Be (somewhat more) consistent about the value of pi

Use M_PI (and friends), where possible, in favor of hand-coded
approximations of various (in)accuracies.  Where that's not available
(e.g. fragment shaders), use the same value that qmath.h uses for
M_PI, for consistency.  Replaced math.h with qmath.h in places that
defined a fall-back in case math.h omits it (it's not in the C++
standard, although M_PI is in POSIX); or removed this entirely where
it wasn't used.

Reworked some code to reduce the amount of arithmetic needed, in the
process; e.g. pulling common factors out of loops.  Revised an
example's doc to not waste time talking about using a six-sig-fig
value for pi (which we no longer do) - it really wasn't relevant, or
anything to be proud of; nor did the doc mention its later use.

Task-number: QTBUG-58083
Change-Id: I5a31e3a2b6a823b97a43209bed61a37b9aa6c05f
Reviewed-by: Thiago Macieira <thiago.macieira@intel.com>

1 files changed, 12 insertions, 13 deletions

diff --git a/examples/opengl/hellowindow/hellowindow.cpp b/examples/opengl/hellowindow/hellowindow.cpp
index dc48cc4b76..235775f09a 100644
--- a/examples/opengl/hellowindow/hellowindow.cpp
+++ b/examples/opengl/hellowindow/hellowindow.cpp
@@ -276,21 +276,20 @@ void Renderer::createGeometry()
     extrude(x4, y4, y4, x4);
     extrude(y4, x4, y3, x3);
 
-    const qreal Pi = 3.14159f;
     const int NumSectors = 100;
-
+    const qreal sectorAngle = 2 * qreal(M_PI) / NumSectors;
     for (int i = 0; i < NumSectors; ++i) {
-        qreal angle1 = (i * 2 * Pi) / NumSectors;
-        qreal x5 = 0.30 * qSin(angle1);
-        qreal y5 = 0.30 * qCos(angle1);
-        qreal x6 = 0.20 * qSin(angle1);
-        qreal y6 = 0.20 * qCos(angle1);
-
-        qreal angle2 = ((i + 1) * 2 * Pi) / NumSectors;
-        qreal x7 = 0.20 * qSin(angle2);
-        qreal y7 = 0.20 * qCos(angle2);
-        qreal x8 = 0.30 * qSin(angle2);
-        qreal y8 = 0.30 * qCos(angle2);
+        qreal angle = i * sectorAngle;
+        qreal x5 = 0.30 * qSin(angle);
+        qreal y5 = 0.30 * qCos(angle);
+        qreal x6 = 0.20 * qSin(angle);
+        qreal y6 = 0.20 * qCos(angle);
+
+        angle += sectorAngle;
+        qreal x7 = 0.20 * qSin(angle);
+        qreal y7 = 0.20 * qCos(angle);
+        qreal x8 = 0.30 * qSin(angle);
+        qreal y8 = 0.30 * qCos(angle);
 
         quad(x5, y5, x6, y6, x7, y7, x8, y8);