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qt6windows7/tests/auto/gui/math3d/qquaternion/tst_qquaternion.cpp

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qt 6.5.1 original
2023-10-30 06:33:08 +08:00
// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR GPL-3.0-only WITH Qt-GPL-exception-1.0
#include <QTest>
#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
public:
tst_QQuaternion() {}
~tst_QQuaternion() {}
private slots:
void create();
void dotProduct_data();
void dotProduct();
void length_data();
void length();
void normalized_data();
void normalized();
void normalize_data();
void normalize();
void inverted_data();
void inverted();
void compare();
void add_data();
void add();
void subtract_data();
void subtract();
void multiply_data();
void multiply();
void multiplyFactor_data();
void multiplyFactor();
void divide_data();
void divide();
void negate_data();
void negate();
void conjugated_data();
void conjugated();
void fromAxisAndAngle_data();
void fromAxisAndAngle();
void fromRotationMatrix_data();
void fromRotationMatrix();
void fromAxes_data();
void fromAxes();
void rotationTo_data();
void rotationTo();
void fromDirection_data();
void fromDirection();
void fromEulerAngles_data();
void fromEulerAngles();
void slerp_data();
void slerp();
void nlerp_data();
void nlerp();
void properties();
void metaTypes();
};
// Test the creation of QQuaternion objects in various ways:
// construct, copy, and modify.
void tst_QQuaternion::create()
{
QQuaternion identity;
QCOMPARE(identity.x(), 0.0f);
QCOMPARE(identity.y(), 0.0f);
QCOMPARE(identity.z(), 0.0f);
QCOMPARE(identity.scalar(), 1.0f);
QVERIFY(identity.isIdentity());
QQuaternion negativeZeroIdentity(1.0f, -0.0f, -0.0f, -0.0f);
QCOMPARE(negativeZeroIdentity.x(), -0.0f);
QCOMPARE(negativeZeroIdentity.y(), -0.0f);
QCOMPARE(negativeZeroIdentity.z(), -0.0f);
QCOMPARE(negativeZeroIdentity.scalar(), 1.0f);
QVERIFY(negativeZeroIdentity.isIdentity());
QQuaternion v1(34.0f, 1.0f, 2.5f, -89.25f);
QCOMPARE(v1.x(), 1.0f);
QCOMPARE(v1.y(), 2.5f);
QCOMPARE(v1.z(), -89.25f);
QCOMPARE(v1.scalar(), 34.0f);
QVERIFY(!v1.isNull());
QQuaternion v1i(34, 1, 2, -89);
QCOMPARE(v1i.x(), 1.0f);
QCOMPARE(v1i.y(), 2.0f);
QCOMPARE(v1i.z(), -89.0f);
QCOMPARE(v1i.scalar(), 34.0f);
QVERIFY(!v1i.isNull());
QQuaternion v2(v1);
QCOMPARE(v2.x(), 1.0f);
QCOMPARE(v2.y(), 2.5f);
QCOMPARE(v2.z(), -89.25f);
QCOMPARE(v2.scalar(), 34.0f);
QVERIFY(!v2.isNull());
QQuaternion v4;
QCOMPARE(v4.x(), 0.0f);
QCOMPARE(v4.y(), 0.0f);
QCOMPARE(v4.z(), 0.0f);
QCOMPARE(v4.scalar(), 1.0f);
QVERIFY(v4.isIdentity());
v4 = v1;
QCOMPARE(v4.x(), 1.0f);
QCOMPARE(v4.y(), 2.5f);
QCOMPARE(v4.z(), -89.25f);
QCOMPARE(v4.scalar(), 34.0f);
QVERIFY(!v4.isNull());
QQuaternion v9(34, QVector3D(1.0f, 2.5f, -89.25f));
QCOMPARE(v9.x(), 1.0f);
QCOMPARE(v9.y(), 2.5f);
QCOMPARE(v9.z(), -89.25f);
QCOMPARE(v9.scalar(), 34.0f);
QVERIFY(!v9.isNull());
v1.setX(3.0f);
QCOMPARE(v1.x(), 3.0f);
QCOMPARE(v1.y(), 2.5f);
QCOMPARE(v1.z(), -89.25f);
QCOMPARE(v1.scalar(), 34.0f);
QVERIFY(!v1.isNull());
v1.setY(10.5f);
QCOMPARE(v1.x(), 3.0f);
QCOMPARE(v1.y(), 10.5f);
QCOMPARE(v1.z(), -89.25f);
QCOMPARE(v1.scalar(), 34.0f);
QVERIFY(!v1.isNull());
v1.setZ(15.5f);
QCOMPARE(v1.x(), 3.0f);
QCOMPARE(v1.y(), 10.5f);
QCOMPARE(v1.z(), 15.5f);
QCOMPARE(v1.scalar(), 34.0f);
QVERIFY(!v1.isNull());
v1.setScalar(6.0f);
QCOMPARE(v1.x(), 3.0f);
QCOMPARE(v1.y(), 10.5f);
QCOMPARE(v1.z(), 15.5f);
QCOMPARE(v1.scalar(), 6.0f);
QVERIFY(!v1.isNull());
v1.setVector(2.0f, 6.5f, -1.25f);
QCOMPARE(v1.x(), 2.0f);
QCOMPARE(v1.y(), 6.5f);
QCOMPARE(v1.z(), -1.25f);
QCOMPARE(v1.scalar(), 6.0f);
QVERIFY(!v1.isNull());
QVERIFY(v1.vector() == QVector3D(2.0f, 6.5f, -1.25f));
v1.setVector(QVector3D(-2.0f, -6.5f, 1.25f));
QCOMPARE(v1.x(), -2.0f);
QCOMPARE(v1.y(), -6.5f);
QCOMPARE(v1.z(), 1.25f);
QCOMPARE(v1.scalar(), 6.0f);
QVERIFY(!v1.isNull());
QVERIFY(v1.vector() == QVector3D(-2.0f, -6.5f, 1.25f));
v1.setX(0.0f);
v1.setY(0.0f);
v1.setZ(0.0f);
v1.setScalar(0.0f);
QCOMPARE(v1.x(), 0.0f);
QCOMPARE(v1.y(), 0.0f);
QCOMPARE(v1.z(), 0.0f);
QCOMPARE(v1.scalar(), 0.0f);
QVERIFY(v1.isNull());
QVector4D v10 = v9.toVector4D();
QCOMPARE(v10.x(), 1.0f);
QCOMPARE(v10.y(), 2.5f);
QCOMPARE(v10.z(), -89.25f);
QCOMPARE(v10.w(), 34.0f);
}
// Test the computation of dot product.
void tst_QQuaternion::dotProduct_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("scalar1");
QTest::addColumn<float>("x2");
QTest::addColumn<float>("y2");
QTest::addColumn<float>("z2");
QTest::addColumn<float>("scalar2");
QTest::addColumn<float>("dot");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 0.0f;
QTest::newRow("identity")
<< 0.0f << 0.0f << 0.0f << 1.0f
<< 0.0f << 0.0f << 0.0f << 1.0f
<< 1.0f;
QTest::newRow("unitvec")
<< 1.0f << 0.0f << 0.0f << 0.0f
<< 0.0f << 1.0f << 0.0f << 0.0f
<< 0.0f;
QTest::newRow("complex")
<< 1.0f << 2.0f << 3.0f << 4.0f
<< 4.0f << 5.0f << 6.0f << 7.0f
<< 60.0f;
}
void tst_QQuaternion::dotProduct()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, scalar1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, scalar2);
QFETCH(float, dot);
QQuaternion q1(scalar1, x1, y1, z1);
QQuaternion q2(scalar2, x2, y2, z2);
QCOMPARE(QQuaternion::dotProduct(q1, q2), dot);
QCOMPARE(QQuaternion::dotProduct(q2, q1), dot);
}
// Test length computation for quaternions.
void tst_QQuaternion::length_data()
{
QTest::addColumn<float>("x");
QTest::addColumn<float>("y");
QTest::addColumn<float>("z");
QTest::addColumn<float>("w");
QTest::addColumn<float>("len");
QTest::newRow("null") << 0.0f << 0.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("1x") << 1.0f << 0.0f << 0.0f << 0.0f << 1.0f;
QTest::newRow("1y") << 0.0f << 1.0f << 0.0f << 0.0f << 1.0f;
QTest::newRow("1z") << 0.0f << 0.0f << 1.0f << 0.0f << 1.0f;
QTest::newRow("1w") << 0.0f << 0.0f << 0.0f << 1.0f << 1.0f;
QTest::newRow("-1x") << -1.0f << 0.0f << 0.0f << 0.0f << 1.0f;
QTest::newRow("-1y") << 0.0f << -1.0f << 0.0f << 0.0f << 1.0f;
QTest::newRow("-1z") << 0.0f << 0.0f << -1.0f << 0.0f << 1.0f;
QTest::newRow("-1w") << 0.0f << 0.0f << 0.0f << -1.0f << 1.0f;
QTest::newRow("two") << 2.0f << -2.0f << 2.0f << 2.0f << std::sqrt(16.0f);
}
void tst_QQuaternion::length()
{
QFETCH(float, x);
QFETCH(float, y);
QFETCH(float, z);
QFETCH(float, w);
QFETCH(float, len);
QQuaternion v(w, x, y, z);
QCOMPARE(v.length(), len);
QCOMPARE(v.lengthSquared(), x * x + y * y + z * z + w * w);
}
// Test the unit vector conversion for quaternions.
void tst_QQuaternion::normalized_data()
{
// Use the same test data as the length test.
length_data();
}
void tst_QQuaternion::normalized()
{
QFETCH(float, x);
QFETCH(float, y);
QFETCH(float, z);
QFETCH(float, w);
QFETCH(float, len);
QQuaternion v(w, x, y, z);
QQuaternion u = v.normalized();
if (v.isNull())
QVERIFY(u.isNull());
else
QCOMPARE(u.length(), 1.0f);
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 unit vector conversion for quaternions.
void tst_QQuaternion::normalize_data()
{
// Use the same test data as the length test.
length_data();
}
void tst_QQuaternion::normalize()
{
QFETCH(float, x);
QFETCH(float, y);
QFETCH(float, z);
QFETCH(float, w);
QQuaternion v(w, x, y, z);
bool isNull = v.isNull();
v.normalize();
if (isNull)
QVERIFY(v.isNull());
else
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()
{
QQuaternion v1(8, 1, 2, 4);
QQuaternion v2(8, 1, 2, 4);
QQuaternion v3(8, 3, 2, 4);
QQuaternion v4(8, 1, 3, 4);
QQuaternion v5(8, 1, 2, 3);
QQuaternion v6(3, 1, 2, 4);
QCOMPARE(v1, v2);
QVERIFY(v1 != v3);
QVERIFY(v1 != v4);
QVERIFY(v1 != v5);
QVERIFY(v1 != v6);
}
// Test addition for quaternions.
void tst_QQuaternion::add_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("w1");
QTest::addColumn<float>("x2");
QTest::addColumn<float>("y2");
QTest::addColumn<float>("z2");
QTest::addColumn<float>("w2");
QTest::addColumn<float>("x3");
QTest::addColumn<float>("y3");
QTest::addColumn<float>("z3");
QTest::addColumn<float>("w3");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 0.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("xonly")
<< 1.0f << 0.0f << 0.0f << 0.0f
<< 2.0f << 0.0f << 0.0f << 0.0f
<< 3.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("yonly")
<< 0.0f << 1.0f << 0.0f << 0.0f
<< 0.0f << 2.0f << 0.0f << 0.0f
<< 0.0f << 3.0f << 0.0f << 0.0f;
QTest::newRow("zonly")
<< 0.0f << 0.0f << 1.0f << 0.0f
<< 0.0f << 0.0f << 2.0f << 0.0f
<< 0.0f << 0.0f << 3.0f << 0.0f;
QTest::newRow("wonly")
<< 0.0f << 0.0f << 0.0f << 1.0f
<< 0.0f << 0.0f << 0.0f << 2.0f
<< 0.0f << 0.0f << 0.0f << 3.0f;
QTest::newRow("all")
<< 1.0f << 2.0f << 3.0f << 8.0f
<< 4.0f << 5.0f << -6.0f << 9.0f
<< 5.0f << 7.0f << -3.0f << 17.0f;
}
void tst_QQuaternion::add()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, w2);
QFETCH(float, x3);
QFETCH(float, y3);
QFETCH(float, z3);
QFETCH(float, w3);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(w2, x2, y2, z2);
QQuaternion v3(w3, x3, y3, z3);
QVERIFY((v1 + v2) == v3);
QQuaternion v4(v1);
v4 += v2;
QCOMPARE(v4, v3);
QCOMPARE(v4.x(), v1.x() + v2.x());
QCOMPARE(v4.y(), v1.y() + v2.y());
QCOMPARE(v4.z(), v1.z() + v2.z());
QCOMPARE(v4.scalar(), v1.scalar() + v2.scalar());
}
// Test subtraction for quaternions.
void tst_QQuaternion::subtract_data()
{
// Use the same test data as the add test.
add_data();
}
void tst_QQuaternion::subtract()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, w2);
QFETCH(float, x3);
QFETCH(float, y3);
QFETCH(float, z3);
QFETCH(float, w3);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(w2, x2, y2, z2);
QQuaternion v3(w3, x3, y3, z3);
QVERIFY((v3 - v1) == v2);
QVERIFY((v3 - v2) == v1);
QQuaternion v4(v3);
v4 -= v1;
QCOMPARE(v4, v2);
QCOMPARE(v4.x(), v3.x() - v1.x());
QCOMPARE(v4.y(), v3.y() - v1.y());
QCOMPARE(v4.z(), v3.z() - v1.z());
QCOMPARE(v4.scalar(), v3.scalar() - v1.scalar());
QQuaternion v5(v3);
v5 -= v2;
QCOMPARE(v5, v1);
QCOMPARE(v5.x(), v3.x() - v2.x());
QCOMPARE(v5.y(), v3.y() - v2.y());
QCOMPARE(v5.z(), v3.z() - v2.z());
QCOMPARE(v5.scalar(), v3.scalar() - v2.scalar());
}
// Test quaternion multiplication.
void tst_QQuaternion::multiply_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("w1");
QTest::addColumn<float>("x2");
QTest::addColumn<float>("y2");
QTest::addColumn<float>("z2");
QTest::addColumn<float>("w2");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 0.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("unitvec")
<< 1.0f << 0.0f << 0.0f << 1.0f
<< 0.0f << 1.0f << 0.0f << 1.0f;
QTest::newRow("complex")
<< 1.0f << 2.0f << 3.0f << 7.0f
<< 4.0f << 5.0f << 6.0f << 8.0f;
for (float w = -1.0f; w <= 1.0f; w += 0.5f)
for (float x = -1.0f; x <= 1.0f; x += 0.5f)
for (float y = -1.0f; y <= 1.0f; y += 0.5f)
for (float z = -1.0f; z <= 1.0f; z += 0.5f) {
QTest::addRow("exhaustive: (%.1f, %.1f, %.1f), %.1f", x, y, z, w)
<< x << y << z << w
<< z << w << y << x;
}
}
void tst_QQuaternion::multiply()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, w2);
QQuaternion q1(w1, x1, y1, z1);
QQuaternion q2(w2, x2, y2, z2);
// Use the simple algorithm at:
// http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q53
// to calculate the answer we expect to get.
QVector3D v1(x1, y1, z1);
QVector3D v2(x2, y2, z2);
float scalar = w1 * w2 - QVector3D::dotProduct(v1, v2);
QVector3D vector = w1 * v2 + w2 * v1 + QVector3D::crossProduct(v1, v2);
QQuaternion result(scalar, vector);
QVERIFY((q1 * q2) == result);
}
// Test multiplication by a factor for quaternions.
void tst_QQuaternion::multiplyFactor_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("w1");
QTest::addColumn<float>("factor");
QTest::addColumn<float>("x2");
QTest::addColumn<float>("y2");
QTest::addColumn<float>("z2");
QTest::addColumn<float>("w2");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f
<< 100.0f
<< 0.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("xonly")
<< 1.0f << 0.0f << 0.0f << 0.0f
<< 2.0f
<< 2.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("yonly")
<< 0.0f << 1.0f << 0.0f << 0.0f
<< 2.0f
<< 0.0f << 2.0f << 0.0f << 0.0f;
QTest::newRow("zonly")
<< 0.0f << 0.0f << 1.0f << 0.0f
<< 2.0f
<< 0.0f << 0.0f << 2.0f << 0.0f;
QTest::newRow("wonly")
<< 0.0f << 0.0f << 0.0f << 1.0f
<< 2.0f
<< 0.0f << 0.0f << 0.0f << 2.0f;
QTest::newRow("all")
<< 1.0f << 2.0f << -3.0f << 4.0f
<< 2.0f
<< 2.0f << 4.0f << -6.0f << 8.0f;
QTest::newRow("allzero")
<< 1.0f << 2.0f << -3.0f << 4.0f
<< 0.0f
<< 0.0f << 0.0f << 0.0f << 0.0f;
}
void tst_QQuaternion::multiplyFactor()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QFETCH(float, factor);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, w2);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(w2, x2, y2, z2);
QVERIFY((v1 * factor) == v2);
QVERIFY((factor * v1) == v2);
QQuaternion v3(v1);
v3 *= factor;
QCOMPARE(v3, v2);
QCOMPARE(v3.x(), v1.x() * factor);
QCOMPARE(v3.y(), v1.y() * factor);
QCOMPARE(v3.z(), v1.z() * factor);
QCOMPARE(v3.scalar(), v1.scalar() * factor);
}
// Test division by a factor for quaternions.
void tst_QQuaternion::divide_data()
{
// Use the same test data as the multiply test.
multiplyFactor_data();
}
void tst_QQuaternion::divide()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QFETCH(float, factor);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, w2);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(w2, x2, y2, z2);
if (factor == 0.0f)
return;
QVERIFY((v2 / factor) == v1);
QQuaternion v3(v2);
v3 /= factor;
QCOMPARE(v3, v1);
QCOMPARE(v3.x(), v2.x() / factor);
QCOMPARE(v3.y(), v2.y() / factor);
QCOMPARE(v3.z(), v2.z() / factor);
QCOMPARE(v3.scalar(), v2.scalar() / factor);
}
// Test negation for quaternions.
void tst_QQuaternion::negate_data()
{
// Use the same test data as the add test.
add_data();
}
void tst_QQuaternion::negate()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(-w1, -x1, -y1, -z1);
QCOMPARE(-v1, v2);
}
// Test quaternion conjugate calculations.
void tst_QQuaternion::conjugated_data()
{
// Use the same test data as the add test.
add_data();
}
void tst_QQuaternion::conjugated()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, w1);
QQuaternion v1(w1, x1, y1, z1);
QQuaternion v2(w1, -x1, -y1, -z1);
QCOMPARE(v1.conjugated(), v2);
}
// Test quaternion creation from an axis and an angle.
void tst_QQuaternion::fromAxisAndAngle_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("angle");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f;
QTest::newRow("xonly")
<< 1.0f << 0.0f << 0.0f << 90.0f;
QTest::newRow("yonly")
<< 0.0f << 1.0f << 0.0f << 180.0f;
QTest::newRow("zonly")
<< 0.0f << 0.0f << 1.0f << 270.0f;
QTest::newRow("complex")
<< 1.0f << 2.0f << -3.0f << 45.0f;
}
void tst_QQuaternion::fromAxisAndAngle()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, angle);
// Use a straight-forward implementation of the algorithm at:
// http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
// to calculate the answer we expect to get.
QVector3D vector = QVector3D(x1, y1, z1).normalized();
const float a = qDegreesToRadians(angle) / 2.0;
const float sin_a = std::sin(a);
const float cos_a = std::cos(a);
QQuaternion result(cos_a,
(vector.x() * sin_a),
(vector.y() * sin_a),
(vector.z() * sin_a));
result = result.normalized();
QQuaternion answer = QQuaternion::fromAxisAndAngle(QVector3D(x1, y1, z1), angle);
QCOMPARE(answer.x(), result.x());
QCOMPARE(answer.y(), result.y());
QCOMPARE(answer.z(), result.z());
QCOMPARE(answer.scalar(), result.scalar());
{
QVector3D answerAxis;
float answerAngle;
answer.getAxisAndAngle(&answerAxis, &answerAngle);
QCOMPARE(answerAxis.x(), vector.x());
QCOMPARE(answerAxis.y(), vector.y());
QCOMPARE(answerAxis.z(), vector.z());
QCOMPARE(answerAngle, angle);
}
answer = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle);
QCOMPARE(answer.x(), result.x());
QCOMPARE(answer.y(), result.y());
QCOMPARE(answer.z(), result.z());
QCOMPARE(answer.scalar(), result.scalar());
{
float answerAxisX, answerAxisY, answerAxisZ;
float answerAngle;
answer.getAxisAndAngle(&answerAxisX, &answerAxisY, &answerAxisZ, &answerAngle);
QCOMPARE(answerAxisX, vector.x());
QCOMPARE(answerAxisY, vector.y());
QCOMPARE(answerAxisZ, vector.z());
QCOMPARE(answerAngle, angle);
}
}
// Test quaternion convertion to and from rotation matrix.
void tst_QQuaternion::fromRotationMatrix_data()
{
fromAxisAndAngle_data();
}
void tst_QQuaternion::fromRotationMatrix()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, angle);
QQuaternion result = QQuaternion::fromAxisAndAngle(QVector3D(x1, y1, z1), angle);
QMatrix3x3 rot3x3 = result.toRotationMatrix();
QQuaternion answer = QQuaternion::fromRotationMatrix(rot3x3);
QVERIFY(qFuzzyCompare(answer, result) || qFuzzyCompare(-answer, result));
}
// Test quaternion convertion to and from orthonormal axes.
void tst_QQuaternion::fromAxes_data()
{
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");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << 0.0f
<< QVector3D(1, 0, 0) << QVector3D(0, 1, 0) << QVector3D(0, 0, 1);
QTest::newRow("xonly")
<< 1.0f << 0.0f << 0.0f << 90.0f
<< QVector3D(1, 0, 0) << QVector3D(0, 0, 1) << QVector3D(0, -1, 0);
QTest::newRow("yonly")
<< 0.0f << 1.0f << 0.0f << 180.0f
<< QVector3D(-1, 0, 0) << QVector3D(0, 1, 0) << QVector3D(0, 0, -1);
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(0.728028f, -0.525105f, -0.440727f) << QVector3D(0.608789f, 0.790791f, 0.0634566f) << QVector3D(0.315202f, -0.314508f, 0.895395f);
}
void tst_QQuaternion::fromAxes()
{
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 shortest arc quaternion.
void tst_QQuaternion::rotationTo_data()
{
QTest::addColumn<QVector3D>("from");
QTest::addColumn<QVector3D>("to");
// same
QTest::newRow("+X -> +X") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(10.0f, 0.0f, 0.0f);
QTest::newRow("-X -> -X") << QVector3D(-10.0f, 0.0f, 0.0f) << QVector3D(-10.0f, 0.0f, 0.0f);
QTest::newRow("+Y -> +Y") << QVector3D(0.0f, 10.0f, 0.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("-Y -> -Y") << QVector3D(0.0f, -10.0f, 0.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("+Z -> +Z") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, 0.0f, 10.0f);
QTest::newRow("-Z -> -Z") << QVector3D(0.0f, 0.0f, -10.0f) << QVector3D(0.0f, 0.0f, -10.0f);
QTest::newRow("+X+Y+Z -> +X+Y+Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(10.0f, 10.0f, 10.0f);
QTest::newRow("-X-Y-Z -> -X-Y-Z") << QVector3D(-10.0f, -10.0f, -10.0f) << QVector3D(-10.0f, -10.0f, -10.0f);
// arbitrary
QTest::newRow("+Z -> +X") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(10.0f, 0.0f, 0.0f);
QTest::newRow("+Z -> -X") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(-10.0f, 0.0f, 0.0f);
QTest::newRow("+Z -> +Y") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("+Z -> -Y") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("-Z -> +X") << QVector3D(0.0f, 0.0f, -10.0f) << QVector3D(10.0f, 0.0f, 0.0f);
QTest::newRow("-Z -> -X") << QVector3D(0.0f, 0.0f, -10.0f) << QVector3D(-10.0f, 0.0f, 0.0f);
QTest::newRow("-Z -> +Y") << QVector3D(0.0f, 0.0f, -10.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("-Z -> -Y") << QVector3D(0.0f, 0.0f, -10.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("+X -> +Y") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("+X -> -Y") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("-X -> +Y") << QVector3D(-10.0f, 0.0f, 0.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("-X -> -Y") << QVector3D(-10.0f, 0.0f, 0.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("+X+Y+Z -> +X-Y-Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(10.0f, -10.0f, -10.0f);
QTest::newRow("-X-Y+Z -> -X+Y-Z") << QVector3D(-10.0f, -10.0f, 10.0f) << QVector3D(-10.0f, 10.0f, -10.0f);
QTest::newRow("+X+Y+Z -> +Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(0.0f, 0.0f, 10.0f);
// collinear
QTest::newRow("+X -> -X") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(-10.0f, 0.0f, 0.0f);
QTest::newRow("+Y -> -Y") << QVector3D(0.0f, 10.0f, 0.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("+Z -> -Z") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, 0.0f, -10.0f);
QTest::newRow("+X+Y+Z -> -X-Y-Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(-10.0f, -10.0f, -10.0f);
}
void tst_QQuaternion::rotationTo()
{
QFETCH(QVector3D, from);
QFETCH(QVector3D, to);
QQuaternion q1 = QQuaternion::rotationTo(from, to);
QVERIFY(myFuzzyCompare(q1, q1.normalized()));
QVector3D vec1(q1 * from);
vec1 *= (to.length() / from.length()); // discard rotated length
QVERIFY(myFuzzyCompare(vec1, to));
QQuaternion q2 = QQuaternion::rotationTo(to, from);
QVERIFY(myFuzzyCompare(q2, q2.normalized()));
QVector3D vec2(q2 * to);
vec2 *= (from.length() / to.length()); // discard rotated length
QVERIFY(myFuzzyCompare(vec2, from));
}
// Test quaternion convertion to and from orthonormal axes.
void tst_QQuaternion::fromDirection_data()
{
QTest::addColumn<QVector3D>("direction");
QTest::addColumn<QVector3D>("up");
QList<QQuaternion> orientations;
orientations << QQuaternion();
for (int angle = 45; angle <= 360; angle += 45) {
orientations << QQuaternion::fromAxisAndAngle(QVector3D(1, 0, 0), angle)
<< QQuaternion::fromAxisAndAngle(QVector3D(0, 1, 0), angle)
<< QQuaternion::fromAxisAndAngle(QVector3D(0, 0, 1), angle)
<< QQuaternion::fromAxisAndAngle(QVector3D(1, 0, 0), angle)
* QQuaternion::fromAxisAndAngle(QVector3D(0, 1, 0), angle)
* QQuaternion::fromAxisAndAngle(QVector3D(0, 0, 1), angle);
}
// othonormal up and dir
foreach (const QQuaternion &q, orientations) {
QVector3D xAxis, yAxis, zAxis;
q.getAxes(&xAxis, &yAxis, &zAxis);
QTest::addRow("ortho dirs: (%.1f,%.1f,%.1f), (%.1f,%.1f,%.1f), (%.1f,%.1f,%.1f)",
xAxis.x(), xAxis.y(), xAxis.z(),
yAxis.x(), yAxis.y(), yAxis.z(),
zAxis.x(), zAxis.y(), zAxis.z())
<< zAxis * 10.0f << yAxis * 10.0f;
}
// collinear up and dir
QTest::newRow("dir: +X, up: +X") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(10.0f, 0.0f, 0.0f);
QTest::newRow("dir: +X, up: -X") << QVector3D(10.0f, 0.0f, 0.0f) << QVector3D(-10.0f, 0.0f, 0.0f);
QTest::newRow("dir: +Y, up: +Y") << QVector3D(0.0f, 10.0f, 0.0f) << QVector3D(0.0f, 10.0f, 0.0f);
QTest::newRow("dir: +Y, up: -Y") << QVector3D(0.0f, 10.0f, 0.0f) << QVector3D(0.0f, -10.0f, 0.0f);
QTest::newRow("dir: +Z, up: +Z") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, 0.0f, 10.0f);
QTest::newRow("dir: +Z, up: -Z") << QVector3D(0.0f, 0.0f, 10.0f) << QVector3D(0.0f, 0.0f, -10.0f);
QTest::newRow("dir: +X+Y+Z, up: +X+Y+Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(10.0f, 10.0f, 10.0f);
QTest::newRow("dir: +X+Y+Z, up: -X-Y-Z") << QVector3D(10.0f, 10.0f, 10.0f) << QVector3D(-10.0f, -10.0f, -10.0f);
// invalid up
foreach (const QQuaternion &q, orientations) {
QVector3D xAxis, yAxis, zAxis;
q.getAxes(&xAxis, &yAxis, &zAxis);
QTest::addRow("bad dirs: (%.1f,%.1f,%.1f), (%.1f,%.1f,%.1f), (%.1f,%.1f,%.1f)",
xAxis.x(), xAxis.y(), xAxis.z(),
yAxis.x(), yAxis.y(), yAxis.z(),
zAxis.x(), zAxis.y(), zAxis.z())
<< zAxis * 10.0f << QVector3D();
}
}
void tst_QQuaternion::fromDirection()
{
QFETCH(QVector3D, direction);
QFETCH(QVector3D, up);
QVector3D expextedZ(direction != QVector3D() ? direction.normalized() : QVector3D(0, 0, 1));
QVector3D expextedY(up.normalized());
QQuaternion result = QQuaternion::fromDirection(direction, up);
QVERIFY(myFuzzyCompare(result, result.normalized()));
QVector3D xAxis, yAxis, zAxis;
result.getAxes(&xAxis, &yAxis, &zAxis);
QVERIFY(myFuzzyCompare(zAxis, expextedZ));
if (!qFuzzyIsNull(QVector3D::crossProduct(expextedZ, expextedY).lengthSquared())) {
QVector3D expextedX(QVector3D::crossProduct(expextedY, expextedZ));
QVERIFY(myFuzzyCompare(yAxis, expextedY));
QVERIFY(myFuzzyCompare(xAxis, expextedX));
}
}
// Test quaternion creation from an axis and an angle.
void tst_QQuaternion::fromEulerAngles_data()
{
QTest::addColumn<float>("pitch");
QTest::addColumn<float>("yaw");
QTest::addColumn<float>("roll");
QTest::addColumn<QQuaternion>("quaternion");
QTest::newRow("null")
<< 0.0f << 0.0f << 0.0f << QQuaternion(1.0f, 0.0f, 0.0f, 0.0f);
QTest::newRow("xonly")
<< 90.0f << 0.0f << 0.0f << QQuaternion(0.707107f, 0.707107f, 0.0f, 0.0f);
QTest::newRow("yonly")
<< 0.0f << 180.0f << 0.0f << QQuaternion(0.0f, 0.0f, 1.0f, 0.0f);
QTest::newRow("zonly")
<< 0.0f << 0.0f << 270.0f << QQuaternion(-0.707107f, 0.0f, 0.0f, 0.707107f);
QTest::newRow("x+z")
<< 30.0f << 0.0f << 45.0f << QQuaternion(0.892399f, 0.239118f, -0.099046f, 0.369644f);
QTest::newRow("x+y")
<< 30.0f << 90.0f << 0.0f << QQuaternion(0.683013f, 0.183013f, 0.683013f, -0.183013f);
QTest::newRow("y+z")
<< 0.0f << 45.0f << 30.0f << QQuaternion(0.892399f, 0.099046f, 0.369644f, 0.239118f);
QTest::newRow("complex")
<< 30.0f << 240.0f << -45.0f << QQuaternion(-0.531976f, -0.43968f, 0.723317f, -0.02226f);
// Three gimbal_lock cases are not unique for the conversions from quaternion
// to euler, Qt will use only XY rotations for these cases.
// For example, QQuaternion(0.5f, 0.5f, -0.5f, 0.5f) can be EulerXYZ(90.0f, 0.0f, 90.0f), too.
// But Qt will always convert it to EulerXYZ(90.0f, -90.0f, 0.0f) without Z-rotation.
QTest::newRow("gimbal_lock_1")
<< 90.0f << -90.0f << 0.0f << QQuaternion(0.5f, 0.5f, -0.5f, 0.5f);
QTest::newRow("gimbal_lock_2")
<< 90.0f << 40.0f << 0.0f << QQuaternion(0.664463f, 0.664463f, 0.241845f, -0.241845f);
QTest::newRow("gimbal_lock_3") << 90.0f << 170.0f << 0.0f
<< QQuaternion(0.0616285f, 0.0616285f, 0.704416f, -0.704416f);
// These four examples have a fraction of errors that would bypass normalize() threshold
// and could make Gimbal lock detection fail.
QTest::newRow("gimbal_lock_fraction_1")
<< -90.0f << 90.001152f << 0.0f << QQuaternion(0.499989986f, -0.5f, 0.5f, 0.5f);
QTest::newRow("gimbal_lock_fraction_2")
<< -90.0f << -179.999985f << 0.0f
<< QQuaternion(1.00000001e-07f, 1.00000001e-10f, -0.707106769f, -0.707105756f);
QTest::newRow("gimbal_lock_fraction_3")
<< -90.0f << 90.0011597f << 0.0f << QQuaternion(0.499989986f, -0.49999994f, 0.5f, 0.5f);
QTest::newRow("gimbal_lock_fraction_4")
<< -90.0f << -180.0f << 0.0f
<< QQuaternion(9.99999996e-12f, 9.99999996e-12f, -0.707106769f, -0.707096756f);
}
void tst_QQuaternion::fromEulerAngles()
{
QFETCH(float, pitch);
QFETCH(float, yaw);
QFETCH(float, roll);
QFETCH(QQuaternion, quaternion);
// Use a straight-forward implementation of the algorithm at:
// http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q60
// to calculate the answer we expect to get.
QQuaternion qx = QQuaternion::fromAxisAndAngle(QVector3D(1, 0, 0), pitch);
QQuaternion qy = QQuaternion::fromAxisAndAngle(QVector3D(0, 1, 0), yaw);
QQuaternion qz = QQuaternion::fromAxisAndAngle(QVector3D(0, 0, 1), roll);
QQuaternion result = qy * (qx * qz);
QQuaternion answer = QQuaternion::fromEulerAngles(QVector3D(pitch, yaw, roll));
QVERIFY(myFuzzyCompare(answer.x(), result.x()));
QVERIFY(myFuzzyCompare(answer.y(), result.y()));
QVERIFY(myFuzzyCompare(answer.z(), result.z()));
QVERIFY(myFuzzyCompare(answer.scalar(), result.scalar()));
// quaternion should be the same as the result
QVERIFY(myFuzzyCompare(answer.x(), quaternion.x()));
QVERIFY(myFuzzyCompare(answer.y(), quaternion.y()));
QVERIFY(myFuzzyCompare(answer.z(), quaternion.z()));
QVERIFY(myFuzzyCompare(answer.scalar(), quaternion.scalar()));
{
QVector3D answerEulerAngles = answer.toEulerAngles();
QVERIFY(myFuzzyCompareDegrees(answerEulerAngles.x(), pitch));
QVERIFY(myFuzzyCompareDegrees(answerEulerAngles.y(), yaw));
QVERIFY(myFuzzyCompareDegrees(answerEulerAngles.z(), roll));
QVector3D quaternionEulerAngles = quaternion.toEulerAngles();
QVERIFY(myFuzzyCompareDegrees(quaternionEulerAngles.x(), pitch));
QVERIFY(myFuzzyCompareDegrees(quaternionEulerAngles.y(), yaw));
QVERIFY(myFuzzyCompareDegrees(quaternionEulerAngles.z(), roll));
}
answer = QQuaternion::fromEulerAngles(pitch, yaw, roll);
QVERIFY(myFuzzyCompare(answer.x(), result.x()));
QVERIFY(myFuzzyCompare(answer.y(), result.y()));
QVERIFY(myFuzzyCompare(answer.z(), result.z()));
QVERIFY(myFuzzyCompare(answer.scalar(), result.scalar()));
{
float answerPitch, answerYaw, answerRoll;
answer.getEulerAngles(&answerPitch, &answerYaw, &answerRoll);
QVERIFY(myFuzzyCompareDegrees(answerPitch, pitch));
QVERIFY(myFuzzyCompareDegrees(answerYaw, yaw));
QVERIFY(myFuzzyCompareDegrees(answerRoll, roll));
float quaternionPitch, quaternionYaw, quaternionRoll;
quaternion.getEulerAngles(&quaternionPitch, &quaternionYaw, &quaternionRoll);
QVERIFY(myFuzzyCompareDegrees(quaternionPitch, pitch));
QVERIFY(myFuzzyCompareDegrees(quaternionYaw, yaw));
QVERIFY(myFuzzyCompareDegrees(quaternionRoll, roll));
}
}
// Test spherical interpolation of quaternions.
void tst_QQuaternion::slerp_data()
{
QTest::addColumn<float>("x1");
QTest::addColumn<float>("y1");
QTest::addColumn<float>("z1");
QTest::addColumn<float>("angle1");
QTest::addColumn<float>("x2");
QTest::addColumn<float>("y2");
QTest::addColumn<float>("z2");
QTest::addColumn<float>("angle2");
QTest::addColumn<float>("t");
QTest::addColumn<float>("x3");
QTest::addColumn<float>("y3");
QTest::addColumn<float>("z3");
QTest::addColumn<float>("angle3");
QTest::newRow("first")
<< 1.0f << 2.0f << -3.0f << 90.0f
<< 1.0f << 2.0f << -3.0f << 180.0f
<< 0.0f
<< 1.0f << 2.0f << -3.0f << 90.0f;
QTest::newRow("first2")
<< 1.0f << 2.0f << -3.0f << 90.0f
<< 1.0f << 2.0f << -3.0f << 180.0f
<< -0.5f
<< 1.0f << 2.0f << -3.0f << 90.0f;
QTest::newRow("second")
<< 1.0f << 2.0f << -3.0f << 90.0f
<< 1.0f << 2.0f << -3.0f << 180.0f
<< 1.0f
<< 1.0f << 2.0f << -3.0f << 180.0f;
QTest::newRow("second2")
<< 1.0f << 2.0f << -3.0f << 90.0f
<< 1.0f << 2.0f << -3.0f << 180.0f
<< 1.5f
<< 1.0f << 2.0f << -3.0f << 180.0f;
QTest::newRow("middle")
<< 1.0f << 2.0f << -3.0f << 90.0f
<< 1.0f << 2.0f << -3.0f << 180.0f
<< 0.5f
<< 1.0f << 2.0f << -3.0f << 135.0f;
QTest::newRow("wide angle")
<< 1.0f << 2.0f << -3.0f << 0.0f
<< 1.0f << 2.0f << -3.0f << 270.0f
<< 0.5f
<< 1.0f << 2.0f << -3.0f << -45.0f;
}
void tst_QQuaternion::slerp()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, angle1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, angle2);
QFETCH(float, t);
QFETCH(float, x3);
QFETCH(float, y3);
QFETCH(float, z3);
QFETCH(float, angle3);
QQuaternion q1 = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle1);
QQuaternion q2 = QQuaternion::fromAxisAndAngle(x2, y2, z2, angle2);
QQuaternion q3 = QQuaternion::fromAxisAndAngle(x3, y3, z3, angle3);
QQuaternion result = QQuaternion::slerp(q1, q2, t);
QCOMPARE(result.x(), q3.x());
QCOMPARE(result.y(), q3.y());
QCOMPARE(result.z(), q3.z());
QCOMPARE(result.scalar(), q3.scalar());
}
// Test normalized linear interpolation of quaternions.
void tst_QQuaternion::nlerp_data()
{
slerp_data();
}
void tst_QQuaternion::nlerp()
{
QFETCH(float, x1);
QFETCH(float, y1);
QFETCH(float, z1);
QFETCH(float, angle1);
QFETCH(float, x2);
QFETCH(float, y2);
QFETCH(float, z2);
QFETCH(float, angle2);
QFETCH(float, t);
QQuaternion q1 = QQuaternion::fromAxisAndAngle(x1, y1, z1, angle1);
QQuaternion q2 = QQuaternion::fromAxisAndAngle(x2, y2, z2, angle2);
QQuaternion result = QQuaternion::nlerp(q1, q2, t);
float resultx, resulty, resultz, resultscalar;
if (t <= 0.0f) {
resultx = q1.x();
resulty = q1.y();
resultz = q1.z();
resultscalar = q1.scalar();
} else if (t >= 1.0f) {
resultx = q2.x();
resulty = q2.y();
resultz = q2.z();
resultscalar = q2.scalar();
} else if (qAbs(angle1 - angle2) <= 180.f) {
resultx = q1.x() * (1 - t) + q2.x() * t;
resulty = q1.y() * (1 - t) + q2.y() * t;
resultz = q1.z() * (1 - t) + q2.z() * t;
resultscalar = q1.scalar() * (1 - t) + q2.scalar() * t;
} else {
// Angle greater than 180 degrees: negate q2.
resultx = q1.x() * (1 - t) - q2.x() * t;
resulty = q1.y() * (1 - t) - q2.y() * t;
resultz = q1.z() * (1 - t) - q2.z() * t;
resultscalar = q1.scalar() * (1 - t) - q2.scalar() * t;
}
QQuaternion q3 = QQuaternion(resultscalar, resultx, resulty, resultz).normalized();
QCOMPARE(result.x(), q3.x());
QCOMPARE(result.y(), q3.y());
QCOMPARE(result.z(), q3.z());
QCOMPARE(result.scalar(), q3.scalar());
}
class tst_QQuaternionProperties : public QObject
{
Q_OBJECT
Q_PROPERTY(QQuaternion quaternion READ quaternion WRITE setQuaternion)
public:
tst_QQuaternionProperties(QObject *parent = nullptr) : QObject(parent) {}
QQuaternion quaternion() const { return q; }
void setQuaternion(const QQuaternion& value) { q = value; }
private:
QQuaternion q;
};
// Test getting and setting quaternion properties via the metaobject system.
void tst_QQuaternion::properties()
{
tst_QQuaternionProperties obj;
obj.setQuaternion(QQuaternion(6.0f, 7.0f, 8.0f, 9.0f));
QQuaternion q = qvariant_cast<QQuaternion>(obj.property("quaternion"));
QCOMPARE(q.scalar(), 6.0f);
QCOMPARE(q.x(), 7.0f);
QCOMPARE(q.y(), 8.0f);
QCOMPARE(q.z(), 9.0f);
obj.setProperty("quaternion",
QVariant::fromValue(QQuaternion(-6.0f, -7.0f, -8.0f, -9.0f)));
q = qvariant_cast<QQuaternion>(obj.property("quaternion"));
QCOMPARE(q.scalar(), -6.0f);
QCOMPARE(q.x(), -7.0f);
QCOMPARE(q.y(), -8.0f);
QCOMPARE(q.z(), -9.0f);
}
void tst_QQuaternion::metaTypes()
{
QCOMPARE(QMetaType::fromName("QQuaternion").id(), int(QMetaType::QQuaternion));
QCOMPARE(QByteArray(QMetaType(QMetaType::QQuaternion).name()), QByteArray("QQuaternion"));
QVERIFY(QMetaType::isRegistered(QMetaType::QQuaternion));
QCOMPARE(qMetaTypeId<QQuaternion>(), int(QMetaType::QQuaternion));
}
QTEST_APPLESS_MAIN(tst_QQuaternion)
#include "tst_qquaternion.moc"
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