Add support for boundingGeoRectangle to QGeoShape

this patch introduces QGeoShape::boundingGeoRectangle,
which returns a QGeoRectangle containing the latitudinal/longitudinal bounds
of a geoshape.
The bounding geo rectangle is projection independent, as it returns
a georectangle containing the min/max latitudes/longitudes of the
shape.

Change-Id: Ie3a83ec41f87ea3753899d2278e664fe2469f778
Reviewed-by: Alex Blasche <alexander.blasche@qt.io>

10 files changed, 288 insertions, 109 deletions

diff --git a/src/positioning/qgeocircle.cpp b/src/positioning/qgeocircle.cpp
index 3f2707a4..9552ac37 100644
--- a/src/positioning/qgeocircle.cpp
+++ b/src/positioning/qgeocircle.cpp
@@ -42,9 +42,11 @@
 
 #include "qgeocoordinate.h"
 #include "qnumeric.h"
+#include "qlocationutils_p.h"
 
 #include "qdoublevector2d_p.h"
 #include "qdoublevector3d_p.h"
+#include <cmath>
 QT_BEGIN_NAMESPACE
 
 /*!
@@ -191,12 +193,12 @@ bool QGeoCircle::operator!=(const QGeoCircle &other) const
 
 bool QGeoCirclePrivate::isValid() const
 {
-    return m_center.isValid() && !qIsNaN(radius) && radius >= -1e-7;
+    return m_center.isValid() && !qIsNaN(m_radius) && m_radius >= -1e-7;
 }
 
 bool QGeoCirclePrivate::isEmpty() const
 {
-    return !isValid() || radius <= 1e-7;
+    return !isValid() || m_radius <= 1e-7;
 }
 
 /*!
@@ -206,7 +208,7 @@ void QGeoCircle::setCenter(const QGeoCoordinate &center)
 {
     Q_D(QGeoCircle);
 
-    d->m_center = center;
+    d->setCenter(center);
 }
 
 /*!
@@ -226,7 +228,7 @@ void QGeoCircle::setRadius(qreal radius)
 {
     Q_D(QGeoCircle);
 
-    d->radius = radius;
+    d->setRadius(radius);
 }
 
 /*!
@@ -236,7 +238,7 @@ qreal QGeoCircle::radius() const
 {
     Q_D(const QGeoCircle);
 
-    return d->radius;
+    return d->m_radius;
 }
 
 bool QGeoCirclePrivate::contains(const QGeoCoordinate &coordinate) const
@@ -246,7 +248,7 @@ bool QGeoCirclePrivate::contains(const QGeoCoordinate &coordinate) const
 
     // see QTBUG-41447 for details
     qreal distance = m_center.distanceTo(coordinate);
-    if (qFuzzyCompare(distance, radius) || distance <= radius)
+    if (qFuzzyCompare(distance, m_radius) || distance <= m_radius)
         return true;
 
     return false;
@@ -257,6 +259,103 @@ QGeoCoordinate QGeoCirclePrivate::center() const
     return m_center;
 }
 
+QGeoRectangle QGeoCirclePrivate::boundingGeoRectangle() const
+{
+    return m_bbox;
+}
+
+void QGeoCirclePrivate::updateBoundingBox()
+{
+    if (isEmpty()) {
+        if (m_center.isValid()) {
+            m_bbox.setTopLeft(m_center);
+            m_bbox.setBottomRight(m_center);
+        }
+        return;
+    }
+
+    bool crossNorth = crossNorthPole();
+    bool crossSouth = crossSouthPole();
+
+    if (crossNorth && crossSouth) {
+        // Circle crossing both poles fills the whole map
+        m_bbox = QGeoRectangle(QGeoCoordinate(90.0, -180.0), QGeoCoordinate(-90.0, 180.0));
+    } else if (crossNorth) {
+        // Circle crossing one pole fills the map in the longitudinal direction
+        m_bbox = QGeoRectangle(QGeoCoordinate(90.0, -180.0), QGeoCoordinate(m_center.atDistanceAndAzimuth(m_radius, 180.0).latitude(), 180.0));
+    } else if (crossSouth) {
+        m_bbox = QGeoRectangle(QGeoCoordinate(m_center.atDistanceAndAzimuth(m_radius, 0.0).latitude(), -180.0), QGeoCoordinate(-90, 180.0));
+    } else {
+        // Regular circle not crossing anything
+
+        // Calculate geo bounding box of the circle
+        //
+        // A circle tangential point with a meridian, together with pole and
+        // the circle center create a spherical triangle.
+        // Finding the tangential point with the spherical law of sines:
+        //
+        // * lon_delta_in_rad : delta between the circle center and a tangential
+        //   point (absolute value).
+        // * r_in_rad : angular radius of the circle
+        // * lat_in_rad : latitude of the circle center
+        // * alpha_in_rad : angle between meridian and radius of the circle.
+        //   At the tangential point, sin(alpha_in_rad) == 1.
+        // * lat_delta_in_rad - absolute delta of latitudes between the circle center and
+        //   any of the two points where the great circle going through the circle
+        //   center and the pole crosses the circle. In other words, the points
+        //   on the circle with azimuth 0 or 180.
+        //
+        //  Using:
+        //  sin(lon_delta_in_rad)/sin(r_in_rad) = sin(alpha_in_rad)/sin(pi/2 - lat_in_rad)
+
+        double r_in_rad = m_radius / QLocationUtils::earthMeanRadius(); // angular r
+        double lat_delta_in_deg = QLocationUtils::degrees(r_in_rad);
+        double lon_delta_in_deg = QLocationUtils::degrees(std::asin(
+               std::sin(r_in_rad) /
+               std::cos(QLocationUtils::radians(m_center.latitude()))
+            ));
+
+        QGeoCoordinate topLeft;
+        topLeft.setLatitude(m_center.latitude() + lat_delta_in_deg);
+        topLeft.setLongitude(m_center.longitude() - lon_delta_in_deg);
+        QGeoCoordinate bottomRight;
+        bottomRight.setLatitude(m_center.latitude() - lat_delta_in_deg);
+        bottomRight.setLongitude(m_center.longitude() + lon_delta_in_deg);
+
+        m_bbox = QGeoRectangle(topLeft, bottomRight);
+    }
+}
+
+void QGeoCirclePrivate::setCenter(const QGeoCoordinate &c)
+{
+    m_center = c;
+    updateBoundingBox();
+}
+
+void QGeoCirclePrivate::setRadius(const qreal r)
+{
+    m_radius = r;
+    updateBoundingBox();
+}
+
+bool QGeoCirclePrivate::crossNorthPole() const
+{
+    const QGeoCoordinate northPole(90.0, m_center.longitude());
+    qreal distanceToPole = m_center.distanceTo(northPole);
+    if (distanceToPole < m_radius)
+        return true;
+    return false;
+}
+
+bool QGeoCirclePrivate::crossSouthPole() const
+{
+    const QGeoCoordinate southPole(-90.0, m_center.longitude());
+    qreal distanceToPole = m_center.distanceTo(southPole);
+    if (distanceToPole < m_radius)
+        return true;
+    return false;
+}
+
 /*!
   Extends the circle to include \a coordinate
 */
@@ -265,7 +364,7 @@ void QGeoCirclePrivate::extendShape(const QGeoCoordinate &coordinate)
     if (!isValid() || !coordinate.isValid() || contains(coordinate))
         return;
 
-    radius = m_center.distanceTo(coordinate);
+    setRadius(m_center.distanceTo(coordinate));
 }
 
 /*!
@@ -307,7 +406,7 @@ void QGeoCircle::translate(double degreesLatitude, double degreesLongitude)
             lon -= 180;
     }
 
-    d->m_center = QGeoCoordinate(lat, lon);
+    d->setCenter(QGeoCoordinate(lat, lon));
 }
 
 /*!
@@ -349,18 +448,19 @@ QString QGeoCircle::toString() const
 *******************************************************************************/
 
 QGeoCirclePrivate::QGeoCirclePrivate()
-:   QGeoShapePrivate(QGeoShape::CircleType), radius(-1.0)
+:   QGeoShapePrivate(QGeoShape::CircleType), m_radius(-1.0)
 {
 }
 
 QGeoCirclePrivate::QGeoCirclePrivate(const QGeoCoordinate &center, qreal radius)
-:   QGeoShapePrivate(QGeoShape::CircleType), m_center(center), radius(radius)
+:   QGeoShapePrivate(QGeoShape::CircleType), m_center(center), m_radius(radius)
 {
+    updateBoundingBox();
 }
 
 QGeoCirclePrivate::QGeoCirclePrivate(const QGeoCirclePrivate &other)
 :   QGeoShapePrivate(QGeoShape::CircleType), m_center(other.m_center),
-    radius(other.radius)
+    m_radius(other.m_radius), m_bbox(other.m_bbox)
 {
 }
 
@@ -378,8 +478,7 @@ bool QGeoCirclePrivate::operator==(const QGeoShapePrivate &other) const
 
     const QGeoCirclePrivate &otherCircle = static_cast<const QGeoCirclePrivate &>(other);
 
-    return radius == otherCircle.radius && m_center == otherCircle.m_center;
+    return m_radius == otherCircle.m_radius && m_center == otherCircle.m_center;
 }
 
 QT_END_NAMESPACE
-
diff --git a/src/positioning/qgeocircle.h b/src/positioning/qgeocircle.h
index b4b6c45e..e8632fe9 100644
--- a/src/positioning/qgeocircle.h
+++ b/src/positioning/qgeocircle.h
@@ -75,8 +75,8 @@ public:
     void setRadius(qreal radius);
     qreal radius() const;
 
-    void translate(double degreesLatitude, double degreesLongitude);
-    QGeoCircle translated(double degreesLatitude, double degreesLongitude) const;
+    Q_INVOKABLE void translate(double degreesLatitude, double degreesLongitude);
+    Q_INVOKABLE QGeoCircle translated(double degreesLatitude, double degreesLongitude) const;
 
     Q_INVOKABLE QString toString() const;
 
diff --git a/src/positioning/qgeocircle_p.h b/src/positioning/qgeocircle_p.h
index 311aba8b..07d79db4 100644
--- a/src/positioning/qgeocircle_p.h
+++ b/src/positioning/qgeocircle_p.h
@@ -70,6 +70,14 @@ public:
 
     QGeoCoordinate center() const Q_DECL_OVERRIDE;
 
+    QGeoRectangle boundingGeoRectangle() const Q_DECL_OVERRIDE;
+
+    bool crossNorthPole() const;
+    bool crossSouthPole() const;
+    void updateBoundingBox();
+    void setCenter(const QGeoCoordinate &c);
+    void setRadius(const qreal r);
+
     void extendShape(const QGeoCoordinate &coordinate) Q_DECL_OVERRIDE;
 
     QGeoShapePrivate *clone() const Q_DECL_OVERRIDE;
@@ -77,7 +85,8 @@ public:
     bool operator==(const QGeoShapePrivate &other) const Q_DECL_OVERRIDE;
 
     QGeoCoordinate m_center;
-    qreal radius;
+    qreal m_radius;
+    QGeoRectangle m_bbox;
 };
 
 QT_END_NAMESPACE
diff --git a/src/positioning/qgeorectangle.cpp b/src/positioning/qgeorectangle.cpp
index bbcafd6b..a8d74414 100644
--- a/src/positioning/qgeorectangle.cpp
+++ b/src/positioning/qgeorectangle.cpp
@@ -40,6 +40,8 @@
 #include "qgeorectangle.h"
 #include "qgeorectangle_p.h"
 
+#include "qgeoprojection_p.h"
+#include "qdoublevector2d_p.h"
 #include "qgeocoordinate.h"
 #include "qnumeric.h"
 #include <QList>
@@ -614,10 +616,7 @@ double QGeoRectangle::height() const
 
     Q_D(const QGeoRectangle);
 
-    double result = d->topLeft.latitude() - d->bottomRight.latitude();
-    if (result < 0.0)
-        result = qQNaN();
-    return result;
+    return d->topLeft.latitude() - d->bottomRight.latitude();
 }
 
 bool QGeoRectanglePrivate::contains(const QGeoCoordinate &coordinate) const
@@ -674,6 +673,11 @@ QGeoCoordinate QGeoRectanglePrivate::center() const
     return QGeoCoordinate(cLat, cLon);
 }
 
+QGeoRectangle QGeoRectanglePrivate::boundingGeoRectangle() const
+{
+    return QGeoRectangle(topLeft, bottomRight);
+}
+
 /*!
     Returns whether the geo rectangle \a rectangle is contained within this
     geo rectangle.
diff --git a/src/positioning/qgeorectangle.h b/src/positioning/qgeorectangle.h
index 7e921730..9e9acf91 100644
--- a/src/positioning/qgeorectangle.h
+++ b/src/positioning/qgeorectangle.h
@@ -42,89 +42,7 @@
 
 #include <QtPositioning/QGeoShape>
 
-QT_BEGIN_NAMESPACE
-
-class QGeoCoordinate;
-class QGeoRectanglePrivate;
-
-class Q_POSITIONING_EXPORT QGeoRectangle : public QGeoShape
-{
-    Q_GADGET
-    Q_PROPERTY(QGeoCoordinate bottomLeft READ bottomLeft WRITE setBottomLeft)
-    Q_PROPERTY(QGeoCoordinate bottomRight READ bottomRight WRITE setBottomRight)
-    Q_PROPERTY(QGeoCoordinate topLeft READ topLeft WRITE setTopLeft)
-    Q_PROPERTY(QGeoCoordinate topRight READ topRight WRITE setTopRight)
-    Q_PROPERTY(QGeoCoordinate center READ center WRITE setCenter)
-    Q_PROPERTY(double height READ height WRITE setHeight)
-    Q_PROPERTY(double width READ width WRITE setWidth)
-
-public:
-    QGeoRectangle();
-    QGeoRectangle(const QGeoCoordinate &center, double degreesWidth, double degreesHeight);
-    QGeoRectangle(const QGeoCoordinate &topLeft, const QGeoCoordinate &bottomRight);
-    QGeoRectangle(const QList<QGeoCoordinate> &coordinates);
-    QGeoRectangle(const QGeoRectangle &other);
-    QGeoRectangle(const QGeoShape &other);
-
-    ~QGeoRectangle();
-
-    QGeoRectangle &operator=(const QGeoRectangle &other);
-
-    using QGeoShape::operator==;
-    bool operator==(const QGeoRectangle &other) const;
-
-    using QGeoShape::operator!=;
-    bool operator!=(const QGeoRectangle &other) const;
-
-    void setTopLeft(const QGeoCoordinate &topLeft);
-    QGeoCoordinate topLeft() const;
-
-    void setTopRight(const QGeoCoordinate &topRight);
-    QGeoCoordinate topRight() const;
-
-    void setBottomLeft(const QGeoCoordinate &bottomLeft);
-    QGeoCoordinate bottomLeft() const;
-
-    void setBottomRight(const QGeoCoordinate &bottomRight);
-    QGeoCoordinate bottomRight() const;
-
-    void setCenter(const QGeoCoordinate &center);
-    QGeoCoordinate center() const;
-
-    void setWidth(double degreesWidth);
-    double width() const;
-
-    void setHeight(double degreesHeight);
-    double height() const;
-
-    using QGeoShape::contains;
-    bool contains(const QGeoRectangle &rectangle) const;
-    bool intersects(const QGeoRectangle &rectangle) const;
-
-    void translate(double degreesLatitude, double degreesLongitude);
-    QGeoRectangle translated(double degreesLatitude, double degreesLongitude) const;
-
-    QGeoRectangle united(const QGeoRectangle &rectangle) const;
-    QGeoRectangle operator|(const QGeoRectangle &rectangle) const;
-    QGeoRectangle &operator|=(const QGeoRectangle &rectangle);
-
-    Q_INVOKABLE QString toString() const;
-
-private:
-    inline QGeoRectanglePrivate *d_func();
-    inline const QGeoRectanglePrivate *d_func() const;
-};
-
-Q_DECLARE_TYPEINFO(QGeoRectangle, Q_MOVABLE_TYPE);
-
-inline QGeoRectangle QGeoRectangle::operator|(const QGeoRectangle &rectangle) const
-{
-    return united(rectangle);
-}
-
-QT_END_NAMESPACE
-
-Q_DECLARE_METATYPE(QGeoRectangle)
+// QGeoRectangle declaration now in qgeoshape.h.
+// This file remains for compatibility.
 
 #endif
-
diff --git a/src/positioning/qgeorectangle_p.h b/src/positioning/qgeorectangle_p.h
index 188e5548..ee1b1732 100644
--- a/src/positioning/qgeorectangle_p.h
+++ b/src/positioning/qgeorectangle_p.h
@@ -70,6 +70,8 @@ public:
 
     QGeoCoordinate center() const Q_DECL_OVERRIDE;
 
+    QGeoRectangle boundingGeoRectangle() const Q_DECL_OVERRIDE;
+
     void extendShape(const QGeoCoordinate &coordinate) Q_DECL_OVERRIDE;
 
     QGeoShapePrivate *clone() const Q_DECL_OVERRIDE;
diff --git a/src/positioning/qgeoshape.cpp b/src/positioning/qgeoshape.cpp
index bac37605..dd358fb5 100644
--- a/src/positioning/qgeoshape.cpp
+++ b/src/positioning/qgeoshape.cpp
@@ -227,6 +227,22 @@ bool QGeoShape::contains(const QGeoCoordinate &coordinate) const
 }
 
 /*!
+    Returns a \a QGeoRectangle representing the geographical bounding rectangle of the
+    geo shape, that defines the latitudinal/longitudinal bounds of the geo shape.
+
+    \since 5.9
+*/
+QGeoRectangle QGeoShape::boundingGeoRectangle() const
+{
+    Q_D(const QGeoShape);
+
+    if (d)
+        return d->boundingGeoRectangle();
+    else
+        return QGeoRectangle();
+}
+
+/*!
     Returns the coordinate located at the geometric center of the geo shape.
 
     \since 5.5
diff --git a/src/positioning/qgeoshape.h b/src/positioning/qgeoshape.h
index f8a30358..58e17c7d 100644
--- a/src/positioning/qgeoshape.h
+++ b/src/positioning/qgeoshape.h
@@ -47,6 +47,7 @@ QT_BEGIN_NAMESPACE
 
 class QDebug;
 class QGeoShapePrivate;
+class QGeoRectangle;
 
 class Q_POSITIONING_EXPORT QGeoShape
 {
@@ -72,10 +73,10 @@ public:
     bool isValid() const;
     bool isEmpty() const;
     Q_INVOKABLE bool contains(const QGeoCoordinate &coordinate) const;
+    Q_INVOKABLE QGeoRectangle boundingGeoRectangle() const;
+    Q_INVOKABLE QGeoCoordinate center() const;
 
-    QGeoCoordinate center() const;
-
-    void extendShape(const QGeoCoordinate &coordinate);
+    Q_INVOKABLE void extendShape(const QGeoCoordinate &coordinate);
 
     bool operator==(const QGeoShape &other) const;
     bool operator!=(const QGeoShape &other) const;
@@ -104,9 +105,89 @@ Q_POSITIONING_EXPORT QDataStream &operator<<(QDataStream &stream, const QGeoShap
 Q_POSITIONING_EXPORT QDataStream &operator>>(QDataStream &stream, QGeoShape &shape);
 #endif
 
+
+
+// QGeoRectangle is declared here because of QGeoShape::boundingGeoRectangle
+class QGeoRectanglePrivate;
+
+class Q_POSITIONING_EXPORT QGeoRectangle : public QGeoShape
+{
+    Q_GADGET
+    Q_PROPERTY(QGeoCoordinate bottomLeft READ bottomLeft WRITE setBottomLeft)
+    Q_PROPERTY(QGeoCoordinate bottomRight READ bottomRight WRITE setBottomRight)
+    Q_PROPERTY(QGeoCoordinate topLeft READ topLeft WRITE setTopLeft)
+    Q_PROPERTY(QGeoCoordinate topRight READ topRight WRITE setTopRight)
+    Q_PROPERTY(QGeoCoordinate center READ center WRITE setCenter)
+    Q_PROPERTY(double height READ height WRITE setHeight)
+    Q_PROPERTY(double width READ width WRITE setWidth)
+
+public:
+    QGeoRectangle();
+    QGeoRectangle(const QGeoCoordinate &center, double degreesWidth, double degreesHeight);
+    QGeoRectangle(const QGeoCoordinate &topLeft, const QGeoCoordinate &bottomRight);
+    QGeoRectangle(const QList<QGeoCoordinate> &coordinates);
+    QGeoRectangle(const QGeoRectangle &other);
+    QGeoRectangle(const QGeoShape &other);
+
+    ~QGeoRectangle();
+
+    QGeoRectangle &operator=(const QGeoRectangle &other);
+
+    using QGeoShape::operator==;
+    bool operator==(const QGeoRectangle &other) const;
+
+    using QGeoShape::operator!=;
+    bool operator!=(const QGeoRectangle &other) const;
+
+    void setTopLeft(const QGeoCoordinate &topLeft);
+    QGeoCoordinate topLeft() const;
+
+    void setTopRight(const QGeoCoordinate &topRight);
+    QGeoCoordinate topRight() const;
+
+    void setBottomLeft(const QGeoCoordinate &bottomLeft);
+    QGeoCoordinate bottomLeft() const;
+
+    void setBottomRight(const QGeoCoordinate &bottomRight);
+    QGeoCoordinate bottomRight() const;
+
+    void setCenter(const QGeoCoordinate &center);
+    QGeoCoordinate center() const;
+
+    void setWidth(double degreesWidth);
+    double width() const;
+
+    void setHeight(double degreesHeight);
+    double height() const;
+
+    using QGeoShape::contains;
+    bool contains(const QGeoRectangle &rectangle) const;
+    Q_INVOKABLE bool intersects(const QGeoRectangle &rectangle) const;
+
+    Q_INVOKABLE void translate(double degreesLatitude, double degreesLongitude);
+    Q_INVOKABLE QGeoRectangle translated(double degreesLatitude, double degreesLongitude) const;
+
+    Q_INVOKABLE QGeoRectangle united(const QGeoRectangle &rectangle) const;
+    QGeoRectangle operator|(const QGeoRectangle &rectangle) const;
+    QGeoRectangle &operator|=(const QGeoRectangle &rectangle);
+
+    Q_INVOKABLE QString toString() const;
+
+private:
+    inline QGeoRectanglePrivate *d_func();
+    inline const QGeoRectanglePrivate *d_func() const;
+};
+
+Q_DECLARE_TYPEINFO(QGeoRectangle, Q_MOVABLE_TYPE);
+
+inline QGeoRectangle QGeoRectangle::operator|(const QGeoRectangle &rectangle) const
+{
+    return united(rectangle);
+}
+
 QT_END_NAMESPACE
 
 Q_DECLARE_METATYPE(QGeoShape)
+Q_DECLARE_METATYPE(QGeoRectangle)
 
 #endif
-
diff --git a/src/positioning/qgeoshape_p.h b/src/positioning/qgeoshape_p.h
index 275886ff..251e872c 100644
--- a/src/positioning/qgeoshape_p.h
+++ b/src/positioning/qgeoshape_p.h
@@ -69,6 +69,8 @@ public:
 
     virtual QGeoCoordinate center() const = 0;
 
+    virtual QGeoRectangle boundingGeoRectangle() const = 0;
+
     virtual void extendShape(const QGeoCoordinate &coordinate) = 0;
 
     virtual QGeoShapePrivate *clone() const = 0;
@@ -89,4 +91,3 @@ Q_INLINE_TEMPLATE QGeoShapePrivate *QSharedDataPointer<QGeoShapePrivate>::clone(
 QT_END_NAMESPACE
 
 #endif
-
diff --git a/src/positioning/qlocationutils_p.h b/src/positioning/qlocationutils_p.h
index 00c4d3e3..32addb63 100644
--- a/src/positioning/qlocationutils_p.h
+++ b/src/positioning/qlocationutils_p.h
@@ -53,6 +53,14 @@
 #include <QtCore/QtGlobal>
 #include <math.h>
 
+#ifndef M_1_180
+#define M_1_180 0.0055555555555555555555555555555555555555556
+#endif
+
+#ifndef M_1_PI
+#define M_1_PI   0.31830988618379067154
+#endif
+
 QT_BEGIN_NAMESPACE
 class QTime;
 class QByteArray;
@@ -176,6 +184,47 @@ public:
             return CardinalNNW;
     }
 
+    // For values exceeding +- 720.0
+    inline static double wrapLongExt(double lng) {
+        double remainder = fmod(lng + 180.0, 360.0);
+        return fmod(remainder + 360.0, 360.0) - 180.0;
+    }
+
+    // Mirrors the azimuth against the X axis. Azimuth assumed to be in [0,360[
+    inline static double mirrorAzimuthX(double azimuth) {
+        if (azimuth <= 90.0)
+             return 180.0 - azimuth;
+         else
+             return 180.0 + (360.0 - azimuth);
+    }
+
+    // Mirrors the azimuth against the Y axis. Azimuth assumed to be in [0,360[
+    inline static double mirrorAzimuthY(double azimuth) {
+        if (azimuth == 0.0)
+            return 0.0;
+        return 360.0 - azimuth;
+    }
+
+    inline static double radians(double degrees)
+    {
+        return degrees * M_PI * M_1_180;
+    }
+
+    inline static double degrees(double radians)
+    {
+        return radians * 180.0 * M_1_PI;
+    }
+
+    inline static double earthMeanRadius()
+    {
+        return 6371007.2;
+    }
+
+    inline static double mercatorMaxLatitude()
+    {
+        return 85.05113;
+    }
+
     /*
         Creates a QGeoPositionInfo from a GGA, GLL, RMC, VTG or ZDA sentence.