Introduce QQuaternion::inverted()

Change-Id: I6de77082bb7c32e48fb7f7d765a58fdbe68db1fd
Reviewed-by: Sean Harmer <sean.harmer@kdab.com>

src/gui/math3d/qquaternion.cpp

@@ -273,6 +273,16 @@ void QQuaternion::normalize()
     wp /= len;
 }
 
+/*!
+    \fn QQuaternion QQuaternion::inverted() const
+    \since 5.5
+
+    Returns the inverse of this quaternion.
+    If this quaternion is null, then a null quaternion is returned.
+
+    \sa isNull(), length()
+*/
+
 /*!
     \fn QQuaternion QQuaternion::conjugate() const
 

src/gui/math3d/qquaternion.h

@@ -82,6 +82,8 @@ public:
     QQuaternion normalized() const;
     void normalize();
 
+    inline QQuaternion inverted() const;
+
     QQuaternion conjugate() const;
 
     QVector3D rotatedVector(const QVector3D& vector) const;
@@ -152,6 +154,18 @@ inline void QQuaternion::setY(float aY) { yp = aY; }
 inline void QQuaternion::setZ(float aZ) { zp = aZ; }
 inline void QQuaternion::setScalar(float aScalar) { wp = aScalar; }
 
+inline QQuaternion QQuaternion::inverted() const
+{
+    // Need some extra precision if the length is very small.
+    double len = double(xp) * double(xp) +
+                 double(yp) * double(yp) +
+                 double(zp) * double(zp) +
+                 double(wp) * double(wp);
+    if (!qFuzzyIsNull(len))
+        return QQuaternion(wp / len, -xp / len, -yp / len, -zp / len);
+    return QQuaternion(0.0f, 0.0f, 0.0f, 0.0f);
+}
+
 inline QQuaternion QQuaternion::conjugate() const
 {
     return QQuaternion(wp, -xp, -yp, -zp);

tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp

@@ -54,6 +54,9 @@ private slots:
     void normalize_data();
     void normalize();
 
+    void inverted_data();
+    void inverted();
+
     void compare();
 
     void add_data();
@@ -291,6 +294,32 @@ void tst_QQuaternion::normalize()
         QCOMPARE(v.length(), 1.0f);
 }
 
+void tst_QQuaternion::inverted_data()
+{
+    // Use the same test data as the length test.
+    length_data();
+}
+void tst_QQuaternion::inverted()
+{
+    QFETCH(float, x);
+    QFETCH(float, y);
+    QFETCH(float, z);
+    QFETCH(float, w);
+    QFETCH(float, len);
+
+    QQuaternion v(w, x, y, z);
+    QQuaternion u = v.inverted();
+    if (v.isNull()) {
+        QVERIFY(u.isNull());
+    } else {
+        len *= len;
+        QCOMPARE(-u.x() * len, v.x());
+        QCOMPARE(-u.y() * len, v.y());
+        QCOMPARE(-u.z() * len, v.z());
+        QCOMPARE(u.scalar() * len, v.scalar());
+    }
+}
+
 // Test the comparison operators for quaternions.
 void tst_QQuaternion::compare()
 {