diff --git a/src/atlas.cpp b/src/atlas.cpp
index 4cc2e625..85a93238 100644
--- a/src/atlas.cpp
+++ b/src/atlas.cpp
@@ -30,17 +30,17 @@ static bool yCmp(const OfflineMap *m1, const OfflineMap *m2)
 	return TL(m1).y() > TL(m2).y();
 }
 
-bool Atlas::isAtlas(const QFileInfoList &files)
+bool Atlas::isAtlas(Tar &tar, const QFileInfoList &files)
 {
 	for (int i = 0; i < files.count(); i++) {
 		const QString &fileName = files.at(i).fileName();
 		if (fileName.endsWith(".tar")) {
-			if (!_tar.load(files.at(i).absoluteFilePath())) {
+			if (!tar.load(files.at(i).absoluteFilePath())) {
 				qWarning("%s: %s: error loading tar file", qPrintable(_name),
 				  qPrintable(fileName));
 				return false;
 			}
-			QStringList tarFiles = _tar.files();
+			QStringList tarFiles = tar.files();
 			for (int j = 0; j < tarFiles.size(); j++)
 				if (tarFiles.at(j).endsWith(".tba"))
 					return true;
@@ -102,6 +102,8 @@ void Atlas::computeBounds()
 
 Atlas::Atlas(const QString &path, QObject *parent) : Map(parent)
 {
+	Tar tar;
+
 	_valid = false;
 	_zoom = 0;
 
@@ -110,7 +112,7 @@ Atlas::Atlas(const QString &path, QObject *parent) : Map(parent)
 
 	QDir dir(path);
 	QFileInfoList files = dir.entryInfoList(QDir::Files);
-	if (!isAtlas(files))
+	if (!isAtlas(tar, files))
 		return;
 
 	QFileInfoList layers = dir.entryInfoList(QDir::Dirs | QDir::NoDotAndDotDot);
@@ -120,8 +122,8 @@ Atlas::Atlas(const QString &path, QObject *parent) : Map(parent)
 		  | QDir::NoDotAndDotDot);
 		for (int i = 0; i < maps.count(); i++) {
 			OfflineMap *map;
-			if (_tar.isOpen())
-				map = new OfflineMap(_tar, maps.at(i).absoluteFilePath(), this);
+			if (tar.isOpen())
+				map = new OfflineMap(tar, maps.at(i).absoluteFilePath(), this);
 			else
 				map = new OfflineMap(maps.at(i).absoluteFilePath(), this);
 			if (map->isValid())
diff --git a/src/atlas.h b/src/atlas.h
index 9970a5c1..c3882d46 100644
--- a/src/atlas.h
+++ b/src/atlas.h
@@ -33,14 +33,13 @@ public:
 
 private:
 	void draw(QPainter *painter, const QRectF &rect, int mapIndex);
-	bool isAtlas(const QFileInfoList &files);
+	bool isAtlas(Tar &tar, const QFileInfoList &files);
 	void computeZooms();
 	void computeBounds();
 
 	QString _name;
 	bool _valid;
 
-	Tar _tar;
 	QList<OfflineMap*> _maps;
 	QVector<QPair<int, int> > _zooms;
 	QVector<QPair<QRectF, QRectF> > _bounds;
diff --git a/src/offlinemap.cpp b/src/offlinemap.cpp
index 01f90a94..18ea9eed 100644
--- a/src/offlinemap.cpp
+++ b/src/offlinemap.cpp
@@ -226,6 +226,7 @@ bool OfflineMap::computeTransformation(const QList<ReferencePoint> &points)
 
 	_transform = QTransform(M.m(0,3), M.m(0,4), M.m(1,3), M.m(1,4), M.m(2,3),
 	  M.m(2,4));
+	_inverted = _transform.inverted();
 
 	return true;
 }
@@ -571,28 +572,3 @@ void OfflineMap::draw(QPainter *painter, const QRectF &rect)
 		}
 	}
 }
-
-QPointF OfflineMap::ll2xy(const Coordinates &c) const
-{
-	return _transform.map(_projection->ll2xy(c));
-}
-
-Coordinates OfflineMap::xy2ll(const QPointF &p) const
-{
-	return _projection->xy2ll(_transform.inverted().map(p));
-}
-
-QPointF OfflineMap::ll2pp(const Coordinates &c) const
-{
-	return _projection->ll2xy(c);
-}
-
-QPointF OfflineMap::xy2pp(const QPointF &p) const
-{
-	return _transform.inverted().map(p);
-}
-
-QPointF OfflineMap::pp2xy(const QPointF &p) const
-{
-	return _transform.map(p);
-}
diff --git a/src/offlinemap.h b/src/offlinemap.h
index 138bfd26..e0726f16 100644
--- a/src/offlinemap.h
+++ b/src/offlinemap.h
@@ -5,10 +5,11 @@
 #include "map.h"
 #include "tar.h"
 #include "coordinates.h"
+#include "projection.h"
+
 
 class QIODevice;
 class QImage;
-class Projection;
 
 class OfflineMap : public Map
 {
@@ -29,8 +30,10 @@ public:
 	qreal zoomIn();
 	qreal zoomOut();
 
-	QPointF ll2xy(const Coordinates &c) const;
-	Coordinates xy2ll(const QPointF &p) const;
+	QPointF ll2xy(const Coordinates &c) const
+	  {return _transform.map(_projection->ll2xy(c));}
+	Coordinates xy2ll(const QPointF &p) const
+	  {return _projection->xy2ll(_inverted.map(p));}
 
 	void draw(QPainter *painter, const QRectF &rect);
 
@@ -39,9 +42,12 @@ public:
 
 	bool isValid() {return _valid;}
 
-	QPointF ll2pp(const Coordinates &c) const;
-	QPointF xy2pp(const QPointF &p) const;
-	QPointF pp2xy(const QPointF &p) const;
+	QPointF ll2pp(const Coordinates &c) const
+	  {return _projection->ll2xy(c);}
+	QPointF xy2pp(const QPointF &p) const
+	  {return _inverted.map(p);}
+	QPointF pp2xy(const QPointF &p) const
+	  {return _transform.map(p);}
 
 private:
 	typedef struct {
@@ -75,7 +81,7 @@ private:
 	QString _name;
 	QSize _size;
 	Projection *_projection;
-	QTransform _transform;
+	QTransform _transform, _inverted;
 	qreal _resolution;
 
 	Tar _tar;