smesh/src/SMESHUtils/SMESH_Triangulate.cxx

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// Copyright (C) 2007-2021 CEA/DEN, EDF R&D, OPEN CASCADE
//
// Copyright (C) 2003-2007 OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
// CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library 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
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
//
// See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
//
// File : SMESH_Triangulate.cxx
// Created : Thu Jan 18 18:00:13 2018
// Author : Edward AGAPOV (eap)
// Extracted from ../DriverSTL/DriverSTL_W_SMDS_Mesh.cxx
#include "SMESH_MeshAlgos.hxx"
#include <Standard_ErrorHandler.hxx>
#include <Standard_Failure.hxx>
#include <gp_Ax2.hxx>
#include <boost/container/flat_set.hpp>
using namespace SMESH_MeshAlgos;
namespace
{
struct Node // node of a triangle
{
size_t _triaIndex; // triangle index == index of the 1st triangle node in triangulation array
size_t _nodeIndex; // node index within triangle [0-2]
//! return node index within the node array
size_t Index() const { return _triaIndex + _nodeIndex; }
//! return local 3-d index [0-2]
static size_t ThirdIndex( size_t i1, size_t i2 )
{
size_t i3 = ( i2 + 1 ) % 3;
if ( i3 == i1 )
i3 = ( i2 + 2 ) % 3;
return i3;
}
//! return 3-d node index within the node array
static size_t ThirdIndex( const Node& n1, const Node& n2 )
{
return n1._triaIndex + ThirdIndex( n1._nodeIndex, n2._nodeIndex );
}
bool operator<(const Node& other) const { return _triaIndex < other._triaIndex; }
};
typedef boost::container::flat_set< Node > TriaNodeSet;
}
/*!
* \brief Vertex of a polygon. Together with 2 neighbor Vertices represents a triangle
*/
struct Triangulate::PolyVertex
{
SMESH_NodeXYZ _nxyz;
size_t _index;
gp_XY _xy;
PolyVertex* _prev;
PolyVertex* _next;
void SetNodeAndNext( const SMDS_MeshNode* n, PolyVertex& v, size_t index );
void GetTriaNodes( const SMDS_MeshNode** nodes, size_t* nodeIndices) const;
double TriaArea() const;
bool IsInsideTria( const PolyVertex* v );
PolyVertex* Delete();
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// compare PolyVertex'es by node
bool operator()(const PolyVertex* a, const PolyVertex* b) const
{
return ( a->_nxyz.Node() < b->_nxyz.Node() );
}
// set of PolyVertex sorted by mesh node
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typedef boost::container::flat_set< PolyVertex*, PolyVertex > PVSet;
};
struct Triangulate::Data
{
std::vector< PolyVertex > _pv;
std::vector< size_t > _nodeIndex;
PolyVertex::PVSet _uniqueNodePV;
};
struct Triangulate::Optimizer
{
std::vector< TriaNodeSet > _nodeUsage; // inclusions of a node in triangles
//================================================================================
/*!
* \brief Optimize triangles by edge swapping
* \param [inout] nodes - polygon triangulation, i.e. connectivity of all triangles to optimize
* \param [in] points - coordinates of nodes of the input polygon
* \param [in] nodeIndices - indices of triangulation nodes within the input polygon
*/
//================================================================================
void optimize( std::vector< const SMDS_MeshNode*>& nodes,
std::vector< PolyVertex > & points,
std::vector< size_t > & nodeIndices)
{
// for each node of the polygon, remember triangles using it
_nodeUsage.resize( points.size() );
for ( size_t i = 0; i < points.size(); ++i ) // clear old data
{
_nodeUsage[ i ].clear();
}
for ( size_t i = 0, iTria = 0; i < nodeIndices.size(); ++iTria )
{
_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 0 });
_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 1 });
_nodeUsage[ nodeIndices[ i++ ]].insert({ iTria * 3, 2 });
}
// optimization
for ( size_t iTria = 0; iTria < nodeIndices.size(); iTria += 3 )
{
double badness1 = computeBadness( nodeIndices[ iTria + 0 ],
nodeIndices[ iTria + 1 ],
nodeIndices[ iTria + 2 ],
points );
for ( size_t i = 0; i < 3; ++i ) // loop on triangle edges to find a neighbor triangle
{
size_t i1 = iTria + i; // node index in nodeIndices
size_t i2 = iTria + ( i + 1 ) % 3;
size_t ind1 = nodeIndices[ i1 ]; // node index in points
size_t ind2 = nodeIndices[ i2 ];
TriaNodeSet & usage1 = _nodeUsage[ ind1 ]; // triangles using a node
TriaNodeSet & usage2 = _nodeUsage[ ind2 ];
if ( usage1.size() < 2 ||
usage2.size() < 2 )
continue;
// look for another triangle using two nodes
TriaNodeSet::iterator usIt1 = usage1.begin();
for ( ; usIt1 != usage1.end(); ++usIt1 )
{
if ( usIt1->_triaIndex == iTria )
continue; // current triangle
TriaNodeSet::iterator usIt2 = usage2.find( *usIt1 );
if ( usIt2 == usage2.end() )
continue; // no common _triaIndex in two usages
size_t i3 = iTria + ( i + 2 ) % 3;
size_t i4 = Node::ThirdIndex( *usIt1, *usIt2 ); // 4th node of quadrangle
size_t ind3 = nodeIndices[ i3 ];
size_t ind4 = nodeIndices[ i4 ];
double badness2 = computeBadness( ind2, ind1, ind4, points );
double badness3 = computeBadness( ind1, ind4, ind3, points, /*checkArea=*/true );
double badness4 = computeBadness( ind2, ind3, ind4, points, /*checkArea=*/true );
if ( Max( badness1, badness2 ) < Max( badness3, badness4 ))
continue;
// swap edge by modifying nodeIndices
nodeIndices[ i2 ] = ind4;
_nodeUsage[ ind4 ].insert({ iTria, i2 - iTria });
_nodeUsage[ ind2 ].erase ({ iTria, i2 - iTria });
i1 = usIt1->Index();
nodeIndices[ i1 ] = ind3;
_nodeUsage[ ind3 ].insert( *usIt1 );
_nodeUsage[ ind1 ].erase ( *usIt1 );
--i; // to re-check a current edge
badness1 = badness3;
break;
}
}
}
// update nodes by updated nodeIndices
for ( size_t i = 0; i < nodeIndices.size(); ++i )
nodes[ i ] = points[ nodeIndices[ i ]]._nxyz.Node();
return;
}
//================================================================================
/*!
* \brief Return 1./area. Initially: max cos^2 of triangle angles
*/
//================================================================================
double computeBadness( size_t i1, size_t i2, size_t i3,
std::vector< PolyVertex > & points,
bool checkArea = false )
{
if ( checkArea )
{
points[ i2 ]._prev = & points[ i1 ];
points[ i2 ]._next = & points[ i3 ];
double a = points[ i2 ].TriaArea();
// if ( a < 0 )
// return std::numeric_limits<double>::max();
// return 1. / a;
if ( a < 0 )
return 2;
}
const gp_XY & p1 = points[ i1 ]._xy;
const gp_XY & p2 = points[ i2 ]._xy;
const gp_XY & p3 = points[ i3 ]._xy;
gp_XY vec[3] = { p2 - p1,
p3 - p2,
p1 - p3 };
double len[3] = { vec[0].SquareModulus(),
vec[1].SquareModulus(),
vec[2].SquareModulus() };
if ( len[0] < gp::Resolution() ||
len[1] < gp::Resolution() ||
len[2] < gp::Resolution() )
return 2;
double maxCos2 = 0;
for ( int i = 0; i < 3; ++i )
{
int i2 = ( i+1 ) % 3;
double dot = -vec[ i ] * vec[ i2 ];
if ( dot > 0 )
maxCos2 = Max( maxCos2, dot * dot / len[ i ] / len[ i2 ] );
}
return maxCos2;
}
};
//================================================================================
/*!
* \brief Initialization
*/
//================================================================================
void Triangulate::PolyVertex::SetNodeAndNext( const SMDS_MeshNode* n,
PolyVertex& v,
size_t index )
{
_nxyz.Set( n );
_next = &v;
v._prev = this;
_index = index;
}
//================================================================================
/*!
* \brief Remove self from a polygon
*/
//================================================================================
Triangulate::PolyVertex* Triangulate::PolyVertex::Delete()
{
_prev->_next = _next;
_next->_prev = _prev;
return _next;
}
//================================================================================
/*!
* \brief Return nodes of a triangle
*/
//================================================================================
void Triangulate::PolyVertex::GetTriaNodes( const SMDS_MeshNode** nodes,
size_t* nodeIndices) const
{
nodes[0] = _prev->_nxyz._node;
nodes[1] = this->_nxyz._node;
nodes[2] = _next->_nxyz._node;
nodeIndices[0] = _prev->_index;
nodeIndices[1] = this->_index;
nodeIndices[2] = _next->_index;
}
//================================================================================
/*!
* \brief Compute triangle area
*/
//================================================================================
inline static double Area( const gp_XY& xy0, const gp_XY& xy1, const gp_XY& xy2 )
{
gp_XY vPrev = xy0 - xy1;
gp_XY vNext = xy2 - xy1;
return vNext ^ vPrev;
}
//================================================================================
/*!
* \brief Compute triangle area
*/
//================================================================================
double Triangulate::PolyVertex::TriaArea() const
{
return Area( _prev->_xy, this->_xy, _next->_xy );
}
//================================================================================
/*!
* \brief Check if a vertex is inside a triangle
*/
//================================================================================
bool Triangulate::PolyVertex::IsInsideTria( const PolyVertex* v )
{
if ( this ->_nxyz == v->_nxyz ||
_prev->_nxyz == v->_nxyz ||
_next->_nxyz == v->_nxyz )
return false;
gp_XY p = _prev->_xy - v->_xy;
gp_XY t = this->_xy - v->_xy;
gp_XY n = _next->_xy - v->_xy;
const double tol = -1e-7;
return (( p ^ t ) >= tol &&
( t ^ n ) >= tol &&
( n ^ p ) >= tol );
// return ( Area( _prev, this, v ) > 0 &&
// Area( this, _next, v ) > 0 &&
// Area( _next, _prev, v ) > 0 );
}
//================================================================================
/*!
* \brief Triangulate a polygon. Assure correct orientation for concave polygons
*/
//================================================================================
bool Triangulate::triangulate( std::vector< const SMDS_MeshNode*>& nodes,
const size_t nbNodes)
{
std::vector< PolyVertex >& _pv = _data->_pv;
std::vector< size_t >& _nodeIndex = _data->_nodeIndex;
PolyVertex::PVSet& _uniqueNodePV = _data->_uniqueNodePV;
// connect nodes into a ring
_pv.resize( nbNodes );
for ( size_t i = 1; i < nbNodes; ++i )
_pv[i-1].SetNodeAndNext( nodes[i-1], _pv[i], /*index=*/i-1 );
_pv[ nbNodes-1 ].SetNodeAndNext( nodes[ nbNodes-1 ], _pv[0], nbNodes-1 );
// assure correctness of PolyVertex::_index as a node can encounter more than once
// within a polygon boundary
if ( _optimizer && nbNodes > 4 )
{
_uniqueNodePV.clear();
for ( size_t i = 0; i < nbNodes; ++i )
{
PolyVertex::PVSet::iterator pv = _uniqueNodePV.insert( &_pv[i] ).first;
_pv[i]._index = (*pv)->_index;
}
}
// get a polygon normal
gp_XYZ normal(0,0,0), p0,v01,v02;
p0 = _pv[0]._nxyz;
v01 = _pv[1]._nxyz - p0;
for ( size_t i = 2; i < nbNodes; ++i )
{
v02 = _pv[i]._nxyz - p0;
normal += v01 ^ v02;
v01 = v02;
}
// project nodes to the found plane
gp_Ax2 axes;
try {
axes = gp_Ax2( p0, normal, v01 );
}
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catch ( Standard_Failure& ) {
return false;
}
double factor = 1.0, modulus = normal.Modulus();
if ( modulus < 1e-2 )
factor = 1. / sqrt( modulus );
for ( size_t i = 0; i < nbNodes; ++i )
{
gp_XYZ p = _pv[i]._nxyz - p0;
_pv[i]._xy.SetX( axes.XDirection().XYZ() * p * factor);
_pv[i]._xy.SetY( axes.YDirection().XYZ() * p * factor );
}
// compute minimal triangle area
double sumArea = 0;
if ( factor == 1.0 )
sumArea = modulus;
else
for ( size_t i = 0; i < nbNodes; ++i )
sumArea += _pv[i].TriaArea();
const double minArea = 1e-6 * sumArea / ( nbNodes - 2 );
// in a loop, find triangles with positive area and having no vertices inside
int iN = 0, nbTria = nbNodes - 2;
nodes.resize( nbTria * 3 );
_nodeIndex.resize( nbTria * 3 );
PolyVertex* v = &_pv[0], *vi;
int nbVertices = nbNodes, nbBadTria = 0, isGoodTria;
while ( nbBadTria < nbVertices )
{
if (( isGoodTria = v->TriaArea() > minArea ))
{
for ( vi = v->_next->_next;
vi != v->_prev;
vi = vi->_next )
{
if ( v->IsInsideTria( vi ))
break;
}
isGoodTria = ( vi == v->_prev );
}
if ( isGoodTria )
{
v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
iN += 3;
v = v->Delete();
if ( --nbVertices == 3 )
{
// last triangle remains
v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
if ( _optimizer )
_optimizer->optimize( nodes, _pv, _nodeIndex );
return true;
}
nbBadTria = 0;
}
else
{
v = v->_next;
++nbBadTria;
}
}
// the polygon is invalid; add triangles with positive area
nbBadTria = 0;
while ( nbBadTria < nbVertices )
{
isGoodTria = v->TriaArea() > minArea;
if ( isGoodTria )
{
v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
iN += 3;
v = v->Delete();
if ( --nbVertices == 3 )
{
// last triangle remains
v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
return true;
}
nbBadTria = 0;
}
else
{
v = v->_next;
++nbBadTria;
}
}
// add all the rest triangles
while ( nbVertices >= 3 )
{
v->GetTriaNodes( &nodes[ iN ], &_nodeIndex[ iN ] );
iN += 3;
v = v->Delete();
--nbVertices;
}
return true;
} // triangulate()
//================================================================================
/*!
* \brief Constructor
*/
//================================================================================
Triangulate::Triangulate( bool optimize ): _optimizer(0)
{
_data = new Data;
if ( optimize )
_optimizer = new Optimizer;
}
//================================================================================
/*!
* \brief Destructor
*/
//================================================================================
Triangulate::~Triangulate()
{
delete _data;
delete _optimizer;
_optimizer = 0;
}
//================================================================================
/*!
* \brief Return nb triangles in a decomposed mesh face
* \retval int - number of triangles
*/
//================================================================================
int Triangulate::GetNbTriangles( const SMDS_MeshElement* face )
{
// WARNING: counting triangles must be coherent with GetTriangles()
switch ( face->GetEntityType() )
{
case SMDSEntity_BiQuad_Triangle:
case SMDSEntity_BiQuad_Quadrangle:
return face->NbNodes() - 1;
// case SMDSEntity_Triangle:
// case SMDSEntity_Quad_Triangle:
// case SMDSEntity_Quadrangle:
// case SMDSEntity_Quad_Quadrangle:
// case SMDSEntity_Polygon:
// case SMDSEntity_Quad_Polygon:
default:
return face->NbNodes() - 2;
}
return 0;
}
//================================================================================
/*!
* \brief Decompose a mesh face into triangles
* \retval int - number of triangles
*/
//================================================================================
int Triangulate::GetTriangles( const SMDS_MeshElement* face,
std::vector< const SMDS_MeshNode*>& nodes)
{
if ( face->GetType() != SMDSAbs_Face )
return 0;
// WARNING: decomposing into triangles must be coherent with getNbTriangles()
int nbTria, i = 0, nbNodes = face->NbNodes();
SMDS_NodeIteratorPtr nIt = face->interlacedNodesIterator();
nodes.resize( nbNodes * 3 );
nodes[ i++ ] = nIt->next();
nodes[ i++ ] = nIt->next();
const SMDSAbs_EntityType type = face->GetEntityType();
switch ( type )
{
case SMDSEntity_BiQuad_Triangle:
case SMDSEntity_BiQuad_Quadrangle:
nbTria = ( type == SMDSEntity_BiQuad_Triangle ) ? 6 : 8;
nodes[ i++ ] = face->GetNode( nbTria );
for ( i = 3; i < 3*(nbTria-1); i += 3 )
{
nodes[ i+0 ] = nodes[ i-2 ];
nodes[ i+1 ] = nIt->next();
nodes[ i+2 ] = nodes[ 2 ];
}
nodes[ i+0 ] = nodes[ i-2 ];
nodes[ i+1 ] = nodes[ 0 ];
nodes[ i+2 ] = nodes[ 2 ];
break;
case SMDSEntity_Triangle:
nbTria = 1;
nodes[ i++ ] = nIt->next();
break;
default:
// case SMDSEntity_Quad_Triangle:
// case SMDSEntity_Quadrangle:
// case SMDSEntity_Quad_Quadrangle:
// case SMDSEntity_Polygon:
// case SMDSEntity_Quad_Polygon:
nbTria = nbNodes - 2;
while ( nIt->more() )
nodes[ i++ ] = nIt->next();
if ( nbTria > 1 && !triangulate( nodes, nbNodes ))
{
nIt = face->interlacedNodesIterator();
nodes[ 0 ] = nIt->next();
nodes[ 1 ] = nIt->next();
nodes[ 2 ] = nIt->next();
for ( i = 3; i < 3*nbTria; i += 3 )
{
nodes[ i+0 ] = nodes[ 0 ];
nodes[ i+1 ] = nodes[ i-1 ];
nodes[ i+2 ] = nIt->next();
}
}
}
return nbTria;
}