qgsgeometryutils.cpp

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/***************************************************************************
                      qgsgeometryutils.cpp
-------------------------------------------------------------------
Date                 : 21 Nov 2014
Copyright            : (C) 2014 by Marco Hugentobler
email                : marco.hugentobler at sourcepole 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 "qgsgeometryutils.h"
 
#include <limits>
#include <memory>
#include <nlohmann/json.hpp>
 
#include "qgsabstractgeometry.h"
#include "qgscircularstring.h"
#include "qgscompoundcurve.h"
#include "qgscurve.h"
#include "qgscurvepolygon.h"
#include "qgsgeometrycollection.h"
#include "qgslinestring.h"
#include "qgslogger.h"
#include "qgspoint.h"
#include "qgsvertexid.h"
#include "qgswkbptr.h"
 
#include <QRegularExpression>
#include <QString>
#include <QStringList>
#include <QVector>
 
using namespace Qt::StringLiterals;
 
QVector<QgsLineString *> QgsGeometryUtils::extractLineStrings( const QgsAbstractGeometry *geom )
{
  QVector< QgsLineString * > linestrings;
  if ( !geom )
    return linestrings;
 
  QVector< const QgsAbstractGeometry * > geometries;
  geometries << geom;
  while ( ! geometries.isEmpty() )
  {
    const QgsAbstractGeometry *g = geometries.takeFirst();
    if ( const QgsCurve *curve = qgsgeometry_cast< const QgsCurve * >( g ) )
    {
      linestrings << static_cast< QgsLineString * >( curve->segmentize() );
    }
    else if ( const QgsGeometryCollection *collection = qgsgeometry_cast< const QgsGeometryCollection * >( g ) )
    {
      for ( int i = 0; i < collection->numGeometries(); ++i )
      {
        geometries.append( collection->geometryN( i ) );
      }
    }
    else if ( const QgsCurvePolygon *curvePolygon = qgsgeometry_cast< const QgsCurvePolygon * >( g ) )
    {
      if ( curvePolygon->exteriorRing() )
        linestrings << static_cast< QgsLineString * >( curvePolygon->exteriorRing()->segmentize() );
 
      for ( int i = 0; i < curvePolygon->numInteriorRings(); ++i )
      {
        linestrings << static_cast< QgsLineString * >( curvePolygon->interiorRing( i )->segmentize() );
      }
    }
  }
  return linestrings;
}
 
QgsPoint QgsGeometryUtils::closestVertex( const QgsAbstractGeometry &geom, const QgsPoint &pt, QgsVertexId &id )
{
  double minDist = std::numeric_limits<double>::max();
  double currentDist = 0;
  QgsPoint minDistPoint;
  id = QgsVertexId(); // set as invalid
 
  if ( geom.isEmpty() || pt.isEmpty() )
    return minDistPoint;
 
  QgsVertexId vertexId;
  QgsPoint vertex;
  while ( geom.nextVertex( vertexId, vertex ) )
  {
    currentDist = QgsGeometryUtils::sqrDistance2D( pt, vertex );
    // The <= is on purpose: for geometries with closing vertices, this ensures
    // that the closing vertex is returned. For the vertex tool, the rubberband
    // of the closing vertex is above the opening vertex, hence with the <=
    // situations where the covered opening vertex rubberband is selected are
    // avoided.
    if ( currentDist <= minDist )
    {
      minDist = currentDist;
      minDistPoint = vertex;
      id.part = vertexId.part;
      id.ring = vertexId.ring;
      id.vertex = vertexId.vertex;
      id.type = vertexId.type;
    }
  }
 
  return minDistPoint;
}
 
QgsPoint QgsGeometryUtils::closestPoint( const QgsAbstractGeometry &geometry, const QgsPoint &point )
{
  QgsPoint closestPoint;
  QgsVertexId vertexAfter;
  geometry.closestSegment( point, closestPoint, vertexAfter, nullptr, Qgis::DEFAULT_SEGMENT_EPSILON );
  if ( vertexAfter.isValid() )
  {
    const QgsPoint pointAfter = geometry.vertexAt( vertexAfter );
    if ( vertexAfter.vertex > 0 )
    {
      QgsVertexId vertexBefore = vertexAfter;
      vertexBefore.vertex--;
      const QgsPoint pointBefore = geometry.vertexAt( vertexBefore );
      const double length = pointBefore.distance( pointAfter );
      const double distance = pointBefore.distance( closestPoint );
 
      if ( qgsDoubleNear( distance, 0.0 ) )
        closestPoint = pointBefore;
      else if ( qgsDoubleNear( distance, length ) )
        closestPoint = pointAfter;
      else
      {
        if ( QgsWkbTypes::hasZ( geometry.wkbType() ) && length )
          closestPoint.addZValue( pointBefore.z() + ( pointAfter.z() - pointBefore.z() ) * distance / length );
        if ( QgsWkbTypes::hasM( geometry.wkbType() ) )
          closestPoint.addMValue( pointBefore.m() + ( pointAfter.m() - pointBefore.m() ) * distance / length );
      }
    }
  }
 
  return closestPoint;
}
 
double QgsGeometryUtils::distanceToVertex( const QgsAbstractGeometry &geom, QgsVertexId id )
{
  double currentDist = 0;
  QgsVertexId vertexId;
  QgsPoint vertex;
  while ( geom.nextVertex( vertexId, vertex ) )
  {
    if ( vertexId == id )
    {
      //found target vertex
      return currentDist;
    }
    currentDist += geom.segmentLength( vertexId );
  }
 
  //could not find target vertex
  return -1;
}
 
bool QgsGeometryUtils::verticesAtDistance( const QgsAbstractGeometry &geometry, double distance, QgsVertexId &previousVertex, QgsVertexId &nextVertex )
{
  double currentDist = 0;
  previousVertex = QgsVertexId();
  nextVertex = QgsVertexId();
 
  if ( geometry.isEmpty() )
  {
    return false;
  }
 
  QgsPoint point;
  QgsPoint previousPoint;
 
  if ( qgsDoubleNear( distance, 0.0 ) )
  {
    geometry.nextVertex( previousVertex, point );
    nextVertex = previousVertex;
    return true;
  }
 
  bool first = true;
  while ( currentDist < distance && geometry.nextVertex( nextVertex, point ) )
  {
    if ( !first && nextVertex.part == previousVertex.part && nextVertex.ring == previousVertex.ring )
    {
      currentDist += std::sqrt( QgsGeometryUtils::sqrDistance2D( previousPoint, point ) );
    }
 
    if ( qgsDoubleNear( currentDist, distance ) )
    {
      // exact hit!
      previousVertex = nextVertex;
      return true;
    }
 
    if ( currentDist > distance )
    {
      return true;
    }
 
    previousVertex = nextVertex;
    previousPoint = point;
    first = false;
  }
 
  //could not find target distance
  return false;
}
 
double QgsGeometryUtils::distToInfiniteLine( const QgsPoint &point, const QgsPoint &linePoint1, const QgsPoint &linePoint2, double epsilon )
{
  const double area = std::abs(
                        ( linePoint1.x() - linePoint2.x() ) * ( point.y() - linePoint2.y() ) -
                        ( linePoint1.y() - linePoint2.y() ) * ( point.x() - linePoint2.x() )
                      );
 
  const double length = std::sqrt(
                          std::pow( linePoint1.x() - linePoint2.x(), 2 ) +
                          std::pow( linePoint1.y() - linePoint2.y(), 2 )
                        );
 
  const double distance = area / length;
  return qgsDoubleNear( distance, 0.0, epsilon ) ? 0.0 : distance;
}
 
bool QgsGeometryUtils::lineCircleIntersection( const QgsPointXY &center, const double radius,
    const QgsPointXY &linePoint1, const QgsPointXY &linePoint2,
    QgsPointXY &intersection )
{
  // formula taken from http://mathworld.wolfram.com/Circle-LineIntersection.html
 
  const double x1 = linePoint1.x() - center.x();
  const double y1 = linePoint1.y() - center.y();
  const double x2 = linePoint2.x() - center.x();
  const double y2 = linePoint2.y() - center.y();
  const double dx = x2 - x1;
  const double dy = y2 - y1;
 
  const double dr2 = std::pow( dx, 2 ) + std::pow( dy, 2 );
  const double d = x1 * y2 - x2 * y1;
 
  const double disc = std::pow( radius, 2 ) * dr2 - std::pow( d, 2 );
 
  if ( disc < 0 )
  {
    //no intersection or tangent
    return false;
  }
  else
  {
    // two solutions
    const int sgnDy = dy < 0 ? -1 : 1;
 
    const double sqrDisc = std::sqrt( disc );
 
    const double ax = center.x() + ( d * dy + sgnDy * dx * sqrDisc ) / dr2;
    const double ay = center.y() + ( -d * dx + std::fabs( dy ) * sqrDisc ) / dr2;
    const QgsPointXY p1( ax, ay );
 
    const double bx = center.x() + ( d * dy - sgnDy * dx * sqrDisc ) / dr2;
    const double by = center.y() + ( -d * dx - std::fabs( dy ) * sqrDisc ) / dr2;
    const QgsPointXY p2( bx, by );
 
    // snap to nearest intersection
 
    if ( intersection.sqrDist( p1 ) < intersection.sqrDist( p2 ) )
    {
      intersection.set( p1.x(), p1.y() );
    }
    else
    {
      intersection.set( p2.x(), p2.y() );
    }
    return true;
  }
}
 
// based on public domain work by 3/26/2005 Tim Voght
// see http://paulbourke.net/geometry/circlesphere/tvoght.c
int QgsGeometryUtils::circleCircleIntersections( const QgsPointXY &center1, const double r1, const QgsPointXY &center2, const double r2, QgsPointXY &intersection1, QgsPointXY &intersection2 )
{
  // determine the straight-line distance between the centers
  const double d = center1.distance( center2 );
 
  // check if the circles intersect at only 1 point, either "externally" or "internally"
  const bool singleSolutionExt = qgsDoubleNear( d, r1 + r2 );
  const bool singleSolutionInt = qgsDoubleNear( d, std::fabs( r1 - r2 ) );
 
  // check for solvability
  if ( !singleSolutionExt && d > ( r1 + r2 ) )
  {
    // no solution. circles do not intersect.
    return 0;
  }
  else if ( !singleSolutionInt && d < std::fabs( r1 - r2 ) )
  {
    // no solution. one circle is contained in the other
    return 0;
  }
  else if ( qgsDoubleNear( d, 0 ) && ( qgsDoubleNear( r1, r2 ) ) )
  {
    // no solutions, the circles coincide
    return 0;
  }
 
  /* 'point 2' is the point where the line through the circle
   * intersection points crosses the line between the circle
   * centers.
  */
 
  /* Determine the distance 'a' from point 0 to point 2.
   * In the general case, a = ( ( r1 * r1 ) - ( r2 * r2 ) + ( d * d ) ) / ( 2.0 * d ).
   * If d = r1 + r2 or d = r1 - r2 (i.e. r1 > r2), then a = r1; if d = r2 - r1 (i.e. r2 > r1), then a = -r1.
  */
  const double a = singleSolutionExt ? r1 : ( singleSolutionInt ? ( r1 > r2 ? r1 : -r1 ) : ( ( r1 * r1 ) - ( r2 * r2 ) + ( d * d ) ) / ( 2.0 * d ) );
 
  /* dx and dy are the vertical and horizontal distances between
   * the circle centers.
   */
  const double dx = center2.x() - center1.x();
  const double dy = center2.y() - center1.y();
 
  // Determine the coordinates of point 2.
  const double x2 = center1.x() + ( dx * a / d );
  const double y2 = center1.y() + ( dy * a / d );
 
  // only 1 solution
  if ( singleSolutionExt || singleSolutionInt )
  {
    intersection1 = QgsPointXY( x2, y2 );
    intersection2 = QgsPointXY( x2, y2 );
 
    return 1;
  }
 
  // 2 solutions
 
  /* Determine the distance from point 2 to either of the
   * intersection points.
   */
  const double h = std::sqrt( ( r1 * r1 ) - ( a * a ) );
 
  /* Now determine the offsets of the intersection points from
   * point 2.
   */
  const double rx = dy * ( h / d );
  const double ry = dx * ( h / d );
 
  // determine the absolute intersection points
  intersection1 = QgsPointXY( x2 + rx, y2 - ry );
  intersection2 = QgsPointXY( x2 - rx, y2 +  ry );
 
  return 2;
}
 
// Using https://stackoverflow.com/a/1351794/1861260
// and inspired by http://csharphelper.com/blog/2014/11/find-the-tangent-lines-between-a-point-and-a-circle-in-c/
bool QgsGeometryUtils::tangentPointAndCircle( const QgsPointXY &center, double radius, const QgsPointXY &p, QgsPointXY &pt1, QgsPointXY &pt2 )
{
  // distance from point to center of circle
  const double dx = center.x() - p.x();
  const double dy = center.y() - p.y();
  const double distanceSquared = dx * dx + dy * dy;
  const double radiusSquared = radius * radius;
  if ( distanceSquared < radiusSquared )
  {
    // point is inside circle!
    return false;
  }
 
  // distance from point to tangent point, using pythagoras
  const double distanceToTangent = std::sqrt( distanceSquared - radiusSquared );
 
  // tangent points are those where the original circle intersects a circle centered
  // on p with radius distanceToTangent
  circleCircleIntersections( center, radius, p, distanceToTangent, pt1, pt2 );
 
  return true;
}
 
// inspired by http://csharphelper.com/blog/2014/12/find-the-tangent-lines-between-two-circles-in-c/
int QgsGeometryUtils::circleCircleOuterTangents( const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2 )
{
  if ( radius1 > radius2 )
    return circleCircleOuterTangents( center2, radius2, center1, radius1, line1P1, line1P2, line2P1, line2P2 );
 
  const double radius2a = radius2 - radius1;
  if ( !tangentPointAndCircle( center2, radius2a, center1, line1P2, line2P2 ) )
  {
    // there are no tangents
    return 0;
  }
 
  // get the vector perpendicular to the
  // first tangent with length radius1
  QgsVector v1( -( line1P2.y() - center1.y() ), line1P2.x() - center1.x() );
  const double v1Length = v1.length();
  v1 = v1 * ( radius1 / v1Length );
 
  // offset the tangent vector's points
  line1P1 = center1 + v1;
  line1P2 = line1P2 + v1;
 
  // get the vector perpendicular to the
  // second tangent with length radius1
  QgsVector v2( line2P2.y() - center1.y(), -( line2P2.x() - center1.x() ) );
  const double v2Length = v2.length();
  v2 = v2 * ( radius1 / v2Length );
 
  // offset the tangent vector's points
  line2P1 = center1 + v2;
  line2P2 = line2P2 + v2;
 
  return 2;
}
 
// inspired by http://csharphelper.com/blog/2014/12/find-the-tangent-lines-between-two-circles-in-c/
int QgsGeometryUtils::circleCircleInnerTangents( const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2 )
{
  if ( radius1 > radius2 )
    return circleCircleInnerTangents( center2, radius2, center1, radius1, line1P1, line1P2, line2P1, line2P2 );
 
  // determine the straight-line distance between the centers
  const double d = center1.distance( center2 );
  const double radius1a = radius1 + radius2;
 
  // check for solvability
  if ( d <= radius1a || qgsDoubleNear( d, radius1a ) )
  {
    // no solution. circles intersect or touch.
    return 0;
  }
 
  if ( !tangentPointAndCircle( center1, radius1a, center2, line1P2, line2P2 ) )
  {
    // there are no tangents
    return 0;
  }
 
  // get the vector perpendicular to the
  // first tangent with length radius2
  QgsVector v1( ( line1P2.y() - center2.y() ), -( line1P2.x() - center2.x() ) );
  const double v1Length = v1.length();
  v1 = v1 * ( radius2 / v1Length );
 
  // offset the tangent vector's points
  line1P1 = center2 + v1;
  line1P2 = line1P2 + v1;
 
  // get the vector perpendicular to the
  // second tangent with length radius2
  QgsVector v2( -( line2P2.y() - center2.y() ), line2P2.x() - center2.x() );
  const double v2Length = v2.length();
  v2 = v2 * ( radius2 / v2Length );
 
  // offset the tangent vector's points in opposite direction
  line2P1 = center2 + v2;
  line2P2 = line2P2 + v2;
 
  return 2;
}
 
QVector<QgsGeometryUtils::SelfIntersection> QgsGeometryUtils::selfIntersections( const QgsAbstractGeometry *geom, int part, int ring, double tolerance )
{
  QVector<SelfIntersection> intersections;
 
  const int n = geom->vertexCount( part, ring );
  const bool isClosed = geom->vertexAt( QgsVertexId( part, ring, 0 ) ) == geom->vertexAt( QgsVertexId( part, ring, n - 1 ) );
 
  // Check every pair of segments for intersections
  for ( int i = 0, j = 1; j < n; i = j++ )
  {
    const QgsPoint pi = geom->vertexAt( QgsVertexId( part, ring, i ) );
    const QgsPoint pj = geom->vertexAt( QgsVertexId( part, ring, j ) );
    if ( QgsGeometryUtils::sqrDistance2D( pi, pj ) < tolerance * tolerance ) continue;
 
    // Don't test neighboring edges
    const int start = j + 1;
    const int end = i == 0 && isClosed ? n - 1 : n;
    for ( int k = start, l = start + 1; l < end; k = l++ )
    {
      const QgsPoint pk = geom->vertexAt( QgsVertexId( part, ring, k ) );
      const QgsPoint pl = geom->vertexAt( QgsVertexId( part, ring, l ) );
 
      QgsPoint inter;
      bool intersection = false;
      if ( !QgsGeometryUtils::segmentIntersection( pi, pj, pk, pl, inter, intersection, tolerance ) ) continue;
 
      SelfIntersection s;
      s.segment1 = i;
      s.segment2 = k;
      if ( s.segment1 > s.segment2 )
      {
        std::swap( s.segment1, s.segment2 );
      }
      s.point = inter;
      intersections.append( s );
    }
  }
  return intersections;
}
 
int QgsGeometryUtils::leftOfLine( const QgsPoint &point, const QgsPoint &p1, const QgsPoint &p2 )
{
  return QgsGeometryUtilsBase::leftOfLine( point.x(), point.y(), p1.x(), p1.y(), p2.x(), p2.y() );
}
 
QgsPoint QgsGeometryUtils::pointOnLineWithDistance( const QgsPoint &startPoint, const QgsPoint &directionPoint, double distance )
{
  double x, y;
  QgsGeometryUtilsBase::pointOnLineWithDistance( startPoint.x(), startPoint.y(), directionPoint.x(), directionPoint.y(), distance, x, y );
  return QgsPoint( x, y );
}
 
 
QgsPoint QgsGeometryUtils::interpolatePointOnArc( const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double distance )
{
  double centerX, centerY, radius;
  circleCenterRadius( pt1, pt2, pt3, radius, centerX, centerY );
 
  const double theta = distance / radius; // angle subtended
  const double anglePt1 = std::atan2( pt1.y() - centerY, pt1.x() - centerX );
  const double anglePt2 = std::atan2( pt2.y() - centerY, pt2.x() - centerX );
  const double anglePt3 = std::atan2( pt3.y() - centerY, pt3.x() - centerX );
  const bool isClockwise = QgsGeometryUtilsBase::circleClockwise( anglePt1, anglePt2, anglePt3 );
  const double angleDest = anglePt1 + ( isClockwise ? -theta : theta );
 
  const double x = centerX + radius * ( std::cos( angleDest ) );
  const double y = centerY + radius * ( std::sin( angleDest ) );
 
  const double z = pt1.is3D() ?
                   QgsGeometryUtilsBase::interpolateArcValue( angleDest, anglePt1, anglePt2, anglePt3, pt1.z(), pt2.z(), pt3.z() )
                   : 0;
  const double m = pt1.isMeasure() ?
                   QgsGeometryUtilsBase::interpolateArcValue( angleDest, anglePt1, anglePt2, anglePt3, pt1.m(), pt2.m(), pt3.m() )
                   : 0;
 
  return QgsPoint( pt1.wkbType(), x, y, z, m );
}
 
QgsPoint QgsGeometryUtils::interpolatePointOnCubicBezier( const QgsPoint &p0, const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &p3, double t )
{
  const bool hasZ = p0.is3D() && p1.is3D() && p2.is3D() && p3.is3D();
  const bool hasM = p0.isMeasure() && p1.isMeasure() && p2.isMeasure() && p3.isMeasure();
 
  double x, y;
  double z = std::numeric_limits<double>::quiet_NaN();
  double m = std::numeric_limits<double>::quiet_NaN();
 
  QgsGeometryUtilsBase::interpolatePointOnCubicBezier( p0.x(), p0.y(), p0.z(), p0.m(),
      p1.x(), p1.y(), p1.z(), p1.m(),
      p2.x(), p2.y(), p2.z(), p2.m(),
      p3.x(), p3.y(), p3.z(), p3.m(),
      t, hasZ, hasM,
      x, y, z, m );
 
  Qgis::WkbType wkbType = Qgis::WkbType::Point;
  if ( hasZ && hasM )
    wkbType = Qgis::WkbType::PointZM;
  else if ( hasZ )
    wkbType = Qgis::WkbType::PointZ;
  else if ( hasM )
    wkbType = Qgis::WkbType::PointM;
 
  return QgsPoint( wkbType, x, y, z, m );
}
 
void QgsGeometryUtilsBase::interpolatePointOnCubicBezier(
  double p0x, double p0y, double p0z, double p0m,
  double p1x, double p1y, double p1z, double p1m,
  double p2x, double p2y, double p2z, double p2m,
  double p3x, double p3y, double p3z, double p3m,
  double t, bool hasZ, bool hasM,
  double &outX, double &outY, double &outZ, double &outM )
{
  // Cubic Bézier formula: B(t) = (1-t)³P₀ + 3(1-t)²tP₁ + 3(1-t)t²P₂ + t³P₃
  const double t1 = 1.0 - t;
  const double t1_2 = t1 * t1;
  const double t1_3 = t1_2 * t1;
  const double t_2 = t * t;
  const double t_3 = t_2 * t;
 
  outX = t1_3 * p0x + 3.0 * t1_2 * t * p1x + 3.0 * t1 * t_2 * p2x + t_3 * p3x;
  outY = t1_3 * p0y + 3.0 * t1_2 * t * p1y + 3.0 * t1 * t_2 * p2y + t_3 * p3y;
 
  if ( hasZ )
  {
    outZ = t1_3 * p0z + 3.0 * t1_2 * t * p1z + 3.0 * t1 * t_2 * p2z + t_3 * p3z;
  }
 
  if ( hasM )
  {
    outM = t1_3 * p0m + 3.0 * t1_2 * t * p1m + 3.0 * t1 * t_2 * p2m + t_3 * p3m;
  }
}
 
bool QgsGeometryUtils::segmentMidPoint( const QgsPoint &p1, const QgsPoint &p2, QgsPoint &result, double radius, const QgsPoint &mousePos )
{
  const QgsPoint midPoint( ( p1.x() + p2.x() ) / 2.0, ( p1.y() + p2.y() ) / 2.0 );
  const double midDist = std::sqrt( sqrDistance2D( p1, midPoint ) );
  if ( radius < midDist )
  {
    return false;
  }
  const double centerMidDist = std::sqrt( radius * radius - midDist * midDist );
  const double dist = radius - centerMidDist;
 
  const double midDx = midPoint.x() - p1.x();
  const double midDy = midPoint.y() - p1.y();
 
  //get the four possible midpoints
  QVector<QgsPoint> possibleMidPoints;
  possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPoint( midPoint.x() - midDy, midPoint.y() + midDx ), dist ) );
  possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPoint( midPoint.x() - midDy, midPoint.y() + midDx ), 2 * radius - dist ) );
  possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPoint( midPoint.x() + midDy, midPoint.y() - midDx ), dist ) );
  possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPoint( midPoint.x() + midDy, midPoint.y() - midDx ), 2 * radius - dist ) );
 
  //take the closest one
  double minDist = std::numeric_limits<double>::max();
  int minDistIndex = -1;
  for ( int i = 0; i < possibleMidPoints.size(); ++i )
  {
    const double currentDist = sqrDistance2D( mousePos, possibleMidPoints.at( i ) );
    if ( currentDist < minDist )
    {
      minDistIndex = i;
      minDist = currentDist;
    }
  }
 
  if ( minDistIndex == -1 )
  {
    return false;
  }
 
  result = possibleMidPoints.at( minDistIndex );
 
  // add z and m support if necessary
  QgsGeometryUtils::transferFirstZOrMValueToPoint( QgsPointSequence() << p1 << p2, result );
 
  return true;
}
 
QgsPoint QgsGeometryUtils::segmentMidPointFromCenter( const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &center, const bool useShortestArc )
{
  double midPointAngle = QgsGeometryUtilsBase::averageAngle( QgsGeometryUtilsBase::lineAngle( center.x(), center.y(), p1.x(), p1.y() ),
                         QgsGeometryUtilsBase::lineAngle( center.x(), center.y(), p2.x(), p2.y() ) );
  if ( !useShortestArc )
    midPointAngle += M_PI;
  return center.project( center.distance( p1 ), midPointAngle * 180 / M_PI );
}
 
double QgsGeometryUtils::circleTangentDirection( const QgsPoint &tangentPoint, const QgsPoint &cp1,
    const QgsPoint &cp2, const QgsPoint &cp3 )
{
  //calculate circle midpoint
  double mX, mY, radius;
  circleCenterRadius( cp1, cp2, cp3, radius, mX, mY );
 
  const double p1Angle = QgsGeometryUtilsBase::ccwAngle( cp1.y() - mY, cp1.x() - mX );
  const double p2Angle = QgsGeometryUtilsBase::ccwAngle( cp2.y() - mY, cp2.x() - mX );
  const double p3Angle = QgsGeometryUtilsBase::ccwAngle( cp3.y() - mY, cp3.x() - mX );
  double angle = 0;
  if ( QgsGeometryUtilsBase::circleClockwise( p1Angle, p2Angle, p3Angle ) )
  {
    angle = QgsGeometryUtilsBase::lineAngle( tangentPoint.x(), tangentPoint.y(), mX, mY ) - M_PI_2;
  }
  else
  {
    angle = QgsGeometryUtilsBase::lineAngle( mX, mY, tangentPoint.x(), tangentPoint.y() ) - M_PI_2;
  }
  if ( angle < 0 )
    angle += 2 * M_PI;
  return angle;
}
 
// Ported from PostGIS' pt_continues_arc
bool QgsGeometryUtils::pointContinuesArc( const QgsPoint &a1, const QgsPoint &a2, const QgsPoint &a3, const QgsPoint &b, double distanceTolerance, double pointSpacingAngleTolerance )
{
  double centerX = 0;
  double centerY = 0;
  double radius = 0;
  circleCenterRadius( a1, a2, a3, radius, centerX, centerY );
 
  // Co-linear a1/a2/a3
  if ( radius < 0.0 )
    return false;
 
  // distance of candidate point to center of arc a1-a2-a3
  const double bDistance = std::sqrt( ( b.x() - centerX ) * ( b.x() - centerX ) +
                                      ( b.y() - centerY ) * ( b.y() - centerY ) );
 
  double diff = std::fabs( radius - bDistance );
 
  auto arcAngle = []( const QgsPoint & a, const QgsPoint & b, const QgsPoint & c )->double
  {
    const double abX = b.x() - a.x();
    const double abY = b.y() - a.y();
 
    const double cbX = b.x() - c.x();
    const double cbY = b.y() - c.y();
 
    const double dot = ( abX * cbX + abY * cbY ); /* dot product */
    const double cross = ( abX * cbY - abY * cbX ); /* cross product */
 
    const double alpha = std::atan2( cross, dot );
 
    return alpha;
  };
 
  // Is the point b on the circle?
  if ( diff < distanceTolerance )
  {
    const double angle1 = arcAngle( a1, a2, a3 );
    const double angle2 = arcAngle( a2, a3, b );
 
    // Is the sweep angle similar to the previous one?
    // We only consider a segment replaceable by an arc if the points within
    // it are regularly spaced
    diff = std::fabs( angle1 - angle2 );
    if ( diff > pointSpacingAngleTolerance )
    {
      return false;
    }
 
    const int a2Side = QgsGeometryUtilsBase::leftOfLine( a2.x(), a2.y(), a1.x(), a1.y(), a3.x(), a3.y() );
    const int bSide  = QgsGeometryUtilsBase::leftOfLine( b.x(), b.y(), a1.x(), a1.y(), a3.x(), a3.y() );
 
    // Is the point b on the same side of a1/a3 as the mid-point a2 is?
    // If not, it's in the unbounded part of the circle, so it continues the arc, return true.
    if ( bSide != a2Side )
      return true;
  }
  return false;
}
 
void QgsGeometryUtils::segmentizeArc( const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &p3, QgsPointSequence &points, double tolerance, QgsAbstractGeometry::SegmentationToleranceType toleranceType, bool hasZ, bool hasM )
{
  bool reversed = false;
  const int segSide = segmentSide( p1, p3, p2 );
 
  QgsPoint circlePoint1;
  const QgsPoint &circlePoint2 = p2;
  QgsPoint circlePoint3;
 
  if ( segSide == -1 )
  {
    // Reverse !
    circlePoint1 = p3;
    circlePoint3 = p1;
    reversed = true;
  }
  else
  {
    circlePoint1 = p1;
    circlePoint3 = p3;
  }
 
  //adapted code from PostGIS
  double radius = 0;
  double centerX = 0;
  double centerY = 0;
  circleCenterRadius( circlePoint1, circlePoint2, circlePoint3, radius, centerX, centerY );
 
  if ( circlePoint1 != circlePoint3 && ( radius < 0 || qgsDoubleNear( segSide, 0.0 ) ) ) //points are colinear
  {
    points.append( p1 );
    points.append( p2 );
    points.append( p3 );
    return;
  }
 
  double increment = tolerance; //one segment per degree
  if ( toleranceType == QgsAbstractGeometry::MaximumDifference )
  {
    // Ensure tolerance is not higher than twice the radius
    tolerance = std::min( tolerance, radius * 2 );
    const double halfAngle = std::acos( -tolerance / radius + 1 );
    increment = 2 * halfAngle;
  }
 
  //angles of pt1, pt2, pt3
  const double a1 = std::atan2( circlePoint1.y() - centerY, circlePoint1.x() - centerX );
  double a2 = std::atan2( circlePoint2.y() - centerY, circlePoint2.x() - centerX );
  double a3 = std::atan2( circlePoint3.y() - centerY, circlePoint3.x() - centerX );
 
  // Make segmentation symmetric
  const bool symmetric = true;
  if ( symmetric )
  {
    double angle = a3 - a1;
    // angle == 0 when full circle
    if ( angle <= 0 ) angle += M_PI * 2;
 
    /* Number of segments in output */
    const int segs = ceil( angle / increment );
    /* Tweak increment to be regular for all the arc */
    increment = angle / segs;
  }
 
  /* Adjust a3 up so we can increment from a1 to a3 cleanly */
  // a3 == a1 when full circle
  if ( a3 <= a1 )
    a3 += 2.0 * M_PI;
  if ( a2 < a1 )
    a2 += 2.0 * M_PI;
 
  double x, y;
  double z = 0;
  double m = 0;
 
  QVector<QgsPoint> stringPoints;
  stringPoints.insert( 0, circlePoint1 );
  if ( circlePoint2 != circlePoint3 && circlePoint1 != circlePoint2 ) //draw straight line segment if two points have the same position
  {
    Qgis::WkbType pointWkbType = Qgis::WkbType::Point;
    if ( hasZ )
      pointWkbType = QgsWkbTypes::addZ( pointWkbType );
    if ( hasM )
      pointWkbType = QgsWkbTypes::addM( pointWkbType );
 
    // As we're adding the last point in any case, we'll avoid
    // including a point which is at less than 1% increment distance
    // from it (may happen to find them due to numbers approximation).
    // NOTE that this effectively allows in output some segments which
    //      are more distant than requested. This is at most 1% off
    //      from requested MaxAngle and less for MaxError.
    const double tolError = increment / 100;
    const double stopAngle = a3 - tolError;
    for ( double angle = a1 + increment; angle < stopAngle; angle += increment )
    {
      x = centerX + radius * std::cos( angle );
      y = centerY + radius * std::sin( angle );
 
      if ( hasZ )
      {
        z = QgsGeometryUtilsBase::interpolateArcValue( angle, a1, a2, a3, circlePoint1.z(), circlePoint2.z(), circlePoint3.z() );
      }
      if ( hasM )
      {
        m = QgsGeometryUtilsBase::interpolateArcValue( angle, a1, a2, a3, circlePoint1.m(), circlePoint2.m(), circlePoint3.m() );
      }
 
      stringPoints.insert( stringPoints.size(), QgsPoint( pointWkbType, x, y, z, m ) );
    }
  }
  stringPoints.insert( stringPoints.size(), circlePoint3 );
 
  // TODO: check if or implement QgsPointSequence directly taking an iterator to append
  if ( reversed )
  {
    std::reverse( stringPoints.begin(), stringPoints.end() );
  }
  if ( ! points.empty() && stringPoints.front() == points.back() ) stringPoints.pop_front();
  points.append( stringPoints );
}
 
int QgsGeometryUtils::segmentSide( const QgsPoint &pt1, const QgsPoint &pt3, const QgsPoint &pt2 )
{
  const double side = ( ( pt2.x() - pt1.x() ) * ( pt3.y() - pt1.y() ) - ( pt3.x() - pt1.x() ) * ( pt2.y() - pt1.y() ) );
  if ( side == 0.0 )
  {
    return 0;
  }
  else
  {
    if ( side < 0 )
    {
      return -1;
    }
    if ( side > 0 )
    {
      return 1;
    }
    return 0;
  }
}
 
QgsPointSequence QgsGeometryUtils::pointsFromWKT( const QString &wktCoordinateList, bool is3D, bool isMeasure )
{
  const int dim = 2 + is3D + isMeasure;
  QgsPointSequence points;
 
  const QStringList coordList = wktCoordinateList.split( ',', Qt::SkipEmptyParts );
 
  //first scan through for extra unexpected dimensions
  bool foundZ = false;
  bool foundM = false;
  const thread_local QRegularExpression rx( u"\\s"_s );
  const thread_local QRegularExpression rxIsNumber( u"^[+-]?(\\d\\.?\\d*[Ee][+\\-]?\\d+|(\\d+\\.\\d*|\\d*\\.\\d+)|\\d+)$"_s );
  for ( const QString &pointCoordinates : coordList )
  {
    const QStringList coordinates = pointCoordinates.split( rx, Qt::SkipEmptyParts );
 
    // exit with an empty set if one list contains invalid value.
    if ( coordinates.filter( rxIsNumber ).size() != coordinates.size() )
      return points;
 
    if ( coordinates.size() == 3 && !foundZ && !foundM && !is3D && !isMeasure )
    {
      // 3 dimensional coordinates, but not specifically marked as such. We allow this
      // anyway and upgrade geometry to have Z dimension
      foundZ = true;
    }
    else if ( coordinates.size() >= 4 && ( !( is3D || foundZ ) || !( isMeasure || foundM ) ) )
    {
      // 4 (or more) dimensional coordinates, but not specifically marked as such. We allow this
      // anyway and upgrade geometry to have Z&M dimensions
      foundZ = true;
      foundM = true;
    }
  }
 
  for ( const QString &pointCoordinates : coordList )
  {
    QStringList coordinates = pointCoordinates.split( rx, Qt::SkipEmptyParts );
    if ( coordinates.size() < dim )
      continue;
 
    int idx = 0;
    const double x = coordinates[idx++].toDouble();
    const double y = coordinates[idx++].toDouble();
 
    double z = 0;
    if ( ( is3D || foundZ ) && coordinates.length() > idx )
      z = coordinates[idx++].toDouble();
 
    double m = 0;
    if ( ( isMeasure || foundM ) && coordinates.length() > idx )
      m = coordinates[idx++].toDouble();
 
    Qgis::WkbType t = Qgis::WkbType::Point;
    if ( is3D || foundZ )
    {
      if ( isMeasure || foundM )
        t = Qgis::WkbType::PointZM;
      else
        t = Qgis::WkbType::PointZ;
    }
    else
    {
      if ( isMeasure || foundM )
        t = Qgis::WkbType::PointM;
      else
        t = Qgis::WkbType::Point;
    }
 
    points.append( QgsPoint( t, x, y, z, m ) );
  }
 
  return points;
}
 
void QgsGeometryUtils::pointsToWKB( QgsWkbPtr &wkb, const QgsPointSequence &points, bool is3D, bool isMeasure, QgsAbstractGeometry::WkbFlags flags )
{
  wkb << static_cast<quint32>( points.size() );
  for ( const QgsPoint &point : points )
  {
    wkb << point.x() << point.y();
    if ( is3D )
    {
      double z = point.z();
      if ( flags & QgsAbstractGeometry::FlagExportNanAsDoubleMin
           && std::isnan( z ) )
        z = -std::numeric_limits<double>::max();
 
      wkb << z;
    }
    if ( isMeasure )
    {
      double m = point.m();
      if ( flags & QgsAbstractGeometry::FlagExportNanAsDoubleMin
           && std::isnan( m ) )
        m = -std::numeric_limits<double>::max();
 
      wkb << m;
    }
  }
}
 
QString QgsGeometryUtils::pointsToWKT( const QgsPointSequence &points, int precision, bool is3D, bool isMeasure )
{
  QString wkt = u"("_s;
  for ( const QgsPoint &p : points )
  {
    wkt += qgsDoubleToString( p.x(), precision );
    wkt += ' ' + qgsDoubleToString( p.y(), precision );
    if ( is3D )
      wkt += ' ' + qgsDoubleToString( p.z(), precision );
    if ( isMeasure )
      wkt += ' ' + qgsDoubleToString( p.m(), precision );
    wkt += ", "_L1;
  }
  if ( wkt.endsWith( ", "_L1 ) )
    wkt.chop( 2 ); // Remove last ", "
  wkt += ')';
  return wkt;
}
 
QDomElement QgsGeometryUtils::pointsToGML2( const QgsPointSequence &points, QDomDocument &doc, int precision, const QString &ns, QgsAbstractGeometry::AxisOrder axisOrder )
{
  QDomElement elemCoordinates = doc.createElementNS( ns, u"coordinates"_s );
 
  // coordinate separator
  const QString cs = u","_s;
  // tuple separator
  const QString ts = u" "_s;
 
  elemCoordinates.setAttribute( u"cs"_s, cs );
  elemCoordinates.setAttribute( u"ts"_s, ts );
 
  QString strCoordinates;
 
  for ( const QgsPoint &p : points )
    if ( axisOrder == QgsAbstractGeometry::AxisOrder::XY )
      strCoordinates += qgsDoubleToString( p.x(), precision ) + cs + qgsDoubleToString( p.y(), precision ) + ts;
    else
      strCoordinates += qgsDoubleToString( p.y(), precision ) + cs + qgsDoubleToString( p.x(), precision ) + ts;
 
  if ( strCoordinates.endsWith( ts ) )
    strCoordinates.chop( 1 ); // Remove trailing space
 
  elemCoordinates.appendChild( doc.createTextNode( strCoordinates ) );
  return elemCoordinates;
}
 
QDomElement QgsGeometryUtils::pointsToGML3( const QgsPointSequence &points, QDomDocument &doc, int precision, const QString &ns, bool is3D, QgsAbstractGeometry::AxisOrder axisOrder )
{
  QDomElement elemPosList = doc.createElementNS( ns, u"posList"_s );
  elemPosList.setAttribute( u"srsDimension"_s, is3D ? 3 : 2 );
 
  QString strCoordinates;
  for ( const QgsPoint &p : points )
  {
    if ( axisOrder == QgsAbstractGeometry::AxisOrder::XY )
      strCoordinates += qgsDoubleToString( p.x(), precision ) + ' ' + qgsDoubleToString( p.y(), precision ) + ' ';
    else
      strCoordinates += qgsDoubleToString( p.y(), precision ) + ' ' + qgsDoubleToString( p.x(), precision ) + ' ';
    if ( is3D )
      strCoordinates += qgsDoubleToString( p.z(), precision ) + ' ';
  }
  if ( strCoordinates.endsWith( ' ' ) )
    strCoordinates.chop( 1 ); // Remove trailing space
 
  elemPosList.appendChild( doc.createTextNode( strCoordinates ) );
  return elemPosList;
}
 
QString QgsGeometryUtils::pointsToJSON( const QgsPointSequence &points, int precision )
{
  QString json = u"[ "_s;
  for ( const QgsPoint &p : points )
  {
    json += '[' + qgsDoubleToString( p.x(), precision ) + ", "_L1 + qgsDoubleToString( p.y(), precision ) + "], "_L1;
  }
  if ( json.endsWith( ", "_L1 ) )
  {
    json.chop( 2 ); // Remove last ", "
  }
  json += ']';
  return json;
}
 
 
json QgsGeometryUtils::pointsToJson( const QgsPointSequence &points, int precision )
{
  json coordinates( json::array() );
  for ( const QgsPoint &p : points )
  {
    if ( p.is3D() )
    {
      coordinates.push_back( { qgsRound( p.x(), precision ), qgsRound( p.y(), precision ), qgsRound( p.z(), precision ) } );
    }
    else
    {
      coordinates.push_back( { qgsRound( p.x(), precision ), qgsRound( p.y(), precision ) } );
    }
  }
  return coordinates;
}
 
QPair<Qgis::WkbType, QString> QgsGeometryUtils::wktReadBlock( const QString &wkt )
{
  QString wktParsed = wkt;
  QString contents;
  bool isEmpty = false;
  const QLatin1String empty { "EMPTY" };
  if ( wkt.contains( empty, Qt::CaseInsensitive ) )
  {
    const thread_local QRegularExpression whiteSpaces( "\\s" );
    wktParsed.remove( whiteSpaces );
    const int index = wktParsed.indexOf( empty, 0, Qt::CaseInsensitive );
 
    if ( index == wktParsed.length() - empty.size() )
    {
      // "EMPTY" found at the end of the QString
      // Extract the part of the QString to the left of "EMPTY"
      wktParsed = wktParsed.left( index );
      contents = empty;
      isEmpty = true;
    }
    else
    {
      wktParsed = wkt; // reset to original content
    }
  }
  if ( !isEmpty )
  {
    const int openedParenthesisCount = wktParsed.count( '(' );
    const int closedParenthesisCount = wktParsed.count( ')' );
    // closes missing parentheses
    for ( int i = 0 ;  i < openedParenthesisCount - closedParenthesisCount; ++i )
      wktParsed.push_back( ')' );
    // removes extra parentheses
    wktParsed.truncate( wktParsed.size() - ( closedParenthesisCount - openedParenthesisCount ) );
 
    const thread_local QRegularExpression cooRegEx( u"^[^\\(]*\\((.*)\\)[^\\)]*$"_s, QRegularExpression::DotMatchesEverythingOption );
    const QRegularExpressionMatch match = cooRegEx.match( wktParsed );
    contents = match.hasMatch() ? match.captured( 1 ) : QString();
  }
  const Qgis::WkbType wkbType = QgsWkbTypes::parseType( wktParsed );
  return qMakePair( wkbType, contents );
}
 
QStringList QgsGeometryUtils::wktGetChildBlocks( const QString &wkt, const QString &defaultType )
{
  int level = 0;
  QString block;
  block.reserve( wkt.size() );
  QStringList blocks;
 
  const QChar *wktData = wkt.data();
  const int wktLength = wkt.length();
  for ( int i = 0, n = wktLength; i < n; ++i, ++wktData )
  {
    if ( ( wktData->isSpace() || *wktData == '\n' || *wktData == '\t' ) && level == 0 )
      continue;
 
    if ( *wktData == ',' && level == 0 )
    {
      if ( !block.isEmpty() )
      {
        if ( block.startsWith( '(' ) && !defaultType.isEmpty() )
          block.prepend( defaultType + ' ' );
        blocks.append( block );
      }
      block.resize( 0 );
      continue;
    }
    if ( *wktData == '(' )
      ++level;
    else if ( *wktData == ')' )
      --level;
    block += *wktData;
  }
  if ( !block.isEmpty() )
  {
    if ( block.startsWith( '(' ) && !defaultType.isEmpty() )
      block.prepend( defaultType + ' ' );
    blocks.append( block );
  }
  return blocks;
}
 
QgsPoint QgsGeometryUtils::midpoint( const QgsPoint &pt1, const QgsPoint &pt2 )
{
  Qgis::WkbType pType( Qgis::WkbType::Point );
 
 
  const double x = ( pt1.x() + pt2.x() ) / 2.0;
  const double y = ( pt1.y() + pt2.y() ) / 2.0;
  double z = std::numeric_limits<double>::quiet_NaN();
  double m = std::numeric_limits<double>::quiet_NaN();
 
  if ( pt1.is3D() || pt2.is3D() )
  {
    pType = QgsWkbTypes::addZ( pType );
    z = ( pt1.z() + pt2.z() ) / 2.0;
  }
 
  if ( pt1.isMeasure() || pt2.isMeasure() )
  {
    pType = QgsWkbTypes::addM( pType );
    m = ( pt1.m() + pt2.m() ) / 2.0;
  }
 
  return QgsPoint( pType, x, y, z, m );
}
 
QgsPoint QgsGeometryUtils::interpolatePointOnLine( const QgsPoint &p1, const QgsPoint &p2, const double fraction )
{
  const double _fraction = 1 - fraction;
  return QgsPoint( p1.wkbType(),
                   p1.x() * _fraction + p2.x() * fraction,
                   p1.y() * _fraction + p2.y() * fraction,
                   p1.is3D() ? p1.z() * _fraction + p2.z() * fraction : std::numeric_limits<double>::quiet_NaN(),
                   p1.isMeasure() ? p1.m() * _fraction + p2.m() * fraction : std::numeric_limits<double>::quiet_NaN() );
}
 
QgsPointXY QgsGeometryUtils::interpolatePointOnLine( const double x1, const double y1, const double x2, const double y2, const double fraction )
{
  const double deltaX = ( x2 - x1 ) * fraction;
  const double deltaY = ( y2 - y1 ) * fraction;
  return QgsPointXY( x1 + deltaX, y1 + deltaY );
}
 
QgsPointXY QgsGeometryUtils::interpolatePointOnLineByValue( const double x1, const double y1, const double v1, const double x2, const double y2, const double v2, const double value )
{
  if ( qgsDoubleNear( v1, v2 ) )
    return QgsPointXY( x1, y1 );
 
  const double fraction = ( value - v1 ) / ( v2 - v1 );
  return interpolatePointOnLine( x1, y1, x2, y2, fraction );
}
 
double QgsGeometryUtils::gradient( const QgsPoint &pt1, const QgsPoint &pt2 )
{
  const double delta_x = pt2.x() - pt1.x();
  const double delta_y = pt2.y() - pt1.y();
  if ( qgsDoubleNear( delta_x, 0.0 ) )
  {
    return INFINITY;
  }
 
  return delta_y / delta_x;
}
 
void QgsGeometryUtils::coefficients( const QgsPoint &pt1, const QgsPoint &pt2, double &a, double &b, double &c )
{
  if ( qgsDoubleNear( pt1.x(), pt2.x() ) )
  {
    a = 1;
    b = 0;
    c = -pt1.x();
  }
  else if ( qgsDoubleNear( pt1.y(), pt2.y() ) )
  {
    a = 0;
    b = 1;
    c = -pt1.y();
  }
  else
  {
    a = pt1.y() - pt2.y();
    b = pt2.x() - pt1.x();
    c = pt1.x() * pt2.y() - pt1.y() * pt2.x();
  }
 
}
 
QgsLineString QgsGeometryUtils::perpendicularSegment( const QgsPoint &p, const QgsPoint &s1, const QgsPoint &s2 )
{
  QgsLineString line;
  QgsPoint p2;
 
  if ( ( p == s1 ) || ( p == s2 ) )
  {
    return line;
  }
 
  double a, b, c;
  coefficients( s1, s2, a, b, c );
 
  if ( qgsDoubleNear( a, 0 ) )
  {
    p2 = QgsPoint( p.x(), s1.y() );
  }
  else if ( qgsDoubleNear( b, 0 ) )
  {
    p2 = QgsPoint( s1.x(), p.y() );
  }
  else
  {
    const double y = ( -c - a * p.x() ) / b;
    const double m = gradient( s1, s2 );
    const double d2 = 1 + m * m;
    const double H = p.y() - y;
    const double dx = m * H / d2;
    const double dy = m * dx;
    p2 = QgsPoint( p.x() + dx, y + dy );
  }
 
  line.addVertex( p );
  line.addVertex( p2 );
 
  return line;
}
 
bool QgsGeometryUtils::transferFirstMValueToPoint( const QgsPointSequence &points, QgsPoint &point )
{
  bool rc = false;
 
  for ( const QgsPoint &pt : points )
  {
    if ( pt.isMeasure() )
    {
      point.convertTo( QgsWkbTypes::addM( point.wkbType() ) );
      point.setM( pt.m() );
      rc = true;
      break;
    }
  }
 
  return rc;
}
 
bool QgsGeometryUtils::transferFirstZValueToPoint( const QgsPointSequence &points, QgsPoint &point )
{
  bool rc = false;
 
  for ( const QgsPoint &pt : points )
  {
    if ( pt.is3D() )
    {
      point.convertTo( QgsWkbTypes::addZ( point.wkbType() ) );
      point.setZ( pt.z() );
      rc = true;
      break;
    }
  }
 
  return rc;
}
 
QgsPoint QgsGeometryUtils::createPointWithMatchingDimensions( double x, double y, const QgsPoint &reference )
{
  if ( reference.is3D() && reference.isMeasure() )
    return QgsPoint( Qgis::WkbType::PointZM, x, y, 0.0, 0.0 );
  else if ( reference.is3D() )
    return QgsPoint( Qgis::WkbType::PointZ, x, y, 0.0 );
  else if ( reference.isMeasure() )
    return QgsPoint( Qgis::WkbType::PointM, x, y, 0.0, 0.0 );
  else
    return QgsPoint( x, y );
}
 
QgsPoint QgsGeometryUtils::interpolatePointOnSegment( double x, double y,
    const QgsPoint &segmentStart, const QgsPoint &segmentEnd )
{
  QgsPoint result = createPointWithMatchingDimensions( x, y, segmentStart );
  const double distanceFromStart = QgsGeometryUtilsBase::distance2D( segmentStart.x(), segmentStart.y(), x, y );
 
  if ( segmentStart.is3D() && segmentEnd.is3D() )
  {
    double z1 = segmentStart.z();
    double z2 = segmentEnd.z();
    double interpolatedZ;
    double tempX, tempY;
    QgsGeometryUtilsBase::pointOnLineWithDistance(
      segmentStart.x(), segmentStart.y(), segmentEnd.x(), segmentEnd.y(),
      distanceFromStart, tempX, tempY, &z1, &z2, &interpolatedZ );
    result.setZ( interpolatedZ );
  }
 
  if ( segmentStart.isMeasure() && segmentEnd.isMeasure() )
  {
    double m1 = segmentStart.m();
    double m2 = segmentEnd.m();
    double interpolatedM;
    double tempX, tempY;
    QgsGeometryUtilsBase::pointOnLineWithDistance(
      segmentStart.x(), segmentStart.y(), segmentEnd.x(), segmentEnd.y(),
      distanceFromStart, tempX, tempY, nullptr, nullptr, nullptr, &m1, &m2, &interpolatedM );
    result.setM( interpolatedM );
  }
 
  return result;
}
 
bool QgsGeometryUtils::createChamfer( const QgsPoint &segment1Start, const QgsPoint &segment1End,
                                      const QgsPoint &segment2Start, const QgsPoint &segment2End,
                                      double distance1, double distance2,
                                      QgsPoint &chamferStart, QgsPoint &chamferEnd,
                                      double epsilon )
{
  // Create chamfer points using the utility function
  double chamferStartX, chamferStartY, chamferEndX, chamferEndY;
 
  QgsGeometryUtilsBase::createChamfer(
    segment1Start.x(), segment1Start.y(), segment1End.x(), segment1End.y(),
    segment2Start.x(), segment2Start.y(), segment2End.x(), segment2End.y(),
    distance1, distance2,
    chamferStartX, chamferStartY,
    chamferEndX, chamferEndY,
    nullptr, nullptr, nullptr, nullptr,
    nullptr, nullptr, nullptr, nullptr,
    epsilon
  );
 
  chamferStart = interpolatePointOnSegment( chamferStartX, chamferStartY, segment1Start, segment1End );
  chamferEnd = interpolatePointOnSegment( chamferEndX, chamferEndY, segment2Start, segment2End );
 
  return true;
}
 
bool QgsGeometryUtils::createFillet( const QgsPoint &segment1Start, const QgsPoint &segment1End,
                                     const QgsPoint &segment2Start, const QgsPoint &segment2End,
                                     double radius,
                                     QgsPoint &filletPoint1,
                                     QgsPoint &filletMidPoint,
                                     QgsPoint &filletPoint2,
                                     double epsilon )
{
  // Create fillet arc using the utility function
  double filletPointsX[3], filletPointsY[3];
 
  QgsGeometryUtilsBase::createFillet(
    segment1Start.x(), segment1Start.y(), segment1End.x(), segment1End.y(),
    segment2Start.x(), segment2Start.y(), segment2End.x(), segment2End.y(),
    radius,
    filletPointsX, filletPointsY,
    nullptr, nullptr, nullptr, nullptr,
    nullptr, nullptr, nullptr, nullptr,
    epsilon
  );
 
  filletPoint1 = interpolatePointOnSegment( filletPointsX[0], filletPointsY[0], segment1Start, segment1End );
  filletMidPoint = createPointWithMatchingDimensions( filletPointsX[1], filletPointsY[1], segment1Start );
  filletPoint2 = interpolatePointOnSegment( filletPointsX[2], filletPointsY[2], segment2Start, segment2End );
 
  // Interpolate Z and M for midpoint
  if ( segment1Start.is3D() && segment1End.is3D() && segment2Start.is3D() && segment2End.is3D() )
  {
    filletMidPoint.setZ( ( filletPoint1.z() + filletPoint2.z() ) / 2.0 );
  }
  if ( segment1Start.isMeasure() && segment1End.isMeasure() && segment2Start.isMeasure() && segment2End.isMeasure() )
  {
    filletMidPoint.setM( ( filletPoint1.m() + filletPoint2.m() ) / 2.0 );
  }
 
  return true;
}
 
bool QgsGeometryUtils::createFilletArray( const QgsPoint &segment1Start, const QgsPoint &segment1End,
    const QgsPoint &segment2Start, const QgsPoint &segment2End,
    double radius,
    QgsPoint filletPoints[3],
    double epsilon )
{
  QgsPoint p1, p2, p3;
  createFillet( segment1Start, segment1End, segment2Start, segment2End, radius, p1, p2, p3, epsilon );
  filletPoints[0] = p1;
  filletPoints[1] = p2;
  filletPoints[2] = p3;
  return true;
}
 
std::unique_ptr<QgsLineString> QgsGeometryUtils::createChamferGeometry(
  const QgsPoint &segment1Start, const QgsPoint &segment1End,
  const QgsPoint &segment2Start, const QgsPoint &segment2End,
  double distance1, double distance2 )
{
  QgsPoint chamferStart, chamferEnd;
  createChamfer( segment1Start, segment1End, segment2Start, segment2End, distance1, distance2, chamferStart, chamferEnd );
 
  return std::make_unique<QgsLineString>(
           QVector<QgsPoint> { segment1Start, chamferStart, chamferEnd, segment2Start } );
}
 
std::unique_ptr<QgsAbstractGeometry> QgsGeometryUtils::createFilletGeometry(
  const QgsPoint &segment1Start, const QgsPoint &segment1End,
  const QgsPoint &segment2Start, const QgsPoint &segment2End,
  double radius, int segments )
{
  QgsPoint filletPoints[3];
  createFilletArray( segment1Start, segment1End, segment2Start, segment2End, radius, filletPoints );
 
  // Calculate far endpoints for complete geometry
  double intersectionX, intersectionY;
  bool isIntersection;
  QgsGeometryUtilsBase::segmentIntersection(
    segment1Start.x(), segment1Start.y(), segment1End.x(), segment1End.y(),
    segment2Start.x(), segment2Start.y(), segment2End.x(), segment2End.y(),
    intersectionX, intersectionY, isIntersection, 1e-8, true );
 
  if ( !isIntersection )
  {
    throw QgsInvalidArgumentException( "Segments do not intersect." );
  }
 
  const double dist1ToStart = QgsGeometryUtilsBase::distance2D( intersectionX, intersectionY, segment1Start.x(), segment1Start.y() );
  const double dist1ToEnd = QgsGeometryUtilsBase::distance2D( intersectionX, intersectionY, segment1End.x(), segment1End.y() );
  const double dist2ToStart = QgsGeometryUtilsBase::distance2D( intersectionX, intersectionY, segment2Start.x(), segment2Start.y() );
  const double dist2ToEnd = QgsGeometryUtilsBase::distance2D( intersectionX, intersectionY, segment2End.x(), segment2End.y() );
 
  const QgsPoint segment1FarEnd = ( dist1ToStart < dist1ToEnd ) ? segment1End : segment1Start;
  const QgsPoint segment2FarEnd = ( dist2ToStart < dist2ToEnd ) ? segment2End : segment2Start;
 
  if ( segments <= 0 )
  {
    // Return CompoundCurve with circular arc
    auto completeCurve = std::make_unique<QgsCompoundCurve>();
 
    // First linear segment
    auto firstSegment = std::make_unique<QgsLineString>(
                          QVector<QgsPoint> { segment1FarEnd, filletPoints[0] } );
    completeCurve->addCurve( firstSegment.release() );
 
    // Circular arc segment
    auto circularString = std::make_unique<QgsCircularString>();
    circularString->setPoints( {filletPoints[0], filletPoints[1], filletPoints[2]} );
    completeCurve->addCurve( circularString.release() );
 
    // Last linear segment
    auto lastSegment = std::make_unique<QgsLineString>(
                         QVector<QgsPoint> { filletPoints[2], segment2FarEnd } );
    completeCurve->addCurve( lastSegment.release() );
 
    return completeCurve;
  }
  else
  {
    // Return segmented LineString
    QVector<QgsPoint> points;
    points.append( segment1FarEnd );
 
    // Convert circular arc to line segments with specified number of segments
    QgsCircularString tempArc;
    tempArc.setPoints( {filletPoints[0], filletPoints[1], filletPoints[2]} );
 
    // Calculate appropriate tolerance based on desired number of segments
    // Calculate the actual arc angle and divide by desired number of segments
    // Note: segmentizeArc uses ceil(angle/tolerance), so we need to ensure we get exactly the desired number of segments
    double angleTolerance = M_PI / 180.0; // Default to 1 degree
    if ( segments > 0 )
    {
      double radius, centerX, centerY;
      QgsGeometryUtils::circleCenterRadius( filletPoints[0], filletPoints[1], filletPoints[2], radius, centerX, centerY );
      const double arcAngle = std::abs( QgsGeometryUtilsBase::sweepAngle( centerX, centerY,
                                        filletPoints[0].x(), filletPoints[0].y(),
                                        filletPoints[1].x(), filletPoints[1].y(),
                                        filletPoints[2].x(), filletPoints[2].y() ) ) * M_PI / 180.0; // Convert to radians
      // Add small epsilon to avoid ceil() rounding up due to numerical precision
      angleTolerance = arcAngle / segments * ( 1.0 + 1e-10 );
    }
 
    std::unique_ptr<QgsLineString> segmentizedArc( tempArc.curveToLine( angleTolerance, QgsAbstractGeometry::MaximumAngle ) );
 
    for ( int i = 0; i < segmentizedArc->numPoints(); ++i )
    {
      points.append( segmentizedArc->vertexAt( QgsVertexId( 0, 0, i ) ) );
    }
 
    points.append( segment2FarEnd );
 
    return std::make_unique<QgsLineString>( points );
  }
}
 
double QgsGeometryUtils::maxFilletRadius( const QgsPoint &segment1Start, const QgsPoint &segment1End,
    const QgsPoint &segment2Start, const QgsPoint &segment2End,
    double epsilon )
{
  return QgsGeometryUtilsBase::maximumFilletRadius( segment1Start.x(), segment1Start.y(), segment1End.x(), segment1End.y(), segment2Start.x(), segment2Start.y(), segment2End.x(), segment2End.y(), epsilon );
}
 
std::unique_ptr<QgsAbstractGeometry> QgsGeometryUtils::chamferVertex(
  const QgsCurve *curve, int vertexIndex,
  double distance1, double distance2 )
{
  return doChamferFilletOnVertex( QgsGeometry::ChamferFilletOperationType::Chamfer, curve, vertexIndex, distance1, distance2, 0 );
}
 
std::unique_ptr<QgsAbstractGeometry> QgsGeometryUtils::filletVertex(
  const QgsCurve *curve, int vertexIndex,
  double radius, int segments )
{
  return doChamferFilletOnVertex( QgsGeometry::ChamferFilletOperationType::Fillet, curve, vertexIndex, radius, 0.0, segments );
}
 
std::unique_ptr< QgsAbstractGeometry > QgsGeometryUtils::doChamferFilletOnVertex(
  QgsGeometry::ChamferFilletOperationType operation, const QgsCurve *curve, int vertexIndex,
  double value1, double value2, int segments
)
{
  if ( !curve )
    throw QgsInvalidArgumentException( "Curve is null." );
  if ( curve->isClosed() )
  {
    if ( curve->numPoints() < 4 )
      throw QgsInvalidArgumentException( "Closed curve must have at least 4 vertex." );
    if ( vertexIndex < 0 || vertexIndex > curve->numPoints() - 1 )
      throw QgsInvalidArgumentException( u"Vertex index out of range. %1 must be in [0, %2]."_s.arg( vertexIndex ).arg( curve->numPoints() - 1 ) );
  }
  else
  {
    if ( curve->numPoints() < 3 )
      throw QgsInvalidArgumentException( "Opened curve must have at least 3 points." );
    if ( vertexIndex <= 0 || vertexIndex >= curve->numPoints() - 1 )
      throw QgsInvalidArgumentException( u"Vertex index out of range. %1 must be in (0, %2)."_s.arg( vertexIndex ).arg( curve->numPoints() - 1 ) );
  }
 
  // Extract the three consecutive vertices
  QgsPoint pPrev = curve->vertexAt( QgsVertexId( 0, 0, vertexIndex - 1 ) );
  const QgsPoint p = curve->vertexAt( QgsVertexId( 0, 0, vertexIndex ) );
  QgsPoint pNext = curve->vertexAt( QgsVertexId( 0, 0, vertexIndex + 1 ) );
  if ( curve->isClosed() )
  {
    if ( vertexIndex - 1 < 0 )
      pPrev = curve->vertexAt( QgsVertexId( 0, 0, curve->numPoints() - 2 ) );
    if ( vertexIndex + 1 >= curve->numPoints() )
      pNext = curve->vertexAt( QgsVertexId( 0, 0, 1 ) );
  }
 
  QgsPoint firstNewPoint, middlePoint, lastNewPoint;
 
  if ( operation == QgsGeometry::ChamferFilletOperationType::Fillet )
  {
    double rad = std::min( value1, pPrev.distance( p ) * 0.95 );
    rad = std::min( rad, pNext.distance( p ) * 0.95 );
 
    // Create fillet
    QgsPoint filletPoints[3];
    createFilletArray( pPrev, p, p, pNext, rad, filletPoints );
 
    firstNewPoint = filletPoints[0];
    middlePoint = filletPoints[1];
    lastNewPoint = filletPoints[2];
  }
  else if ( operation == QgsGeometry::ChamferFilletOperationType::Chamfer )
  {
    // Create chamfer
    createChamfer( pPrev, p, p, pNext, value1, value2, firstNewPoint, lastNewPoint );
  }
  else
    throw QgsInvalidArgumentException( u"Operation '%1' is unknown."_s.arg( qgsEnumValueToKey( operation ) ) );
 
  // Handle LineString geometries
  if ( qgsgeometry_cast<const QgsLineString *>( curve ) )
  {
    QVector<QgsPoint> points;
 
    int min = 0;
    if ( curve->isClosed() && vertexIndex == curve->numPoints() - 1 )
      min = 1;
 
    // Add points before the operated vertex
    for ( int i = min; i < vertexIndex; ++i )
    {
      points.append( curve->vertexAt( QgsVertexId( 0, 0, i ) ) );
    }
 
    if ( operation == QgsGeometry::ChamferFilletOperationType::Fillet )
    {
      // Add fillet arc as line segments with proper segmentation
      if ( firstNewPoint != pPrev )
        points.append( firstNewPoint );
 
      if ( segments > 0 )
      {
        QgsCircularString tempArc;
        tempArc.setPoints( { firstNewPoint, middlePoint, lastNewPoint } );
 
        // Calculate the actual arc angle and divide by desired number of segments
        // Note: segmentizeArc uses ceil(angle/tolerance), so we need to ensure we get exactly the desired number of segments
        double radius, centerX, centerY;
        QgsGeometryUtils::circleCenterRadius( firstNewPoint, middlePoint, lastNewPoint, radius, centerX, centerY );
        const double arcAngle = std::abs( QgsGeometryUtilsBase::sweepAngle( centerX, centerY,
                                          firstNewPoint.x(), firstNewPoint.y(),
                                          middlePoint.x(), middlePoint.y(),
                                          lastNewPoint.x(), lastNewPoint.y() ) ) * M_PI / 180.0; // Convert to radians
        // Add small epsilon to avoid ceil() rounding up due to numerical precision
        const double angleTolerance = arcAngle / segments * ( 1.0 + 1e-10 );
        std::unique_ptr<QgsLineString> segmentizedArc( tempArc.curveToLine( angleTolerance, QgsAbstractGeometry::MaximumAngle ) );
 
        for ( int i = 1; i < segmentizedArc->numPoints() - 1; ++i )
        {
          points.append( segmentizedArc->vertexAt( QgsVertexId( 0, 0, i ) ) );
        }
      }
      else
      {
        points.append( middlePoint );
      }
 
      if ( lastNewPoint != pNext )
        points.append( lastNewPoint );
    }
    else
    {
      if ( firstNewPoint != pPrev )
        points.append( firstNewPoint );
      if ( lastNewPoint != pNext )
        points.append( lastNewPoint );
    }
 
    int max = curve->numPoints();
    if ( curve->isClosed() && vertexIndex == 0 )
      max = curve->numPoints() - 1;
 
    for ( int i = vertexIndex + 1; i < max; ++i )
    {
      points.append( curve->vertexAt( QgsVertexId( 0, 0, i ) ) );
    }
 
    return std::make_unique<QgsLineString>( points );
  }
 
  if ( const QgsCompoundCurve *compound = qgsgeometry_cast<const QgsCompoundCurve *>( curve ) )
  {
    auto newCompound = std::make_unique<QgsCompoundCurve>();
 
    int globalVertexIndex = 0;
    int targetCurveIndex = -1;
    int vertexInCurve = -1;
 
    for ( int curveIdx = 0; curveIdx < compound->nCurves(); ++curveIdx )
    {
      const QgsCurve *subcurve = compound->curveAt( curveIdx );
      const int subcurvePoints = subcurve->numPoints();
 
      if ( globalVertexIndex + subcurvePoints > vertexIndex )
      {
        targetCurveIndex = curveIdx;
        vertexInCurve = vertexIndex - globalVertexIndex;
        break;
      }
      globalVertexIndex += subcurvePoints - 1;
    }
 
    if ( targetCurveIndex == -1 )
    {
      throw QgsInvalidArgumentException( "While generating output: unable to find curve within compound." );
    }
 
    const QgsCurve *targetCurve = compound->curveAt( targetCurveIndex );
 
    // Add curves before the target curve
    for ( int i = 0; i < targetCurveIndex; ++i )
    {
      std::unique_ptr<QgsCurve> tmpCurv( compound->curveAt( i )->clone() );
      if ( curve->isClosed() && vertexIndex == curve->numPoints() - 1 )
      {
        tmpCurv->insertVertex( QgsVertexId( 0, 0, 1 ), lastNewPoint );
        tmpCurv->deleteVertex( QgsVertexId( 0, 0, 0 ) );
      }
      newCompound->addCurve( tmpCurv.release() );
    }
 
    // Handle the curve containing the vertex
    if ( vertexInCurve > 0 )
    {
      QVector<QgsPoint> beforePoints;
      for ( int j = 0; j < vertexInCurve; ++j )
      {
        beforePoints.append( targetCurve->vertexAt( QgsVertexId( 0, 0, j ) ) );
      }
      beforePoints.append( firstNewPoint );
 
      if ( beforePoints.size() > 1 )
      {
        auto beforeVertex = std::make_unique<QgsLineString>( beforePoints );
        newCompound->addCurve( beforeVertex.release() );
      }
    }
 
    if ( operation == QgsGeometry::ChamferFilletOperationType::Fillet )
    {
      // Add the fillet arc - for CompoundCurve, preserve circular nature unless segments > 0
      if ( segments <= 0 )
      {
        // Preserve circular arc
        auto filletArc = std::make_unique<QgsCircularString>();
        filletArc->setPoints( { firstNewPoint, middlePoint, lastNewPoint } );
        newCompound->addCurve( filletArc.release() );
      }
      else
      {
        // Segmentize the arc
        QgsCircularString tempArc;
        tempArc.setPoints( { firstNewPoint, middlePoint, lastNewPoint } );
 
        const double angleTolerance = ( 2.0 * M_PI ) / ( 4.0 * segments );
        std::unique_ptr<QgsLineString> segmentizedArc( tempArc.curveToLine( angleTolerance, QgsAbstractGeometry::MaximumAngle ) );
 
        newCompound->addCurve( segmentizedArc.release() );
      }
    }
    else
    {
      auto chamferLine = std::make_unique<QgsLineString>(
                           QVector<QgsPoint> { firstNewPoint, lastNewPoint }
                         );
      newCompound->addCurve( chamferLine.release() );
    }
 
    if ( vertexInCurve < targetCurve->numPoints() - 1 )
    {
      QVector<QgsPoint> afterPoints;
      afterPoints.append( lastNewPoint );
      for ( int j = vertexInCurve + 1; j < targetCurve->numPoints(); ++j )
      {
        afterPoints.append( targetCurve->vertexAt( QgsVertexId( 0, 0, j ) ) );
      }
 
      if ( afterPoints.size() > 1 )
      {
        auto afterVertex = std::make_unique<QgsLineString>( afterPoints );
        newCompound->addCurve( afterVertex.release() );
      }
    }
 
    // Add curves after the target curve
    for ( int i = targetCurveIndex + 1; i < compound->nCurves(); ++i )
    {
      std::unique_ptr<QgsCurve> tmpCurv( compound->curveAt( i )->clone() );
      if ( curve->isClosed() && vertexIndex == 0 )
      {
        tmpCurv->insertVertex( QgsVertexId( 0, 0, tmpCurv->numPoints() - 1 ), firstNewPoint );
        tmpCurv->deleteVertex( QgsVertexId( 0, 0, tmpCurv->numPoints() - 1 ) );
      }
      newCompound->addCurve( tmpCurv.release() );
    }
 
    return newCompound;
  }
 
  throw QgsInvalidArgumentException( "While generating output: curse is not a QgsLineString nor a QgsCompoundCurve." );
}
 
bool QgsGeometryUtils::pointsAreCollinear( const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double epsilon )
{
  if ( pt1.is3D() )
  {
    return QgsGeometryUtilsBase::points3DAreCollinear( pt1.x(), pt1.y(), pt1.z(), pt2.x(), pt2.y(), pt2.z(), pt3.x(), pt3.y(), pt3.z(), epsilon );
  }
  else
  {
    return QgsGeometryUtilsBase::pointsAreCollinear( pt1.x(), pt1.y(), pt2.x(), pt2.y(), pt3.x(), pt3.y(), epsilon );
  }
}
 
bool QgsGeometryUtils::checkWeaklyFor3DPlane( const QgsAbstractGeometry *geom, QgsPoint &pt1, QgsPoint &pt2, QgsPoint &pt3, double epsilon )
{
  if ( !geom || !geom->is3D() || geom->nCoordinates() < 3  || qgsgeometry_cast< const QgsGeometryCollection * >( geom ) )
  {
    return false;
  }
 
  const QgsCurve *ring = nullptr;
  if ( const QgsCurve *curve = qgsgeometry_cast< const QgsCurve * >( geom ) )
  {
    ring = curve;
  }
  else if ( const QgsCurvePolygon *curvePolygon = qgsgeometry_cast< const QgsCurvePolygon * >( geom ) )
  {
    // curve polygon case, consider exterior ring only
    ring = curvePolygon->exteriorRing();
  }
 
  if ( ring )
  {
    QgsVertexIterator ringIt = ring->vertices();
    pt1 = ringIt.next();
 
    // Find a second distinct point
    while ( ringIt.hasNext() )
    {
      pt2 = ringIt.next();
      if ( !pt2.fuzzyEqual( pt1, epsilon ) )
      {
        // Find a third non-collinear point
        while ( ringIt.hasNext() )
        {
          pt3 = ringIt.next();
          if ( !QgsGeometryUtils::pointsAreCollinear( pt1, pt2, pt3, epsilon ) )
          {
            return true;
          }
        }
      }
    }
  }
 
  return false;
}