Added templated Math::Constants structure to replace PI #define.

And added sqrt(2) and sqrt(3) constants while we are at it.

src/Math/Math.h

@@ -32,8 +32,27 @@ namespace Magnum {
 */
 namespace Math {
 
-/** @brief Pi */
-#define PI 3.1415926535
+/** @brief Numeric constants */
+template<class T> struct Constants {
+    #ifdef DOXYGEN_GENERATING_OUTPUT
+    static constexpr T Pi;      /**< @brief Pi */
+    static constexpr T Sqrt2;   /**< @brief Square root of 2 */
+    static constexpr T Sqrt3;   /**< @brief Square root of 3 */
+    #endif
+};
+
+#ifndef DOXYGEN_GENERATING_OUTPUT
+template<> struct Constants<double> {
+    static constexpr double Pi = 3.14159265359;
+    static constexpr double Sqrt2 = 1.41421356237;
+    static constexpr double Sqrt3 = 1.73205080757;
+};
+template<> struct Constants<float> {
+    static constexpr float Pi = 3.14159265359f;
+    static constexpr float Sqrt2 = 1.41421356237f;
+    static constexpr float Sqrt3 = 1.73205080757f;
+};
+#endif
 
 /**
  * @brief Integral power
@@ -61,7 +80,7 @@ size_t MAGNUM_EXPORT log(size_t base, size_t number);
  * Function to make angle entering less error-prone. Converts the value to
  * radians at compile time. For example `deg(180.0f)` is converted to `3.14f`.
  */
-template<class T> inline constexpr T deg(T value) { return value*PI/180; }
+template<class T> inline constexpr T deg(T value) { return value*Constants<T>::Pi/180; }
 
 /**
  * @brief Angle in radians

src/Math/Test/MathTest.cpp

@@ -24,12 +24,9 @@ QTEST_APPLESS_MAIN(Magnum::Math::Test::MathTest)
 namespace Magnum { namespace Math { namespace Test {
 
 void MathTest::degrad() {
-    QCOMPARE(deg(90.0), PI/2);
-    QCOMPARE(deg(90.0f), float(PI/2));
-    QCOMPARE(rad(PI/2), PI/2);
-
-    QEXPECT_FAIL(0, "Integral parameter is not converted to floating point", Continue);
-    QVERIFY(deg(90) == PI/2);
+    QCOMPARE(deg(90.0), Constants<double>::Pi/2);
+    QCOMPARE(deg(90.0f), Constants<float>::Pi/2);
+    QCOMPARE(rad(Constants<double>::Pi/2), Constants<double>::Pi/2);
 }
 
 void MathTest::pow() {

src/Primitives/Capsule.cpp

@@ -24,13 +24,13 @@ Capsule::Capsule(unsigned int rings, unsigned int segments, GLfloat length, Text
 
     GLfloat height = 2.0f+length;
     GLfloat textureCoordsVIncrement = 1.0f/(rings*height);
-    GLfloat ringAngleIncrement = PI/(2*rings);
+    GLfloat ringAngleIncrement = Math::Constants<GLfloat>::Pi/(2*rings);
 
     /* Bottom cap vertex */
     capVertex(-height/2, -1.0f, 0.0f);
 
     /* Rings of bottom hemisphere */
-    vertexRings(rings, -length/2, -PI/2+ringAngleIncrement, ringAngleIncrement, textureCoordsVIncrement, textureCoordsVIncrement);
+    vertexRings(rings, -length/2, -Math::Constants<GLfloat>::Pi/2+ringAngleIncrement, ringAngleIncrement, textureCoordsVIncrement, textureCoordsVIncrement);
 
     /* Rings of top hemisphere */
     vertexRings(rings, length/2, 0.0f, ringAngleIncrement, (1.0f + length)/height, textureCoordsVIncrement);
@@ -53,7 +53,7 @@ void Capsule::capVertex(GLfloat y, GLfloat normalY, GLfloat textureCoordsV) {
 }
 
 void Capsule::vertexRings(unsigned int count, GLfloat centerY, GLfloat startRingAngle, GLfloat ringAngleIncrement, GLfloat startTextureCoordsV, GLfloat textureCoordsVIncrement) {
-    GLfloat segmentAngleIncrement = 2*PI/segments;
+    GLfloat segmentAngleIncrement = 2*Math::Constants<GLfloat>::Pi/segments;
     GLfloat x, y, z;
     for(unsigned int i = 0; i != count; ++i) {
         GLfloat ringAngle = startRingAngle + i*ringAngleIncrement;

src/Primitives/UVSphere.cpp

@@ -24,13 +24,13 @@ UVSphere::UVSphere(unsigned int rings, unsigned int segments, TextureCoords text
     CORRADE_ASSERT(rings >= 2 && segments >= 3, "UVSphere must have at least two rings and three segments", )
 
     GLfloat textureCoordsVIncrement = 1.0f/rings;
-    GLfloat ringAngleIncrement = PI/rings;
+    GLfloat ringAngleIncrement = Math::Constants<GLfloat>::Pi/rings;
 
     /* Bottom cap vertex */
     capVertex(-1.0f, -1.0f, 0.0f);
 
     /* Vertex rings */
-    vertexRings(rings-1, 0.0f, -PI/2+ringAngleIncrement, ringAngleIncrement, textureCoordsVIncrement, textureCoordsVIncrement);
+    vertexRings(rings-1, 0.0f, -Math::Constants<GLfloat>::Pi/2+ringAngleIncrement, ringAngleIncrement, textureCoordsVIncrement, textureCoordsVIncrement);
 
     /* Top cap vertex */
     capVertex(1.0f, 1.0f, 1.0f);