Use qRadiansToDegrees() and qDegreesToRadians() more widely

Especially in examples, where we should show off our convenience
functions, prefer calling these functions over doing arithmetic with
M_PI (or approximations thereto) and 180 (give or take simple
factors).  This incidentally documents what's going on, just by the
name of the function used (and reveals at least one place where
variables were misnamed; the return from atan is in radians, *not*
degrees).

Task-number: QTBUG-58083
Change-Id: I6e5d66721cafab423378f970af525400423e971e
Reviewed-by: Jüri Valdmann <juri.valdmann@qt.io>
Reviewed-by: Allan Sandfeld Jensen <allan.jensen@qt.io>
Reviewed-by: Marc Mutz <marc.mutz@kdab.com>

17 files changed, 39 insertions, 66 deletions

diff --git a/examples/dbus/remotecontrolledcar/car/car.cpp b/examples/dbus/remotecontrolledcar/car/car.cpp
index 67daac79ba..2de4e6447a 100644
--- a/examples/dbus/remotecontrolledcar/car/car.cpp
+++ b/examples/dbus/remotecontrolledcar/car/car.cpp
@@ -50,9 +50,7 @@
 
 #include "car.h"
 #include <QtWidgets/QtWidgets>
-#include <math.h>
-
-static const double Pi = 3.14159265358979323846264338327950288419717;
+#include <qmath.h>
 
 QRectF Car::boundingRect() const
 {
@@ -135,10 +133,10 @@ void Car::timerEvent(QTimerEvent *event)
     Q_UNUSED(event);
 
     const qreal axelDistance = 54;
-    qreal wheelsAngleRads = (wheelsAngle * Pi) / 180;
+    qreal wheelsAngleRads = qDegreesToRadians(wheelsAngle);
     qreal turnDistance = ::cos(wheelsAngleRads) * axelDistance * 2;
     qreal turnRateRads = wheelsAngleRads / turnDistance;  // rough estimate
-    qreal turnRate = (turnRateRads * 180) / Pi;
+    qreal turnRate = qRadiansToDegrees(turnRateRads);
     qreal rotation = speed * turnRate;
 
     setTransform(QTransform().rotate(rotation), true);
diff --git a/examples/embedded/lightmaps/slippymap.cpp b/examples/embedded/lightmaps/slippymap.cpp
index 7e847c2501..0bd5f44075 100644
--- a/examples/embedded/lightmaps/slippymap.cpp
+++ b/examples/embedded/lightmaps/slippymap.cpp
@@ -48,15 +48,10 @@
 **
 ****************************************************************************/
 
-#include <math.h>
-
 #include <QtWidgets>
 #include <QtNetwork>
 #include "slippymap.h"
-
-#ifndef M_PI
-#define M_PI 3.14159265358979323846
-#endif
+#include "qmath.h"
 
 uint qHash(const QPoint& p)
 {
@@ -68,10 +63,10 @@ const int tdim = 256;
 
 QPointF tileForCoordinate(qreal lat, qreal lng, int zoom)
 {
+    qreal radianLat = qDegreesToRadians(lat);
     qreal zn = static_cast<qreal>(1 << zoom);
     qreal tx = (lng + 180.0) / 360.0;
-    qreal ty = (1.0 - log(tan(lat * M_PI / 180.0) +
-                          1.0 / cos(lat * M_PI / 180.0)) / M_PI) / 2.0;
+    qreal ty = 0.5 - log(tan(radianLat) + 1.0 / cos(radianLat)) / M_PI / 2.0;
     return QPointF(tx * zn, ty * zn);
 }
 
@@ -86,8 +81,7 @@ qreal latitudeFromTile(qreal ty, int zoom)
 {
     qreal zn = static_cast<qreal>(1 << zoom);
     qreal n = M_PI - 2 * M_PI * ty / zn;
-    qreal lng = 180.0 / M_PI * atan(0.5 * (exp(n) - exp(-n)));
-    return lng;
+    return qRadiansToDegrees(atan(0.5 * (exp(n) - exp(-n))));
 }
 
 
diff --git a/examples/widgets/animation/stickman/stickman.cpp b/examples/widgets/animation/stickman/stickman.cpp
index 7a4629c4d2..b7a2d87ada 100644
--- a/examples/widgets/animation/stickman/stickman.cpp
+++ b/examples/widgets/animation/stickman/stickman.cpp
@@ -53,13 +53,7 @@
 
 #include <QPainter>
 #include <QTimer>
-
-#define _USE_MATH_DEFINES
-#include <math.h>
-
-#ifndef M_PI
-#define M_PI 3.14159265358979323846
-#endif
+#include <qmath.h>
 
 static const qreal Coords[NodeCount * 2] = {
     0.0, -150.0, // head, #0
@@ -300,7 +294,7 @@ void StickMan::paint(QPainter *painter, const QStyleOptionGraphicsItem *, QWidge
             QPointF dist = node2->pos() - node1->pos();
 
             qreal sinAngle = dist.x() / sqrt(pow(dist.x(), 2) + pow(dist.y(), 2));
-            qreal angle = asin(sinAngle) * 180.0 / M_PI;
+            qreal angle = qRadiansToDegrees(asin(sinAngle));
 
             QPointF headPos = node1->pos();
             painter->translate(headPos);
diff --git a/examples/widgets/effects/lighting/lighting.cpp b/examples/widgets/effects/lighting/lighting.cpp
index 68350f32b7..1ba7dd9ce7 100644
--- a/examples/widgets/effects/lighting/lighting.cpp
+++ b/examples/widgets/effects/lighting/lighting.cpp
@@ -49,14 +49,9 @@
 ****************************************************************************/
 
 #include "lighting.h"
-
 #include <QtWidgets>
 #include <QtCore/qmath.h>
 
-#ifndef M_PI
-#define M_PI 3.14159265358979323846
-#endif
-
 Lighting::Lighting(QWidget *parent): QGraphicsView(parent), angle(0.0)
 {
     setScene(&m_scene);
@@ -120,7 +115,7 @@ void Lighting::setupScene()
 
 void Lighting::animate()
 {
-    angle += (M_PI / 30);
+    angle += qDegreesToRadians(qreal(6));
     qreal xs = 200 * qSin(angle) - 40 + 25;
     qreal ys = 200 * qCos(angle) - 40 + 25;
     m_lightSource->setPos(xs, ys);
diff --git a/examples/widgets/graphicsview/boxes/glbuffers.cpp b/examples/widgets/graphicsview/boxes/glbuffers.cpp
index 1481292e76..851cd17796 100644
--- a/examples/widgets/graphicsview/boxes/glbuffers.cpp
+++ b/examples/widgets/graphicsview/boxes/glbuffers.cpp
@@ -50,11 +50,11 @@
 
 #include "glbuffers.h"
 #include <QtGui/qmatrix4x4.h>
-
+#include <QtCore/qmath.h>
 
 void qgluPerspective(GLdouble fovy, GLdouble aspect, GLdouble zNear, GLdouble zFar)
 {
-    const GLdouble ymax = zNear * tan(fovy * M_PI / 360.0);
+    const GLdouble ymax = zNear * tan(qDegreesToRadians(fovy) / 2.0);
     const GLdouble ymin = -ymax;
     const GLdouble xmin = ymin * aspect;
     const GLdouble xmax = ymax * aspect;
diff --git a/examples/widgets/graphicsview/boxes/trackball.cpp b/examples/widgets/graphicsview/boxes/trackball.cpp
index 15f3af77d1..c350f6adee 100644
--- a/examples/widgets/graphicsview/boxes/trackball.cpp
+++ b/examples/widgets/graphicsview/boxes/trackball.cpp
@@ -50,6 +50,7 @@
 
 #include "trackball.h"
 #include "scene.h"
+#include <qmath.h>
 #include <cmath>
 
 //============================================================================//
@@ -101,10 +102,11 @@ void TrackBall::move(const QPointF& p, const QQuaternion &transformation)
     case Plane:
         {
             QLineF delta(m_lastPos, p);
-            m_angularVelocity = 180*delta.length() / (PI*msecs);
+            const float angleDelta = qRadiansToDegrees(float(delta.length()));
+            m_angularVelocity = angleDelta / msecs;
             m_axis = QVector3D(-delta.dy(), delta.dx(), 0.0f).normalized();
             m_axis = transformation.rotatedVector(m_axis);
-            m_rotation = QQuaternion::fromAxisAndAngle(m_axis, 180 / PI * delta.length()) * m_rotation;
+            m_rotation = QQuaternion::fromAxisAndAngle(m_axis, angleDelta) * m_rotation;
         }
         break;
     case Sphere:
@@ -124,7 +126,7 @@ void TrackBall::move(const QPointF& p, const QQuaternion &transformation)
                 currentPos3D.normalize();
 
             m_axis = QVector3D::crossProduct(lastPos3D, currentPos3D);
-            float angle = 180 / PI * std::asin(std::sqrt(QVector3D::dotProduct(m_axis, m_axis)));
+            float angle = qRadiansToDegrees(std::asin(std::sqrt(QVector3D::dotProduct(m_axis, m_axis))));
 
             m_angularVelocity = angle / msecs;
             m_axis.normalize();
diff --git a/examples/widgets/itemviews/chart/pieview.cpp b/examples/widgets/itemviews/chart/pieview.cpp
index 942bbe5ca5..3f85e397ee 100644
--- a/examples/widgets/itemviews/chart/pieview.cpp
+++ b/examples/widgets/itemviews/chart/pieview.cpp
@@ -49,12 +49,8 @@
 ****************************************************************************/
 
 #include <QtWidgets>
+#include <qmath.h>
 #include <cmath>
-
-#ifndef M_PI
-#define M_PI 3.1415927
-#endif
-
 #include "pieview.h"
 
 PieView::PieView(QWidget *parent)
@@ -125,7 +121,7 @@ QModelIndex PieView::indexAt(const QPoint &point) const
             return QModelIndex();
 
         // Determine the angle of the point.
-        double angle = (180 / M_PI) * std::atan2(cy, cx);
+        double angle = qRadiansToDegrees(std::atan2(cy, cx));
         if (angle < 0)
             angle = 360 + angle;
 
diff --git a/src/gui/math3d/qmatrix4x4.cpp b/src/gui/math3d/qmatrix4x4.cpp
index 6b18e1ab03..d016f07522 100644
--- a/src/gui/math3d/qmatrix4x4.cpp
+++ b/src/gui/math3d/qmatrix4x4.cpp
@@ -1128,7 +1128,7 @@ void QMatrix4x4::rotate(float angle, float x, float y, float z)
         s = 0.0f;
         c = -1.0f;
     } else {
-        float a = angle * M_PI / 180.0f;
+        float a = qDegreesToRadians(angle);
         c = std::cos(a);
         s = std::sin(a);
     }
@@ -1237,7 +1237,7 @@ void QMatrix4x4::projectedRotate(float angle, float x, float y, float z)
         s = 0.0f;
         c = -1.0f;
     } else {
-        float a = angle * M_PI / 180.0f;
+        float a = qDegreesToRadians(angle);
         c = std::cos(a);
         s = std::sin(a);
     }
@@ -1496,7 +1496,7 @@ void QMatrix4x4::perspective(float verticalAngle, float aspectRatio, float nearP
 
     // Construct the projection.
     QMatrix4x4 m(1);
-    float radians = (verticalAngle / 2.0f) * M_PI / 180.0f;
+    float radians = qDegreesToRadians(verticalAngle / 2.0f);
     float sine = std::sin(radians);
     if (sine == 0.0f)
         return;
diff --git a/src/gui/math3d/qquaternion.cpp b/src/gui/math3d/qquaternion.cpp
index e3262c8830..fe1b0425a8 100644
--- a/src/gui/math3d/qquaternion.cpp
+++ b/src/gui/math3d/qquaternion.cpp
@@ -408,7 +408,7 @@ QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D& axis, float angle)
     // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
     // We normalize the result just in case the values are close
     // to zero, as suggested in the above FAQ.
-    float a = (angle / 2.0f) * M_PI / 180.0f;
+    float a = qDegreesToRadians(angle / 2.0f);
     float s = std::sin(a);
     float c = std::cos(a);
     QVector3D ax = axis.normalized();
@@ -467,7 +467,7 @@ QQuaternion QQuaternion::fromAxisAndAngle
         y /= length;
         z /= length;
     }
-    float a = (angle / 2.0f) * M_PI / 180.0f;
+    float a = qDegreesToRadians(angle / 2.0f);
     float s = std::sin(a);
     float c = std::cos(a);
     return QQuaternion(c, x * s, y * s, z * s).normalized();
diff --git a/src/gui/text/qdistancefield.cpp b/src/gui/text/qdistancefield.cpp
index 746200fd9c..af13b96c32 100644
--- a/src/gui/text/qdistancefield.cpp
+++ b/src/gui/text/qdistancefield.cpp
@@ -516,7 +516,7 @@ static void makeDistanceField(QDistanceFieldData *data, const QPainterPath &path
     for (int i = 0; i < imgWidth * imgHeight; ++i)
         bits[i] = exteriorColor;
 
-    const qreal angleStep = qreal(15 * 3.141592653589793238 / 180);
+    const qreal angleStep = qDegreesToRadians(qreal(15));
     const QPoint rotation(qRound(qCos(angleStep) * 0x4000),
                           qRound(qSin(angleStep) * 0x4000)); // 2:14 signed
 
diff --git a/src/plugins/generic/tuiotouch/qtuiohandler.cpp b/src/plugins/generic/tuiotouch/qtuiohandler.cpp
index ac410b7415..bb18ba5085 100644
--- a/src/plugins/generic/tuiotouch/qtuiohandler.cpp
+++ b/src/plugins/generic/tuiotouch/qtuiohandler.cpp
@@ -523,7 +523,7 @@ QWindowSystemInterface::TouchPoint QTuioHandler::tokenToTouchPoint(const QTuioTo
     QPointF delta = relPos - relPos.toPoint();
     tp.area.moveCenter(win->mapToGlobal(relPos.toPoint()) + delta);
     tp.velocity = QVector2D(win->size().width() * tc.vx(), win->size().height() * tc.vy());
-    tp.rotation = tc.angle() * 180.0 / M_PI; // convert radians to degrees
+    tp.rotation = qRadiansToDegrees(tc.angle());
     return tp;
 }
 
diff --git a/src/plugins/platforms/android/androidjniinput.cpp b/src/plugins/platforms/android/androidjniinput.cpp
index ef95b80dd4..75cffe3854 100644
--- a/src/plugins/platforms/android/androidjniinput.cpp
+++ b/src/plugins/platforms/android/androidjniinput.cpp
@@ -50,6 +50,7 @@
 
 #include <QGuiApplication>
 #include <QDebug>
+#include <QtMath>
 
 QT_BEGIN_NAMESPACE
 
@@ -251,7 +252,7 @@ namespace QtAndroidInput
         QWindowSystemInterface::TouchPoint touchPoint;
         touchPoint.id = id;
         touchPoint.pressure = pressure;
-        touchPoint.rotation = rotation * 180 / M_PI;
+        touchPoint.rotation = qRadiansToDegrees(rotation);
         touchPoint.normalPosition = QPointF(double(x / dw), double(y / dh));
         touchPoint.state = state;
         touchPoint.area = QRectF(x - double(minor),
diff --git a/src/plugins/platforms/windows/qwindowstabletsupport.cpp b/src/plugins/platforms/windows/qwindowstabletsupport.cpp
index 7e1017426f..299497a35b 100644
--- a/src/plugins/platforms/windows/qwindowstabletsupport.cpp
+++ b/src/plugins/platforms/windows/qwindowstabletsupport.cpp
@@ -463,13 +463,13 @@ bool QWindowsTabletSupport::translateTabletPacketEvent()
             // Z = sin(altitude)
             // X Tilt = arctan(X / Z)
             // Y Tilt = arctan(Y / Z)
-            const double radAzim = (packet.pkOrientation.orAzimuth / 10.0) * (M_PI / 180);
-            const double tanAlt = std::tan((std::abs(packet.pkOrientation.orAltitude / 10.0)) * (M_PI / 180));
+            const double radAzim = qDegreesToRadians(packet.pkOrientation.orAzimuth / 10.0);
+            const double tanAlt = std::tan(qDegreesToRadians(std::abs(packet.pkOrientation.orAltitude / 10.0)));
 
             const double degX = std::atan(std::sin(radAzim) / tanAlt);
             const double degY = std::atan(std::cos(radAzim) / tanAlt);
-            tiltX = int(degX * (180 / M_PI));
-            tiltY = int(-degY * (180 / M_PI));
+            tiltX = int(qRadiansToDegrees(degX));
+            tiltY = int(qRadiansToDegrees(-degY));
             rotation = 360.0 - (packet.pkOrientation.orTwist / 10.0);
             if (rotation > 180.0)
                 rotation -= 360.0;
diff --git a/tests/auto/gui/math3d/qmatrixnxn/tst_qmatrixnxn.cpp b/tests/auto/gui/math3d/qmatrixnxn/tst_qmatrixnxn.cpp
index c2c04b69c5..96d983c8f7 100644
--- a/tests/auto/gui/math3d/qmatrixnxn/tst_qmatrixnxn.cpp
+++ b/tests/auto/gui/math3d/qmatrixnxn/tst_qmatrixnxn.cpp
@@ -2278,8 +2278,8 @@ void tst_QMatrixNxN::rotate4x4_data()
     float y = 2.0f;
     float z = -6.0f;
     float angle = -45.0f;
-    float c = std::cos(angle * M_PI / 180.0f);
-    float s = std::sin(angle * M_PI / 180.0f);
+    float c = std::cos(qDegreesToRadians(angle));
+    float s = std::sin(qDegreesToRadians(angle));
     float len = std::sqrt(x * x + y * y + z * z);
     float xu = x / len;
     float yu = y / len;
diff --git a/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp b/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
index 53af65e010..097dd111d3 100644
--- a/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
+++ b/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
@@ -815,7 +815,7 @@ void tst_QQuaternion::fromAxisAndAngle()
     // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
     // to calculate the answer we expect to get.
     QVector3D vector = QVector3D(x1, y1, z1).normalized();
-    const float a = (angle * M_PI / 180.0) / 2.0;
+    const float a = qDegreesToRadians(angle) / 2.0;
     const float sin_a = std::sin(a);
     const float cos_a = std::cos(a);
     QQuaternion result(cos_a,
diff --git a/tests/auto/gui/painting/qwmatrix/tst_qwmatrix.cpp b/tests/auto/gui/painting/qwmatrix/tst_qwmatrix.cpp
index 46420b49c5..da88a868f3 100644
--- a/tests/auto/gui/painting/qwmatrix/tst_qwmatrix.cpp
+++ b/tests/auto/gui/painting/qwmatrix/tst_qwmatrix.cpp
@@ -114,12 +114,8 @@ void tst_QWMatrix::mapping_data()
                                 << QRect( 0, 0, 30, 40 )
                                 << QPolygon( QRect( -300, -400, 300, 400 ) );
 
-#if defined(Q_OS_WIN) && !defined(M_PI)
-#define M_PI 3.14159265897932384626433832795f
-#endif
-
     const auto rotate = [](qreal degrees) {
-        const qreal rad = M_PI * degrees / 180.;
+        const qreal rad = qDegreesToRadians(degrees);
         return QMatrix(std::cos(rad), -std::sin(rad),
                        std::sin(rad),  std::cos(rad), 0, 0);
     };
@@ -140,7 +136,7 @@ void tst_QWMatrix::mapping_data()
 
 #if 0
     const auto rotScale = [](qreal degrees, qreal scale) {
-        const qreal rad = M_PI * degrees / 180.;
+        const qreal rad = qDegreesToRadians(degrees);
         return QMatrix(scale * std::cos(rad), -scale * std::sin(rad),
                        scale * std::sin(rad),  scale * std::cos(rad), 0, 0);
     };
diff --git a/tests/benchmarks/gui/painting/qpainter/tst_qpainter.cpp b/tests/benchmarks/gui/painting/qpainter/tst_qpainter.cpp
index ea08af7608..f2e6973e27 100644
--- a/tests/benchmarks/gui/painting/qpainter/tst_qpainter.cpp
+++ b/tests/benchmarks/gui/painting/qpainter/tst_qpainter.cpp
@@ -33,10 +33,7 @@
 #include <QImage>
 #include <QPaintEngine>
 #include <QTileRules>
-#include <math.h>
-#ifndef M_PI
-#define M_PI 3.14159265358979323846
-#endif
+#include <qmath.h>
 
 #include <private/qpixmap_raster_p.h>
 
@@ -1232,7 +1229,7 @@ QTransform tst_QPainter::transformForAngle(qreal angle)
     QTransform rotTrans2;
     rotTrans2.translate(40, 0);
 
-    qreal rad = angle * 2. * M_PI / 360.;
+    qreal rad = qDegreesToRadians(angle);
     qreal c = ::cos(rad);
     qreal s = ::sin(rad);