Add reflect and refract function

src/Magnum/Math/Functions.h

@@ -654,6 +654,32 @@ template<std::size_t size, class T> inline Vector<size, T> sqrtInverted(const Ve
     return Vector<size, T>(T(1))/Math::sqrt(a);
 }
 
+
+/**
+@brief Reflect a vector off a surface given the surface outward normal. Note that the normal vector must be normalized.
+
+@m_keyword{reflect(),GLSL reflect(),}
+*/
+template<std::size_t size, class T> inline Vector<size, T> reflect(const Vector<size, T>& v, const Vector<size, T>& n) {
+    return v - T(2) * dot(v, n) * n;
+}
+
+
+/**
+@brief Refract a vector through a medium given the surface outward normal and ratio of indices of refraction eta. Note that the normal vector must be normalized.
+
+@m_keyword{refract(),GLSL refract(),}
+*/
+template<std::size_t size, class T> inline Vector<size, T> refract(const Vector<size, T>& v, const Vector<size, T>& n, T eta) {
+    const Vector<size, T> vi = v.normalized();
+    const T dt = dot(vi, n);
+    const T k  = T(1) - eta * eta * (T(1) - dt * dt);
+    if(k > 0) {
+        return eta * (vi - n * dt) - n * std::sqrt(k);
+    }
+	return Vector<size, T>{};
+}
+
 /*@}*/
 
 }}

src/Magnum/Math/Test/FunctionsTest.cpp

@@ -69,6 +69,9 @@ struct FunctionsTest: Corrade::TestSuite::Tester {
     void isNan();
     void isNanfVector();
 	
+	void reflect();
+	void refract();
+
     void trigonometric();
     void trigonometricWithBase();
     template<class T> void sincos();
@@ -125,6 +128,9 @@ FunctionsTest::FunctionsTest() {
               &FunctionsTest::isNan,
               &FunctionsTest::isNanfVector,
 			  
+			  &FunctionsTest::reflect,
+              &FunctionsTest::refract,
+
               &FunctionsTest::trigonometric,
               &FunctionsTest::trigonometricWithBase,
               &FunctionsTest::sincos<Float>,
@@ -440,6 +446,16 @@ void FunctionsTest::isNanfVector() {
     CORRADE_COMPARE(Math::isNan(Vector3{0.3f, -Constants::inf(), 1.0f}), Math::BoolVector<3>{0x00});
 }
 
+void FunctionsTest::reflect() {
+    CORRADE_COMPARE(Math::reflect(Vector3{1.0f, 2.0f, 3.0f}, Vector3{0.0f, 1.0f, 0.0f}), (Vector3{1.0f, -2.0f, 3.0f}));
+    CORRADE_COMPARE(Math::reflect(Vector3{2.0f, 1.0f, 1.0f}, Vector3{1.0f, -1.0f, 1.0f}.normalized()), (Vector3{2.0f / 3.0f, 2.0f + 1.0f/3.0f, -1.0f/3.0f}));
+}
+
+void FunctionsTest::refract() {
+    CORRADE_COMPARE(Math::refract(Vector3{1.0f, 0.0f, 1.0f}, Vector3{0.0f, 0.0f, -1.0f}, Float{1.0f / 1.5f}), (Vector3{0.471405, 0, 0.881917}));
+	CORRADE_COMPARE(Math::refract(Vector3{4.0f, 1.0f, 1.0f}, Vector3{0.0f, -2.0f, -1.0f}.normalized(), Float{1.0f / 1.5f}), (Vector3{0.628539, 0.661393, 0.409264}));
+}
+
 void FunctionsTest::trigonometric() {
     CORRADE_COMPARE(Math::sin(Deg(30.0f)), 0.5f);
     CORRADE_COMPARE(Math::sin(Rad(Constants::pi()/6)), 0.5f);