# 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 noexcept]`

QVector3D::QVector3D()

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

`[constexpr noexcept]`

QVector3D::QVector3D(float *xpos*, float *ypos*, float *zpos*)

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

`[explicit constexpr noexcept]`

QVector3D::QVector3D(QPoint *point*)

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

`[explicit constexpr noexcept]`

QVector3D::QVector3D(QPointF *point*)

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

`[explicit constexpr noexcept]`

QVector3D::QVector3D(QVector2D *vector*)

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

**See also **toVector2D().

`[constexpr noexcept]`

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 noexcept]`

QVector3D::QVector3D(QVector4D *vector*)

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

**See also **toVector4D().

`[static constexpr noexcept]`

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().

`[noexcept]`

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 noexcept]`

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().

`[noexcept]`

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().

`[noexcept]`

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 noexcept]`

float QVector3D::dotProduct(QVector3D *v1*, QVector3D *v2*)

Returns the dot product of *v1* and *v2*.

`[constexpr noexcept]`

bool QVector3D::isNull() const

Returns `true`

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

.

`[noexcept]`

float QVector3D::length() const

Returns the length of the vector from the origin.

**See also **lengthSquared() and normalized().

`[constexpr noexcept]`

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 noexcept]`

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 noexcept]`

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().

`[noexcept]`

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().

`[noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

QPointF QVector3D::toPointF() const

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

**See also **toPoint() and toVector2D().

`[constexpr noexcept]`

QVector2D QVector3D::toVector2D() const

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

**See also **toVector4D() and toPoint().

`[constexpr noexcept]`

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 noexcept]`

float QVector3D::x() const

Returns the x coordinate of this point.

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

`[constexpr noexcept]`

float QVector3D::y() const

Returns the y coordinate of this point.

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

`[constexpr noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

QVector3D &QVector3D::operator+=(QVector3D *vector*)

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

**See also **operator-=().

`[constexpr noexcept]`

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

`[noexcept]`

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 noexcept]`

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 noexcept]`

QVector3D operator*(float *factor*, QVector3D *vector*)

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

**See also **QVector3D::operator*=().

`[constexpr noexcept]`

QVector3D operator*(QVector3D *vector*, float *factor*)

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

**See also **QVector3D::operator*=().

`[constexpr noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

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 noexcept]`

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.

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