
      }
    }
  }
  // find the water node closest to the bottom of the ball
  for (auto n_it = m.node_begin(); (*n_it).index() != water_nodes; ++n_it) {
    if (norm(Point((*n_it).position().x,(*n_it).position().y,0)-Point(bottom_loc.x,bottom_loc.y,0)) < water_dis){
      water_dis = norm(Point((*n_it).position().x,(*n_it).position().y,0)-Point(bottom_loc.x,bottom_loc.y,0));
      water_loc = Point((*n_it).position().x,(*n_it).position().y,(*n_it).value().q.h);
    }
  }

  // apply contraints of neccessary
  c(m,ball_bottom);

  // determines if the ball fell below shallow water and updates height submerged
  if (bottom_loc.z < water_loc.z)
    submerged_height += dh;
  return Point(bottom_loc.x, bottom_loc.y, submerged_height);
}

/*
 * implementation of euler approximation of the shallow water PDE
 * @pre: a valid Mesh class instance @mesh
 * @post: all triangle in the mesh class have new value() = old value - dt/area() * total flux, 
		  where total flux is calculated by all three edges of the triangle
   @return: return total time t+dt
*/
double hyperbolic_step(MESH& mesh, FLUX& f, double t, double dt) {
  // Step the finite volume model in time by dt.
  // Implement Equation 7 from your pseudocode here.

  for (auto it = mesh.tri_begin(); it!=mesh.tri_end() ; ++it)
  {
	// value function will return the flux
	QVar total_flux=QVar(0,0,0);
	QVar qm = QVar(0,0,0);
	// iterate through 3 edges of a triangle
	auto edgetemp = (*it).edge1();
	for (int num = 0; num < 3; num++)
	{	
		if (num ==0)
			edgetemp= (*it).edge1();
		else if (num==1)
			edgetemp = (*it).edge2();
		else	
			edgetemp = (*it).edge3();
			
		if (  mesh.has_neighbor(edgetemp.index()) ) // it has a common triangle
		{
			auto nx =  ((*it).norm_vector(edgetemp)).x;
			auto ny =  ((*it).norm_vector(edgetemp)).y;
			
			// find the neighbour of a common edge
			for (auto i = mesh.tri_edge_begin(edgetemp.index()); i != mesh.tri_edge_end(edgetemp.index()); ++i){	
				if (!(*i==*it))
					qm = (*i).value();
			}
			// calculat the total flux
			total_flux += f(nx, ny, dt, (*it).value(), qm);
		}
		else{
			// when it doesnt have a neighbour shared with this edge
			auto nx =  ((*it).norm_vector(edgetemp)).x;
			auto ny =  ((*it).norm_vector(edgetemp)).y;
			qm = QVar((*it).value().h, 0, 0 ); // approximation

			total_flux += f(nx, ny, dt, (*it).value(), qm);
		}
	}
	
	(*it).value() +=  total_flux * (- dt / (*it).area());
  }
  
  
  return t + dt;
}

    //! Get required faces of every element and store the unqiue ones
    static void apply( const MESH & mesh,
                       const std::vector<Face> & faces,
                       FaceMesh & faceMesh )
    {
        // 1. Allocate space for nodes and face elements
        const std::size_t numNodes = std::distance( mesh.nodesBegin(),
                                                    mesh.nodesEnd() );
        const std::size_t numElements = faces.size();
        faceMesh.allocate( numNodes, numElements );

        // 2. Copy nodes (not just the pointers!!!)
        typename MESH::NodePtrConstIter sourceNode = mesh.nodesBegin();
        typename MESH::NodePtrConstIter finalNode  = mesh.nodesEnd();
        typename FaceMesh::NodePtrIter  copyNode   = faceMesh.nodesBegin();
        for ( ; sourceNode != finalNode; ++sourceNode, ++copyNode ) {

            // Copy the global ID
            (*copyNode) -> setID( (*sourceNode) -> getID() );

            // Copy the coordinates
            std::vector<double> x( Node::dim );
            (*sourceNode) -> getX( x.begin() );
            (*copyNode)   -> setX( x.begin() );
        }
        

        // 3. Generate new elements from faces
        typename FaceMesh::ElementPtrIter elemIter = faceMesh.elementsBegin();
        typename FaceMesh::ElementPtrIter elemEnd  = faceMesh.elementsEnd();
        typename std::vector<Face>::const_iterator faceIter = faces.begin();
        for ( ; elemIter != elemEnd; ++elemIter, ++faceIter ) {

            // Extract face's node IDs
            Face nodeIDs;
            for ( unsigned v = 0; v < nodeIDs.size(); v ++ )
                nodeIDs[v] = faceIter -> at( v );

            // Set face element connectivity
            typename FaceMesh::Element::NodePtrIter node =
                (*elemIter) -> nodesBegin();
            for ( unsigned v = 0; v < Face::size(); v++, ++node ) {

                (*node) = mesh.nodePtr( nodeIDs[v] );
            }
            
        }
        return;
    }

/*************
 * DESCRIPTION:	create mesh dialog
 * INPUT:			ID		dialog ID
 * OUTPUT:			-
 *************/
void CDoc::CreateMesh(int ID)
{
	UNDO_CREATE *pUndo;
	MESH *pMesh;
	BOOL bErr;

	nDialogID = ID;
	CCMeshDlg dialog;

	if (dialog.DoModal() == IDOK)
	{
		pMesh = new MESH;
		if (pMesh)
		{
			pMesh->selected = TRUE;
			pMesh->surf = new SURFACE;
			if (pMesh->surf)
			{
				switch (nDialogID)
				{
					case IDD_CUBE:   bErr = pMesh->CreateCube(&dialog.m_vSize); break;
					case IDD_TORUS:  bErr = pMesh->CreateTorus(dialog.m_Radius, dialog.m_Thickness, dialog.m_nDivs, dialog.m_nSlices); break;
					case IDD_SPHERE: bErr = pMesh->CreateSphere(dialog.m_Radius, dialog.m_nDivs, dialog.m_nSlices); break;
					case IDD_TUBE:   bErr = pMesh->CreateTube(dialog.m_Radius, dialog.m_Height, dialog.m_nDivs, dialog.m_nSlices, dialog.m_bClosedBottom, dialog.m_bClosedTop); break;
					case IDD_PLANE:  bErr = pMesh->CreatePlane(&dialog.m_vSize, dialog.m_nXDivs, dialog.m_nZDivs); break;
					case IDD_CONE:   bErr = pMesh->CreateCone(dialog.m_Radius, dialog.m_Height, dialog.m_nDivs, dialog.m_nSlices, dialog.m_bClosedBottom); break;
				}
				if (!bErr)
					delete pMesh;
				else
				{
					DeselectAll();
					pMesh->Append();
					pMesh->IsFirstSelected();
					
					pUndo = new UNDO_CREATE;
					if (pUndo)
					{
						if (pUndo->AddCreated(pMesh))
							pUndo->Add();
						else
							delete pUndo;
					}	
					sciBrowserBuild();
 				}
			}
			else
				delete pMesh;
		}
	}
	sciRedraw();
}

void post_process(MESH& m) {
  // HW4B: Post-processing step
  // Translate the triangle-averaged values to node-averaged values
  // Implement Equation 9 from your pseudocode here
  for (auto nit = m.node_begin(); nit != m.node_end(); ++nit) {
      double total_area = 0;
      QVar Q_tot(0, 0, 0);
      int count = 0;
  
      for (auto tri_it = m.adjacent_triangle_begin(*nit); tri_it != m.adjacent_triangle_end(*nit); ++tri_it) {
        Q_tot = Q_tot + (*tri_it).value() * (*tri_it).area();
        total_area += (*tri_it).area();
        ++count;
      }
      (*nit).value() = Q_tot / total_area;
  }
}

double giveRadius( const MESH& mesh, const FIELD& field )
{
    typename MESH::NodePtrConstIter nIter = mesh.nodesBegin();
    
    typename FIELD::DoFPtrConstIter dIter = field.doFsBegin();

    return
        ((*nIter) -> getX())[0] +
        ((*dIter) -> getValue(0));
}

/*	
 * post process of a mesh instance to update the values of all the nodes values
 * @pre: a valid mesh instance
 * @post: update the nodes values based on approximation of the average of neighbours values
		  refer to equation 9 on the notes
*/
void post_process(MESH& m) {
  // Translate the triangle-averaged values to node-averaged values
  // Implement Equation 8 from your pseudocode here
  	// iterate through all the nodes
  for ( auto it = m.node_begin(); it!= m.node_end(); ++it)
  {
	
	QVar sum = QVar(0,0,0);
	double sumTriArea = 0;
	// for each node, iterate through its adjacent triangles
	
	for (auto adji = m.vertex_begin((*it).index()); adji !=  m.vertex_end((*it).index()); ++ adji)
	{
		auto tri = (*adji);
		sum += tri.area() * tri.value();
		sumTriArea += tri.area();  
	}

	(*it).value() = sum/sumTriArea; // update nodes value
  }
}