- Qt 6.5
- Qt GUI
- C++ Classes
- QVector3D
- Qt 6.5.0 Reference Documentation

# QVector3D Class

The QVector3D class represents a vector or vertex in 3D space. More...

Header: | #include <QVector3D>
CMake: | find_package(Qt6 REQUIRED COMPONENTS Gui) target_link_libraries(mytarget PRIVATE Qt6::Gui)
qmake: | QT += gui

- List of all members, including inherited members
- QVector3D is part of Rendering in 3D.

## Public Functions

| QVector3D()
| QVector3D(float xpos, float ypos, float zpos)
| QVector3D(QPoint point)
| QVector3D(QPointF point)
| QVector3D(QVector2D vector)
| QVector3D(QVector2D vector, float zpos)
| QVector3D(QVector4D vector)
float | distanceToLine(QVector3D point, QVector3D direction) const
float | distanceToPlane(QVector3D plane, QVector3D normal) const
float | distanceToPlane(QVector3D plane1, QVector3D plane2, QVector3D plane3) const
float | distanceToPoint(QVector3D point) const
bool | isNull() const
float | length() const
float | lengthSquared() const
void | normalize()
QVector3D | normalized() const
QVector3D | project(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const
void | setX(float x)
void | setY(float y)
void | setZ(float z)
QPoint | toPoint() const
QPointF | toPointF() const
QVector2D | toVector2D() const
QVector4D | toVector4D() const
QVector3D | unproject(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const
float | x() const
float | y() const
float | z() const
QVariant | operator QVariant() const
QVector3D & | operator*=(float factor)
QVector3D & | operator*=(QVector3D vector)
QVector3D & | operator+=(QVector3D vector)
QVector3D & | operator-=(QVector3D vector)
QVector3D & | operator/=(float divisor)
QVector3D & | operator/=(QVector3D vector)
float & | operator[](int i)
float | operator[](int i) const

## Static Public Members

QVector3D | crossProduct(QVector3D v1, QVector3D v2)
float | dotProduct(QVector3D v1, QVector3D v2)
QVector3D | normal(QVector3D v1, QVector3D v2)
QVector3D | normal(QVector3D v1, QVector3D v2, QVector3D v3)

## Related Non-Members

bool | qFuzzyCompare(QVector3D v1, QVector3D v2)
bool | operator!=(QVector3D v1, QVector3D v2)
QVector3D | operator*(float factor, QVector3D vector)
QVector3D | operator*(QVector3D vector, float factor)
QVector3D | operator*(QVector3D v1, QVector3D v2)
QVector3D | operator+(QVector3D v1, QVector3D v2)
QVector3D | operator-(QVector3D v1, QVector3D v2)
QVector3D | operator-(QVector3D vector)
QVector3D | operator/(QVector3D vector, float divisor)
QVector3D | operator/(QVector3D vector, QVector3D divisor)
QDataStream & | operator<<(QDataStream &stream, QVector3D vector)
bool | operator==(QVector3D v1, QVector3D v2)
QDataStream & | operator>>(QDataStream &stream, QVector3D &vector)

## Detailed Description

Vectors are one of the main building blocks of 3D representation and drawing. They consist of three finite floating-point coordinates, traditionally called x, y, and z.

The QVector3D class can also be used to represent vertices in 3D space. We therefore do not need to provide a separate vertex class.

See also QVector2D, QVector4D, and QQuaternion.

## Member Function Documentation

### `[constexpr]` QVector3D::QVector3D()

Constructs a null vector, i.e. with coordinates (0, 0, 0).

### `[constexpr]` QVector3D::QVector3D(float xpos, float ypos, float zpos)

Constructs a vector with coordinates (xpos, ypos, zpos). All parameters must be finite.

### `[explicit constexpr]` QVector3D::QVector3D(QPoint point)

Constructs a vector with x and y coordinates from a 2D point, and a z coordinate of 0.

### `[explicit constexpr]` QVector3D::QVector3D(QPointF point)

Constructs a vector with x and y coordinates from a 2D point, and a z coordinate of 0.

### `[explicit constexpr]` QVector3D::QVector3D(QVector2D vector)

Constructs a 3D vector from the specified 2D vector. The z coordinate is set to zero.

See also toVector2D().

### `[constexpr]` QVector3D::QVector3D(QVector2D vector, float zpos)

Constructs a 3D vector from the specified 2D vector. The z coordinate is set to zpos, which must be finite.

See also toVector2D().

### `[explicit constexpr]` QVector3D::QVector3D(QVector4D vector)

Constructs a 3D vector from the specified 4D vector. The w coordinate is dropped.

See also toVector4D().

### `[static constexpr]` QVector3D QVector3D::crossProduct(QVector3D v1, QVector3D v2)

Returns the cross-product of vectors v1 and v2, which is normal to the plane spanned by v1 and v2. It will be zero if the two vectors are parallel.

See also normal().

### float QVector3D::distanceToLine(QVector3D point, QVector3D direction) const

Returns the distance that this vertex is from a line defined by point and the unit vector direction.

If direction is a null vector, then it does not define a line. In that case, the distance from point to this vertex is returned.

See also distanceToPlane().

### `[constexpr]` float QVector3D::distanceToPlane(QVector3D plane, QVector3D normal) const

Returns the distance from this vertex to a plane defined by the vertex plane and a normal unit vector. The normal parameter is assumed to have been normalized to a unit vector.

The return value will be negative if the vertex is below the plane, or zero if it is on the plane.

See also normal() and distanceToLine().

### float QVector3D::distanceToPlane(QVector3D plane1, QVector3D plane2, QVector3D plane3) const

Returns the distance from this vertex to a plane defined by the vertices plane1, plane2 and plane3.

The return value will be negative if the vertex is below the plane, or zero if it is on the plane.

The two vectors that define the plane are plane2 - plane1 and plane3 - plane1.

See also normal() and distanceToLine().

### float QVector3D::distanceToPoint(QVector3D point) const

Returns the distance from this vertex to a point defined by the vertex point.

See also distanceToPlane() and distanceToLine().

### `[static constexpr]` float QVector3D::dotProduct(QVector3D v1, QVector3D v2)

Returns the dot product of v1 and v2.

### `[constexpr]` bool QVector3D::isNull() const

Returns `true` if the x, y, and z coordinates are set to 0.0, otherwise returns `false`.

### float QVector3D::length() const

Returns the length of the vector from the origin.

See also lengthSquared() and normalized().

### `[constexpr]` float QVector3D::lengthSquared() const

Returns the squared length of the vector from the origin. This is equivalent to the dot product of the vector with itself.

See also length() and dotProduct().

### `[static]` QVector3D QVector3D::normal(QVector3D v1, QVector3D v2)

Returns the unit normal vector of a plane spanned by vectors v1 and v2, which must not be parallel to one another.

Use crossProduct() to compute the cross-product of v1 and v2 if you do not need the result to be normalized to a unit vector.

See also crossProduct() and distanceToPlane().

### `[static]` QVector3D QVector3D::normal(QVector3D v1, QVector3D v2, QVector3D v3)

Returns the unit normal vector of a plane spanned by vectors v2 - v1 and v3 - v1, which must not be parallel to one another.

Use crossProduct() to compute the cross-product of v2 - v1 and v3 - v1 if you do not need the result to be normalized to a unit vector.

See also crossProduct() and distanceToPlane().

### void QVector3D::normalize()

Normalizes the current vector in place. Nothing happens if this vector is a null vector or the length of the vector is very close to 1.

See also length() and normalized().

### QVector3D QVector3D::normalized() const

Returns the normalized unit vector form of this vector.

If this vector is null, then a null vector is returned. If the length of the vector is very close to 1, then the vector will be returned as-is. Otherwise the normalized form of the vector of length 1 will be returned.

See also length() and normalize().

### QVector3D QVector3D::project(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const

Returns the window coordinates of this vector initially in object/model coordinates using the model view matrix modelView, the projection matrix projection and the viewport dimensions viewport.

When transforming from clip to normalized space, a division by the w component on the vector components takes place. To prevent dividing by 0 if w equals to 0, it is set to 1.

Note: the returned y coordinates are in OpenGL orientation. OpenGL expects the bottom to be 0 whereas for Qt top is 0.

See also unproject().

### `[constexpr]` void QVector3D::setX(float x)

Sets the x coordinate of this point to the given finite x coordinate.

See also x(), setY(), and setZ().

### `[constexpr]` void QVector3D::setY(float y)

Sets the y coordinate of this point to the given finite y coordinate.

See also y(), setX(), and setZ().

### `[constexpr]` void QVector3D::setZ(float z)

Sets the z coordinate of this point to the given finite z coordinate.

See also z(), setX(), and setY().

### `[constexpr]` QPoint QVector3D::toPoint() const

Returns the QPoint form of this 3D vector. The z coordinate is dropped. The x and y coordinates are rounded to nearest integers.

See also toPointF() and toVector2D().

### `[constexpr]` QPointF QVector3D::toPointF() const

Returns the QPointF form of this 3D vector. The z coordinate is dropped.

See also toPoint() and toVector2D().

### `[constexpr]` QVector2D QVector3D::toVector2D() const

Returns the 2D vector form of this 3D vector, dropping the z coordinate.

See also toVector4D() and toPoint().

### `[constexpr]` QVector4D QVector3D::toVector4D() const

Returns the 4D form of this 3D vector, with the w coordinate set to zero.

See also toVector2D() and toPoint().

### QVector3D QVector3D::unproject(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const

Returns the object/model coordinates of this vector initially in window coordinates using the model view matrix modelView, the projection matrix projection and the viewport dimensions viewport.

When transforming from clip to normalized space, a division by the w component of the vector components takes place. To prevent dividing by 0 if w equals to 0, it is set to 1.

Note: y coordinates in viewport should use OpenGL orientation. OpenGL expects the bottom to be 0 whereas for Qt top is 0.

See also project().

### `[constexpr]` float QVector3D::x() const

Returns the x coordinate of this point.

See also setX(), y(), and z().

### `[constexpr]` float QVector3D::y() const

Returns the y coordinate of this point.

See also setY(), x(), and z().

### `[constexpr]` float QVector3D::z() const

Returns the z coordinate of this point.

See also setZ(), x(), and y().

### QVariant QVector3D::operator QVariant() const

Returns the 3D vector as a QVariant.

### `[constexpr]` QVector3D &QVector3D::operator*=(float factor)

Multiplies this vector's coordinates by the given finite factor and returns a reference to this vector.

See also operator/=() and operator*().

### `[constexpr]` QVector3D &QVector3D::operator*=(QVector3D vector)

This is an overloaded function.

Multiplies each component of this vector by the corresponding component in vector and returns a reference to this vector.

Note: this is not the same as the crossProduct() of this vector and vector. (Its components add up to the dot product of this vector and vector.)

See also crossProduct(), operator/=(), and operator*().

### `[constexpr]` QVector3D &QVector3D::operator+=(QVector3D vector)

Adds the given vector to this vector and returns a reference to this vector.

See also operator-=().

### `[constexpr]` QVector3D &QVector3D::operator-=(QVector3D vector)

Subtracts the given vector from this vector and returns a reference to this vector.

See also operator+=().

### `[constexpr]` QVector3D &QVector3D::operator/=(float divisor)

Divides this vector's coordinates by the given divisor, and returns a reference to this vector. The divisor must not be either zero or NaN.

See also operator*=() and operator/().

### `[constexpr]` QVector3D &QVector3D::operator/=(QVector3D vector)

Divides each component of this vector by the corresponding component in vector and returns a reference to this vector.

The vector must have no component that is either zero or NaN.

See also operator*=() and operator/().

### `[constexpr]` float &QVector3D::operator[](int i)

Returns the component of the vector at index position i as a modifiable reference.

i must be a valid index position in the vector (i.e., 0 <= i < 3).

### `[constexpr]` float QVector3D::operator[](int i) const

Returns the component of the vector at index position i.

i must be a valid index position in the vector (i.e., 0 <= i < 3).

## Related Non-Members

### bool qFuzzyCompare(QVector3D v1, QVector3D v2)

Returns `true` if v1 and v2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

### `[constexpr]` bool operator!=(QVector3D v1, QVector3D v2)

Returns `true` if v1 is not equal to v2; otherwise returns `false`. This operator uses an exact floating-point comparison.

### `[constexpr]` QVector3D operator*(float factor, QVector3D vector)

Returns a copy of the given vector, multiplied by the given finite factor.

See also QVector3D::operator*=().

### `[constexpr]` QVector3D operator*(QVector3D vector, float factor)

Returns a copy of the given vector, multiplied by the given finite factor.

See also QVector3D::operator*=().

### `[constexpr]` QVector3D operator*(QVector3D v1, QVector3D v2)

Returns the QVector3D object formed by multiplying each component of v1 by the corresponding component of v2.

Note: This is not the same as the crossProduct() of v1 and v2. (Its components add up to the dot product of v1 and v2.)

See also QVector3D::crossProduct().

### `[constexpr]` QVector3D operator+(QVector3D v1, QVector3D v2)

Returns a QVector3D object that is the sum of the given vectors, v1 and v2; each component is added separately.

See also QVector3D::operator+=().

### `[constexpr]` QVector3D operator-(QVector3D v1, QVector3D v2)

Returns a QVector3D object that is formed by subtracting v2 from v1; each component is subtracted separately.

See also QVector3D::operator-=().

### `[constexpr]` QVector3D operator-(QVector3D vector)

This is an overloaded function.

Returns a QVector3D object that is formed by changing the sign of each component of the given vector.

Equivalent to `QVector3D(0,0,0) - vector`.

### `[constexpr]` QVector3D operator/(QVector3D vector, float divisor)

Returns the QVector3D object formed by dividing each component of the given vector by the given divisor.

The divisor must not be either zero or NaN.

See also QVector3D::operator/=().

### `[constexpr]` QVector3D operator/(QVector3D vector, QVector3D divisor)

Returns the QVector3D object formed by dividing each component of the given vector by the corresponding component of the given divisor.

The divisor must have no component that is either zero or NaN.

See also QVector3D::operator/=().

### QDataStream &operator<<(QDataStream &stream, QVector3D vector)

Writes the given vector to the given stream and returns a reference to the stream.

See also Serializing Qt Data Types.

### `[constexpr]` bool operator==(QVector3D v1, QVector3D v2)

Returns `true` if v1 is equal to v2; otherwise returns `false`. This operator uses an exact floating-point comparison.

### QDataStream &operator>>(QDataStream &stream, QVector3D &vector)

Reads a 3D vector from the given stream into the given vector and returns a reference to the stream.

See also Serializing Qt Data Types.