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+/****************************************************************************
+**
+** Copyright (C) 2016 The Qt Company Ltd.
+** Copyright (C) 2020 Klarälvdalens Datakonsult AB, a KDAB Group company, info@kdab.com, author Giuseppe D'Angelo <giuseppe.dangelo@kdab.com>
+** Contact: https://www.qt.io/licensing/
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** Commercial License Usage
+** Licensees holding valid commercial Qt licenses may use this file in
+** accordance with the commercial license agreement provided with the
+** Software or, alternatively, in accordance with the terms contained in
+** a written agreement between you and The Qt Company. For licensing terms
+** and conditions see https://www.qt.io/terms-conditions. For further
+** information use the contact form at https://www.qt.io/contact-us.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 3 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL3 included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU Lesser General Public License version 3 requirements
+** will be met: https://www.gnu.org/licenses/lgpl-3.0.html.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 2.0 or (at your option) the GNU General
+** Public license version 3 or any later version approved by the KDE Free
+** Qt Foundation. The licenses are as published by the Free Software
+** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3
+** included in the packaging of this file. Please review the following
+** information to ensure the GNU General Public License requirements will
+** be met: https://www.gnu.org/licenses/gpl-2.0.html and
+** https://www.gnu.org/licenses/gpl-3.0.html.
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#ifndef QVECTORND_H
+#define QVECTORND_H
+
+#include <QtGui/qtguiglobal.h>
+#include <QtCore/qpoint.h>
+#include <QtCore/qrect.h>
+#include <QtCore/qmath.h>
+
+QT_BEGIN_NAMESPACE
+
+class QVector2D;
+class QVector3D;
+class QVector4D;
+class QMatrix4x4;
+class QVariant;
+
+/***************************** QVector2D *****************************/
+
+#ifndef QT_NO_VECTOR2D
+
+class QVector2D
+{
+public:
+ constexpr QVector2D() noexcept;
+ explicit QVector2D(Qt::Initialization) noexcept {}
+ constexpr QVector2D(float xpos, float ypos) noexcept;
+ constexpr explicit QVector2D(QPoint point) noexcept;
+ constexpr explicit QVector2D(QPointF point) noexcept;
+#ifndef QT_NO_VECTOR3D
+ constexpr explicit QVector2D(QVector3D vector) noexcept;
+#endif
+#ifndef QT_NO_VECTOR4D
+ constexpr explicit QVector2D(QVector4D vector) noexcept;
+#endif
+
+ constexpr bool isNull() const noexcept;
+
+ constexpr float x() const noexcept;
+ constexpr float y() const noexcept;
+
+ constexpr void setX(float x) noexcept;
+ constexpr void setY(float y) noexcept;
+
+ constexpr float &operator[](int i);
+ constexpr float operator[](int i) const;
+
+ [[nodiscard]] float length() const noexcept;
+ [[nodiscard]] constexpr float lengthSquared() const noexcept;
+
+ [[nodiscard]] QVector2D normalized() const noexcept;
+ void normalize() noexcept;
+
+ [[nodiscard]] float distanceToPoint(QVector2D point) const noexcept;
+ [[nodiscard]] float distanceToLine(QVector2D point, QVector2D direction) const noexcept;
+
+ constexpr QVector2D &operator+=(QVector2D vector) noexcept;
+ constexpr QVector2D &operator-=(QVector2D vector) noexcept;
+ constexpr QVector2D &operator*=(float factor) noexcept;
+ constexpr QVector2D &operator*=(QVector2D vector) noexcept;
+ constexpr QVector2D &operator/=(float divisor);
+ constexpr QVector2D &operator/=(QVector2D vector);
+
+ [[nodiscard]] static constexpr float dotProduct(QVector2D v1, QVector2D v2) noexcept;
+
+QT_WARNING_PUSH
+QT_WARNING_DISABLE_FLOAT_COMPARE
+ constexpr friend inline bool operator==(QVector2D v1, QVector2D v2) noexcept
+ {
+ return v1.v[0] == v2.v[0] && v1.v[1] == v2.v[1];
+ }
+
+ constexpr friend inline bool operator!=(QVector2D v1, QVector2D v2) noexcept
+ {
+ return v1.v[0] != v2.v[0] || v1.v[1] != v2.v[1];
+ }
+QT_WARNING_POP
+
+ constexpr friend inline QVector2D operator+(QVector2D v1, QVector2D v2) noexcept
+ {
+ return QVector2D(v1.v[0] + v2.v[0], v1.v[1] + v2.v[1]);
+ }
+
+ constexpr friend inline QVector2D operator-(QVector2D v1, QVector2D v2) noexcept
+ {
+ return QVector2D(v1.v[0] - v2.v[0], v1.v[1] - v2.v[1]);
+ }
+
+ constexpr friend inline QVector2D operator*(float factor, QVector2D vector) noexcept
+ {
+ return QVector2D(vector.v[0] * factor, vector.v[1] * factor);
+ }
+
+ constexpr friend inline QVector2D operator*(QVector2D vector, float factor) noexcept
+ {
+ return QVector2D(vector.v[0] * factor, vector.v[1] * factor);
+ }
+
+ constexpr friend inline QVector2D operator*(QVector2D v1, QVector2D v2) noexcept
+ {
+ return QVector2D(v1.v[0] * v2.v[0], v1.v[1] * v2.v[1]);
+ }
+
+ constexpr friend inline QVector2D operator-(QVector2D vector) noexcept
+ {
+ return QVector2D(-vector.v[0], -vector.v[1]);
+ }
+
+ constexpr friend inline QVector2D operator/(QVector2D vector, float divisor)
+ {
+ return QVector2D(vector.v[0] / divisor, vector.v[1] / divisor);
+ }
+
+ constexpr friend inline QVector2D operator/(QVector2D vector, QVector2D divisor)
+ {
+ return QVector2D(vector.v[0] / divisor.v[0], vector.v[1] / divisor.v[1]);
+ }
+
+ constexpr friend inline bool qFuzzyCompare(QVector2D v1, QVector2D v2) noexcept;
+
+#ifndef QT_NO_VECTOR3D
+ constexpr QVector3D toVector3D() const noexcept;
+#endif
+#ifndef QT_NO_VECTOR4D
+ constexpr QVector4D toVector4D() const noexcept;
+#endif
+
+ constexpr QPoint toPoint() const noexcept;
+ constexpr QPointF toPointF() const noexcept;
+
+ Q_GUI_EXPORT operator QVariant() const;
+
+private:
+ float v[2];
+
+ friend class QVector3D;
+ friend class QVector4D;
+};
+
+Q_DECLARE_TYPEINFO(QVector2D, Q_PRIMITIVE_TYPE);
+
+#endif // QT_NO_VECTOR2D
+
+
+
+/***************************** QVector3D *****************************/
+
+#ifndef QT_NO_VECTOR3D
+
+class QVector3D
+{
+public:
+ constexpr QVector3D() noexcept;
+ explicit QVector3D(Qt::Initialization) noexcept {}
+ constexpr QVector3D(float xpos, float ypos, float zpos) noexcept : v{xpos, ypos, zpos} {}
+
+ constexpr explicit QVector3D(QPoint point) noexcept;
+ constexpr explicit QVector3D(QPointF point) noexcept;
+#ifndef QT_NO_VECTOR2D
+ constexpr QVector3D(QVector2D vector) noexcept;
+ constexpr QVector3D(QVector2D vector, float zpos) noexcept;
+#endif
+#ifndef QT_NO_VECTOR4D
+ constexpr explicit QVector3D(QVector4D vector) noexcept;
+#endif
+
+ constexpr bool isNull() const noexcept;
+
+ constexpr float x() const noexcept;
+ constexpr float y() const noexcept;
+ constexpr float z() const noexcept;
+
+ constexpr void setX(float x) noexcept;
+ constexpr void setY(float y) noexcept;
+ constexpr void setZ(float z) noexcept;
+
+ constexpr float &operator[](int i);
+ constexpr float operator[](int i) const;
+
+ [[nodiscard]] float length() const noexcept;
+ [[nodiscard]] constexpr float lengthSquared() const noexcept;
+
+ [[nodiscard]] QVector3D normalized() const noexcept;
+ void normalize() noexcept;
+
+ constexpr QVector3D &operator+=(QVector3D vector) noexcept;
+ constexpr QVector3D &operator-=(QVector3D vector) noexcept;
+ constexpr QVector3D &operator*=(float factor) noexcept;
+ constexpr QVector3D &operator*=(QVector3D vector) noexcept;
+ constexpr QVector3D &operator/=(float divisor);
+ constexpr QVector3D &operator/=(QVector3D vector);
+
+ [[nodiscard]] static constexpr float dotProduct(QVector3D v1, QVector3D v2) noexcept;
+ [[nodiscard]] static constexpr QVector3D crossProduct(QVector3D v1, QVector3D v2) noexcept;
+
+ [[nodiscard]] static QVector3D normal(QVector3D v1, QVector3D v2) noexcept;
+ [[nodiscard]] static QVector3D normal(QVector3D v1, QVector3D v2, QVector3D v3) noexcept;
+
+ Q_GUI_EXPORT QVector3D project(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const;
+ Q_GUI_EXPORT QVector3D unproject(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const;
+
+QT_WARNING_PUSH
+QT_WARNING_DISABLE_FLOAT_COMPARE
+ constexpr friend inline bool operator==(QVector3D v1, QVector3D v2) noexcept
+ {
+ return v1.v[0] == v2.v[0] && v1.v[1] == v2.v[1] && v1.v[2] == v2.v[2];
+ }
+
+ constexpr friend inline bool operator!=(QVector3D v1, QVector3D v2) noexcept
+ {
+ return v1.v[0] != v2.v[0] || v1.v[1] != v2.v[1] || v1.v[2] != v2.v[2];
+ }
+QT_WARNING_POP
+ float distanceToPoint(QVector3D point) const noexcept;
+ constexpr float distanceToPlane(QVector3D plane, QVector3D normal) const noexcept;
+ float distanceToPlane(QVector3D plane1, QVector3D plane2, QVector3D plane3) const noexcept;
+ float distanceToLine(QVector3D point, QVector3D direction) const noexcept;
+
+
+ constexpr friend inline QVector3D operator+(QVector3D v1, QVector3D v2) noexcept
+ {
+ return QVector3D(v1.v[0] + v2.v[0], v1.v[1] + v2.v[1], v1.v[2] + v2.v[2]);
+ }
+
+ constexpr friend inline QVector3D operator-(QVector3D v1, QVector3D v2) noexcept
+ {
+ return QVector3D(v1.v[0] - v2.v[0], v1.v[1] - v2.v[1], v1.v[2] - v2.v[2]);
+ }
+
+ constexpr friend inline QVector3D operator*(float factor, QVector3D vector) noexcept
+ {
+ return QVector3D(vector.v[0] * factor, vector.v[1] * factor, vector.v[2] * factor);
+ }
+
+ constexpr friend inline QVector3D operator*(QVector3D vector, float factor) noexcept
+ {
+ return QVector3D(vector.v[0] * factor, vector.v[1] * factor, vector.v[2] * factor);
+ }
+
+ constexpr friend inline QVector3D operator*(QVector3D v1, QVector3D v2) noexcept
+ {
+ return QVector3D(v1.v[0] * v2.v[0], v1.v[1] * v2.v[1], v1.v[2] * v2.v[2]);
+ }
+
+ constexpr friend inline QVector3D operator-(QVector3D vector) noexcept
+ {
+ return QVector3D(-vector.v[0], -vector.v[1], -vector.v[2]);
+ }
+
+ constexpr friend inline QVector3D operator/(QVector3D vector, float divisor)
+ {
+ return QVector3D(vector.v[0] / divisor, vector.v[1] / divisor, vector.v[2] / divisor);
+ }
+
+ constexpr friend inline QVector3D operator/(QVector3D vector, QVector3D divisor)
+ {
+ return QVector3D(vector.v[0] / divisor.v[0], vector.v[1] / divisor.v[1], vector.v[2] / divisor.v[2]);
+ }
+
+ constexpr friend inline bool qFuzzyCompare(QVector3D v1, QVector3D v2) noexcept;
+
+#ifndef QT_NO_VECTOR2D
+ constexpr QVector2D toVector2D() const noexcept;
+#endif
+#ifndef QT_NO_VECTOR4D
+ constexpr QVector4D toVector4D() const noexcept;
+#endif
+
+ constexpr QPoint toPoint() const noexcept;
+ constexpr QPointF toPointF() const noexcept;
+
+ Q_GUI_EXPORT operator QVariant() const;
+
+private:
+ float v[3];
+
+ friend class QVector2D;
+ friend class QVector4D;
+#ifndef QT_NO_MATRIX4X4
+ friend QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix);
+ friend QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector);
+#endif
+};
+
+Q_DECLARE_TYPEINFO(QVector3D, Q_PRIMITIVE_TYPE);
+
+#endif // QT_NO_VECTOR3D
+
+
+
+/***************************** QVector4D *****************************/
+
+#ifndef QT_NO_VECTOR4D
+
+class QVector4D
+{
+public:
+ constexpr QVector4D() noexcept;
+ explicit QVector4D(Qt::Initialization) noexcept {}
+ constexpr QVector4D(float xpos, float ypos, float zpos, float wpos) noexcept;
+ constexpr explicit QVector4D(QPoint point) noexcept;
+ constexpr explicit QVector4D(QPointF point) noexcept;
+#ifndef QT_NO_VECTOR2D
+ constexpr QVector4D(QVector2D vector) noexcept;
+ constexpr QVector4D(QVector2D vector, float zpos, float wpos) noexcept;
+#endif
+#ifndef QT_NO_VECTOR3D
+ constexpr QVector4D(QVector3D vector) noexcept;
+ constexpr QVector4D(QVector3D vector, float wpos) noexcept;
+#endif
+
+ constexpr bool isNull() const noexcept;
+
+ constexpr float x() const noexcept;
+ constexpr float y() const noexcept;
+ constexpr float z() const noexcept;
+ constexpr float w() const noexcept;
+
+ constexpr void setX(float x) noexcept;
+ constexpr void setY(float y) noexcept;
+ constexpr void setZ(float z) noexcept;
+ constexpr void setW(float w) noexcept;
+
+ constexpr float &operator[](int i);
+ constexpr float operator[](int i) const;
+
+ [[nodiscard]] float length() const noexcept;
+ [[nodiscard]] constexpr float lengthSquared() const noexcept;
+
+ [[nodiscard]] QVector4D normalized() const noexcept;
+ void normalize() noexcept;
+
+ constexpr QVector4D &operator+=(QVector4D vector) noexcept;
+ constexpr QVector4D &operator-=(QVector4D vector) noexcept;
+ constexpr QVector4D &operator*=(float factor) noexcept;
+ constexpr QVector4D &operator*=(QVector4D vector) noexcept;
+ constexpr QVector4D &operator/=(float divisor);
+ constexpr inline QVector4D &operator/=(QVector4D vector);
+
+ [[nodiscard]] static constexpr float dotProduct(QVector4D v1, QVector4D v2) noexcept;
+
+QT_WARNING_PUSH
+QT_WARNING_DISABLE_FLOAT_COMPARE
+ constexpr friend inline bool operator==(QVector4D v1, QVector4D v2) noexcept
+ {
+ return v1.v[0] == v2.v[0] && v1.v[1] == v2.v[1] && v1.v[2] == v2.v[2] && v1.v[3] == v2.v[3];
+ }
+
+ constexpr friend inline bool operator!=(QVector4D v1, QVector4D v2) noexcept
+ {
+ return v1.v[0] != v2.v[0] || v1.v[1] != v2.v[1] || v1.v[2] != v2.v[2] || v1.v[3] != v2.v[3];
+ }
+QT_WARNING_POP
+ constexpr friend inline QVector4D operator+(QVector4D v1, QVector4D v2) noexcept
+ {
+ return QVector4D(v1.v[0] + v2.v[0], v1.v[1] + v2.v[1], v1.v[2] + v2.v[2], v1.v[3] + v2.v[3]);
+ }
+
+ constexpr friend inline QVector4D operator-(QVector4D v1, QVector4D v2) noexcept
+ {
+ return QVector4D(v1.v[0] - v2.v[0], v1.v[1] - v2.v[1], v1.v[2] - v2.v[2], v1.v[3] - v2.v[3]);
+ }
+
+ constexpr friend inline QVector4D operator*(float factor, QVector4D vector) noexcept
+ {
+ return QVector4D(vector.v[0] * factor, vector.v[1] * factor, vector.v[2] * factor, vector.v[3] * factor);
+ }
+
+ constexpr friend inline QVector4D operator*(QVector4D vector, float factor) noexcept
+ {
+ return QVector4D(vector.v[0] * factor, vector.v[1] * factor, vector.v[2] * factor, vector.v[3] * factor);
+ }
+
+ constexpr friend inline QVector4D operator*(QVector4D v1, QVector4D v2) noexcept
+ {
+ return QVector4D(v1.v[0] * v2.v[0], v1.v[1] * v2.v[1], v1.v[2] * v2.v[2], v1.v[3] * v2.v[3]);
+ }
+
+ constexpr friend inline QVector4D operator-(QVector4D vector) noexcept
+ {
+ return QVector4D(-vector.v[0], -vector.v[1], -vector.v[2], -vector.v[3]);
+ }
+
+ constexpr friend inline QVector4D operator/(QVector4D vector, float divisor)
+ {
+ return QVector4D(vector.v[0] / divisor, vector.v[1] / divisor, vector.v[2] / divisor, vector.v[3] / divisor);
+ }
+
+ constexpr friend inline QVector4D operator/(QVector4D vector, QVector4D divisor)
+ {
+ return QVector4D(vector.v[0] / divisor.v[0], vector.v[1] / divisor.v[1], vector.v[2] / divisor.v[2], vector.v[3] / divisor.v[3]);
+ }
+
+ constexpr friend inline bool qFuzzyCompare(QVector4D v1, QVector4D v2) noexcept;
+
+#ifndef QT_NO_VECTOR2D
+ constexpr QVector2D toVector2D() const noexcept;
+ constexpr QVector2D toVector2DAffine() const noexcept;
+#endif
+#ifndef QT_NO_VECTOR3D
+ constexpr QVector3D toVector3D() const noexcept;
+ constexpr QVector3D toVector3DAffine() const noexcept;
+#endif
+
+ constexpr QPoint toPoint() const noexcept;
+ constexpr QPointF toPointF() const noexcept;
+
+ Q_GUI_EXPORT operator QVariant() const;
+
+private:
+ float v[4];
+
+ friend class QVector2D;
+ friend class QVector3D;
+#ifndef QT_NO_MATRIX4X4
+ friend QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix);
+ friend QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector);
+#endif
+};
+
+Q_DECLARE_TYPEINFO(QVector4D, Q_PRIMITIVE_TYPE);
+
+#endif // QT_NO_VECTOR4D
+
+
+
+/***************************** QVector2D *****************************/
+
+#ifndef QT_NO_VECTOR2D
+
+constexpr inline QVector2D::QVector2D() noexcept : v{0.0f, 0.0f} {}
+
+constexpr inline QVector2D::QVector2D(float xpos, float ypos) noexcept : v{xpos, ypos} {}
+
+constexpr inline QVector2D::QVector2D(QPoint point) noexcept : v{float(point.x()), float(point.y())} {}
+
+constexpr inline QVector2D::QVector2D(QPointF point) noexcept : v{float(point.x()), float(point.y())} {}
+
+#ifndef QT_NO_VECTOR3D
+constexpr inline QVector2D::QVector2D(QVector3D vector) noexcept : v{vector[0], vector[1]} {}
+#endif
+#ifndef QT_NO_VECTOR4D
+constexpr inline QVector2D::QVector2D(QVector4D vector) noexcept : v{vector[0], vector[1]} {}
+#endif
+
+constexpr inline bool QVector2D::isNull() const noexcept
+{
+ return qIsNull(v[0]) && qIsNull(v[1]);
+}
+
+constexpr inline float QVector2D::x() const noexcept { return v[0]; }
+constexpr inline float QVector2D::y() const noexcept { return v[1]; }
+
+constexpr inline void QVector2D::setX(float aX) noexcept { v[0] = aX; }
+constexpr inline void QVector2D::setY(float aY) noexcept { v[1] = aY; }
+
+constexpr inline float &QVector2D::operator[](int i)
+{
+ Q_ASSERT(uint(i) < 2u);
+ return v[i];
+}
+
+constexpr inline float QVector2D::operator[](int i) const
+{
+ Q_ASSERT(uint(i) < 2u);
+ return v[i];
+}
+
+inline float QVector2D::length() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]);
+ return float(std::sqrt(len));
+}
+
+constexpr inline float QVector2D::lengthSquared() const noexcept
+{
+ return v[0] * v[0] + v[1] * v[1];
+}
+
+inline QVector2D QVector2D::normalized() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]);
+ if (qFuzzyIsNull(len - 1.0)) {
+ return *this;
+ } else if (!qFuzzyIsNull(len)) {
+ double sqrtLen = std::sqrt(len);
+ return QVector2D(float(double(v[0]) / sqrtLen), float(double(v[1]) / sqrtLen));
+ } else {
+ return QVector2D();
+ }
+}
+
+inline void QVector2D::normalize() noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]);
+ if (qFuzzyIsNull(len - 1.0) || qFuzzyIsNull(len))
+ return;
+
+ len = std::sqrt(len);
+
+ v[0] = float(double(v[0]) / len);
+ v[1] = float(double(v[1]) / len);
+}
+
+inline float QVector2D::distanceToPoint(QVector2D point) const noexcept
+{
+ return (*this - point).length();
+}
+
+inline float QVector2D::distanceToLine(QVector2D point, QVector2D direction) const noexcept
+{
+ if (direction.isNull())
+ return (*this - point).length();
+ QVector2D p = point + dotProduct(*this - point, direction) * direction;
+ return (*this - p).length();
+}
+
+constexpr inline QVector2D &QVector2D::operator+=(QVector2D vector) noexcept
+{
+ v[0] += vector.v[0];
+ v[1] += vector.v[1];
+ return *this;
+}
+
+constexpr inline QVector2D &QVector2D::operator-=(QVector2D vector) noexcept
+{
+ v[0] -= vector.v[0];
+ v[1] -= vector.v[1];
+ return *this;
+}
+
+constexpr inline QVector2D &QVector2D::operator*=(float factor) noexcept
+{
+ v[0] *= factor;
+ v[1] *= factor;
+ return *this;
+}
+
+constexpr inline QVector2D &QVector2D::operator*=(QVector2D vector) noexcept
+{
+ v[0] *= vector.v[0];
+ v[1] *= vector.v[1];
+ return *this;
+}
+
+constexpr inline QVector2D &QVector2D::operator/=(float divisor)
+{
+ v[0] /= divisor;
+ v[1] /= divisor;
+ return *this;
+}
+
+constexpr inline QVector2D &QVector2D::operator/=(QVector2D vector)
+{
+ v[0] /= vector.v[0];
+ v[1] /= vector.v[1];
+ return *this;
+}
+
+constexpr inline float QVector2D::dotProduct(QVector2D v1, QVector2D v2) noexcept
+{
+ return v1.v[0] * v2.v[0] + v1.v[1] * v2.v[1];
+}
+
+constexpr inline bool qFuzzyCompare(QVector2D v1, QVector2D v2) noexcept
+{
+ return qFuzzyCompare(v1.v[0], v2.v[0]) && qFuzzyCompare(v1.v[1], v2.v[1]);
+}
+
+#ifndef QT_NO_VECTOR3D
+constexpr inline QVector3D QVector2D::toVector3D() const noexcept
+{
+ return QVector3D(v[0], v[1], 0.0f);
+}
+#endif
+#ifndef QT_NO_VECTOR4D
+constexpr inline QVector4D QVector2D::toVector4D() const noexcept
+{
+ return QVector4D(v[0], v[1], 0.0f, 0.0f);
+}
+#endif
+
+
+constexpr inline QPoint QVector2D::toPoint() const noexcept
+{
+ return QPoint(qRound(v[0]), qRound(v[1]));
+}
+
+constexpr inline QPointF QVector2D::toPointF() const noexcept
+{
+ return QPointF(qreal(v[0]), qreal(v[1]));
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+Q_GUI_EXPORT QDebug operator<<(QDebug dbg, QVector2D vector);
+#endif
+
+#ifndef QT_NO_DATASTREAM
+Q_GUI_EXPORT QDataStream &operator<<(QDataStream &, QVector2D );
+Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QVector2D &);
+#endif
+
+#endif // QT_NO_VECTOR2D
+
+
+
+/***************************** QVector3D *****************************/
+
+#ifndef QT_NO_VECTOR3D
+
+constexpr inline QVector3D::QVector3D() noexcept : v{0.0f, 0.0f, 0.0f} {}
+
+constexpr inline QVector3D::QVector3D(QPoint point) noexcept : v{float(point.x()), float(point.y()), 0.0f} {}
+
+constexpr inline QVector3D::QVector3D(QPointF point) noexcept : v{float(point.x()), float(point.y()), 0.0f} {}
+
+#ifndef QT_NO_VECTOR2D
+constexpr inline QVector3D::QVector3D(QVector2D vector) noexcept : v{vector[0], vector[1], 0.0f} {}
+constexpr inline QVector3D::QVector3D(QVector2D vector, float zpos) noexcept : v{vector[0], vector[1], zpos} {}
+#endif
+
+#ifndef QT_NO_VECTOR4D
+constexpr inline QVector3D::QVector3D(QVector4D vector) noexcept : v{vector[0], vector[1], vector[2]} {}
+#endif
+
+constexpr inline bool QVector3D::isNull() const noexcept
+{
+ return qIsNull(v[0]) && qIsNull(v[1]) && qIsNull(v[2]);
+}
+
+constexpr inline float QVector3D::x() const noexcept { return v[0]; }
+constexpr inline float QVector3D::y() const noexcept { return v[1]; }
+constexpr inline float QVector3D::z() const noexcept { return v[2]; }
+
+constexpr inline void QVector3D::setX(float aX) noexcept { v[0] = aX; }
+constexpr inline void QVector3D::setY(float aY) noexcept { v[1] = aY; }
+constexpr inline void QVector3D::setZ(float aZ) noexcept { v[2] = aZ; }
+
+constexpr inline float &QVector3D::operator[](int i)
+{
+ Q_ASSERT(uint(i) < 3u);
+ return v[i];
+}
+
+constexpr inline float QVector3D::operator[](int i) const
+{
+ Q_ASSERT(uint(i) < 3u);
+ return v[i];
+}
+
+inline float QVector3D::length() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]);
+ return float(std::sqrt(len));
+}
+
+inline QVector3D QVector3D::normalized() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]);
+ if (qFuzzyIsNull(len - 1.0)) {
+ return *this;
+ } else if (!qFuzzyIsNull(len)) {
+ double sqrtLen = std::sqrt(len);
+ return QVector3D(float(double(v[0]) / sqrtLen),
+ float(double(v[1]) / sqrtLen),
+ float(double(v[2]) / sqrtLen));
+ } else {
+ return QVector3D();
+ }
+}
+
+inline void QVector3D::normalize() noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]);
+ if (qFuzzyIsNull(len - 1.0) || qFuzzyIsNull(len))
+ return;
+
+ len = std::sqrt(len);
+
+ v[0] = float(double(v[0]) / len);
+ v[1] = float(double(v[1]) / len);
+ v[2] = float(double(v[2]) / len);
+}
+
+constexpr inline float QVector3D::lengthSquared() const noexcept
+{
+ return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
+}
+
+constexpr inline QVector3D &QVector3D::operator+=(QVector3D vector) noexcept
+{
+ v[0] += vector.v[0];
+ v[1] += vector.v[1];
+ v[2] += vector.v[2];
+ return *this;
+}
+
+constexpr inline QVector3D &QVector3D::operator-=(QVector3D vector) noexcept
+{
+ v[0] -= vector.v[0];
+ v[1] -= vector.v[1];
+ v[2] -= vector.v[2];
+ return *this;
+}
+
+constexpr inline QVector3D &QVector3D::operator*=(float factor) noexcept
+{
+ v[0] *= factor;
+ v[1] *= factor;
+ v[2] *= factor;
+ return *this;
+}
+
+constexpr inline QVector3D &QVector3D::operator*=(QVector3D vector) noexcept
+{
+ v[0] *= vector.v[0];
+ v[1] *= vector.v[1];
+ v[2] *= vector.v[2];
+ return *this;
+}
+
+constexpr inline QVector3D &QVector3D::operator/=(float divisor)
+{
+ v[0] /= divisor;
+ v[1] /= divisor;
+ v[2] /= divisor;
+ return *this;
+}
+
+constexpr inline QVector3D &QVector3D::operator/=(QVector3D vector)
+{
+ v[0] /= vector.v[0];
+ v[1] /= vector.v[1];
+ v[2] /= vector.v[2];
+ return *this;
+}
+
+constexpr inline float QVector3D::dotProduct(QVector3D v1, QVector3D v2) noexcept
+{
+ return v1.v[0] * v2.v[0] + v1.v[1] * v2.v[1] + v1.v[2] * v2.v[2];
+}
+
+constexpr inline QVector3D QVector3D::crossProduct(QVector3D v1, QVector3D v2) noexcept
+{
+ return QVector3D(v1.v[1] * v2.v[2] - v1.v[2] * v2.v[1],
+ v1.v[2] * v2.v[0] - v1.v[0] * v2.v[2],
+ v1.v[0] * v2.v[1] - v1.v[1] * v2.v[0]);
+}
+
+inline QVector3D QVector3D::normal(QVector3D v1, QVector3D v2) noexcept
+{
+ return crossProduct(v1, v2).normalized();
+}
+
+inline QVector3D QVector3D::normal(QVector3D v1, QVector3D v2, QVector3D v3) noexcept
+{
+ return crossProduct((v2 - v1), (v3 - v1)).normalized();
+}
+
+inline float QVector3D::distanceToPoint(QVector3D point) const noexcept
+{
+ return (*this - point).length();
+}
+
+constexpr inline float QVector3D::distanceToPlane(QVector3D plane, QVector3D normal) const noexcept
+{
+ return dotProduct(*this - plane, normal);
+}
+
+inline float QVector3D::distanceToPlane(QVector3D plane1, QVector3D plane2, QVector3D plane3) const noexcept
+{
+ QVector3D n = normal(plane2 - plane1, plane3 - plane1);
+ return dotProduct(*this - plane1, n);
+}
+
+inline float QVector3D::distanceToLine(QVector3D point, QVector3D direction) const noexcept
+{
+ if (direction.isNull())
+ return (*this - point).length();
+ QVector3D p = point + dotProduct(*this - point, direction) * direction;
+ return (*this - p).length();
+}
+
+constexpr inline bool qFuzzyCompare(QVector3D v1, QVector3D v2) noexcept
+{
+ return qFuzzyCompare(v1.v[0], v2.v[0]) &&
+ qFuzzyCompare(v1.v[1], v2.v[1]) &&
+ qFuzzyCompare(v1.v[2], v2.v[2]);
+}
+
+#ifndef QT_NO_VECTOR2D
+constexpr inline QVector2D QVector3D::toVector2D() const noexcept
+{
+ return QVector2D(v[0], v[1]);
+}
+#endif
+#ifndef QT_NO_VECTOR4D
+constexpr inline QVector4D QVector3D::toVector4D() const noexcept
+{
+ return QVector4D(v[0], v[1], v[2], 0.0f);
+}
+#endif
+
+constexpr inline QPoint QVector3D::toPoint() const noexcept
+{
+ return QPoint(qRound(v[0]), qRound(v[1]));
+}
+
+constexpr inline QPointF QVector3D::toPointF() const noexcept
+{
+ return QPointF(qreal(v[0]), qreal(v[1]));
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+Q_GUI_EXPORT QDebug operator<<(QDebug dbg, QVector3D vector);
+#endif
+
+#ifndef QT_NO_DATASTREAM
+Q_GUI_EXPORT QDataStream &operator<<(QDataStream &, QVector3D );
+Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QVector3D &);
+#endif
+
+#endif // QT_NO_VECTOR3D
+
+
+
+/***************************** QVector4D *****************************/
+
+#ifndef QT_NO_VECTOR4D
+
+constexpr inline QVector4D::QVector4D() noexcept : v{0.0f, 0.0f, 0.0f, 0.0f} {}
+
+constexpr inline QVector4D::QVector4D(float xpos, float ypos, float zpos, float wpos) noexcept : v{xpos, ypos, zpos, wpos} {}
+
+constexpr inline QVector4D::QVector4D(QPoint point) noexcept : v{float(point.x()), float(point.y()), 0.0f, 0.0f} {}
+
+constexpr inline QVector4D::QVector4D(QPointF point) noexcept : v{float(point.x()), float(point.y()), 0.0f, 0.0f} {}
+
+#ifndef QT_NO_VECTOR2D
+constexpr QVector4D::QVector4D(QVector2D vector) noexcept : v{vector[0], vector[1], 0.0f, 0.0f} {}
+constexpr QVector4D::QVector4D(QVector2D vector, float zpos, float wpos) noexcept : v{vector[0], vector[1], zpos, wpos} {}
+#endif
+#ifndef QT_NO_VECTOR3D
+constexpr QVector4D::QVector4D(QVector3D vector) noexcept : v{vector[0], vector[1], vector[2], 0.0f} {}
+constexpr QVector4D::QVector4D(QVector3D vector, float wpos) noexcept : v{vector[0], vector[1], vector[2], wpos} {}
+#endif
+
+constexpr inline bool QVector4D::isNull() const noexcept
+{
+ return qIsNull(v[0]) && qIsNull(v[1]) && qIsNull(v[2]) && qIsNull(v[3]);
+}
+
+constexpr inline float QVector4D::x() const noexcept { return v[0]; }
+constexpr inline float QVector4D::y() const noexcept { return v[1]; }
+constexpr inline float QVector4D::z() const noexcept { return v[2]; }
+constexpr inline float QVector4D::w() const noexcept { return v[3]; }
+
+constexpr inline void QVector4D::setX(float aX) noexcept { v[0] = aX; }
+constexpr inline void QVector4D::setY(float aY) noexcept { v[1] = aY; }
+constexpr inline void QVector4D::setZ(float aZ) noexcept { v[2] = aZ; }
+constexpr inline void QVector4D::setW(float aW) noexcept { v[3] = aW; }
+
+constexpr inline float &QVector4D::operator[](int i)
+{
+ Q_ASSERT(uint(i) < 4u);
+ return v[i];
+}
+
+constexpr inline float QVector4D::operator[](int i) const
+{
+ Q_ASSERT(uint(i) < 4u);
+ return v[i];
+}
+
+inline float QVector4D::length() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]) +
+ double(v[3]) * double(v[3]);
+ return float(std::sqrt(len));
+}
+
+constexpr inline float QVector4D::lengthSquared() const noexcept
+{
+ return v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3];
+}
+
+inline QVector4D QVector4D::normalized() const noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]) +
+ double(v[3]) * double(v[3]);
+ if (qFuzzyIsNull(len - 1.0)) {
+ return *this;
+ } else if (!qFuzzyIsNull(len)) {
+ double sqrtLen = std::sqrt(len);
+ return QVector4D(float(double(v[0]) / sqrtLen),
+ float(double(v[1]) / sqrtLen),
+ float(double(v[2]) / sqrtLen),
+ float(double(v[3]) / sqrtLen));
+ } else {
+ return QVector4D();
+ }
+}
+
+inline void QVector4D::normalize() noexcept
+{
+ // Need some extra precision if the length is very small.
+ double len = double(v[0]) * double(v[0]) +
+ double(v[1]) * double(v[1]) +
+ double(v[2]) * double(v[2]) +
+ double(v[3]) * double(v[3]);
+ if (qFuzzyIsNull(len - 1.0) || qFuzzyIsNull(len))
+ return;
+
+ len = std::sqrt(len);
+
+ v[0] = float(double(v[0]) / len);
+ v[1] = float(double(v[1]) / len);
+ v[2] = float(double(v[2]) / len);
+ v[3] = float(double(v[3]) / len);
+}
+
+constexpr inline QVector4D &QVector4D::operator+=(QVector4D vector) noexcept
+{
+ v[0] += vector.v[0];
+ v[1] += vector.v[1];
+ v[2] += vector.v[2];
+ v[3] += vector.v[3];
+ return *this;
+}
+
+constexpr inline QVector4D &QVector4D::operator-=(QVector4D vector) noexcept
+{
+ v[0] -= vector.v[0];
+ v[1] -= vector.v[1];
+ v[2] -= vector.v[2];
+ v[3] -= vector.v[3];
+ return *this;
+}
+
+constexpr inline QVector4D &QVector4D::operator*=(float factor) noexcept
+{
+ v[0] *= factor;
+ v[1] *= factor;
+ v[2] *= factor;
+ v[3] *= factor;
+ return *this;
+}
+
+constexpr inline QVector4D &QVector4D::operator*=(QVector4D vector) noexcept
+{
+ v[0] *= vector.v[0];
+ v[1] *= vector.v[1];
+ v[2] *= vector.v[2];
+ v[3] *= vector.v[3];
+ return *this;
+}
+
+constexpr inline QVector4D &QVector4D::operator/=(float divisor)
+{
+ v[0] /= divisor;
+ v[1] /= divisor;
+ v[2] /= divisor;
+ v[3] /= divisor;
+ return *this;
+}
+
+constexpr inline QVector4D &QVector4D::operator/=(QVector4D vector)
+{
+ v[0] /= vector.v[0];
+ v[1] /= vector.v[1];
+ v[2] /= vector.v[2];
+ v[3] /= vector.v[3];
+ return *this;
+}
+
+constexpr float QVector4D::dotProduct(QVector4D v1, QVector4D v2) noexcept
+{
+ return v1.v[0] * v2.v[0] + v1.v[1] * v2.v[1] + v1.v[2] * v2.v[2] + v1.v[3] * v2.v[3];
+}
+
+constexpr inline bool qFuzzyCompare(QVector4D v1, QVector4D v2) noexcept
+{
+ return qFuzzyCompare(v1.v[0], v2.v[0]) &&
+ qFuzzyCompare(v1.v[1], v2.v[1]) &&
+ qFuzzyCompare(v1.v[2], v2.v[2]) &&
+ qFuzzyCompare(v1.v[3], v2.v[3]);
+}
+
+#ifndef QT_NO_VECTOR2D
+
+constexpr inline QVector2D QVector4D::toVector2D() const noexcept
+{
+ return QVector2D(v[0], v[1]);
+}
+
+constexpr inline QVector2D QVector4D::toVector2DAffine() const noexcept
+{
+ if (qIsNull(v[3]))
+ return QVector2D();
+ return QVector2D(v[0] / v[3], v[1] / v[3]);
+}
+
+#endif // QT_NO_VECTOR2D
+
+#ifndef QT_NO_VECTOR3D
+
+constexpr inline QVector3D QVector4D::toVector3D() const noexcept
+{
+ return QVector3D(v[0], v[1], v[2]);
+}
+
+constexpr QVector3D QVector4D::toVector3DAffine() const noexcept
+{
+ if (qIsNull(v[3]))
+ return QVector3D();
+ return QVector3D(v[0] / v[3], v[1] / v[3], v[2] / v[3]);
+}
+
+#endif // QT_NO_VECTOR3D
+
+constexpr inline QPoint QVector4D::toPoint() const noexcept
+{
+ return QPoint(qRound(v[0]), qRound(v[1]));
+}
+
+constexpr inline QPointF QVector4D::toPointF() const noexcept
+{
+ return QPointF(qreal(v[0]), qreal(v[1]));
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+Q_GUI_EXPORT QDebug operator<<(QDebug dbg, QVector4D vector);
+#endif
+
+#ifndef QT_NO_DATASTREAM
+Q_GUI_EXPORT QDataStream &operator<<(QDataStream &, QVector4D );
+Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QVector4D &);
+#endif
+
+#endif // QT_NO_VECTOR4D
+
+
+QT_END_NAMESPACE
+
+#endif // QVECTORND_H
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