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, 7 insertions, 9 deletions

diff --git a/examples/opengl/legacy/grabber/glwidget.cpp b/examples/opengl/legacy/grabber/glwidget.cpp
index 958b8055cd..6be4d30597 100644
--- a/examples/opengl/legacy/grabber/glwidget.cpp
+++ b/examples/opengl/legacy/grabber/glwidget.cpp
@@ -52,8 +52,7 @@
 
 #include <QMouseEvent>
 #include <QTimer>
-
-#include <math.h>
+#include <qmath.h>
 
 GLWidget::GLWidget(QWidget *parent)
     : QGLWidget(parent)
@@ -190,8 +189,6 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
                           GLdouble outerRadius, GLdouble thickness,
                           GLdouble toothSize, GLint toothCount)
 {
-    const double Pi = 3.14159265358979323846;
-
     GLuint list = glGenLists(1);
     glNewList(list, GL_COMPILE);
     glMaterialfv(GL_FRONT, GL_AMBIENT_AND_DIFFUSE, reflectance);
@@ -199,7 +196,8 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
     GLdouble r0 = innerRadius;
     GLdouble r1 = outerRadius - toothSize / 2.0;
     GLdouble r2 = outerRadius + toothSize / 2.0;
-    GLdouble delta = (2.0 * Pi / toothCount) / 4.0;
+    GLdouble toothAngle = 2 * M_PI / toothCount;
+    GLdouble delta = toothAngle / 4.0;
     GLdouble z = thickness / 2.0;
 
     glShadeModel(GL_FLAT);
@@ -211,7 +209,7 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
 
         glBegin(GL_QUAD_STRIP);
         for (int j = 0; j <= toothCount; ++j) {
-            GLdouble angle = 2.0 * Pi * j / toothCount;
+            GLdouble angle = j * toothAngle;
             glVertex3d(r0 * cos(angle), r0 * sin(angle), sign * z);
             glVertex3d(r1 * cos(angle), r1 * sin(angle), sign * z);
             glVertex3d(r0 * cos(angle), r0 * sin(angle), sign * z);
@@ -221,7 +219,7 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
 
         glBegin(GL_QUADS);
         for (int j = 0; j < toothCount; ++j) {
-            GLdouble angle = 2.0 * Pi * j / toothCount;
+            GLdouble angle = j * toothAngle;
             glVertex3d(r1 * cos(angle), r1 * sin(angle), sign * z);
             glVertex3d(r2 * cos(angle + delta), r2 * sin(angle + delta), sign * z);
             glVertex3d(r2 * cos(angle + 2 * delta), r2 * sin(angle + 2 * delta), sign * z);
@@ -233,7 +231,7 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
     glBegin(GL_QUAD_STRIP);
     for (int i = 0; i < toothCount; ++i) {
         for (int j = 0; j < 2; ++j) {
-            GLdouble angle = 2.0 * Pi * (i + j / 2.0) / toothCount;
+            GLdouble angle = (i + j / 2.0) * toothAngle;
             GLdouble s1 = r1;
             GLdouble s2 = r2;
             if (j == 1)
@@ -257,7 +255,7 @@ GLuint GLWidget::makeGear(const GLfloat *reflectance, GLdouble innerRadius,
 
     glBegin(GL_QUAD_STRIP);
     for (int i = 0; i <= toothCount; ++i) {
-        GLdouble angle = i * 2.0 * Pi / toothCount;
+        GLdouble angle = i * toothAngle;
         glNormal3d(-cos(angle), -sin(angle), 0.0);
         glVertex3d(r0 * cos(angle), r0 * sin(angle), +z);
         glVertex3d(r0 * cos(angle), r0 * sin(angle), -z);