qgstriangularmesh.cpp

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/***************************************************************************
                         qgstriangularmesh.cpp
                         ---------------------
    begin                : April 2018
    copyright            : (C) 2018 by Peter Petrik
    email                : zilolv at gmail dot com
 ***************************************************************************/
 
/***************************************************************************
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/
 
#include <memory>
#include <QList>
#include "qgspolygon.h"
#include "qgslinestring.h"
#include "qgstriangularmesh.h"
#include "qgsrendercontext.h"
#include "qgscoordinatetransform.h"
#include "qgsgeometry.h"
#include "qgsrectangle.h"
#include "qgslogger.h"
#include "qgsmeshspatialindex.h"
#include "qgsmeshlayerutils.h"
#include "meshOptimizer/meshoptimizer.h"
 
static void ENP_centroid_step( const QPolygonF &pX, double &cx, double &cy, double &signedArea, int i, int i1 )
{
  double x0 = 0.0; // Current vertex X
  double y0 = 0.0; // Current vertex Y
  double x1 = 0.0; // Next vertex X
  double y1 = 0.0; // Next vertex Y
  double a = 0.0;  // Partial signed area
 
  x0 = pX[i].x();
  y0 = pX[i].y();
  x1 = pX[i1].x();
  y1 = pX[i1].y();
  a = x0 * y1 - x1 * y0;
  signedArea += a;
  cx += ( x0 + x1 ) * a;
  cy += ( y0 + y1 ) * a;
}
 
static void ENP_centroid( const QPolygonF &pX, double &cx, double &cy )
{
  // http://stackoverflow.com/questions/2792443/finding-the-centroid-of-a-polygon/2792459#2792459
  cx = 0;
  cy = 0;
 
  if ( pX.isEmpty() )
    return;
 
  double signedArea = 0.0;
 
  const QPointF &pt0 = pX.first();
  QPolygonF localPolygon( pX.count() );
  for ( int i = 0; i < pX.count(); ++i )
    localPolygon[i] = pX.at( i ) - pt0;
 
  // For all vertices except last
  int i = 0;
  for ( ; i < localPolygon.size() - 1; ++i )
  {
    ENP_centroid_step( localPolygon, cx, cy, signedArea, i, i + 1 );
  }
  // Do last vertex separately to avoid performing an expensive
  // modulus operation in each iteration.
  ENP_centroid_step( localPolygon, cx, cy, signedArea, i, 0 );
 
  signedArea *= 0.5;
  cx /= ( 6.0 * signedArea );
  cy /= ( 6.0 * signedArea );
 
  cx = cx + pt0.x();
  cy = cy + pt0.y();
}
 
static void triangulateFaces( const QgsMeshFace &face,
                              int nativeIndex,
                              QVector<QgsMeshFace> &destinationFaces,
                              QVector<int> &triangularToNative,
                              const QgsMesh &verticesMeshSource )
{
  int vertexCount = face.size();
  if ( vertexCount < 3 )
    return;
 
  while ( vertexCount > 3 )
  {
    // clip one ear from last 2 and first vertex
    const QgsMeshFace ear = { face[vertexCount - 2], face[vertexCount - 1], face[0] };
    if ( !( std::isnan( verticesMeshSource.vertex( ear[0] ).x() )  ||
            std::isnan( verticesMeshSource.vertex( ear[1] ).x() )  ||
            std::isnan( verticesMeshSource.vertex( ear[2] ).x() ) ) )
    {
      destinationFaces.push_back( ear );
      triangularToNative.push_back( nativeIndex );
    }
    --vertexCount;
  }
 
  const QgsMeshFace triangle = { face[1], face[2], face[0] };
  if ( !( std::isnan( verticesMeshSource.vertex( triangle[0] ).x() )  ||
          std::isnan( verticesMeshSource.vertex( triangle[1] ).x() )  ||
          std::isnan( verticesMeshSource.vertex( triangle[2] ).x() ) ) )
  {
    destinationFaces.push_back( triangle );
    triangularToNative.push_back( nativeIndex );
  }
}
 
void QgsTriangularMesh::triangulate( const QgsMeshFace &face, int nativeIndex )
{
  triangulateFaces( face, nativeIndex, mTriangularMesh.faces, mTrianglesToNativeFaces, mTriangularMesh );
}
 
QgsMeshVertex QgsTriangularMesh::transformVertex( const QgsMeshVertex &vertex, Qgis::TransformDirection direction ) const
{
  QgsMeshVertex transformedVertex = vertex;
 
  if ( mCoordinateTransform.isValid() )
  {
    try
    {
      transformedVertex.transform( mCoordinateTransform, direction );
    }
    catch ( QgsCsException &cse )
    {
      Q_UNUSED( cse )
      QgsDebugMsg( QStringLiteral( "Caught CRS exception %1" ).arg( cse.what() ) );
      transformedVertex = QgsMeshVertex();
    }
  }
 
  return transformedVertex;
}
 
QgsMeshVertex QgsTriangularMesh::calculateCentroid( const QgsMeshFace &nativeFace )
{
  return QgsMeshUtils::centroid( nativeFace, mTriangularMesh.vertices );
}
 
double QgsTriangularMesh::averageTriangleSize() const
{
  return mAverageTriangleSize;
}
 
QgsTriangularMesh::~QgsTriangularMesh() = default;
QgsTriangularMesh::QgsTriangularMesh() = default;
 
bool QgsTriangularMesh::update( QgsMesh *nativeMesh, const QgsCoordinateTransform &transform )
{
  Q_ASSERT( nativeMesh );
 
  bool needUpdateVerticesCoordinates = mTriangularMesh.vertices.size() != nativeMesh->vertices.size() ||
                                       ( ( mCoordinateTransform.isValid() || transform.isValid() ) &&
                                         ( mCoordinateTransform.sourceCrs() != transform.sourceCrs() ||
                                             mCoordinateTransform.destinationCrs() != transform.destinationCrs() ||
                                             mCoordinateTransform.isValid() != transform.isValid() ) ) ;
 
  bool needUpdateFrame =  mTriangularMesh.vertices.size() != nativeMesh->vertices.size() ||
                          mNativeMeshFaceCentroids.size() != nativeMesh->faces.size() ||
                          mTriangularMesh.faces.size() < nativeMesh->faces.size() ||
                          mTriangularMesh.edges.size() != nativeMesh->edges.size();
 
 
  // FIND OUT IF UPDATE IS NEEDED
  if ( ! needUpdateVerticesCoordinates  && !needUpdateFrame )
    return false;
 
  // CLEAN-UP
  mTriangularMesh.vertices.clear();
  if ( needUpdateFrame )
  {
    mTriangularMesh.faces.clear();
    mTriangularMesh.edges.clear();
    mEdgesToNativeEdges.clear();
    mTrianglesToNativeFaces.clear();
  }
 
  // TRANSFORM VERTICES
  mCoordinateTransform = transform;
  mTriangularMesh.vertices.resize( nativeMesh->vertices.size() );
  mExtent.setMinimal();
  for ( int i = 0; i < nativeMesh->vertices.size(); ++i )
  {
    mTriangularMesh.vertices[i] = nativeToTriangularCoordinates( nativeMesh->vertices.at( i ) );
    mExtent.include( mTriangularMesh.vertices.at( i ) );
  }
 
  if ( needUpdateFrame )
  {
    // CREATE TRIANGULAR MESH
    for ( int i = 0; i < nativeMesh->faces.size(); ++i )
    {
      const QgsMeshFace &face = nativeMesh->faces.at( i ) ;
      triangulate( face, i );
    }
  }
 
  // CALCULATE CENTROIDS
  mNativeMeshFaceCentroids.resize( nativeMesh->faces.size() );
  for ( int i = 0; i < nativeMesh->faces.size(); ++i )
  {
    const QgsMeshFace &face = nativeMesh->faces.at( i ) ;
    mNativeMeshFaceCentroids[i] = calculateCentroid( face );
  }
 
  // CALCULATE SPATIAL INDEX
  mSpatialFaceIndex = QgsMeshSpatialIndex( mTriangularMesh, nullptr, QgsMesh::ElementType::Face );
 
  if ( needUpdateFrame )
  {
    // SET ALL TRIANGLE CCW AND COMPUTE AVERAGE SIZE
    finalizeTriangles();
  }
 
  // CREATE EDGES
  // remove all edges with invalid vertices
  if ( needUpdateFrame )
  {
    const QVector<QgsMeshEdge> edges = nativeMesh->edges;
    for ( int nativeIndex = 0; nativeIndex < edges.size(); ++nativeIndex )
    {
      const QgsMeshEdge &edge = edges.at( nativeIndex );
      if ( !( std::isnan( mTriangularMesh.vertex( edge.first ).x() )  ||
              std::isnan( mTriangularMesh.vertex( edge.second ).x() ) ) )
      {
        mTriangularMesh.edges.push_back( edge );
        mEdgesToNativeEdges.push_back( nativeIndex );
      }
    }
  }
 
  // CALCULATE CENTROIDS
  mNativeMeshEdgeCentroids.resize( nativeMesh->edgeCount() );
  for ( int i = 0; i < nativeMesh->edgeCount(); ++i )
  {
    const QgsMeshEdge &edge = nativeMesh->edges.at( i ) ;
    const QgsPoint &a = mTriangularMesh.vertices[edge.first];
    const QgsPoint &b = mTriangularMesh.vertices[edge.second];
    mNativeMeshEdgeCentroids[i] = QgsMeshVertex( ( a.x() + b.x() ) / 2.0, ( a.y() + b.y() ) / 2.0, ( a.z() + b.z() ) / 2.0 );
  }
 
  // CALCULATE SPATIAL INDEX
  mSpatialEdgeIndex = QgsMeshSpatialIndex( mTriangularMesh, nullptr, QgsMesh::ElementType::Edge );
 
  return true;
}
 
void QgsTriangularMesh::finalizeTriangles()
{
  mAverageTriangleSize = 0;
  for ( int i = 0; i < mTriangularMesh.faceCount(); ++i )
  {
    QgsMeshFace &face = mTriangularMesh.faces[i];
 
    const QgsMeshVertex &v0 = mTriangularMesh.vertex( face[0] );
    const QgsMeshVertex &v1 = mTriangularMesh.vertex( face[1] );
    const QgsMeshVertex &v2 = mTriangularMesh.vertex( face[2] );
 
    QgsRectangle bbox = QgsMeshLayerUtils::triangleBoundingBox( v0, v1, v2 );
 
    mAverageTriangleSize += std::fmax( bbox.width(), bbox.height() );
 
    QgsMeshUtils::setCounterClockwise( face, v0, v1, v2 );
  }
  mAverageTriangleSize /= mTriangularMesh.faceCount();
}
 
QgsMeshVertex QgsTriangularMesh::nativeToTriangularCoordinates( const QgsMeshVertex &vertex ) const
{
  return transformVertex( vertex, Qgis::TransformDirection::Forward );
}
 
QgsMeshVertex QgsTriangularMesh::triangularToNativeCoordinates( const QgsMeshVertex &vertex ) const
{
  return transformVertex( vertex, Qgis::TransformDirection::Reverse );
}
 
QgsRectangle QgsTriangularMesh::nativeExtent()
{
  QgsRectangle nativeExtent;
  if ( !mCoordinateTransform.isShortCircuited() )
  {
    try
    {
      QgsCoordinateTransform extentTransform = mCoordinateTransform;
      extentTransform.setBallparkTransformsAreAppropriate( true );
      nativeExtent = extentTransform.transformBoundingBox( extent(), Qgis::TransformDirection::Reverse );
    }
    catch ( QgsCsException &cse )
    {
      Q_UNUSED( cse )
      QgsDebugMsg( QStringLiteral( "Caught CRS exception %1" ).arg( cse.what() ) );
    }
  }
  else
    nativeExtent = extent();
 
  return nativeExtent;
}
 
QgsRectangle QgsTriangularMesh::extent() const
{
  if ( !mIsExtentValid )
  {
    mExtent.setMinimal();
    for ( int i = 0; i < mTriangularMesh.vertices.size(); ++i )
      if ( !mTriangularMesh.vertices.at( i ).isEmpty() )
        mExtent.include( mTriangularMesh.vertices.at( i ) );
 
    mIsExtentValid = true;
  }
  return mExtent;
}
 
int QgsTriangularMesh::levelOfDetail() const
{
  return mLod;
}
 
bool QgsTriangularMesh::contains( const QgsMesh::ElementType &type ) const
{
  switch ( type )
  {
    case QgsMesh::ElementType::Vertex:
      return mTriangularMesh.vertexCount() != 0;
    case QgsMesh::ElementType::Edge:
      return mTriangularMesh.edgeCount() != 0;
    case QgsMesh::ElementType::Face:
      return mTriangularMesh.faceCount() != 0;
  }
 
  return false;
}
 
void QgsTriangularMesh::addVertex( const QgsMeshVertex &vertex )
{
  QgsMeshVertex vertexInTriangularCoordinates = nativeToTriangularCoordinates( vertex );
  mTriangularMesh.vertices.append( vertexInTriangularCoordinates );
  if ( !vertexInTriangularCoordinates.isEmpty() )
    mExtent.include( vertexInTriangularCoordinates );
}
 
const QVector<QgsMeshVertex> &QgsTriangularMesh::vertices() const
{
  return mTriangularMesh.vertices;
}
 
const QVector<QgsMeshFace> &QgsTriangularMesh::triangles() const
{
  return mTriangularMesh.faces;
}
 
const QVector<QgsMeshEdge> &QgsTriangularMesh::edges() const
{
  return mTriangularMesh.edges;
}
 
const QVector<QgsMeshVertex> &QgsTriangularMesh::centroids() const
{
  return faceCentroids();
}
 
const QVector<QgsMeshVertex> &QgsTriangularMesh::faceCentroids() const
{
  return mNativeMeshFaceCentroids;
}
 
const QVector<QgsMeshVertex> &QgsTriangularMesh::edgeCentroids() const
{
  return mNativeMeshEdgeCentroids;
}
 
const QVector<int> &QgsTriangularMesh::trianglesToNativeFaces() const
{
  return mTrianglesToNativeFaces;
}
 
const QVector<int> &QgsTriangularMesh::edgesToNativeEdges() const
{
  return mEdgesToNativeEdges;
}
 
QgsPointXY QgsTriangularMesh::transformFromLayerToTrianglesCoordinates( const QgsPointXY &point ) const
{
  QgsPointXY mapPoint;
  if ( mCoordinateTransform.isValid() )
  {
    try
    {
      mapPoint = mCoordinateTransform.transform( point );
    }
    catch ( QgsCsException &cse )
    {
      Q_UNUSED( cse )
      QgsDebugMsg( QStringLiteral( "Caught CRS exception %1" ).arg( cse.what() ) );
      mapPoint = point;
    }
  }
  else
    mapPoint = point;
 
  return point;
}
 
int QgsTriangularMesh::faceIndexForPoint( const QgsPointXY &point ) const
{
  const QList<int> faceIndexes = mSpatialFaceIndex.intersects( QgsRectangle( point, point ) );
  for ( const int faceIndex : faceIndexes )
  {
    const QgsMeshFace &face = mTriangularMesh.faces.at( faceIndex );
    const QgsGeometry geom = QgsMeshUtils::toGeometry( face, mTriangularMesh.vertices );
    if ( geom.contains( &point ) )
      return faceIndex;
  }
  return -1;
}
 
int QgsTriangularMesh::nativeFaceIndexForPoint( const QgsPointXY &point ) const
{
  int triangleIndex = faceIndexForPoint_v2( point );
  if ( triangleIndex == -1 )
    return -1;
 
  if ( triangleIndex < mTrianglesToNativeFaces.count() )
    return mTrianglesToNativeFaces.at( triangleIndex );
 
  return -1;
}
 
QList<int> QgsTriangularMesh::nativeFaceIndexForRectangle( const QgsRectangle &rectangle ) const
{
  QSet<int> concernedFaceIndex = QgsMeshUtils::nativeFacesFromTriangles(
                                   faceIndexesForRectangle( rectangle ),
                                   trianglesToNativeFaces() );
  return concernedFaceIndex.values();
}
 
int QgsTriangularMesh::faceIndexForPoint_v2( const QgsPointXY &point ) const
{
  const QList<int> faceIndexes = mSpatialFaceIndex.intersects( QgsRectangle( point, point ) );
 
  for ( const int faceIndex : faceIndexes )
  {
    const QgsMeshFace &face = mTriangularMesh.faces.at( faceIndex );
    if ( QgsMeshUtils::isInTriangleFace( point, face, mTriangularMesh.vertices ) )
      return faceIndex;
  }
  return -1;
}
 
QList<int> QgsTriangularMesh::faceIndexesForRectangle( const QgsRectangle &rectangle ) const
{
  return mSpatialFaceIndex.intersects( rectangle );
}
 
QList<int> QgsTriangularMesh::edgeIndexesForRectangle( const QgsRectangle &rectangle ) const
{
  return mSpatialEdgeIndex.intersects( rectangle );
}
 
QVector<QVector3D> QgsTriangularMesh::vertexNormals( float vertScale ) const
{
  QVector<QVector3D> normales( vertices().count(), QVector3D( 0, 0, 0 ) );
 
  for ( const auto &face : triangles() )
  {
    if ( face.isEmpty() )
      continue;
 
    for ( int i = 0; i < 3; i++ )
    {
      int index1( face.at( i ) );
      int index2( face.at( ( i + 1 ) % 3 ) );
      int index3( face.at( ( i + 2 ) % 3 ) );
 
      const QgsMeshVertex &vert( vertices().at( index1 ) );
      const QgsMeshVertex &otherVert1( vertices().at( index2 ) );
      const QgsMeshVertex &otherVert2( vertices().at( index3 ) );
 
      QVector3D v1( float( otherVert1.x() - vert.x() ), float( otherVert1.y() - vert.y() ), vertScale * float( otherVert1.z() - vert.z() ) );
      QVector3D v2( float( otherVert2.x() - vert.x() ), float( otherVert2.y() - vert.y() ), vertScale * float( otherVert2.z() - vert.z() ) );
 
      normales[index1] += QVector3D::crossProduct( v1, v2 );
    }
  }
  return normales;
}
 
QVector<QgsTriangularMesh *> QgsTriangularMesh::simplifyMesh( double reductionFactor, int minimumTrianglesCount ) const
{
  QVector<QgsTriangularMesh *> simplifiedMeshes;
 
  if ( mTriangularMesh.edgeCount() != 0 )
    return simplifiedMeshes;
 
  if ( !( reductionFactor > 1 ) )
    return simplifiedMeshes;
 
  size_t verticesCount = size_t( mTriangularMesh.vertices.count() );
 
  unsigned int baseIndexCount = mTriangularMesh.faceCount() * 3;
 
  QVector<unsigned int> indexes( mTriangularMesh.faces.count() * 3 );
  for ( int i = 0; i < mTriangularMesh.faceCount(); ++i )
  {
    const QgsMeshFace &f = mTriangularMesh.face( i );
    for ( int j = 0; j < 3; ++j )
      indexes[i * 3 + j] = f.at( j );
  }
 
  QVector<float> vertices( mTriangularMesh.vertices.count() * 3 );
  for ( int i = 0; i < mTriangularMesh.vertices.count(); ++i )
  {
    const QgsMeshVertex &v = mTriangularMesh.vertex( i );
    vertices[i * 3] = v.x() ;
    vertices[i * 3 + 1] = v.y() ;
    vertices[i * 3 + 2] = v.z() ;
  }
 
  int path = 0;
  while ( true )
  {
    QgsTriangularMesh *simplifiedMesh = new QgsTriangularMesh( *this );
    size_t maxNumberOfIndexes = baseIndexCount / pow( reductionFactor, path + 1 );
 
    if ( indexes.size() <= int( maxNumberOfIndexes ) )
    {
      delete simplifiedMesh;
      break;
    }
 
    QVector<unsigned int> returnIndexes( indexes.size() );
    //returned size could be different than goal size but not than the input indexes count
    size_t size = meshopt_simplifySloppy(
                    returnIndexes.data(),
                    indexes.data(),
                    indexes.size(),
                    vertices.data(),
                    verticesCount,
                    sizeof( float ) * 3,
                    maxNumberOfIndexes );
 
 
    returnIndexes.resize( size );
 
    if ( size == 0 || int( size ) >= indexes.size() )
    {
      QgsDebugMsg( QStringLiteral( "Mesh simplification failed after %1 path" ).arg( path + 1 ) );
      delete simplifiedMesh;
      break;
    }
 
    QgsMesh newMesh;
    newMesh.vertices = mTriangularMesh.vertices;
 
    newMesh.faces.resize( returnIndexes.size() / 3 );
    for ( int i = 0; i < newMesh.faces.size(); ++i )
    {
      QgsMeshFace f( 3 );
      for ( size_t j = 0; j < 3 ; ++j )
        f[j] = returnIndexes.at( i * 3 + j ) ;
      newMesh.faces[i ] = f;
    }
 
    simplifiedMesh->mTriangularMesh = newMesh;
    simplifiedMesh->mSpatialFaceIndex = QgsMeshSpatialIndex( simplifiedMesh->mTriangularMesh );
    simplifiedMesh->finalizeTriangles();
    simplifiedMeshes.push_back( simplifiedMesh );
 
    QgsDebugMsgLevel( QStringLiteral( "Simplified mesh created with %1 triangles" ).arg( newMesh.faceCount() ), 2 );
 
    simplifiedMesh->mTrianglesToNativeFaces = QVector<int>( simplifiedMesh->triangles().count(), 0 );
    for ( int i = 0; i < simplifiedMesh->mTrianglesToNativeFaces.count(); ++i )
    {
      QgsMeshFace triangle = simplifiedMesh->triangles().at( i );
      double x = 0;
      double y = 0;
      for ( size_t j = 0; j < 3 ; ++j )
      {
        x += mTriangularMesh.vertex( triangle[j] ).x();
        y += mTriangularMesh.vertex( triangle[j] ).y();
      }
      x /= 3;
      y /= 3;
      QgsPoint centroid( x, y );
      int indexInBaseMesh = faceIndexForPoint_v2( centroid );
 
      if ( indexInBaseMesh == -1 )
      {
        // sometime the centroid of simplified mesh could be outside the base mesh,
        // so try with vertices of the simplified triangle
        int j = 0;
        while ( indexInBaseMesh == -1 && j < 3 )
          indexInBaseMesh = faceIndexForPoint_v2( mTriangularMesh.vertex( triangle[j++] ) );
      }
 
      if ( indexInBaseMesh > -1 && indexInBaseMesh < mTrianglesToNativeFaces.count() )
        simplifiedMesh->mTrianglesToNativeFaces[i] = mTrianglesToNativeFaces[indexInBaseMesh];
    }
 
    simplifiedMesh->mLod = path + 1;
    simplifiedMesh->mBaseTriangularMesh = this;
 
    if ( simplifiedMesh->triangles().count() <  minimumTrianglesCount )
      break;
 
    indexes = returnIndexes;
    ++path;
  }
 
  return simplifiedMeshes;
}
 
std::unique_ptr< QgsPolygon > QgsMeshUtils::toPolygon( const QgsMeshFace &face, const QVector<QgsMeshVertex> &vertices )
{
  QVector<QgsPoint> ring;
  for ( int j = 0; j < face.size(); ++j )
  {
    int vertexId = face[j];
    Q_ASSERT( vertexId < vertices.size() );
    const QgsPoint &vertex = vertices[vertexId];
    ring.append( vertex );
  }
  std::unique_ptr< QgsPolygon > polygon = std::make_unique< QgsPolygon >();
  polygon->setExteriorRing( new QgsLineString( ring ) );
  return polygon;
}
 
QgsGeometry QgsMeshUtils::toGeometry( const QgsMeshFace &face, const QVector<QgsMeshVertex> &vertices )
{
  return QgsGeometry( QgsMeshUtils::toPolygon( face, vertices ) );
}
 
static QSet<int> _nativeElementsFromElements( const QList<int> &indexes, const QVector<int> &elementToNativeElements )
{
  QSet<int> nativeElements;
  for ( const int index : indexes )
  {
    if ( index < elementToNativeElements.count() )
    {
      const int nativeIndex = elementToNativeElements[index];
      nativeElements.insert( nativeIndex );
    }
  }
  return nativeElements;
}
 
QSet<int> QgsMeshUtils::nativeFacesFromTriangles( const QList<int> &triangleIndexes, const QVector<int> &trianglesToNativeFaces )
{
  return _nativeElementsFromElements( triangleIndexes, trianglesToNativeFaces );
}
 
QSet<int> QgsMeshUtils::nativeEdgesFromEdges( const QList<int> &edgesIndexes, const QVector<int> &edgesToNativeEdges )
{
  return _nativeElementsFromElements( edgesIndexes, edgesToNativeEdges );
}
 
 
static double _isLeft2D( const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &p )
{
  return ( p2.x() - p1.x() ) * ( p.y() - p1.y() ) - ( p.x() - p1.x() ) * ( p2.y() - p1.y() );
}
 
static bool _isInTriangle2D( const QgsPoint &p, const QVector<QgsMeshVertex> &triangle )
{
  return ( ( _isLeft2D( triangle[2], triangle[0], p ) * _isLeft2D( triangle[2], triangle[0], triangle[1] ) >= 0 )
           && ( _isLeft2D( triangle[0], triangle[1], p ) * _isLeft2D( triangle[0], triangle[1], triangle[2] ) >= 0 )
           && ( _isLeft2D( triangle[2], triangle[1], p ) * _isLeft2D( triangle[2], triangle[1], triangle[0] ) >= 0 ) );
}
 
bool QgsMeshUtils::isInTriangleFace( const QgsPointXY point, const QgsMeshFace &face, const QVector<QgsMeshVertex> &vertices )
{
  if ( face.count() != 3 )
    return false;
 
  QVector<QgsMeshVertex> triangle( 3 );
  for ( int i = 0; i < 3; ++i )
  {
    if ( face[i] > vertices.count() )
      return false;
    triangle[i] = vertices[face[i]];
  }
 
  const QgsPoint p( point.x(), point.y() );
 
  return _isInTriangle2D( p, triangle );
}
 
QSet<int> QgsMeshUtils::nativeVerticesFromTriangles( const QList<int> &triangleIndexes, const QVector<QgsMeshFace> &triangles )
{
  QSet<int> uniqueVertices;
  for ( int triangleIndex : triangleIndexes )
  {
    const QgsMeshFace triangle = triangles[triangleIndex];
    for ( int i : triangle )
    {
      uniqueVertices.insert( i );
    }
  }
  return uniqueVertices;
}
 
QSet<int> QgsMeshUtils::nativeVerticesFromEdges( const QList<int> &edgesIndexes, const QVector<QgsMeshEdge> &edges )
{
  QSet<int> uniqueVertices;
  for ( int edgeIndex : edgesIndexes )
  {
    const QgsMeshEdge edge = edges[edgeIndex];
    uniqueVertices.insert( edge.first );
    uniqueVertices.insert( edge.second );
  }
  return uniqueVertices;
}
 
void QgsTriangularMesh::applyChanges( const QgsTriangularMesh::Changes &changes )
{
  //if necessary defined removes triangles index
  if ( changes.mRemovedTriangleIndexes.isEmpty() && !changes.mNativeFaceIndexesToRemove.isEmpty() )
  {
    for ( int nf = 0; nf < changes.mNativeFaceIndexesToRemove.count(); ++nf )
    {
      int nativeIndex = changes.mNativeFaceIndexesToRemove.at( nf );
      const QgsMeshFace &nativeFace = changes.mNativeFacesToRemove.at( nf );
      Q_ASSERT( !nativeFace.isEmpty() );
 
      QgsRectangle nativeFaceExtent( mTriangularMesh.vertex( nativeFace.at( 0 ) ), mTriangularMesh.vertex( nativeFace.at( 0 ) ) );
      for ( int i = 1; i < nativeFace.count(); ++i )
      {
        const QgsMeshVertex &triangularVertex = mTriangularMesh.vertex( nativeFace.at( i ) );
        nativeFaceExtent.include( triangularVertex );
      }
 
      QList<int> concernedTriangle = faceIndexesForRectangle( nativeFaceExtent );
      //Remove only those corresponding to the native face
      for ( int i = 0; i < concernedTriangle.count(); ++i )
      {
        int triangleIndex = concernedTriangle.at( i );
        if ( mTrianglesToNativeFaces.at( triangleIndex ) == nativeIndex )
          changes.mRemovedTriangleIndexes.append( triangleIndex );
      }
    }
  }
 
  if ( changes.mOldZValue.isEmpty() && !changes.mNewZValue.isEmpty() )
  {
    changes.mOldZValue.reserve( changes.mNewZValue.count() );
    for ( int i = 0; i < changes.mNewZValue.count(); ++i )
      changes.mOldZValue.append( mTriangularMesh.vertices.at( changes.mChangedVerticesCoordinates.at( i ) ).z() );
  }
 
  if ( changes.mTriangleIndexesGeometryChanged.isEmpty() && !changes.mNativeFaceIndexesGeometryChanged.isEmpty() )
  {
    for ( int i = 0; i < changes.mNativeFaceIndexesGeometryChanged.count(); ++i )
    {
      const QgsMeshFace &nativeFace = changes.mNativeFacesGeometryChanged.at( i );
      if ( nativeFace.count() < 2 )
        continue;
      QgsRectangle bbox( mTriangularMesh.vertices.at( nativeFace.at( 0 ) ), mTriangularMesh.vertices.at( nativeFace.at( 1 ) ) );
 
      for ( int i = 2; i < nativeFace.count(); ++i )
        bbox.include( mTriangularMesh.vertices.at( nativeFace.at( i ) ) );
 
      QList<int> triangleIndexes = faceIndexesForRectangle( bbox );
      int pos = 0;
      while ( pos < triangleIndexes.count() )
      {
        if ( trianglesToNativeFaces().at( triangleIndexes.at( pos ) ) !=
             changes.mNativeFaceIndexesGeometryChanged.at( i ) )
          triangleIndexes.removeAt( pos );
        else
          ++pos;
      }
      changes.mTriangleIndexesGeometryChanged.append( triangleIndexes );
    }
  }
 
  // add vertices
  for ( const QgsMeshVertex &vertex : std::as_const( changes.mAddedVertices ) )
    addVertex( vertex );
 
  // add faces
  if ( !changes.mNativeFacesToAdd.isEmpty() )
  {
    changes.mTrianglesAddedStartIndex = mTriangularMesh.faceCount();
    int firstNewNativeFacesIndex = mNativeMeshFaceCentroids.count();
    for ( int i = 0; i < changes.mNativeFacesToAdd.count(); ++i )
    {
      const QgsMeshFace &nativeFace = changes.mNativeFacesToAdd.at( i );
      triangulate( nativeFace, firstNewNativeFacesIndex + i );
      mNativeMeshFaceCentroids.append( calculateCentroid( nativeFace ) );
    }
 
    for ( int i = changes.mTrianglesAddedStartIndex; i < mTriangularMesh.faceCount(); ++i )
      mSpatialFaceIndex.addFace( i, mTriangularMesh );
  }
 
  // remove faces
  for ( int i = 0; i < changes.mRemovedTriangleIndexes.count(); ++i )
  {
    int triangleIndex = changes.mRemovedTriangleIndexes.at( i );
    mTrianglesToNativeFaces[triangleIndex] = -1;
    mSpatialFaceIndex.removeFace( triangleIndex, mTriangularMesh );
    mTriangularMesh.faces[triangleIndex] = QgsMeshFace();
  }
 
  for ( int i = 0; i < changes.mNativeFaceIndexesToRemove.count(); ++i )
    mNativeMeshFaceCentroids[changes.mNativeFaceIndexesToRemove.at( i )] = QgsMeshVertex();
 
  // remove vertices
  for ( int i = 0; i < changes.mVerticesIndexesToRemove.count(); ++i )
    mTriangularMesh.vertices[changes.mVerticesIndexesToRemove.at( i )] = QgsMeshVertex();
 
  if ( !changes.mVerticesIndexesToRemove.isEmpty() )
    mIsExtentValid = false;
 
  // change Z value
  for ( int i = 0; i < changes.mNewZValue.count(); ++i )
  {
    int vertexIndex = changes.mChangedVerticesCoordinates.at( i );
    mTriangularMesh.vertices[vertexIndex].setZ( changes.mNewZValue.at( i ) );
  }
 
  //remove outdated spatial index
  for ( const int triangleIndex : std::as_const( changes.mTriangleIndexesGeometryChanged ) )
    mSpatialFaceIndex.removeFace( triangleIndex, mTriangularMesh );
 
  // change (X,Y) of vertices
  for ( int i = 0; i < changes.mNewXYValue.count(); ++i )
  {
    const QgsPointXY &nativeCoordinates = changes.mNewXYValue.at( i );
    const QgsMeshVertex nativeVertex( nativeCoordinates.x(),
                                      nativeCoordinates.y(),
                                      mTriangularMesh.vertices.at( changes.mChangedVerticesCoordinates.at( i ) ).z() );
 
    mTriangularMesh.vertices[changes.mChangedVerticesCoordinates.at( i )] = nativeToTriangularCoordinates( nativeVertex );
  }
 
  //restore spatial undex
  for ( const int triangleIndex : std::as_const( changes.mTriangleIndexesGeometryChanged ) )
    mSpatialFaceIndex.addFace( triangleIndex, mTriangularMesh );
 
  //update  native faces
  for ( int i = 0; i < changes.mNativeFaceIndexesGeometryChanged.count(); ++i )
    mNativeMeshFaceCentroids[changes.mNativeFaceIndexesGeometryChanged.at( i )] = calculateCentroid( changes.mNativeFacesGeometryChanged.at( i ) );
}
 
void QgsTriangularMesh::reverseChanges( const QgsTriangularMesh::Changes &changes, const QgsMesh &nativeMesh )
{
  //reverse added faces and added vertices
  if ( !changes.mNativeFacesToAdd.isEmpty() )
  {
    for ( int i = changes.mTrianglesAddedStartIndex; i < mTriangularMesh.faceCount(); ++i )
      mSpatialFaceIndex.removeFace( i, mTriangularMesh );
 
    int initialNativeFacesCount = mNativeMeshFaceCentroids.count() - changes.mNativeFacesToAdd.count();
 
    mTriangularMesh.faces.resize( changes.mTrianglesAddedStartIndex );
    mTrianglesToNativeFaces.resize( changes.mTrianglesAddedStartIndex );
    mNativeMeshFaceCentroids.resize( initialNativeFacesCount );
  }
 
  int initialVerticesCount = mTriangularMesh.vertices.count() - changes.mAddedVertices.count();
  mTriangularMesh.vertices.resize( initialVerticesCount );
 
  if ( !changes.mAddedVertices.isEmpty() )
    mIsExtentValid = false;
 
  // for each vertex to remove we need to update the vertices with the native vertex
  for ( const int i : std::as_const( changes.mVerticesIndexesToRemove ) )
    mTriangularMesh.vertices[i] = nativeToTriangularCoordinates( nativeMesh.vertex( i ) );
 
  if ( !changes.mVerticesIndexesToRemove.isEmpty() )
    mIsExtentValid = false;
 
  // reverse removed faces
  QVector<QgsMeshFace> restoredTriangles;
  QVector<int> restoredTriangularToNative;
  for ( int i = 0; i < changes.mNativeFacesToRemove.count(); ++i )
  {
    const QgsMeshFace &nativeFace = changes.mNativeFacesToRemove.at( i );
    triangulateFaces( nativeFace,
                      changes.mNativeFaceIndexesToRemove.at( i ),
                      restoredTriangles,
                      restoredTriangularToNative,
                      mTriangularMesh );
    mNativeMeshFaceCentroids[changes.mNativeFaceIndexesToRemove.at( i )] = calculateCentroid( nativeFace );
  }
  for ( int i = 0; i < changes.mRemovedTriangleIndexes.count(); ++i )
  {
    int triangleIndex = changes.mRemovedTriangleIndexes.at( i );
    mTriangularMesh.faces[triangleIndex] = restoredTriangles.at( i );
    mSpatialFaceIndex.addFace( triangleIndex, mTriangularMesh );
    mTrianglesToNativeFaces[triangleIndex] = restoredTriangularToNative.at( i );
  }
 
  // reverse Z value
  for ( int i = 0; i < changes.mOldZValue.count(); ++i )
  {
    int vertexIndex = changes.mChangedVerticesCoordinates.at( i );
    mTriangularMesh.vertices[vertexIndex].setZ( changes.mOldZValue.at( i ) );
  }
 
  //remove outdated spatial index
  for ( const int triangleIndex : std::as_const( changes.mTriangleIndexesGeometryChanged ) )
    mSpatialFaceIndex.removeFace( triangleIndex, mTriangularMesh );
 
  // reverse (X,Y) of vertices
  for ( int i = 0; i < changes.mOldXYValue.count(); ++i )
  {
    const QgsPointXY &nativeCoordinates = changes.mOldXYValue.at( i );
    const QgsMeshVertex nativeVertex( nativeCoordinates.x(),
                                      nativeCoordinates.y(),
                                      mTriangularMesh.vertices.at( changes.mChangedVerticesCoordinates.at( i ) ).z() );
 
    mTriangularMesh.vertices[changes.mChangedVerticesCoordinates.at( i )] = nativeToTriangularCoordinates( nativeVertex );
  }
 
  //restore spatial undex
  for ( const int triangleIndex : std::as_const( changes.mTriangleIndexesGeometryChanged ) )
    mSpatialFaceIndex.addFace( triangleIndex, mTriangularMesh );
 
  //update  native faces
  for ( int i = 0; i < changes.mNativeFaceIndexesGeometryChanged.count(); ++i )
    mNativeMeshFaceCentroids[changes.mNativeFaceIndexesGeometryChanged.at( i )] = calculateCentroid( changes.mNativeFacesGeometryChanged.at( i ) );
}
 
QgsTriangularMesh::Changes::Changes( const QgsTopologicalMesh::Changes &topologicalChanges,
                                     const QgsMesh &nativeMesh )
{
  mAddedVertices = topologicalChanges.addedVertices();
  mVerticesIndexesToRemove = topologicalChanges.verticesToRemoveIndexes();
  mNativeFacesToAdd = topologicalChanges.addedFaces();
  mNativeFacesToRemove = topologicalChanges.removedFaces();
  mNativeFaceIndexesToRemove = topologicalChanges.removedFaceIndexes();
  mChangedVerticesCoordinates = topologicalChanges.changedCoordinatesVerticesIndexes();
  mNewZValue = topologicalChanges.newVerticesZValues();
  mNewXYValue = topologicalChanges.newVerticesXYValues();
  mOldXYValue = topologicalChanges.oldVerticesXYValues();
 
  mNativeFaceIndexesGeometryChanged = topologicalChanges.nativeFacesIndexesGeometryChanged();
  mNativeFacesGeometryChanged.resize( mNativeFaceIndexesGeometryChanged.count() );
  for ( int i = 0; i < mNativeFaceIndexesGeometryChanged.count(); ++i )
    mNativeFacesGeometryChanged[i] = nativeMesh.face( mNativeFaceIndexesGeometryChanged.at( i ) );
}
 
QgsMeshVertex QgsMeshUtils::centroid( const QgsMeshFace &face, const QVector<QgsMeshVertex> &vertices )
{
  QVector<QPointF> points( face.size() );
  for ( int j = 0; j < face.size(); ++j )
  {
    int index = face.at( j );
    const QgsMeshVertex &vertex = vertices.at( index ); // we need vertices in map coordinate
    points[j] = vertex.toQPointF();
  }
  QPolygonF poly( points );
  double cx, cy;
  ENP_centroid( poly, cx, cy );
  return QgsMeshVertex( cx, cy );
}
 
void QgsMeshUtils::setCounterClockwise( QgsMeshFace &triangle, const QgsMeshVertex &v0, const QgsMeshVertex &v1, const QgsMeshVertex &v2 )
{
  //To have consistent clock wise orientation of triangles which is necessary for 3D rendering
  //Check the clock wise, and if it is not counter clock wise, swap indexes to make the oientation counter clock wise
  double ux = v1.x() - v0.x();
  double uy = v1.y() - v0.y();
  double vx = v2.x() - v0.x();
  double vy = v2.y() - v0.y();
 
  double crossProduct = ux * vy - uy * vx;
  if ( crossProduct < 0 ) //CW -->change the orientation
  {
    std::swap( triangle[1], triangle[2] );
  }
}