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rGOOSEFEM/src/GooseFEM/MeshTri3.hpp
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MeshTri3.hpp
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/* =================================================================================================
(c - GPLv3) T.W.J. de Geus (Tom) | tom@geus.me | www.geus.me | github.com/tdegeus/GooseFEM
================================================================================================= */
#ifndef GOOSEFEM_MESHTRI3_CPP
#define GOOSEFEM_MESHTRI3_CPP
// -------------------------------------------------------------------------------------------------
#include "MeshTri3.h"
// ===================================== GooseFEM::Mesh::Tri3 ======================================
namespace GooseFEM {
namespace Mesh {
namespace Tri3 {
// ------------------------------------------ constructor ------------------------------------------
inline Regular::Regular(size_t nelx, size_t nely, double h):
m_h(h), m_nelx(nelx), m_nely(nely)
{
assert( m_nelx >= 1 );
assert( m_nely >= 1 );
m_nnode = (m_nelx+1) * (m_nely+1);
m_nelem = m_nelx * m_nely * 2;
}
// -------------------------------------- number of elements ---------------------------------------
inline size_t Regular::nelem() const
{
return m_nelem;
}
// ---------------------------------------- number of nodes ----------------------------------------
inline size_t Regular::nnode() const
{
return m_nnode;
}
// ---------------------------------- number of nodes per element ----------------------------------
inline size_t Regular::nne() const
{
return m_nne;
}
// ------------------------------------- number of dimensions --------------------------------------
inline size_t Regular::ndim() const
{
return m_ndim;
}
// --------------------------------- coordinates (nodal positions) ---------------------------------
inline xt::xtensor<double,2> Regular::coor() const
{
xt::xtensor<double,2> out = xt::empty<double>({m_nnode, m_ndim});
xt::xtensor<double,1> x = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nelx), m_nelx+1);
xt::xtensor<double,1> y = xt::linspace<double>(0.0, m_h*static_cast<double>(m_nely), m_nely+1);
size_t inode = 0;
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy ) {
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix ) {
out(inode,0) = x(ix);
out(inode,1) = y(iy);
++inode;
}
}
return out;
}
// ---------------------------- connectivity (node-numbers per element) ----------------------------
inline xt::xtensor<size_t,2> Regular::conn() const
{
xt::xtensor<size_t,2> out = xt::empty<size_t>({m_nelem,m_nne});
size_t ielem = 0;
for ( size_t iy = 0 ; iy < m_nely ; ++iy ) {
for ( size_t ix = 0 ; ix < m_nelx ; ++ix ) {
out(ielem,0) = (iy )*(m_nelx+1) + (ix );
out(ielem,1) = (iy )*(m_nelx+1) + (ix+1);
out(ielem,2) = (iy+1)*(m_nelx+1) + (ix );
++ielem;
out(ielem,0) = (iy )*(m_nelx+1) + (ix+1);
out(ielem,1) = (iy+1)*(m_nelx+1) + (ix+1);
out(ielem,2) = (iy+1)*(m_nelx+1) + (ix );
++ielem;
}
}
return out;
}
// ------------------------------ node-numbers along the bottom edge -------------------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = ix;
return out;
}
// -------------------------------- node-numbers along the top edge --------------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx+1});
for ( size_t ix = 0 ; ix < m_nelx+1 ; ++ix )
out(ix) = ix + m_nely*(m_nelx+1);
return out;
}
// ------------------------------- node-numbers along the left edge --------------------------------
inline xt::xtensor<size_t,1> Regular::nodesLeftEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1);
return out;
}
// ------------------------------- node-numbers along the right edge -------------------------------
inline xt::xtensor<size_t,1> Regular::nodesRightEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely+1});
for ( size_t iy = 0 ; iy < m_nely+1 ; ++iy )
out(iy) = iy*(m_nelx+1) + m_nelx;
return out;
}
// ---------------------- node-numbers along the bottom edge, without corners ----------------------
inline xt::xtensor<size_t,1> Regular::nodesBottomOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = ix;
return out;
}
// ----------------------- node-numbers along the top edge, without corners ------------------------
inline xt::xtensor<size_t,1> Regular::nodesTopOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nelx-1});
for ( size_t ix = 1 ; ix < m_nelx ; ++ix )
out(ix-1) = ix + m_nely*(m_nelx+1);
return out;
}
// ----------------------- node-numbers along the left edge, without corners -----------------------
inline xt::xtensor<size_t,1> Regular::nodesLeftOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1);
return out;
}
// ---------------------- node-numbers along the right edge, without corners -----------------------
inline xt::xtensor<size_t,1> Regular::nodesRightOpenEdge() const
{
xt::xtensor<size_t,1> out = xt::empty<size_t>({m_nely-1});
for ( size_t iy = 1 ; iy < m_nely ; ++iy )
out(iy-1) = iy*(m_nelx+1) + m_nelx;
return out;
}
// ----------------------------- node-number of the bottom-left corner -----------------------------
inline size_t Regular::nodesBottomLeftCorner() const
{
return 0;
}
// ---------------------------- node-number of the bottom-right corner -----------------------------
inline size_t Regular::nodesBottomRightCorner() const
{
return m_nelx;
}
// ------------------------------ node-number of the top-left corner -------------------------------
inline size_t Regular::nodesTopLeftCorner() const
{
return m_nely*(m_nelx+1);
}
// ------------------------------ node-number of the top-right corner ------------------------------
inline size_t Regular::nodesTopRightCorner() const
{
return m_nely*(m_nelx+1) + m_nelx;
}
// ----------------------------- node-number of the corners (aliases) ------------------------------
inline size_t Regular::nodesLeftBottomCorner() const { return nodesBottomLeftCorner(); }
inline size_t Regular::nodesLeftTopCorner() const { return nodesTopLeftCorner(); }
inline size_t Regular::nodesRightBottomCorner() const { return nodesBottomRightCorner(); }
inline size_t Regular::nodesRightTopCorner() const { return nodesTopRightCorner(); }
// ------------------------------ node-numbers of periodic node-pairs ------------------------------
inline xt::xtensor<size_t,2> Regular::nodesPeriodic() const
{
// edges (without corners)
xt::xtensor<size_t,1> bot = nodesBottomOpenEdge();
xt::xtensor<size_t,1> top = nodesTopOpenEdge();
xt::xtensor<size_t,1> lft = nodesLeftOpenEdge();
xt::xtensor<size_t,1> rgt = nodesRightOpenEdge();
// allocate nodal ties
// - number of tying per category
size_t tedge = bot.size() + lft.size();
size_t tnode = 3;
// - allocate
xt::xtensor<size_t,2> out = xt::empty<size_t>({tedge+tnode, std::size_t(2)});
// counter
size_t i = 0;
// tie all corners to one corner
out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesBottomRightCorner(); ++i;
out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopRightCorner(); ++i;
out(i,0) = nodesBottomLeftCorner(); out(i,1) = nodesTopLeftCorner(); ++i;
// tie all corresponding edges to each other
for ( size_t j = 0 ; j<bot.size() ; ++j ){ out(i,0) = bot(j); out(i,1) = top(j); ++i; }
for ( size_t j = 0 ; j<lft.size() ; ++j ){ out(i,0) = lft(j); out(i,1) = rgt(j); ++i; }
return out;
}
// ------------------------------ node-number that lies in the origin ------------------------------
inline size_t Regular::nodesOrigin() const
{
return nodesBottomLeftCorner();
}
// ------------------------- DOF numbers per node (sequentially numbered) --------------------------
inline xt::xtensor<size_t,2> Regular::dofs() const
{
return GooseFEM::Mesh::dofs(m_nnode,m_ndim);
}
// ------------------------ DOP-numbers with periodic dependencies removed -------------------------
inline xt::xtensor<size_t,2> Regular::dofsPeriodic() const
{
// DOF-numbers for each component of each node (sequential)
xt::xtensor<size_t,2> out = GooseFEM::Mesh::dofs(m_nnode,m_ndim);
// periodic node-pairs
xt::xtensor<size_t,2> nodePer = nodesPeriodic();
// eliminate 'dependent' DOFs; renumber "out" to be sequential for the remaining DOFs
for ( size_t i = 0 ; i < nodePer.shape()[0] ; ++i )
for ( size_t j = 0 ; j < m_ndim ; ++j )
out(nodePer(i,1),j) = out(nodePer(i,0),j);
// renumber "out" to be sequential
return GooseFEM::Mesh::renumber(out);
}
// ------------------------------ get the orientation of each element ------------------------------
inline xt::xtensor<int,1> getOrientation(const xt::xtensor<double,2> &coor, const xt::xtensor<size_t,2> &conn)
{
assert( conn.shape()[1] == 3 );
assert( coor.shape()[1] == 2 );
double k;
size_t nelem = conn.shape()[0];
xt::xtensor<int,1> out = xt::empty<int>({nelem});
for ( size_t ielem = 0 ; ielem < nelem ; ++ielem )
{
auto v1 = xt::view(coor, conn(ielem,0), xt::all()) - xt::view(coor, conn(ielem,1), xt::all());
auto v2 = xt::view(coor, conn(ielem,2), xt::all()) - xt::view(coor, conn(ielem,1), xt::all());
k = v1(0) * v2(1) - v2(0) * v1(1);
if ( k < 0 ) out(ielem) = -1;
else out(ielem) = +1;
}
return out;
}
// ------------------------------ set the orientation of each element ------------------------------
inline xt::xtensor<size_t,2> setOrientation(const xt::xtensor<double,2> &coor, const xt::xtensor<size_t,2> &conn, int orientation)
{
assert( conn.shape()[1] == 3 );
assert( coor.shape()[1] == 2 );
assert( orientation == -1 || orientation == +1 );
xt::xtensor<int,1> val = getOrientation(coor, conn);
return setOrientation(coor, conn, val, orientation);
}
// -------------------- set the orientation of each element to a certain value ---------------------
inline xt::xtensor<size_t,2> setOrientation(const xt::xtensor<double,2> &coor, const xt::xtensor<size_t,2> &conn, const xt::xtensor<int,1> &val, int orientation)
{
assert( conn.shape()[1] == 3 );
assert( coor.shape()[1] == 2 );
assert( conn.shape()[0] == val.size() );
assert( orientation == -1 || orientation == +1 );
// avoid compiler warning
UNUSED(coor);
size_t nelem = conn.shape()[0];
xt::xtensor<size_t,2> out = conn;
for ( size_t ielem = 0 ; ielem < nelem ; ++ielem )
if ( ( orientation == -1 and val(ielem) > 0 ) or ( orientation == +1 and val(ielem) < 0 ) )
std::swap( out(ielem,2) , out(ielem,1) );
return out;
}
// ------------------------------------- re-triangulation API --------------------------------------
inline xt::xtensor<size_t,2> retriangulate(const xt::xtensor<double,2> &coor, const xt::xtensor<size_t,2> &conn, int orientation)
{
// get the orientation of all elements
xt::xtensor<int,1> dir = getOrientation(coor, conn);
// check the orientation
bool eq = static_cast<size_t>(std::abs(xt::sum(dir)[0])) == conn.shape()[0];
// new connectivity
xt::xtensor<size_t,2> out;
// perform re-triangulation
// - use "TriUpdate"
if ( eq )
{
Private::TriUpdate obj(coor,conn);
obj.eval();
out = obj.conn();
}
// - using TriCompute
else
{
throw std::runtime_error("Work-in-progress, has to be re-triangulated using 'TriCompute'");
}
return setOrientation(coor,out,orientation);
}
// ================================= GooseFEM::Mesh::Tri3::Private =================================
namespace Private {
// ------------------------------------------ constructor ------------------------------------------
inline TriUpdate::TriUpdate(const xt::xtensor<double,2> &coor, const xt::xtensor<size_t,2> &conn): m_conn(conn), m_coor(coor)
{
assert( conn.shape()[1] == 3 );
assert( coor.shape()[1] == 2 );
// store shapes
m_nnode = coor.shape()[0];
m_ndim = coor.shape()[1];
m_nelem = conn.shape()[0];
m_nne = conn.shape()[1];
// set default to out-of-bounds, to make clear that nothing happened yet
m_elem = m_nelem * xt::ones<size_t>({2});
m_node = m_nnode * xt::ones<size_t>({4});
edge();
}
// -------------------------- compute neighbors per edge of all elements ---------------------------
inline void TriUpdate::edge()
{
// signal that nothing has been set
m_edge = m_nelem * xt::ones<size_t>({m_nelem , m_nne});
std::vector<size_t> idx = {0,1,2}; // lists to convert connectivity -> edges
std::vector<size_t> jdx = {1,2,0}; // lists to convert connectivity -> edges
std::vector<Edge> edge;
edge.reserve(m_nelem*idx.size());
for ( size_t e = 0 ; e < m_nelem ; ++e )
for ( size_t i = 0 ; i < m_nne ; ++i )
edge.push_back( Edge( m_conn(e,idx[i]), m_conn(e,jdx[i]) , e , i , true ) );
std::sort( edge.begin() , edge.end() , Edge_sort );
for ( size_t i = 0 ; i < edge.size()-1 ; ++i )
{
if ( edge[i].n1 == edge[i+1].n1 and edge[i].n2 == edge[i+1].n2 )
{
m_edge( edge[i ].elem , edge[i ].edge ) = edge[i+1].elem;
m_edge( edge[i+1].elem , edge[i+1].edge ) = edge[i ].elem;
}
}
}
// ---------------------------- update edges around renumbered elements ----------------------------
inline void TriUpdate::chedge(size_t edge, size_t old_elem, size_t new_elem)
{
size_t m;
size_t neigh = m_edge(old_elem , edge);
if ( neigh >= m_nelem ) return;
for ( m = 0 ; m < m_nne ; ++m )
if ( m_edge( neigh , m ) == old_elem )
break;
m_edge( neigh , m ) = new_elem;
}
// --------------------------------- re-triangulate the full mesh ----------------------------------
inline bool TriUpdate::eval()
{
bool change = false;
while ( increment() ) { change = true; }
return change;
}
// ----------------------------------- one re-triangulation step -----------------------------------
inline bool TriUpdate::increment()
{
size_t ielem,jelem,iedge,jedge;
double phi1,phi2;
xt::xtensor_fixed<size_t,xt::xshape<4>> c = xt::empty<size_t>({4});
xt::xtensor_fixed<size_t,xt::xshape<4>> n = xt::empty<size_t>({4});
// loop over all elements
for ( ielem = 0 ; ielem < m_nelem ; ++ielem )
{
// loop over all edges
for ( iedge = 0 ; iedge < m_nne ; ++iedge )
{
// only proceed if the edge is shared with another element
if ( m_edge(ielem,iedge) >= m_nelem )
continue;
// read "jelem"
jelem = m_edge(ielem,iedge);
// find the edge involved for "jelem"
for ( jedge=0; jedge<m_nne; ++jedge ) if ( m_edge(jelem,jedge) == ielem ) break;
// convert to four static nodes
// - read first three from "ielem"
if ( iedge==0 ) { c(0)=m_conn(ielem,2); c(1)=m_conn(ielem,0); c(2)=m_conn(ielem,1); }
else if ( iedge==1 ) { c(0)=m_conn(ielem,0); c(1)=m_conn(ielem,1); c(2)=m_conn(ielem,2); }
else if ( iedge==2 ) { c(0)=m_conn(ielem,1); c(1)=m_conn(ielem,2); c(2)=m_conn(ielem,0); }
// - read last from "jelem"
if ( jedge==0 ) { c(3)=m_conn(jelem,2); }
else if ( jedge==1 ) { c(3)=m_conn(jelem,0); }
else if ( jedge==2 ) { c(3)=m_conn(jelem,1); }
// construct edge vectors
auto a1 = xt::view(m_coor, c(1), xt::all()) - xt::view(m_coor, c(0), xt::all());
auto b1 = xt::view(m_coor, c(2), xt::all()) - xt::view(m_coor, c(0), xt::all());
auto a2 = xt::view(m_coor, c(1), xt::all()) - xt::view(m_coor, c(3), xt::all());
auto b2 = xt::view(m_coor, c(2), xt::all()) - xt::view(m_coor, c(3), xt::all());
// compute angles of the relevant corners
phi1 = std::acos((a1(0)*b1(0)+a1(1)*b1(1))/(std::pow((a1(0)*a1(0)+a1(1)*a1(1)),0.5)*std::pow((b1(0)*b1(0)+b1(1)*b1(1)),0.5)));
phi2 = std::acos((a2(0)*b2(0)+a2(1)*b2(1))/(std::pow((a2(0)*a2(0)+a2(1)*a2(1)),0.5)*std::pow((b2(0)*b2(0)+b2(1)*b2(1)),0.5)));
// update mesh if needed
if ( phi1+phi2 > M_PI )
{
// update connectivity
m_conn(ielem,0) = c(0); m_conn(ielem,1) = c(3); m_conn(ielem,2) = c(2);
m_conn(jelem,0) = c(0); m_conn(jelem,1) = c(1); m_conn(jelem,2) = c(3);
// change list with neighbors for the elements around (only two neighbors change)
if ( iedge==0 ) { chedge(2,ielem,jelem); }
else if ( iedge==1 ) { chedge(0,ielem,jelem); }
else if ( iedge==2 ) { chedge(1,ielem,jelem); }
if ( jedge==0 ) { chedge(2,jelem,ielem); }
else if ( jedge==1 ) { chedge(0,jelem,ielem); }
else if ( jedge==2 ) { chedge(1,jelem,ielem); }
// convert to four static nodes
if ( iedge==0 ) { n(0)=m_edge(ielem,2); n(3)=m_edge(ielem,1); }
else if ( iedge==1 ) { n(0)=m_edge(ielem,0); n(3)=m_edge(ielem,2); }
else if ( iedge==2 ) { n(0)=m_edge(ielem,1); n(3)=m_edge(ielem,0); }
if ( jedge==0 ) { n(1)=m_edge(jelem,1); n(2)=m_edge(jelem,2); }
else if ( jedge==1 ) { n(1)=m_edge(jelem,2); n(2)=m_edge(jelem,0); }
else if ( jedge==2 ) { n(1)=m_edge(jelem,0); n(2)=m_edge(jelem,1); }
// store the neighbors for the changed elements
m_edge(ielem,0) = jelem; m_edge(jelem,0) = n(0) ;
m_edge(ielem,1) = n(2) ; m_edge(jelem,1) = n(1) ;
m_edge(ielem,2) = n(3) ; m_edge(jelem,2) = ielem;
// store information for transfer algorithm
m_node = c;
m_elem(0) = ielem;
m_elem(1) = jelem;
return true;
}
}
}
return false;
}
// ------------------------------------------ constructor ------------------------------------------
inline Edge::Edge(size_t i, size_t j, size_t el, size_t ed, bool sort):
n1(i), n2(j), elem(el), edge(ed)
{
if ( sort && n1>n2 )
std::swap(n1,n2);
}
// --------------------------------------- compare two edges ---------------------------------------
inline bool Edge_cmp(Edge a, Edge b)
{
if ( a.n1 == b.n1 and a.n2 == b.n2 )
return true;
return false;
}
// ----------------------- sort edges by comparing the first and second node -----------------------
inline bool Edge_sort(Edge a, Edge b)
{
if ( a.n1 < b.n1 or a.n2 < b.n2 )
return true;
return false;
}
// -------------------------------------------------------------------------------------------------
} // namespace Private
// -------------------------------------------------------------------------------------------------
}}} // namespace ...
// =================================================================================================
#endif
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