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qgsdistancearea.cpp
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qgsdistancearea.cpp
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/***************************************************************************
qgsdistancearea.cpp - Distance and area calculations on the ellipsoid
---------------------------------------------------------------------------
Date : September 2005
Copyright : (C) 2005 by Martin Dobias
email : won.der at centrum.sk
***************************************************************************
* *
* 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 <cmath>
#include <sqlite3.h>
#include <QDir>
#include <QString>
#include <QLocale>
#include <QObject>
#include "qgis.h"
#include "qgspoint.h"
#include "qgscoordinatetransform.h"
#include "qgscoordinatereferencesystem.h"
#include "qgsgeometry.h"
#include "qgsdistancearea.h"
#include "qgsapplication.h"
#include "qgslogger.h"
#include "qgsmessagelog.h"
// MSVC compiler doesn't have defined M_PI in math.h
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#define DEG2RAD(x) ((x)*M_PI/180)
QgsDistanceArea::QgsDistanceArea()
{
// init with default settings
mEllipsoidalMode = false;
mCoordTransform = new QgsCoordinateTransform;
setSourceCrs( GEOCRS_ID ); // WGS 84
setEllipsoid( GEO_NONE );
}
//! Copy constructor
QgsDistanceArea::QgsDistanceArea( const QgsDistanceArea & origDA )
{
_copy( origDA );
}
QgsDistanceArea::~QgsDistanceArea()
{
delete mCoordTransform;
}
//! Assignment operator
QgsDistanceArea & QgsDistanceArea::operator=( const QgsDistanceArea & origDA )
{
if ( this == & origDA )
{
// Do not copy unto self
return *this;
}
_copy( origDA );
return *this;
}
//! Copy helper. Avoid Sqlite3 accesses.
void QgsDistanceArea::_copy( const QgsDistanceArea & origDA )
{
mEllipsoidalMode = origDA.mEllipsoidalMode;
mEllipsoid = origDA.mEllipsoid;
mSemiMajor = origDA.mSemiMajor;
mSemiMinor = origDA.mSemiMinor;
mInvFlattening = origDA.mInvFlattening;
// Some calculations and trig. Should not be TOO time consuming.
// Alternatively we could copy the temp vars?
computeAreaInit();
mCoordTransform = new QgsCoordinateTransform( origDA.mCoordTransform->sourceCrs(), origDA.mCoordTransform->destCRS() );
}
void QgsDistanceArea::setEllipsoidalMode( bool flag )
{
mEllipsoidalMode = flag;
}
void QgsDistanceArea::setSourceCrs( long srsid )
{
QgsCoordinateReferenceSystem srcCRS;
srcCRS.createFromSrsId( srsid );
mCoordTransform->setSourceCrs( srcCRS );
}
void QgsDistanceArea::setSourceCrs( const QgsCoordinateReferenceSystem& srcCRS )
{
mCoordTransform->setSourceCrs( srcCRS );
}
void QgsDistanceArea::setSourceAuthId( QString authId )
{
QgsCoordinateReferenceSystem srcCRS;
srcCRS.createFromOgcWmsCrs( authId );
mCoordTransform->setSourceCrs( srcCRS );
}
bool QgsDistanceArea::setEllipsoid( const QString& ellipsoid )
{
QString radius, parameter2;
//
// SQLITE3 stuff - get parameters for selected ellipsoid
//
sqlite3 *myDatabase;
const char *myTail;
sqlite3_stmt *myPreparedStatement;
int myResult;
// Shortcut if ellipsoid is none.
if ( ellipsoid == GEO_NONE )
{
mEllipsoid = GEO_NONE;
return true;
}
// Check if we have a custom projection, and set from text string.
// Format is "PARAMETER:<semi-major axis>:<semi minor axis>
// Numbers must be with (optional) decimal point and no other separators (C locale)
// Distances in meters. Flattening is calculated.
if ( ellipsoid.startsWith( "PARAMETER" ) )
{
QStringList paramList = ellipsoid.split( ":" );
bool semiMajorOk, semiMinorOk;
double semiMajor = paramList[1].toDouble( & semiMajorOk );
double semiMinor = paramList[2].toDouble( & semiMinorOk );
if ( semiMajorOk && semiMinorOk )
{
return setEllipsoid( semiMajor, semiMinor );
}
else
{
return false;
}
}
// Continue with PROJ.4 list of ellipsoids.
//check the db is available
myResult = sqlite3_open_v2( QgsApplication::srsDbFilePath().toUtf8().data(), &myDatabase, SQLITE_OPEN_READONLY, NULL );
if ( myResult )
{
QgsMessageLog::logMessage( QObject::tr( "Can't open database: %1" ).arg( sqlite3_errmsg( myDatabase ) ) );
// XXX This will likely never happen since on open, sqlite creates the
// database if it does not exist.
return false;
}
// Set up the query to retrieve the projection information needed to populate the ELLIPSOID list
QString mySql = "select radius, parameter2 from tbl_ellipsoid where acronym='" + ellipsoid + "'";
myResult = sqlite3_prepare( myDatabase, mySql.toUtf8(), mySql.toUtf8().length(), &myPreparedStatement, &myTail );
// XXX Need to free memory from the error msg if one is set
if ( myResult == SQLITE_OK )
{
if ( sqlite3_step( myPreparedStatement ) == SQLITE_ROW )
{
radius = QString(( char * )sqlite3_column_text( myPreparedStatement, 0 ) );
parameter2 = QString(( char * )sqlite3_column_text( myPreparedStatement, 1 ) );
}
}
// close the sqlite3 statement
sqlite3_finalize( myPreparedStatement );
sqlite3_close( myDatabase );
// row for this ellipsoid wasn't found?
if ( radius.isEmpty() || parameter2.isEmpty() )
{
QgsDebugMsg( QString( "setEllipsoid: no row in tbl_ellipsoid for acronym '%1'" ).arg( ellipsoid ) );
return false;
}
// get major semiaxis
if ( radius.left( 2 ) == "a=" )
mSemiMajor = radius.mid( 2 ).toDouble();
else
{
QgsDebugMsg( QString( "setEllipsoid: wrong format of radius field: '%1'" ).arg( radius ) );
return false;
}
// get second parameter
// one of values 'b' or 'f' is in field parameter2
// second one must be computed using formula: invf = a/(a-b)
if ( parameter2.left( 2 ) == "b=" )
{
mSemiMinor = parameter2.mid( 2 ).toDouble();
mInvFlattening = mSemiMajor / ( mSemiMajor - mSemiMinor );
}
else if ( parameter2.left( 3 ) == "rf=" )
{
mInvFlattening = parameter2.mid( 3 ).toDouble();
mSemiMinor = mSemiMajor - ( mSemiMajor / mInvFlattening );
}
else
{
QgsDebugMsg( QString( "setEllipsoid: wrong format of parameter2 field: '%1'" ).arg( parameter2 ) );
return false;
}
QgsDebugMsg( QString( "setEllipsoid: a=%1, b=%2, 1/f=%3" ).arg( mSemiMajor ).arg( mSemiMinor ).arg( mInvFlattening ) );
// get spatial ref system for ellipsoid
QString proj4 = "+proj=longlat +ellps=" + ellipsoid + " +no_defs";
QgsCoordinateReferenceSystem destCRS;
destCRS.createFromProj4( proj4 );
//TODO: createFromProj4 used to save to the user database any new CRS
// this behavior was changed in order to separate creation and saving.
// Not sure if it necessary to save it here, should be checked by someone
// familiar with the code (should also give a more descriptive name to the generated CRS)
if ( destCRS.srsid() == 0 )
{
QString myName = QString( " * %1 (%2)" )
.arg( QObject::tr( "Generated CRS", "A CRS automatically generated from layer info get this prefix for description" ) )
.arg( destCRS.toProj4() );
destCRS.saveAsUserCRS( myName );
}
//
// set transformation from project CRS to ellipsoid coordinates
mCoordTransform->setDestCRS( destCRS );
// precalculate some values for area calculations
computeAreaInit();
mEllipsoid = ellipsoid;
return true;
}
//! Sets ellipsoid by supplied radii
// Inverse flattening is calculated with invf = a/(a-b)
// Also, b = a-(a/invf)
bool QgsDistanceArea::setEllipsoid( double semiMajor, double semiMinor )
{
mEllipsoid = QString( "PARAMETER:%1:%2" ).arg( semiMajor ).arg( semiMinor );
mSemiMajor = semiMajor;
mSemiMinor = semiMinor;
mInvFlattening = mSemiMajor / ( mSemiMajor - mSemiMinor );
computeAreaInit();
return true;
}
double QgsDistanceArea::measure( QgsGeometry* geometry )
{
if ( !geometry )
return 0.0;
const unsigned char* wkb = geometry->asWkb();
if ( !wkb )
return 0.0;
QgsConstWkbPtr wkbPtr( wkb + 1 );
QGis::WkbType wkbType;
wkbPtr >> wkbType;
double res, resTotal = 0;
int count, i;
// measure distance or area based on what is the type of geometry
bool hasZptr = false;
switch ( wkbType )
{
case QGis::WKBLineString25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBLineString:
measureLine( wkb, &res, hasZptr );
QgsDebugMsg( "returning " + QString::number( res ) );
return res;
case QGis::WKBMultiLineString25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBMultiLineString:
wkbPtr >> count;
for ( i = 0; i < count; i++ )
{
wkbPtr = measureLine( wkbPtr, &res, hasZptr );
resTotal += res;
}
QgsDebugMsg( "returning " + QString::number( resTotal ) );
return resTotal;
case QGis::WKBPolygon25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBPolygon:
measurePolygon( wkb, &res, 0, hasZptr );
QgsDebugMsg( "returning " + QString::number( res ) );
return res;
case QGis::WKBMultiPolygon25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBMultiPolygon:
wkbPtr >> count;
for ( i = 0; i < count; i++ )
{
wkbPtr = measurePolygon( wkbPtr, &res, 0, hasZptr );
if ( !wkbPtr )
{
QgsDebugMsg( "measurePolygon returned 0" );
break;
}
resTotal += res;
}
QgsDebugMsg( "returning " + QString::number( resTotal ) );
return resTotal;
default:
QgsDebugMsg( QString( "measure: unexpected geometry type: %1" ).arg( wkbType ) );
return 0;
}
}
double QgsDistanceArea::measurePerimeter( QgsGeometry* geometry )
{
if ( !geometry )
return 0.0;
const unsigned char* wkb = geometry->asWkb();
if ( !wkb )
return 0.0;
QgsConstWkbPtr wkbPtr( wkb + 1 );
QGis::WkbType wkbType;
wkbPtr >> wkbType;
double res = 0.0, resTotal = 0.0;
int count, i;
// measure distance or area based on what is the type of geometry
bool hasZptr = false;
switch ( wkbType )
{
case QGis::WKBLineString25D:
case QGis::WKBLineString:
case QGis::WKBMultiLineString25D:
case QGis::WKBMultiLineString:
return 0.0;
case QGis::WKBPolygon25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBPolygon:
measurePolygon( wkb, 0, &res, hasZptr );
QgsDebugMsg( "returning " + QString::number( res ) );
return res;
case QGis::WKBMultiPolygon25D:
hasZptr = true;
//intentional fall-through
case QGis::WKBMultiPolygon:
wkbPtr >> count;
for ( i = 0; i < count; i++ )
{
wkbPtr = measurePolygon( wkbPtr, 0, &res, hasZptr );
if ( !wkbPtr )
{
QgsDebugMsg( "measurePolygon returned 0" );
break;
}
resTotal += res;
}
QgsDebugMsg( "returning " + QString::number( resTotal ) );
return resTotal;
default:
QgsDebugMsg( QString( "measure: unexpected geometry type: %1" ).arg( wkbType ) );
return 0;
}
}
const unsigned char* QgsDistanceArea::measureLine( const unsigned char* feature, double* area, bool hasZptr )
{
QgsConstWkbPtr wkbPtr( feature + 1 + sizeof( int ) );
int nPoints;
wkbPtr >> nPoints;
QList<QgsPoint> points;
double x, y;
QgsDebugMsg( "This feature WKB has " + QString::number( nPoints ) + " points" );
// Extract the points from the WKB format into the vector
for ( int i = 0; i < nPoints; ++i )
{
wkbPtr >> x >> y;
if ( hasZptr )
{
// totally ignore Z value
wkbPtr += sizeof( double );
}
points.append( QgsPoint( x, y ) );
}
*area = measureLine( points );
return wkbPtr;
}
double QgsDistanceArea::measureLine( const QList<QgsPoint> &points )
{
if ( points.size() < 2 )
return 0;
double total = 0;
QgsPoint p1, p2;
try
{
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
p1 = mCoordTransform->transform( points[0] );
else
p1 = points[0];
for ( QList<QgsPoint>::const_iterator i = points.begin(); i != points.end(); ++i )
{
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
p2 = mCoordTransform->transform( *i );
total += computeDistanceBearing( p1, p2 );
}
else
{
p2 = *i;
total += measureLine( p1, p2 );
}
p1 = p2;
}
return total;
}
catch ( QgsCsException &cse )
{
Q_UNUSED( cse );
QgsMessageLog::logMessage( QObject::tr( "Caught a coordinate system exception while trying to transform a point. Unable to calculate line length." ) );
return 0.0;
}
}
double QgsDistanceArea::measureLine( const QgsPoint &p1, const QgsPoint &p2 )
{
double result;
try
{
QgsPoint pp1 = p1, pp2 = p2;
QgsDebugMsgLevel( QString( "Measuring from %1 to %2" ).arg( p1.toString( 4 ) ).arg( p2.toString( 4 ) ), 3 );
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
QgsDebugMsgLevel( QString( "Ellipsoidal calculations is enabled, using ellipsoid %1" ).arg( mEllipsoid ), 4 );
QgsDebugMsgLevel( QString( "From proj4 : %1" ).arg( mCoordTransform->sourceCrs().toProj4() ), 4 );
QgsDebugMsgLevel( QString( "To proj4 : %1" ).arg( mCoordTransform->destCRS().toProj4() ), 4 );
pp1 = mCoordTransform->transform( p1 );
pp2 = mCoordTransform->transform( p2 );
QgsDebugMsgLevel( QString( "New points are %1 and %2, calculating..." ).arg( pp1.toString( 4 ) ).arg( pp2.toString( 4 ) ), 4 );
result = computeDistanceBearing( pp1, pp2 );
}
else
{
QgsDebugMsgLevel( "Cartesian calculation on canvas coordinates", 4 );
result = computeDistanceFlat( p1, p2 );
}
}
catch ( QgsCsException &cse )
{
Q_UNUSED( cse );
QgsMessageLog::logMessage( QObject::tr( "Caught a coordinate system exception while trying to transform a point. Unable to calculate line length." ) );
result = 0.0;
}
QgsDebugMsgLevel( QString( "The result was %1" ).arg( result ), 3 );
return result;
}
const unsigned char *QgsDistanceArea::measurePolygon( const unsigned char* feature, double* area, double* perimeter, bool hasZptr )
{
if ( !feature )
{
QgsDebugMsg( "no feature to measure" );
return 0;
}
QgsConstWkbPtr wkbPtr( feature + 1 + sizeof( int ) );
// get number of rings in the polygon
int numRings;
wkbPtr >> numRings;
if ( numRings == 0 )
{
QgsDebugMsg( "no rings to measure" );
return 0;
}
// Set pointer to the first ring
QList<QgsPoint> points;
QgsPoint pnt;
double x, y;
if ( area )
*area = 0;
if ( perimeter )
*perimeter = 0;
try
{
for ( int idx = 0; idx < numRings; idx++ )
{
int nPoints;
wkbPtr >> nPoints;
// Extract the points from the WKB and store in a pair of
// vectors.
for ( int jdx = 0; jdx < nPoints; jdx++ )
{
wkbPtr >> x >> y;
if ( hasZptr )
{
// totally ignore Z value
wkbPtr += sizeof( double );
}
pnt = QgsPoint( x, y );
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
pnt = mCoordTransform->transform( pnt );
}
points.append( pnt );
}
if ( points.size() > 2 )
{
if ( area )
{
double areaTmp = computePolygonArea( points );
if ( idx == 0 )
{
// exterior ring
*area += areaTmp;
}
else
{
*area -= areaTmp; // interior rings
}
}
if ( perimeter )
{
if ( idx == 0 )
{
// exterior ring
*perimeter += computeDistance( points );
}
}
}
points.clear();
}
}
catch ( QgsCsException &cse )
{
Q_UNUSED( cse );
QgsMessageLog::logMessage( QObject::tr( "Caught a coordinate system exception while trying to transform a point. Unable to calculate polygon area or perimeter." ) );
}
return wkbPtr;
}
double QgsDistanceArea::measurePolygon( const QList<QgsPoint>& points )
{
try
{
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
QList<QgsPoint> pts;
for ( QList<QgsPoint>::const_iterator i = points.begin(); i != points.end(); ++i )
{
pts.append( mCoordTransform->transform( *i ) );
}
return computePolygonArea( pts );
}
else
{
return computePolygonArea( points );
}
}
catch ( QgsCsException &cse )
{
Q_UNUSED( cse );
QgsMessageLog::logMessage( QObject::tr( "Caught a coordinate system exception while trying to transform a point. Unable to calculate polygon area." ) );
return 0.0;
}
}
double QgsDistanceArea::bearing( const QgsPoint& p1, const QgsPoint& p2 )
{
QgsPoint pp1 = p1, pp2 = p2;
double bearing;
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
pp1 = mCoordTransform->transform( p1 );
pp2 = mCoordTransform->transform( p2 );
computeDistanceBearing( pp1, pp2, &bearing );
}
else //compute simple planar azimuth
{
double dx = p2.x() - p1.x();
double dy = p2.y() - p1.y();
bearing = atan2( dx, dy );
}
return bearing;
}
///////////////////////////////////////////////////////////
// distance calculation
double QgsDistanceArea::computeDistanceBearing(
const QgsPoint& p1, const QgsPoint& p2,
double* course1, double* course2 )
{
if ( p1.x() == p2.x() && p1.y() == p2.y() )
return 0;
// ellipsoid
double a = mSemiMajor;
double b = mSemiMinor;
double f = 1 / mInvFlattening;
double p1_lat = DEG2RAD( p1.y() ), p1_lon = DEG2RAD( p1.x() );
double p2_lat = DEG2RAD( p2.y() ), p2_lon = DEG2RAD( p2.x() );
double L = p2_lon - p1_lon;
double U1 = atan(( 1 - f ) * tan( p1_lat ) );
double U2 = atan(( 1 - f ) * tan( p2_lat ) );
double sinU1 = sin( U1 ), cosU1 = cos( U1 );
double sinU2 = sin( U2 ), cosU2 = cos( U2 );
double lambda = L;
double lambdaP = 2 * M_PI;
double sinLambda = 0;
double cosLambda = 0;
double sinSigma = 0;
double cosSigma = 0;
double sigma = 0;
double alpha = 0;
double cosSqAlpha = 0;
double cos2SigmaM = 0;
double C = 0;
double tu1 = 0;
double tu2 = 0;
int iterLimit = 20;
while ( qAbs( lambda - lambdaP ) > 1e-12 && --iterLimit > 0 )
{
sinLambda = sin( lambda );
cosLambda = cos( lambda );
tu1 = ( cosU2 * sinLambda );
tu2 = ( cosU1 * sinU2 - sinU1 * cosU2 * cosLambda );
sinSigma = sqrt( tu1 * tu1 + tu2 * tu2 );
cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda;
sigma = atan2( sinSigma, cosSigma );
alpha = asin( cosU1 * cosU2 * sinLambda / sinSigma );
cosSqAlpha = cos( alpha ) * cos( alpha );
cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha;
C = f / 16 * cosSqAlpha * ( 4 + f * ( 4 - 3 * cosSqAlpha ) );
lambdaP = lambda;
lambda = L + ( 1 - C ) * f * sin( alpha ) *
( sigma + C * sinSigma * ( cos2SigmaM + C * cosSigma * ( -1 + 2 * cos2SigmaM * cos2SigmaM ) ) );
}
if ( iterLimit == 0 )
return -1; // formula failed to converge
double uSq = cosSqAlpha * ( a * a - b * b ) / ( b * b );
double A = 1 + uSq / 16384 * ( 4096 + uSq * ( -768 + uSq * ( 320 - 175 * uSq ) ) );
double B = uSq / 1024 * ( 256 + uSq * ( -128 + uSq * ( 74 - 47 * uSq ) ) );
double deltaSigma = B * sinSigma * ( cos2SigmaM + B / 4 * ( cosSigma * ( -1 + 2 * cos2SigmaM * cos2SigmaM ) -
B / 6 * cos2SigmaM * ( -3 + 4 * sinSigma * sinSigma ) * ( -3 + 4 * cos2SigmaM * cos2SigmaM ) ) );
double s = b * A * ( sigma - deltaSigma );
if ( course1 )
{
*course1 = atan2( tu1, tu2 );
}
if ( course2 )
{
// PI is added to return azimuth from P2 to P1
*course2 = atan2( cosU1 * sinLambda, -sinU1 * cosU2 + cosU1 * sinU2 * cosLambda ) + M_PI;
}
return s;
}
double QgsDistanceArea::computeDistanceFlat( const QgsPoint& p1, const QgsPoint& p2 )
{
return sqrt(( p2.x() - p1.x() ) * ( p2.x() - p1.x() ) + ( p2.y() - p1.y() ) * ( p2.y() - p1.y() ) );
}
double QgsDistanceArea::computeDistance( const QList<QgsPoint>& points )
{
if ( points.size() < 2 )
return 0;
double total = 0;
QgsPoint p1, p2;
try
{
p1 = points[0];
for ( QList<QgsPoint>::const_iterator i = points.begin(); i != points.end(); ++i )
{
p2 = *i;
if ( mEllipsoidalMode && ( mEllipsoid != GEO_NONE ) )
{
total += computeDistanceBearing( p1, p2 );
}
else
{
total += computeDistanceFlat( p1, p2 );
}
p1 = p2;
}
return total;
}
catch ( QgsCsException &cse )
{
Q_UNUSED( cse );
QgsMessageLog::logMessage( QObject::tr( "Caught a coordinate system exception while trying to transform a point. Unable to calculate line length." ) );
return 0.0;
}
}
///////////////////////////////////////////////////////////
// stuff for measuring areas - copied from GRASS
// don't know how does it work, but it's working .)
// see G_begin_ellipsoid_polygon_area() in area_poly1.c
double QgsDistanceArea::getQ( double x )
{
double sinx, sinx2;
sinx = sin( x );
sinx2 = sinx * sinx;
return sinx *( 1 + sinx2 *( m_QA + sinx2 *( m_QB + sinx2 * m_QC ) ) );
}
double QgsDistanceArea::getQbar( double x )
{
double cosx, cosx2;
cosx = cos( x );
cosx2 = cosx * cosx;
return cosx *( m_QbarA + cosx2 *( m_QbarB + cosx2 *( m_QbarC + cosx2 * m_QbarD ) ) );
}
void QgsDistanceArea::computeAreaInit()
{
//don't try to perform calculations if no ellipsoid
if ( mEllipsoid == GEO_NONE )
{
return;
}
double a2 = ( mSemiMajor * mSemiMajor );
double e2 = 1 - ( a2 / ( mSemiMinor * mSemiMinor ) );
double e4, e6;
m_TwoPI = M_PI + M_PI;
e4 = e2 * e2;
e6 = e4 * e2;
m_AE = a2 * ( 1 - e2 );
m_QA = ( 2.0 / 3.0 ) * e2;
m_QB = ( 3.0 / 5.0 ) * e4;
m_QC = ( 4.0 / 7.0 ) * e6;
m_QbarA = -1.0 - ( 2.0 / 3.0 ) * e2 - ( 3.0 / 5.0 ) * e4 - ( 4.0 / 7.0 ) * e6;
m_QbarB = ( 2.0 / 9.0 ) * e2 + ( 2.0 / 5.0 ) * e4 + ( 4.0 / 7.0 ) * e6;
m_QbarC = - ( 3.0 / 25.0 ) * e4 - ( 12.0 / 35.0 ) * e6;
m_QbarD = ( 4.0 / 49.0 ) * e6;
m_Qp = getQ( M_PI / 2 );
m_E = 4 * M_PI * m_Qp * m_AE;
if ( m_E < 0.0 )
m_E = -m_E;
}
double QgsDistanceArea::computePolygonArea( const QList<QgsPoint>& points )
{
double x1, y1, x2, y2, dx, dy;
double Qbar1, Qbar2;
double area;
QgsDebugMsgLevel( "Ellipsoid: " + mEllipsoid, 3 );
if (( ! mEllipsoidalMode ) || ( mEllipsoid == GEO_NONE ) )
{
return computePolygonFlatArea( points );
}
int n = points.size();
x2 = DEG2RAD( points[n-1].x() );
y2 = DEG2RAD( points[n-1].y() );
Qbar2 = getQbar( y2 );
area = 0.0;
for ( int i = 0; i < n; i++ )
{
x1 = x2;
y1 = y2;
Qbar1 = Qbar2;
x2 = DEG2RAD( points[i].x() );
y2 = DEG2RAD( points[i].y() );
Qbar2 = getQbar( y2 );
if ( x1 > x2 )
while ( x1 - x2 > M_PI )
x2 += m_TwoPI;
else if ( x2 > x1 )
while ( x2 - x1 > M_PI )
x1 += m_TwoPI;
dx = x2 - x1;
area += dx * ( m_Qp - getQ( y2 ) );
if (( dy = y2 - y1 ) != 0.0 )
area += dx * getQ( y2 ) - ( dx / dy ) * ( Qbar2 - Qbar1 );
}
if (( area *= m_AE ) < 0.0 )
area = -area;
/* kludge - if polygon circles the south pole the area will be
* computed as if it cirlced the north pole. The correction is
* the difference between total surface area of the earth and
* the "north pole" area.
*/
if ( area > m_E )
area = m_E;
if ( area > m_E / 2 )
area = m_E - area;
return area;
}
double QgsDistanceArea::computePolygonFlatArea( const QList<QgsPoint>& points )
{
// Normal plane area calculations.
double area = 0.0;
int i, size;
size = points.size();
// QgsDebugMsg("New area calc, nr of points: " + QString::number(size));
for ( i = 0; i < size; i++ )
{
// QgsDebugMsg("Area from point: " + (points[i]).toString(2));
// Using '% size', so that we always end with the starting point
// and thus close the polygon.
area = area + points[i].x() * points[( i+1 ) % size].y() - points[( i+1 ) % size].x() * points[i].y();
}
// QgsDebugMsg("Area from point: " + (points[i % size]).toString(2));
area = area / 2.0;
return qAbs( area ); // All areas are positive!
}
QString QgsDistanceArea::textUnit( double value, int decimals, QGis::UnitType u, bool isArea, bool keepBaseUnit )
{
QString unitLabel;
switch ( u )
{
case QGis::Meters:
if ( isArea )
{
if ( keepBaseUnit )
{
unitLabel = QObject::trUtf8( " m²" );
}
else if ( qAbs( value ) > 1000000.0 )
{
unitLabel = QObject::trUtf8( " km²" );
value = value / 1000000.0;
}
else if ( qAbs( value ) > 10000.0 )
{
unitLabel = QObject::tr( " ha" );
value = value / 10000.0;
}
else
{
unitLabel = QObject::trUtf8( " m²" );
}
}
else
{
if ( keepBaseUnit || qAbs( value ) == 0.0 )
{
unitLabel = QObject::tr( " m" );
}
else if ( qAbs( value ) > 1000.0 )
{
unitLabel = QObject::tr( " km" );
value = value / 1000;
}
else if ( qAbs( value ) < 0.01 )
{
unitLabel = QObject::tr( " mm" );
value = value * 1000;
}
else if ( qAbs( value ) < 0.1 )
{
unitLabel = QObject::tr( " cm" );
value = value * 100;
}
else
{
unitLabel = QObject::tr( " m" );
}
}
break;
case QGis::Feet:
if ( isArea )
{
if ( keepBaseUnit || qAbs( value ) <= 0.5*43560.0 )
{
// < 0.5 acre show sq ft
unitLabel = QObject::tr( " sq ft" );
}
else if ( qAbs( value ) <= 0.5*5280.0*5280.0 )
{
// < 0.5 sq mile show acre
unitLabel = QObject::tr( " acres" );
value /= 43560.0;
}
else
{
// above 0.5 acre show sq mi
unitLabel = QObject::tr( " sq mile" );
value /= 5280.0 * 5280.0;
}
}
else
{
if ( qAbs( value ) <= 528.0 || keepBaseUnit )
{
if ( qAbs( value ) == 1.0 )
{
unitLabel = QObject::tr( " foot" );
}
else
{
unitLabel = QObject::tr( " feet" );
}
}
else
{
unitLabel = QObject::tr( " mile" );
value /= 5280.0;
}
}
break;