Math: added Vector::isZero().

src/Math/Test/VectorTest.cpp

@@ -62,6 +62,7 @@ class VectorTest: public Corrade::TestSuite::Tester {
         void constructConversion();
         void constructCopy();
 
+        void isZero();
         void isNormalized();
 
         void convert();
@@ -109,6 +110,7 @@ VectorTest::VectorTest() {
               &VectorTest::constructConversion,
               &VectorTest::constructCopy,
 
+              &VectorTest::isZero,
               &VectorTest::isNormalized,
 
               &VectorTest::convert,
@@ -198,6 +200,11 @@ void VectorTest::constructCopy() {
     CORRADE_COMPARE(b, Vector4(1.0f, 3.5f, 4.0f, -2.7f));
 }
 
+void VectorTest::isZero() {
+    CORRADE_VERIFY(!Vector3(0.01f, 0.0f, 0.0f).isZero());
+    CORRADE_VERIFY(Vector3(0.0f, 0.0f, 0.0f).isZero());
+}
+
 void VectorTest::isNormalized() {
     CORRADE_VERIFY(!Vector3(1.0f, 2.0f, -1.0f).isNormalized());
     CORRADE_VERIFY(Vector3(0.0f, 1.0f, 0.0f).isNormalized());

src/Math/TypeTraits.h

@@ -183,6 +183,14 @@ template<> struct TypeTraits<long double>: Implementation::TypeTraitsFloatingPoi
     constexpr static long double epsilon() { return LONG_DOUBLE_EQUALITY_PRECISION; }
 };
 
+namespace Implementation {
+
+/* Proper comparison should be with epsilon^2, but the value is not
+   representable in given precision. Comparing to epsilon instead. */
+template<class T> inline bool isZeroSquared(T lengthSquared) {
+    return std::abs(lengthSquared) < TypeTraits<T>::epsilon();
+}
+
 /* Comparing squared length to 1 is not sufficient to compare within range
    [1 - epsilon, 1 + epsilon], as e.g. Quaternion with dot() = 1 + 1e-7 when
    converted to matrix has column vectors with dot() = 1 + 1e-6, which is just
@@ -190,10 +198,10 @@ template<> struct TypeTraits<long double>: Implementation::TypeTraitsFloatingPoi
    [1 - epsilon, 1 + epsilon] or dot() in range [1 - 2*epsilon + epsilon^2,
    1 + 2*epsilon + epsilon^2]. Because epsilon^2 is way off machine precision,
    it's omitted. */
-namespace Implementation {
-    template<class T> inline bool isNormalizedSquared(T lengthSquared) {
-        return std::abs(lengthSquared - T(1)) < T(2)*TypeTraits<T>::epsilon();
-    }
+template<class T> inline bool isNormalizedSquared(T lengthSquared) {
+    return std::abs(lengthSquared - T(1)) < T(2)*TypeTraits<T>::epsilon();
+}
+
 }
 #endif
 

src/Math/Vector.h

@@ -220,6 +220,18 @@ template<std::size_t size, class T> class Vector {
         /** @brief Component-wise greater than */
         BoolVector<size> operator>(const Vector<size, T>& other) const;
 
+        /**
+         * @brief Whether the vector is zero
+         *
+         * @f[
+         *      |\boldsymbol a \cdot \boldsymbol a - 0| < \epsilon^2 \cong \epsilon
+         * @f]
+         * @see dot(), normalized()
+         */
+        bool isZero() const {
+            return Implementation::isZeroSquared(dot());
+        }
+
         /**
          * @brief Whether the vector is normalized
          *