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qgsgeometryutils.cpp
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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 "qgscurvev2.h"
#include "qgscurvepolygonv2.h"
#include "qgsgeometrycollectionv2.h"
#include "qgslinestringv2.h"
#include "qgswkbptr.h"
#include <QStringList>
#include <QVector>
QList<QgsLineStringV2*> QgsGeometryUtils::extractLineStrings( const QgsAbstractGeometryV2* geom )
{
QList< QgsLineStringV2* > linestrings;
if ( !geom )
return linestrings;
QList< const QgsAbstractGeometryV2 * > geometries;
geometries << geom;
while ( ! geometries.isEmpty() )
{
const QgsAbstractGeometryV2* g = geometries.takeFirst();
if ( const QgsCurveV2* curve = dynamic_cast< const QgsCurveV2* >( g ) )
{
linestrings << static_cast< QgsLineStringV2* >( curve->segmentize() );
}
else if ( const QgsGeometryCollectionV2* collection = dynamic_cast< const QgsGeometryCollectionV2* >( g ) )
{
for ( int i = 0; i < collection->numGeometries(); ++i )
{
geometries.append( collection->geometryN( i ) );
}
}
else if ( const QgsCurvePolygonV2* curvePolygon = dynamic_cast< const QgsCurvePolygonV2* >( g ) )
{
if ( curvePolygon->exteriorRing() )
linestrings << static_cast< QgsLineStringV2* >( curvePolygon->exteriorRing()->segmentize() );
for ( int i = 0; i < curvePolygon->numInteriorRings(); ++i )
{
linestrings << static_cast< QgsLineStringV2* >( curvePolygon->interiorRing( i )->segmentize() );
}
}
}
return linestrings;
}
QgsPointV2 QgsGeometryUtils::closestVertex( const QgsAbstractGeometryV2& geom, const QgsPointV2& pt, QgsVertexId& id )
{
double minDist = std::numeric_limits<double>::max();
double currentDist = 0;
QgsPointV2 minDistPoint;
id = QgsVertexId(); // set as invalid
QgsVertexId vertexId;
QgsPointV2 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 retuned. For the node 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;
}
}
return minDistPoint;
}
void QgsGeometryUtils::adjacentVertices( const QgsAbstractGeometryV2& geom, QgsVertexId atVertex, QgsVertexId& beforeVertex, QgsVertexId& afterVertex )
{
bool polygonType = ( geom.dimension() == 2 );
QgsCoordinateSequenceV2 coords = geom.coordinateSequence();
//get feature
if ( coords.size() <= atVertex.part )
{
return; //error, no such feature
}
const QgsRingSequenceV2 &part = coords.at( atVertex.part );
//get ring
if ( part.size() <= atVertex.ring )
{
return; //error, no such ring
}
const QgsPointSequenceV2 &ring = part.at( atVertex.ring );
if ( ring.size() <= atVertex.vertex )
{
return;
}
//vertex in the middle
if ( atVertex.vertex > 0 && atVertex.vertex < ring.size() - 1 )
{
beforeVertex.part = atVertex.part;
beforeVertex.ring = atVertex.ring;
beforeVertex.vertex = atVertex.vertex - 1;
afterVertex.part = atVertex.part;
afterVertex.ring = atVertex.ring;
afterVertex.vertex = atVertex.vertex + 1;
}
else if ( atVertex.vertex == 0 )
{
afterVertex.part = atVertex.part;
afterVertex.ring = atVertex.ring;
afterVertex.vertex = atVertex.vertex + 1;
if ( polygonType && ring.size() > 3 )
{
beforeVertex.part = atVertex.part;
beforeVertex.ring = atVertex.ring;
beforeVertex.vertex = ring.size() - 2;
}
else
{
beforeVertex = QgsVertexId(); //before vertex invalid
}
}
else if ( atVertex.vertex == ring.size() - 1 )
{
beforeVertex.part = atVertex.part;
beforeVertex.ring = atVertex.ring;
beforeVertex.vertex = atVertex.vertex - 1;
if ( polygonType )
{
afterVertex.part = atVertex.part;
afterVertex.ring = atVertex.ring;
afterVertex.vertex = 1;
}
else
{
afterVertex = QgsVertexId(); //after vertex invalid
}
}
}
double QgsGeometryUtils::sqrDistance2D( const QgsPointV2& pt1, const QgsPointV2& pt2 )
{
return ( pt1.x() - pt2.x() ) * ( pt1.x() - pt2.x() ) + ( pt1.y() - pt2.y() ) * ( pt1.y() - pt2.y() );
}
double QgsGeometryUtils::sqrDistToLine( double ptX, double ptY, double x1, double y1, double x2, double y2, double& minDistX, double& minDistY, double epsilon )
{
//normal vector
double nx = y2 - y1;
double ny = -( x2 - x1 );
double t;
t = ( ptX * ny - ptY * nx - x1 * ny + y1 * nx ) / (( x2 - x1 ) * ny - ( y2 - y1 ) * nx );
if ( t < 0.0 )
{
minDistX = x1;
minDistY = y1;
}
else if ( t > 1.0 )
{
minDistX = x2;
minDistY = y2;
}
else
{
minDistX = x1 + t * ( x2 - x1 );
minDistY = y1 + t * ( y2 - y1 );
}
double dist = ( minDistX - ptX ) * ( minDistX - ptX ) + ( minDistY - ptY ) * ( minDistY - ptY );
//prevent rounding errors if the point is directly on the segment
if ( qgsDoubleNear( dist, 0.0, epsilon ) )
{
minDistX = ptX;
minDistY = ptY;
return 0.0;
}
return dist;
}
bool QgsGeometryUtils::lineIntersection( const QgsPointV2& p1, QgsVector v, const QgsPointV2& q1, QgsVector w, QgsPointV2& inter )
{
double d = v.y() * w.x() - v.x() * w.y();
if ( qgsDoubleNear( d, 0 ) )
return false;
double dx = q1.x() - p1.x();
double dy = q1.y() - p1.y();
double k = ( dy * w.x() - dx * w.y() ) / d;
inter = QgsPointV2( p1.x() + v.x() * k, p1.y() + v.y() * k );
return true;
}
bool QgsGeometryUtils::segmentIntersection( const QgsPointV2 &p1, const QgsPointV2 &p2, const QgsPointV2 &q1, const QgsPointV2 &q2, QgsPointV2 &inter, double tolerance )
{
QgsVector v( p2.x() - p1.x(), p2.y() - p1.y() );
QgsVector w( q2.x() - q1.x(), q2.y() - q1.y() );
double vl = v.length();
double wl = w.length();
if ( qFuzzyIsNull( vl ) || qFuzzyIsNull( wl ) )
{
return false;
}
v = v / vl;
w = w / wl;
if ( !QgsGeometryUtils::lineIntersection( p1, v, q1, w, inter ) )
return false;
double lambdav = QgsVector( inter.x() - p1.x(), inter.y() - p1.y() ) * v;
if ( lambdav < 0. + tolerance || lambdav > vl - tolerance )
return false;
double lambdaw = QgsVector( inter.x() - q1.x(), inter.y() - q1.y() ) * w;
if ( lambdaw < 0. + tolerance || lambdaw >= wl - tolerance )
return false;
return true;
}
QList<QgsGeometryUtils::SelfIntersection> QgsGeometryUtils::getSelfIntersections( const QgsAbstractGeometryV2 *geom, int part, int ring, double tolerance )
{
QList<SelfIntersection> intersections;
int n = geom->vertexCount( part, ring );
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++ )
{
QgsPointV2 pi = geom->vertexAt( QgsVertexId( part, ring, i ) );
QgsPointV2 pj = geom->vertexAt( QgsVertexId( part, ring, j ) );
if ( QgsGeometryUtils::sqrDistance2D( pi, pj ) < tolerance * tolerance ) continue;
// Don't test neighboring edges
int start = j + 1;
int end = i == 0 && isClosed ? n - 1 : n;
for ( int k = start, l = start + 1; l < end; k = l++ )
{
QgsPointV2 pk = geom->vertexAt( QgsVertexId( part, ring, k ) );
QgsPointV2 pl = geom->vertexAt( QgsVertexId( part, ring, l ) );
QgsPointV2 inter;
if ( !QgsGeometryUtils::segmentIntersection( pi, pj, pk, pl, inter, tolerance ) ) continue;
SelfIntersection s;
s.segment1 = i;
s.segment2 = k;
if ( s.segment1 > s.segment2 )
{
qSwap( s.segment1, s.segment2 );
}
s.point = inter;
intersections.append( s );
}
}
return intersections;
}
double QgsGeometryUtils::leftOfLine( double x, double y, double x1, double y1, double x2, double y2 )
{
double f1 = x - x1;
double f2 = y2 - y1;
double f3 = y - y1;
double f4 = x2 - x1;
return f1*f2 - f3*f4;
}
QgsPointV2 QgsGeometryUtils::pointOnLineWithDistance( const QgsPointV2& startPoint, const QgsPointV2& directionPoint, double distance )
{
double dx = directionPoint.x() - startPoint.x();
double dy = directionPoint.y() - startPoint.y();
double length = sqrt( dx * dx + dy * dy );
if ( qgsDoubleNear( length, 0.0 ) )
{
return startPoint;
}
double scaleFactor = distance / length;
return QgsPointV2( startPoint.x() + dx * scaleFactor, startPoint.y() + dy * scaleFactor );
}
double QgsGeometryUtils::ccwAngle( double dy, double dx )
{
double angle = atan2( dy, dx ) * 180 / M_PI;
if ( angle < 0 )
{
return 360 + angle;
}
else if ( angle > 360 )
{
return 360 - angle;
}
return angle;
}
void QgsGeometryUtils::circleCenterRadius( const QgsPointV2& pt1, const QgsPointV2& pt2, const QgsPointV2& pt3, double& radius, double& centerX, double& centerY )
{
double dx21, dy21, dx31, dy31, h21, h31, d;
//closed circle
if ( qgsDoubleNear( pt1.x(), pt3.x() ) && qgsDoubleNear( pt1.y(), pt3.y() ) )
{
centerX = pt2.x();
centerY = pt2.y();
radius = sqrt( pow( pt2.x() - pt1.x(), 2.0 ) + pow( pt2.y() - pt1.y(), 2.0 ) );
return;
}
// Using cartesian circumcenter eguations from page https://en.wikipedia.org/wiki/Circumscribed_circle
dx21 = pt2.x() - pt1.x();
dy21 = pt2.y() - pt1.y();
dx31 = pt3.x() - pt1.x();
dy31 = pt3.y() - pt1.y();
h21 = pow( dx21, 2.0 ) + pow( dy21, 2.0 );
h31 = pow( dx31, 2.0 ) + pow( dy31, 2.0 );
// 2*Cross product, d<0 means clockwise and d>0 counterclockwise sweeping angle
d = 2 * ( dx21 * dy31 - dx31 * dy21 );
// Check colinearity, Cross product = 0
if ( qgsDoubleNear( fabs( d ), 0.0, 0.00000000001 ) )
{
radius = -1.0;
return;
}
// Calculate centroid coordinates and radius
centerX = pt1.x() + ( h21 * dy31 - h31 * dy21 ) / d;
centerY = pt1.y() - ( h21 * dx31 - h31 * dx21 ) / d;
radius = sqrt( pow( centerX - pt1.x(), 2.0 ) + pow( centerY - pt1.y(), 2.0 ) );
}
bool QgsGeometryUtils::circleClockwise( double angle1, double angle2, double angle3 )
{
if ( angle3 >= angle1 )
{
if ( angle2 > angle1 && angle2 < angle3 )
{
return false;
}
else
{
return true;
}
}
else
{
if ( angle2 > angle1 || angle2 < angle3 )
{
return false;
}
else
{
return true;
}
}
}
bool QgsGeometryUtils::circleAngleBetween( double angle, double angle1, double angle2, bool clockwise )
{
if ( clockwise )
{
if ( angle2 < angle1 )
{
return ( angle <= angle1 && angle >= angle2 );
}
else
{
return ( angle <= angle1 || angle >= angle2 );
}
}
else
{
if ( angle2 > angle1 )
{
return ( angle >= angle1 && angle <= angle2 );
}
else
{
return ( angle >= angle1 || angle <= angle2 );
}
}
}
bool QgsGeometryUtils::angleOnCircle( double angle, double angle1, double angle2, double angle3 )
{
bool clockwise = circleClockwise( angle1, angle2, angle3 );
return circleAngleBetween( angle, angle1, angle3, clockwise );
}
double QgsGeometryUtils::circleLength( double x1, double y1, double x2, double y2, double x3, double y3 )
{
double centerX, centerY, radius;
circleCenterRadius( QgsPointV2( x1, y1 ), QgsPointV2( x2, y2 ), QgsPointV2( x3, y3 ), radius, centerX, centerY );
double length = M_PI / 180.0 * radius * sweepAngle( centerX, centerY, x1, y1, x2, y2, x3, y3 );
if ( length < 0 )
{
length = -length;
}
return length;
}
double QgsGeometryUtils::sweepAngle( double centerX, double centerY, double x1, double y1, double x2, double y2, double x3, double y3 )
{
double p1Angle = QgsGeometryUtils::ccwAngle( y1 - centerY, x1 - centerX );
double p2Angle = QgsGeometryUtils::ccwAngle( y2 - centerY, x2 - centerX );
double p3Angle = QgsGeometryUtils::ccwAngle( y3 - centerY, x3 - centerX );
if ( p3Angle >= p1Angle )
{
if ( p2Angle > p1Angle && p2Angle < p3Angle )
{
return( p3Angle - p1Angle );
}
else
{
return ( - ( p1Angle + ( 360 - p3Angle ) ) );
}
}
else
{
if ( p2Angle < p1Angle && p2Angle > p3Angle )
{
return( -( p1Angle - p3Angle ) );
}
else
{
return( p3Angle + ( 360 - p1Angle ) );
}
}
}
bool QgsGeometryUtils::segmentMidPoint( const QgsPointV2& p1, const QgsPointV2& p2, QgsPointV2& result, double radius, const QgsPointV2& mousePos )
{
QgsPointV2 midPoint(( p1.x() + p2.x() ) / 2.0, ( p1.y() + p2.y() ) / 2.0 );
double midDist = sqrt( sqrDistance2D( p1, midPoint ) );
if ( radius < midDist )
{
return false;
}
double centerMidDist = sqrt( radius * radius - midDist * midDist );
double dist = radius - centerMidDist;
double midDx = midPoint.x() - p1.x();
double midDy = midPoint.y() - p1.y();
//get the four possible midpoints
QVector<QgsPointV2> possibleMidPoints;
possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPointV2( midPoint.x() - midDy, midPoint.y() + midDx ), dist ) );
possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPointV2( midPoint.x() - midDy, midPoint.y() + midDx ), 2 * radius - dist ) );
possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPointV2( midPoint.x() + midDy, midPoint.y() - midDx ), dist ) );
possibleMidPoints.append( pointOnLineWithDistance( midPoint, QgsPointV2( 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 )
{
double currentDist = sqrDistance2D( mousePos, possibleMidPoints.at( i ) );
if ( currentDist < minDist )
{
minDistIndex = i;
minDist = currentDist;
}
}
if ( minDistIndex == -1 )
{
return false;
}
result = possibleMidPoints.at( minDistIndex );
return true;
}
double QgsGeometryUtils::circleTangentDirection( const QgsPointV2& tangentPoint, const QgsPointV2& cp1,
const QgsPointV2& cp2, const QgsPointV2& cp3 )
{
//calculate circle midpoint
double mX, mY, radius;
circleCenterRadius( cp1, cp2, cp3, radius, mX, mY );
double p1Angle = QgsGeometryUtils::ccwAngle( cp1.y() - mY, cp1.x() - mX );
double p2Angle = QgsGeometryUtils::ccwAngle( cp2.y() - mY, cp2.x() - mX );
double p3Angle = QgsGeometryUtils::ccwAngle( cp3.y() - mY, cp3.x() - mX );
if ( circleClockwise( p1Angle, p2Angle, p3Angle ) )
{
return lineAngle( tangentPoint.x(), tangentPoint.y(), mX, mY );
}
else
{
return lineAngle( mX, mY, tangentPoint.x(), tangentPoint.y() );
}
}
QgsPointSequenceV2 QgsGeometryUtils::pointsFromWKT( const QString &wktCoordinateList, bool is3D, bool isMeasure )
{
int dim = 2 + is3D + isMeasure;
QgsPointSequenceV2 points;
QStringList coordList = wktCoordinateList.split( ',', QString::SkipEmptyParts );
//first scan through for extra unexpected dimensions
bool foundZ = false;
bool foundM = false;
Q_FOREACH ( const QString& pointCoordinates, coordList )
{
QStringList coordinates = pointCoordinates.split( ' ', QString::SkipEmptyParts );
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;
}
}
Q_FOREACH ( const QString& pointCoordinates, coordList )
{
QStringList coordinates = pointCoordinates.split( ' ', QString::SkipEmptyParts );
if ( coordinates.size() < dim )
continue;
int idx = 0;
double x = coordinates[idx++].toDouble();
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();
QgsWKBTypes::Type t = QgsWKBTypes::Point;
if ( is3D || foundZ )
{
if ( isMeasure || foundM )
t = QgsWKBTypes::PointZM;
else
t = QgsWKBTypes::PointZ;
}
else
{
if ( isMeasure || foundM )
t = QgsWKBTypes::PointM;
else
t = QgsWKBTypes::Point;
}
points.append( QgsPointV2( t, x, y, z, m ) );
}
return points;
}
void QgsGeometryUtils::pointsToWKB( QgsWkbPtr& wkb, const QgsPointSequenceV2 &points, bool is3D, bool isMeasure )
{
wkb << static_cast<quint32>( points.size() );
Q_FOREACH ( const QgsPointV2& point, points )
{
wkb << point.x() << point.y();
if ( is3D )
{
wkb << point.z();
}
if ( isMeasure )
{
wkb << point.m();
}
}
}
QString QgsGeometryUtils::pointsToWKT( const QgsPointSequenceV2 &points, int precision, bool is3D, bool isMeasure )
{
QString wkt = "(";
Q_FOREACH ( const QgsPointV2& 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 += ", ";
}
if ( wkt.endsWith( ", " ) )
wkt.chop( 2 ); // Remove last ", "
wkt += ')';
return wkt;
}
QDomElement QgsGeometryUtils::pointsToGML2( const QgsPointSequenceV2 &points, QDomDocument& doc, int precision, const QString &ns )
{
QDomElement elemCoordinates = doc.createElementNS( ns, "coordinates" );
// coordinate separator
QString cs = ",";
// tupel separator
QString ts = " ";
elemCoordinates.setAttribute( "cs", cs );
elemCoordinates.setAttribute( "ts", ts );
QString strCoordinates;
Q_FOREACH ( const QgsPointV2& p, points )
strCoordinates += qgsDoubleToString( p.x(), precision ) + cs + qgsDoubleToString( p.y(), precision ) + ts;
if ( strCoordinates.endsWith( ts ) )
strCoordinates.chop( 1 ); // Remove trailing space
elemCoordinates.appendChild( doc.createTextNode( strCoordinates ) );
return elemCoordinates;
}
QDomElement QgsGeometryUtils::pointsToGML3( const QgsPointSequenceV2 &points, QDomDocument& doc, int precision, const QString &ns, bool is3D )
{
QDomElement elemPosList = doc.createElementNS( ns, "posList" );
elemPosList.setAttribute( "srsDimension", is3D ? 3 : 2 );
QString strCoordinates;
Q_FOREACH ( const QgsPointV2& p, points )
{
strCoordinates += qgsDoubleToString( p.x(), precision ) + ' ' + qgsDoubleToString( p.y(), 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 QgsPointSequenceV2 &points, int precision )
{
QString json = "[ ";
Q_FOREACH ( const QgsPointV2& p, points )
{
json += '[' + qgsDoubleToString( p.x(), precision ) + ", " + qgsDoubleToString( p.y(), precision ) + "], ";
}
if ( json.endsWith( ", " ) )
{
json.chop( 2 ); // Remove last ", "
}
json += ']';
return json;
}
double QgsGeometryUtils::normalizedAngle( double angle )
{
double clippedAngle = angle;
if ( clippedAngle >= M_PI * 2 || clippedAngle <= -2 * M_PI )
{
clippedAngle = fmod( clippedAngle, 2 * M_PI );
}
if ( clippedAngle < 0.0 )
{
clippedAngle += 2 * M_PI;
}
return clippedAngle;
}
QPair<QgsWKBTypes::Type, QString> QgsGeometryUtils::wktReadBlock( const QString &wkt )
{
QgsWKBTypes::Type wkbType = QgsWKBTypes::parseType( wkt );
QRegExp cooRegEx( "^[^\\(]*\\((.*)\\)[^\\)]*$" );
QString contents = cooRegEx.indexIn( wkt ) >= 0 ? cooRegEx.cap( 1 ) : QString();
return qMakePair( wkbType, contents );
}
QStringList QgsGeometryUtils::wktGetChildBlocks( const QString &wkt, const QString& defaultType )
{
int level = 0;
QString block;
QStringList blocks;
for ( int i = 0, n = wkt.length(); i < n; ++i )
{
if ( wkt[i].isSpace() && level == 0 )
continue;
if ( wkt[i] == ',' && level == 0 )
{
if ( !block.isEmpty() )
{
if ( block.startsWith( '(' ) && !defaultType.isEmpty() )
block.prepend( defaultType + ' ' );
blocks.append( block );
}
block.clear();
continue;
}
if ( wkt[i] == '(' )
++level;
else if ( wkt[i] == ')' )
--level;
block += wkt[i];
}
if ( !block.isEmpty() )
{
if ( block.startsWith( '(' ) && !defaultType.isEmpty() )
block.prepend( defaultType + ' ' );
blocks.append( block );
}
return blocks;
}
double QgsGeometryUtils::lineAngle( double x1, double y1, double x2, double y2 )
{
double at = atan2( y2 - y1, x2 - x1 );
double a = -at + M_PI / 2.0;
return normalizedAngle( a );
}
double QgsGeometryUtils::linePerpendicularAngle( double x1, double y1, double x2, double y2 )
{
double a = lineAngle( x1, y1, x2, y2 );
a += ( M_PI / 2.0 );
return normalizedAngle( a );
}
double QgsGeometryUtils::averageAngle( double x1, double y1, double x2, double y2, double x3, double y3 )
{
// calc average angle between the previous and next point
double a1 = lineAngle( x1, y1, x2, y2 );
double a2 = lineAngle( x2, y2, x3, y3 );
return averageAngle( a1, a2 );
}
double QgsGeometryUtils::averageAngle( double a1, double a2 )
{
a1 = normalizedAngle( a1 );
a2 = normalizedAngle( a2 );
double clockwiseDiff = 0.0;
if ( a2 >= a1 )
{
clockwiseDiff = a2 - a1;
}
else
{
clockwiseDiff = a2 + ( 2 * M_PI - a1 );
}
double counterClockwiseDiff = 2 * M_PI - clockwiseDiff;
double resultAngle = 0;
if ( clockwiseDiff <= counterClockwiseDiff )
{
resultAngle = a1 + clockwiseDiff / 2.0;
}
else
{
resultAngle = a1 - counterClockwiseDiff / 2.0;
}
return normalizedAngle( resultAngle );
}