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qgslinestring.cpp
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qgslinestring.cpp
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/***************************************************************************
qgslinestring.cpp
-------------------
begin : September 2014
copyright : (C) 2014 by Marco Hugentobler
email : marco at sourcepole dot ch
***************************************************************************/
/***************************************************************************
* *
* 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 "qgslinestring.h"
#include "qgsapplication.h"
#include "qgscompoundcurve.h"
#include "qgscoordinatetransform.h"
#include "qgsgeometryutils.h"
#include "qgsmaptopixel.h"
#include "qgswkbptr.h"
#include <QPainter>
#include <limits>
#include <QDomDocument>
#include <QtCore/qmath.h>
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
QgsLineString::QgsLineString(): QgsCurve()
{
mWkbType = QgsWkbTypes::LineString;
}
QgsLineString::QgsLineString( const QVector<QgsPoint> &points )
{
if ( points.isEmpty() )
{
mWkbType = QgsWkbTypes::LineString;
return;
}
QgsWkbTypes::Type ptType = points.at( 0 ).wkbType();
mWkbType = QgsWkbTypes::zmType( QgsWkbTypes::LineString, QgsWkbTypes::hasZ( ptType ), QgsWkbTypes::hasM( ptType ) );
mX.resize( points.count() );
mY.resize( points.count() );
double *x = mX.data();
double *y = mY.data();
double *z = nullptr;
double *m = nullptr;
if ( QgsWkbTypes::hasZ( mWkbType ) )
{
mZ.resize( points.count() );
z = mZ.data();
}
if ( QgsWkbTypes::hasM( mWkbType ) )
{
mM.resize( points.count() );
m = mM.data();
}
Q_FOREACH ( const QgsPoint &pt, points )
{
*x++ = pt.x();
*y++ = pt.y();
if ( z )
*z++ = pt.z();
if ( m )
*m++ = pt.m();
}
}
QgsLineString::QgsLineString( const QVector<double> &x, const QVector<double> &y, const QVector<double> &z, const QVector<double> &m )
{
mWkbType = QgsWkbTypes::LineString;
int pointCount = qMin( x.size(), y.size() );
if ( x.size() == pointCount )
{
mX = x;
}
else
{
mX = x.mid( 0, pointCount );
}
if ( y.size() == pointCount )
{
mY = y;
}
else
{
mY = y.mid( 0, pointCount );
}
if ( !z.isEmpty() && z.count() >= pointCount )
{
mWkbType = QgsWkbTypes::addZ( mWkbType );
if ( z.size() == pointCount )
{
mZ = z;
}
else
{
mZ = z.mid( 0, pointCount );
}
}
if ( !m.isEmpty() && m.count() >= pointCount )
{
mWkbType = QgsWkbTypes::addM( mWkbType );
if ( m.size() == pointCount )
{
mM = m;
}
else
{
mM = m.mid( 0, pointCount );
}
}
}
QgsLineString::QgsLineString( const QList<QgsPointXY> &points )
{
mWkbType = QgsWkbTypes::LineString;
mX.reserve( points.size() );
mY.reserve( points.size() );
Q_FOREACH ( const QgsPointXY &p, points )
{
mX << p.x();
mY << p.y();
}
}
bool QgsLineString::operator==( const QgsCurve &other ) const
{
const QgsLineString *otherLine = dynamic_cast< const QgsLineString * >( &other );
if ( !otherLine )
return false;
if ( mWkbType != otherLine->mWkbType )
return false;
if ( mX.count() != otherLine->mX.count() )
return false;
for ( int i = 0; i < mX.count(); ++i )
{
if ( !qgsDoubleNear( mX.at( i ), otherLine->mX.at( i ) )
|| !qgsDoubleNear( mY.at( i ), otherLine->mY.at( i ) ) )
return false;
if ( is3D() && !qgsDoubleNear( mZ.at( i ), otherLine->mZ.at( i ) ) )
return false;
if ( isMeasure() && !qgsDoubleNear( mM.at( i ), otherLine->mM.at( i ) ) )
return false;
}
return true;
}
bool QgsLineString::operator!=( const QgsCurve &other ) const
{
return !operator==( other );
}
QgsLineString *QgsLineString::clone() const
{
return new QgsLineString( *this );
}
void QgsLineString::clear()
{
mX.clear();
mY.clear();
mZ.clear();
mM.clear();
mWkbType = QgsWkbTypes::LineString;
clearCache();
}
bool QgsLineString::isEmpty() const
{
return mX.isEmpty();
}
bool QgsLineString::fromWkb( QgsConstWkbPtr &wkbPtr )
{
if ( !wkbPtr )
{
return false;
}
QgsWkbTypes::Type type = wkbPtr.readHeader();
if ( QgsWkbTypes::flatType( type ) != QgsWkbTypes::LineString )
{
return false;
}
mWkbType = type;
importVerticesFromWkb( wkbPtr );
return true;
}
void QgsLineString::fromWkbPoints( QgsWkbTypes::Type type, const QgsConstWkbPtr &wkb )
{
mWkbType = type;
importVerticesFromWkb( wkb );
}
QgsRectangle QgsLineString::calculateBoundingBox() const
{
double xmin = std::numeric_limits<double>::max();
double ymin = std::numeric_limits<double>::max();
double xmax = -std::numeric_limits<double>::max();
double ymax = -std::numeric_limits<double>::max();
Q_FOREACH ( double x, mX )
{
if ( x < xmin )
xmin = x;
if ( x > xmax )
xmax = x;
}
Q_FOREACH ( double y, mY )
{
if ( y < ymin )
ymin = y;
if ( y > ymax )
ymax = y;
}
return QgsRectangle( xmin, ymin, xmax, ymax );
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
bool QgsLineString::fromWkt( const QString &wkt )
{
clear();
QPair<QgsWkbTypes::Type, QString> parts = QgsGeometryUtils::wktReadBlock( wkt );
if ( QgsWkbTypes::flatType( parts.first ) != QgsWkbTypes::LineString )
return false;
mWkbType = parts.first;
setPoints( QgsGeometryUtils::pointsFromWKT( parts.second, is3D(), isMeasure() ) );
return true;
}
QByteArray QgsLineString::asWkb() const
{
int binarySize = sizeof( char ) + sizeof( quint32 ) + sizeof( quint32 );
binarySize += numPoints() * ( 2 + is3D() + isMeasure() ) * sizeof( double );
QByteArray wkbArray;
wkbArray.resize( binarySize );
QgsWkbPtr wkb( wkbArray );
wkb << static_cast<char>( QgsApplication::endian() );
wkb << static_cast<quint32>( wkbType() );
QgsPointSequence pts;
points( pts );
QgsGeometryUtils::pointsToWKB( wkb, pts, is3D(), isMeasure() );
return wkbArray;
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
QString QgsLineString::asWkt( int precision ) const
{
QString wkt = wktTypeStr() + ' ';
QgsPointSequence pts;
points( pts );
wkt += QgsGeometryUtils::pointsToWKT( pts, precision, is3D(), isMeasure() );
return wkt;
}
QDomElement QgsLineString::asGML2( QDomDocument &doc, int precision, const QString &ns ) const
{
QgsPointSequence pts;
points( pts );
QDomElement elemLineString = doc.createElementNS( ns, QStringLiteral( "LineString" ) );
elemLineString.appendChild( QgsGeometryUtils::pointsToGML2( pts, doc, precision, ns ) );
return elemLineString;
}
QDomElement QgsLineString::asGML3( QDomDocument &doc, int precision, const QString &ns ) const
{
QgsPointSequence pts;
points( pts );
QDomElement elemLineString = doc.createElementNS( ns, QStringLiteral( "LineString" ) );
elemLineString.appendChild( QgsGeometryUtils::pointsToGML3( pts, doc, precision, ns, is3D() ) );
return elemLineString;
}
QString QgsLineString::asJSON( int precision ) const
{
QgsPointSequence pts;
points( pts );
return "{\"type\": \"LineString\", \"coordinates\": " + QgsGeometryUtils::pointsToJSON( pts, precision ) + '}';
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
double QgsLineString::length() const
{
double length = 0;
int size = mX.size();
double dx, dy;
for ( int i = 1; i < size; ++i )
{
dx = mX.at( i ) - mX.at( i - 1 );
dy = mY.at( i ) - mY.at( i - 1 );
length += sqrt( dx * dx + dy * dy );
}
return length;
}
QgsPoint QgsLineString::startPoint() const
{
if ( numPoints() < 1 )
{
return QgsPoint();
}
return pointN( 0 );
}
QgsPoint QgsLineString::endPoint() const
{
if ( numPoints() < 1 )
{
return QgsPoint();
}
return pointN( numPoints() - 1 );
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
QgsLineString *QgsLineString::curveToLine( double tolerance, SegmentationToleranceType toleranceType ) const
{
Q_UNUSED( tolerance );
Q_UNUSED( toleranceType );
return static_cast<QgsLineString *>( clone() );
}
int QgsLineString::numPoints() const
{
return mX.size();
}
QgsPoint QgsLineString::pointN( int i ) const
{
if ( i < 0 || i >= mX.size() )
{
return QgsPoint();
}
double x = mX.at( i );
double y = mY.at( i );
double z = 0;
double m = 0;
bool hasZ = is3D();
if ( hasZ )
{
z = mZ.at( i );
}
bool hasM = isMeasure();
if ( hasM )
{
m = mM.at( i );
}
QgsWkbTypes::Type t = QgsWkbTypes::Point;
if ( mWkbType == QgsWkbTypes::LineString25D )
{
t = QgsWkbTypes::Point25D;
}
else if ( hasZ && hasM )
{
t = QgsWkbTypes::PointZM;
}
else if ( hasZ )
{
t = QgsWkbTypes::PointZ;
}
else if ( hasM )
{
t = QgsWkbTypes::PointM;
}
return QgsPoint( t, x, y, z, m );
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
double QgsLineString::xAt( int index ) const
{
if ( index >= 0 && index < mX.size() )
return mX.at( index );
else
return 0.0;
}
double QgsLineString::yAt( int index ) const
{
if ( index >= 0 && index < mY.size() )
return mY.at( index );
else
return 0.0;
}
double QgsLineString::zAt( int index ) const
{
if ( index >= 0 && index < mZ.size() )
return mZ.at( index );
else
return 0.0;
}
double QgsLineString::mAt( int index ) const
{
if ( index >= 0 && index < mM.size() )
return mM.at( index );
else
return 0.0;
}
void QgsLineString::setXAt( int index, double x )
{
if ( index >= 0 && index < mX.size() )
mX[ index ] = x;
clearCache();
}
void QgsLineString::setYAt( int index, double y )
{
if ( index >= 0 && index < mY.size() )
mY[ index ] = y;
clearCache();
}
void QgsLineString::setZAt( int index, double z )
{
if ( index >= 0 && index < mZ.size() )
mZ[ index ] = z;
}
void QgsLineString::setMAt( int index, double m )
{
if ( index >= 0 && index < mM.size() )
mM[ index ] = m;
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::points( QgsPointSequence &pts ) const
{
pts.clear();
int nPoints = numPoints();
for ( int i = 0; i < nPoints; ++i )
{
pts.push_back( pointN( i ) );
}
}
void QgsLineString::setPoints( const QgsPointSequence &points )
{
clearCache(); //set bounding box invalid
if ( points.isEmpty() )
{
clear();
return;
}
//get wkb type from first point
const QgsPoint &firstPt = points.at( 0 );
bool hasZ = firstPt.is3D();
bool hasM = firstPt.isMeasure();
setZMTypeFromSubGeometry( &firstPt, QgsWkbTypes::LineString );
mX.resize( points.size() );
mY.resize( points.size() );
if ( hasZ )
{
mZ.resize( points.size() );
}
else
{
mZ.clear();
}
if ( hasM )
{
mM.resize( points.size() );
}
else
{
mM.clear();
}
for ( int i = 0; i < points.size(); ++i )
{
mX[i] = points.at( i ).x();
mY[i] = points.at( i ).y();
if ( hasZ )
{
mZ[i] = points.at( i ).z();
}
if ( hasM )
{
mM[i] = points.at( i ).m();
}
}
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::append( const QgsLineString *line )
{
if ( !line )
{
return;
}
if ( numPoints() < 1 )
{
setZMTypeFromSubGeometry( line, QgsWkbTypes::LineString );
}
// do not store duplicit points
if ( numPoints() > 0 &&
line->numPoints() > 0 &&
endPoint() == line->startPoint() )
{
mX.pop_back();
mY.pop_back();
if ( is3D() )
{
mZ.pop_back();
}
if ( isMeasure() )
{
mM.pop_back();
}
}
mX += line->mX;
mY += line->mY;
if ( is3D() )
{
if ( line->is3D() )
{
mZ += line->mZ;
}
else
{
// if append line does not have z coordinates, fill with NaN to match number of points in final line
mZ.insert( mZ.count(), mX.size() - mZ.size(), std::numeric_limits<double>::quiet_NaN() );
}
}
if ( isMeasure() )
{
if ( line->isMeasure() )
{
mM += line->mM;
}
else
{
// if append line does not have m values, fill with NaN to match number of points in final line
mM.insert( mM.count(), mX.size() - mM.size(), std::numeric_limits<double>::quiet_NaN() );
}
}
clearCache(); //set bounding box invalid
}
QgsLineString *QgsLineString::reversed() const
{
QgsLineString *copy = clone();
std::reverse( copy->mX.begin(), copy->mX.end() );
std::reverse( copy->mY.begin(), copy->mY.end() );
if ( copy->is3D() )
{
std::reverse( copy->mZ.begin(), copy->mZ.end() );
}
if ( copy->isMeasure() )
{
std::reverse( copy->mM.begin(), copy->mM.end() );
}
return copy;
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::draw( QPainter &p ) const
{
p.drawPolyline( asQPolygonF() );
}
void QgsLineString::addToPainterPath( QPainterPath &path ) const
{
int nPoints = numPoints();
if ( nPoints < 1 )
{
return;
}
if ( path.isEmpty() || path.currentPosition() != QPointF( mX.at( 0 ), mY.at( 0 ) ) )
{
path.moveTo( mX.at( 0 ), mY.at( 0 ) );
}
for ( int i = 1; i < nPoints; ++i )
{
path.lineTo( mX.at( i ), mY.at( i ) );
}
}
void QgsLineString::drawAsPolygon( QPainter &p ) const
{
p.drawPolygon( asQPolygonF() );
}
QgsAbstractGeometry *QgsLineString::toCurveType() const
{
QgsCompoundCurve *compoundCurve = new QgsCompoundCurve();
compoundCurve->addCurve( clone() );
return compoundCurve;
}
void QgsLineString::extend( double startDistance, double endDistance )
{
if ( mX.size() < 2 || mY.size() < 2 )
return;
// start of line
if ( startDistance > 0 )
{
double currentLen = sqrt( qPow( mX.at( 0 ) - mX.at( 1 ), 2 ) +
qPow( mY.at( 0 ) - mY.at( 1 ), 2 ) );
double newLen = currentLen + startDistance;
mX[ 0 ] = mX.at( 1 ) + ( mX.at( 0 ) - mX.at( 1 ) ) / currentLen * newLen;
mY[ 0 ] = mY.at( 1 ) + ( mY.at( 0 ) - mY.at( 1 ) ) / currentLen * newLen;
}
// end of line
if ( endDistance > 0 )
{
int last = mX.size() - 1;
double currentLen = sqrt( qPow( mX.at( last ) - mX.at( last - 1 ), 2 ) +
qPow( mY.at( last ) - mY.at( last - 1 ), 2 ) );
double newLen = currentLen + endDistance;
mX[ last ] = mX.at( last - 1 ) + ( mX.at( last ) - mX.at( last - 1 ) ) / currentLen * newLen;
mY[ last ] = mY.at( last - 1 ) + ( mY.at( last ) - mY.at( last - 1 ) ) / currentLen * newLen;
}
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::transform( const QgsCoordinateTransform &ct, QgsCoordinateTransform::TransformDirection d, bool transformZ )
{
double *zArray = mZ.data();
bool hasZ = is3D();
int nPoints = numPoints();
bool useDummyZ = !hasZ || !transformZ;
if ( useDummyZ )
{
zArray = new double[nPoints];
for ( int i = 0; i < nPoints; ++i )
{
zArray[i] = 0;
}
}
ct.transformCoords( nPoints, mX.data(), mY.data(), zArray, d );
if ( useDummyZ )
{
delete[] zArray;
}
clearCache();
}
void QgsLineString::transform( const QTransform &t )
{
int nPoints = numPoints();
for ( int i = 0; i < nPoints; ++i )
{
qreal x, y;
t.map( mX.at( i ), mY.at( i ), &x, &y );
mX[i] = x;
mY[i] = y;
}
clearCache();
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
bool QgsLineString::insertVertex( QgsVertexId position, const QgsPoint &vertex )
{
if ( position.vertex < 0 || position.vertex > mX.size() )
{
return false;
}
if ( mWkbType == QgsWkbTypes::Unknown || mX.isEmpty() )
{
setZMTypeFromSubGeometry( &vertex, QgsWkbTypes::LineString );
}
mX.insert( position.vertex, vertex.x() );
mY.insert( position.vertex, vertex.y() );
if ( is3D() )
{
mZ.insert( position.vertex, vertex.z() );
}
if ( isMeasure() )
{
mM.insert( position.vertex, vertex.m() );
}
clearCache(); //set bounding box invalid
return true;
}
bool QgsLineString::moveVertex( QgsVertexId position, const QgsPoint &newPos )
{
if ( position.vertex < 0 || position.vertex >= mX.size() )
{
return false;
}
mX[position.vertex] = newPos.x();
mY[position.vertex] = newPos.y();
if ( is3D() && newPos.is3D() )
{
mZ[position.vertex] = newPos.z();
}
if ( isMeasure() && newPos.isMeasure() )
{
mM[position.vertex] = newPos.m();
}
clearCache(); //set bounding box invalid
return true;
}
bool QgsLineString::deleteVertex( QgsVertexId position )
{
if ( position.vertex >= mX.size() || position.vertex < 0 )
{
return false;
}
mX.remove( position.vertex );
mY.remove( position.vertex );
if ( is3D() )
{
mZ.remove( position.vertex );
}
if ( isMeasure() )
{
mM.remove( position.vertex );
}
if ( numPoints() == 1 )
{
clear();
}
clearCache(); //set bounding box invalid
return true;
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::addVertex( const QgsPoint &pt )
{
if ( mWkbType == QgsWkbTypes::Unknown || mX.isEmpty() )
{
setZMTypeFromSubGeometry( &pt, QgsWkbTypes::LineString );
}
mX.append( pt.x() );
mY.append( pt.y() );
if ( is3D() )
{
mZ.append( pt.z() );
}
if ( isMeasure() )
{
mM.append( pt.m() );
}
clearCache(); //set bounding box invalid
}
double QgsLineString::closestSegment( const QgsPoint &pt, QgsPoint &segmentPt, QgsVertexId &vertexAfter, bool *leftOf, double epsilon ) const
{
double sqrDist = std::numeric_limits<double>::max();
double testDist = 0;
double segmentPtX, segmentPtY;
int size = mX.size();
if ( size == 0 || size == 1 )
{
vertexAfter = QgsVertexId( 0, 0, 0 );
return -1;
}
for ( int i = 1; i < size; ++i )
{
double prevX = mX.at( i - 1 );
double prevY = mY.at( i - 1 );
double currentX = mX.at( i );
double currentY = mY.at( i );
testDist = QgsGeometryUtils::sqrDistToLine( pt.x(), pt.y(), prevX, prevY, currentX, currentY, segmentPtX, segmentPtY, epsilon );
if ( testDist < sqrDist )
{
sqrDist = testDist;
segmentPt.setX( segmentPtX );
segmentPt.setY( segmentPtY );
if ( leftOf )
{
*leftOf = ( QgsGeometryUtils::leftOfLine( pt.x(), pt.y(), prevX, prevY, currentX, currentY ) < 0 );
}
vertexAfter.part = 0;
vertexAfter.ring = 0;
vertexAfter.vertex = i;
}
}
return sqrDist;
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
bool QgsLineString::pointAt( int node, QgsPoint &point, QgsVertexId::VertexType &type ) const
{
if ( node < 0 || node >= numPoints() )
{
return false;
}
point = pointN( node );
type = QgsVertexId::SegmentVertex;
return true;
}
QgsPoint QgsLineString::centroid() const
{
if ( mX.isEmpty() )
return QgsPoint();
int numPoints = mX.count();
if ( numPoints == 1 )
return QgsPoint( mX.at( 0 ), mY.at( 0 ) );
double totalLineLength = 0.0;
double prevX = mX.at( 0 );
double prevY = mY.at( 0 );
double sumX = 0.0;
double sumY = 0.0;
for ( int i = 1; i < numPoints ; ++i )
{
double currentX = mX.at( i );
double currentY = mY.at( i );
double segmentLength = sqrt( qPow( currentX - prevX, 2.0 ) +
qPow( currentY - prevY, 2.0 ) );
if ( qgsDoubleNear( segmentLength, 0.0 ) )
continue;
totalLineLength += segmentLength;
sumX += segmentLength * 0.5 * ( currentX + prevX );
sumY += segmentLength * 0.5 * ( currentY + prevY );
prevX = currentX;
prevY = currentY;
}
if ( qgsDoubleNear( totalLineLength, 0.0 ) )
return QgsPoint( mX.at( 0 ), mY.at( 0 ) );
else
return QgsPoint( sumX / totalLineLength, sumY / totalLineLength );
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::sumUpArea( double &sum ) const
{
int maxIndex = numPoints() - 1;
for ( int i = 0; i < maxIndex; ++i )
{
sum += 0.5 * ( mX.at( i ) * mY.at( i + 1 ) - mY.at( i ) * mX.at( i + 1 ) );
}
}
void QgsLineString::importVerticesFromWkb( const QgsConstWkbPtr &wkb )
{
bool hasZ = is3D();
bool hasM = isMeasure();
int nVertices = 0;
wkb >> nVertices;
mX.resize( nVertices );
mY.resize( nVertices );
hasZ ? mZ.resize( nVertices ) : mZ.clear();
hasM ? mM.resize( nVertices ) : mM.clear();
for ( int i = 0; i < nVertices; ++i )
{
wkb >> mX[i];
wkb >> mY[i];
if ( hasZ )
{
wkb >> mZ[i];
}
if ( hasM )
{
wkb >> mM[i];
}
}
clearCache(); //set bounding box invalid
}
/***************************************************************************
* This class is considered CRITICAL and any change MUST be accompanied with
* full unit tests.
* See details in QEP #17
****************************************************************************/
void QgsLineString::close()
{
if ( numPoints() < 1 || isClosed() )
{
return;
}
addVertex( startPoint() );
}
double QgsLineString::vertexAngle( QgsVertexId vertex ) const
{
if ( mX.count() < 2 )
{
//undefined
return 0.0;