[QQuaternion] Add a way to convert to/from orthonormal axes

It is just a convenience wrapper
around convertion to/from the rotation matrix.

Change-Id: I27511b43866827172960b0152f1c7b65da857f6f
Reviewed-by: Lars Knoll <lars.knoll@digia.com>

3 files changed, 149 insertions, 30 deletions

diff --git a/src/gui/math3d/qquaternion.cpp b/src/gui/math3d/qquaternion.cpp
index 141651eda1..d367f74e25 100644
--- a/src/gui/math3d/qquaternion.cpp
+++ b/src/gui/math3d/qquaternion.cpp
@@ -592,7 +592,7 @@ QQuaternion QQuaternion::fromEulerAngles(float pitch, float yaw, float roll)
     \note If this quaternion is not normalized,
     the resulting rotation matrix will contain scaling information.
 
-    \sa fromRotationMatrix()
+    \sa fromRotationMatrix(), getAxes()
 */
 QMatrix3x3 QQuaternion::toRotationMatrix() const
 {
@@ -635,7 +635,7 @@ QMatrix3x3 QQuaternion::toRotationMatrix() const
     \note If a given rotation matrix is not normalized,
     the resulting quaternion will contain scaling information.
 
-    \sa toRotationMatrix()
+    \sa toRotationMatrix(), fromAxes()
 */
 QQuaternion QQuaternion::fromRotationMatrix(const QMatrix3x3 &rot3x3)
 {
@@ -672,6 +672,53 @@ QQuaternion QQuaternion::fromRotationMatrix(const QMatrix3x3 &rot3x3)
     return QQuaternion(scalar, axis[0], axis[1], axis[2]);
 }
 
+#ifndef QT_NO_VECTOR3D
+
+/*!
+    \since 5.5
+
+    Returns the 3 orthonormal axes (\a xAxis, \a yAxis, \a zAxis) defining the quaternion.
+
+    \sa fromAxes(), toRotationMatrix()
+*/
+void QQuaternion::getAxes(QVector3D *xAxis, QVector3D *yAxis, QVector3D *zAxis) const
+{
+    Q_ASSERT(xAxis && yAxis && zAxis);
+
+    const QMatrix3x3 rot3x3(toRotationMatrix());
+
+    *xAxis = QVector3D(rot3x3(0, 0), rot3x3(1, 0), rot3x3(2, 0));
+    *yAxis = QVector3D(rot3x3(0, 1), rot3x3(1, 1), rot3x3(2, 1));
+    *zAxis = QVector3D(rot3x3(0, 2), rot3x3(1, 2), rot3x3(2, 2));
+}
+
+/*!
+    \since 5.5
+
+    Constructs the quaternion using 3 axes (\a xAxis, \a yAxis, \a zAxis).
+
+    \note The axes are assumed to be orthonormal.
+
+    \sa getAxes(), fromRotationMatrix()
+*/
+QQuaternion QQuaternion::fromAxes(const QVector3D &xAxis, const QVector3D &yAxis, const QVector3D &zAxis)
+{
+    QMatrix3x3 rot3x3(Qt::Uninitialized);
+    rot3x3(0, 0) = xAxis.x();
+    rot3x3(1, 0) = xAxis.y();
+    rot3x3(2, 0) = xAxis.z();
+    rot3x3(0, 1) = yAxis.x();
+    rot3x3(1, 1) = yAxis.y();
+    rot3x3(2, 1) = yAxis.z();
+    rot3x3(0, 2) = zAxis.x();
+    rot3x3(1, 2) = zAxis.y();
+    rot3x3(2, 2) = zAxis.z();
+
+    return QQuaternion::fromRotationMatrix(rot3x3);
+}
+
+#endif // QT_NO_VECTOR3D
+
 /*!
     \fn bool operator==(const QQuaternion &q1, const QQuaternion &q2)
     \relates QQuaternion
diff --git a/src/gui/math3d/qquaternion.h b/src/gui/math3d/qquaternion.h
index b4022e8579..6ce3979bbe 100644
--- a/src/gui/math3d/qquaternion.h
+++ b/src/gui/math3d/qquaternion.h
@@ -134,6 +134,11 @@ public:
     QMatrix3x3 toRotationMatrix() const;
     static QQuaternion fromRotationMatrix(const QMatrix3x3 &rot3x3);
 
+#ifndef QT_NO_VECTOR3D
+    void getAxes(QVector3D *xAxis, QVector3D *yAxis, QVector3D *zAxis) const;
+    static QQuaternion fromAxes(const QVector3D &xAxis, const QVector3D &yAxis, const QVector3D &zAxis);
+#endif
+
     static QQuaternion slerp
         (const QQuaternion& q1, const QQuaternion& q2, float t);
     static QQuaternion nlerp
diff --git a/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp b/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
index e358937a62..6b8eeeaca5 100644
--- a/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
+++ b/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp
@@ -35,6 +35,52 @@
 #include <QtCore/qmath.h>
 #include <QtGui/qquaternion.h>
 
+// This is a more tolerant version of qFuzzyCompare that also handles the case
+// where one or more of the values being compare are close to zero
+static inline bool myFuzzyCompare(float p1, float p2)
+{
+    if (qFuzzyIsNull(p1) && qFuzzyIsNull(p2))
+        return true;
+    return qAbs(qAbs(p1) - qAbs(p2)) <= 0.00003f;
+}
+
+static inline bool myFuzzyCompare(const QVector3D &v1, const QVector3D &v2)
+{
+    return myFuzzyCompare(v1.x(), v2.x())
+            && myFuzzyCompare(v1.y(), v2.y())
+            && myFuzzyCompare(v1.z(), v2.z());
+}
+
+static inline bool myFuzzyCompare(const QQuaternion &q1, const QQuaternion &q2)
+{
+    const float d = QQuaternion::dotProduct(q1, q2);
+    return myFuzzyCompare(d * d, 1.0f);
+}
+
+static inline bool myFuzzyCompareRadians(float p1, float p2)
+{
+    static const float fPI = float(M_PI);
+    if (p1 < -fPI)
+        p1 += 2.0f * fPI;
+    else if (p1 > fPI)
+        p1 -= 2.0f * fPI;
+
+    if (p2 < -fPI)
+        p2 += 2.0f * fPI;
+    else if (p2 > fPI)
+        p2 -= 2.0f * fPI;
+
+    return qAbs(qAbs(p1) - qAbs(p2)) <= qDegreesToRadians(0.05f);
+}
+
+static inline bool myFuzzyCompareDegrees(float p1, float p2)
+{
+    p1 = qDegreesToRadians(p1);
+    p2 = qDegreesToRadians(p2);
+    return myFuzzyCompareRadians(p1, p2);
+}
+
+
 class tst_QQuaternion : public QObject
 {
     Q_OBJECT
@@ -89,6 +135,9 @@ private slots:
     void fromRotationMatrix_data();
     void fromRotationMatrix();
 
+    void fromAxes_data();
+    void fromAxes();
+
     void fromEulerAngles_data();
     void fromEulerAngles();
 
@@ -826,40 +875,58 @@ void tst_QQuaternion::fromRotationMatrix()
     QVERIFY(qFuzzyCompare(answer, result) || qFuzzyCompare(-answer, result));
 }
 
-// This is a more tolerant version of qFuzzyCompare that also handles the case
-// where one or more of the values being compare are close to zero
-static inline bool myFuzzyCompare(float p1, float p2)
+// Test quaternion convertion to and from orthonormal axes.
+void tst_QQuaternion::fromAxes_data()
 {
-    if (qFuzzyIsNull(p1))
-        return qFuzzyIsNull(p2);
-    if (qFuzzyIsNull(p2))
-        return false;
-    // a very slightly looser version of qFuzzyCompare
-    // for use with values that are not very close to zero
-    return qAbs(p1 - p2) <= 0.00003f * qMin(qAbs(p1), qAbs(p2));
-}
+    QTest::addColumn<float>("x1");
+    QTest::addColumn<float>("y1");
+    QTest::addColumn<float>("z1");
+    QTest::addColumn<float>("angle");
+    QTest::addColumn<QVector3D>("xAxis");
+    QTest::addColumn<QVector3D>("yAxis");
+    QTest::addColumn<QVector3D>("zAxis");
 
-static inline bool myFuzzyCompareRadians(float p1, float p2)
-{
-    static const float fPI = float(M_PI);
-    if (p1 < -fPI)
-        p1 += 2.0f * fPI;
-    else if (p1 > fPI)
-        p1 -= 2.0f * fPI;
+    QTest::newRow("null")
+        << 0.0f << 0.0f << 0.0f << 0.0f
+        << QVector3D(1, 0, 0) << QVector3D(0, 1, 0) << QVector3D(0, 0, 1);
 
-    if (p2 < -fPI)
-        p2 += 2.0f * fPI;
-    else if (p2 > fPI)
-        p2 -= 2.0f * fPI;
+    QTest::newRow("xonly")
+        << 1.0f << 0.0f << 0.0f << 90.0f
+        << QVector3D(1, 0, 0) << QVector3D(0, 0, 1) << QVector3D(0, -1, 0);
 
-    return qAbs(qAbs(p1) - qAbs(p2)) <= qDegreesToRadians(0.05f);
-}
+    QTest::newRow("yonly")
+        << 0.0f << 1.0f << 0.0f << 180.0f
+        << QVector3D(-1, 0, 0) << QVector3D(0, 1, 0) << QVector3D(0, 0, -1);
 
-static inline bool myFuzzyCompareDegrees(float p1, float p2)
+    QTest::newRow("zonly")
+        << 0.0f << 0.0f << 1.0f << 270.0f
+        << QVector3D(0, -1, 0) << QVector3D(1, 0, 0) << QVector3D(0, 0, 1);
+
+    QTest::newRow("complex")
+        << 1.0f << 2.0f << -3.0f << 45.0f
+        << QVector3D(0.728028, -0.525105, -0.440727) << QVector3D(0.608789, 0.790791, 0.0634566) << QVector3D(0.315202, -0.314508, 0.895395);
+}
+void tst_QQuaternion::fromAxes()
 {
-    p1 = qDegreesToRadians(p1);
-    p2 = qDegreesToRadians(p2);
-    return myFuzzyCompareRadians(p1, p2);
+    QFETCH(float, x1);
+    QFETCH(float, y1);
+    QFETCH(float, z1);
+    QFETCH(float, angle);
+    QFETCH(QVector3D, xAxis);
+    QFETCH(QVector3D, yAxis);
+    QFETCH(QVector3D, zAxis);
+
+    QQuaternion result = QQuaternion::fromAxisAndAngle(QVector3D(x1, y1, z1), angle);
+
+    QVector3D axes[3];
+    result.getAxes(&axes[0], &axes[1], &axes[2]);
+    QVERIFY(myFuzzyCompare(axes[0], xAxis));
+    QVERIFY(myFuzzyCompare(axes[1], yAxis));
+    QVERIFY(myFuzzyCompare(axes[2], zAxis));
+
+    QQuaternion answer = QQuaternion::fromAxes(axes[0], axes[1], axes[2]);
+
+    QVERIFY(qFuzzyCompare(answer, result) || qFuzzyCompare(-answer, result));
 }
 
 // Test quaternion creation from an axis and an angle.