# QVector3D Class

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

Header: | #include <QVector3D> |

qmake: | QT += gui |

Since: | Qt 4.6 |

## Public Functions

QVector3D() | |

QVector3D(float xpos, float ypos, float zpos) | |

QVector3D(const QPoint & point) | |

QVector3D(const QPointF & point) | |

QVector3D(const QVector2D & vector) | |

QVector3D(const QVector2D & vector, float zpos) | |

QVector3D(const QVector4D & vector) | |

float | distanceToLine(const QVector3D & point, const QVector3D & direction) const |

float | distanceToPlane(const QVector3D & plane, const QVector3D & normal) const |

float | distanceToPlane(const QVector3D & plane1, const QVector3D & plane2, const QVector3D & plane3) const |

float | distanceToPoint(const 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 |

operator QVariant() const | |

QVector3D & | operator*=(float factor) |

QVector3D & | operator*=(const QVector3D & vector) |

QVector3D & | operator+=(const QVector3D & vector) |

QVector3D & | operator-=(const QVector3D & vector) |

QVector3D & | operator/=(float divisor) |

QVector3D & | operator/=(const QVector3D & vector) |

float & | operator[](int i) |

float | operator[](int i) const |

## Static Public Members

QVector3D | crossProduct(const QVector3D & v1, const QVector3D & v2) |

float | dotProduct(const QVector3D & v1, const QVector3D & v2) |

QVector3D | normal(const QVector3D & v1, const QVector3D & v2) |

QVector3D | normal(const QVector3D & v1, const QVector3D & v2, const QVector3D & v3) |

## Related Non-Members

bool | qFuzzyCompare(const QVector3D & v1, const QVector3D & v2) |

bool | operator!=(const QVector3D & v1, const QVector3D & v2) |

const QVector3D | operator*(float factor, const QVector3D & vector) |

const QVector3D | operator*(const QVector3D & vector, float factor) |

const QVector3D | operator*(const QVector3D & v1, const QVector3D & v2) |

const QVector3D | operator+(const QVector3D & v1, const QVector3D & v2) |

const QVector3D | operator-(const QVector3D & v1, const QVector3D & v2) |

const QVector3D | operator-(const QVector3D & vector) |

const QVector3D | operator/(const QVector3D & vector, float divisor) |

const QVector3D | operator/(const QVector3D & vector, const QVector3D & divisor) |

QDataStream & | operator<<(QDataStream & stream, const QVector3D & vector) |

bool | operator==(const QVector3D & v1, const QVector3D & v2) |

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

## Detailed Description

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

Vectors are one of the main building blocks of 3D representation and drawing. They consist of three 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

### QVector3D::QVector3D()

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

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

Constructs a vector with coordinates (*xpos*, *ypos*, *zpos*).

### QVector3D::QVector3D(const QPoint &* point*)

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

### QVector3D::QVector3D(const QPointF &* point*)

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

### QVector3D::QVector3D(const QVector2D &* vector*)

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

**See also **toVector2D().

### QVector3D::QVector3D(const QVector2D &* vector*, float* zpos*)

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

**See also **toVector2D().

### QVector3D::QVector3D(const QVector4D &* vector*)

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

**See also **toVector4D().

`[static] `

QVector3D QVector3D::crossProduct(const QVector3D &* v1*, const QVector3D &* v2*)

Returns the cross-product of vectors *v1* and *v2*, which corresponds to the normal vector of a plane defined by *v1* and *v2*.

**See also **normal().

### float QVector3D::distanceToLine(const QVector3D &* point*, const 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().

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

This is an overloaded function.

Returns the distance from this vertex 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(const QVector3D &* point*) const

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

This function was introduced in Qt 5.1.

**See also **distanceToPlane() and distanceToLine().

`[static] `

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

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

### 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().

### 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(const QVector3D &* v1*, const QVector3D &* v2*)

Returns the normal vector of a plane defined by vectors *v1* and *v2*, normalized to be a unit vector.

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(const QVector3D &* v1*, const QVector3D &* v2*, const QVector3D &* v3*)

This is an overloaded function.

Returns the normal vector of a plane defined by vectors *v2* - *v1* and *v3* - *v1*, normalized to be a unit vector.

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 currect 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.

This function was introduced in Qt 5.5.

**See also **unproject().

### void QVector3D::setX(float* x*)

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

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

### void QVector3D::setY(float* y*)

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

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

### void QVector3D::setZ(float* z*)

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

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

### QPoint QVector3D::toPoint() const

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

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

### QPointF QVector3D::toPointF() const

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

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

### QVector2D QVector3D::toVector2D() const

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

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

### 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.

This function was introduced in Qt 5.5.

**See also **project().

### float QVector3D::x() const

Returns the x coordinate of this point.

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

### float QVector3D::y() const

Returns the y coordinate of this point.

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

### float QVector3D::z() const

Returns the z coordinate of this point.

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

### QVector3D::operator QVariant() const

Returns the 3D vector as a QVariant.

### QVector3D & QVector3D::operator*=(float* factor*)

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

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

### QVector3D & QVector3D::operator*=(const QVector3D &* vector*)

This is an overloaded function.

Multiplies the components of this vector by the corresponding components in *vector*.

Note: this is not the same as the crossProduct() of this vector and *vector*.

**See also **crossProduct().

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

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

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

### QVector3D & QVector3D::operator-=(const QVector3D &* vector*)

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

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

### QVector3D & QVector3D::operator/=(float* divisor*)

Divides this vector's coordinates by the given *divisor*, and returns a reference to this vector.

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

### QVector3D & QVector3D::operator/=(const QVector3D &* vector*)

Divides the components of this vector by the corresponding components in *vector*.

This function was introduced in Qt 5.5.

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

### 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).

This function was introduced in Qt 5.2.

### 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).

This function was introduced in Qt 5.2.

## Related Non-Members

### bool qFuzzyCompare(const QVector3D &* v1*, const QVector3D &* v2*)

Returns `true`

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

### bool operator!=(const QVector3D &* v1*, const QVector3D &* v2*)

Returns `true`

if *v1* is not equal to *v2*; otherwise returns `false`

. This operator uses an exact floating-point comparison.

### const QVector3D operator*(float* factor*, const QVector3D &* vector*)

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

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

### const QVector3D operator*(const QVector3D &* vector*, float* factor*)

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

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

### const QVector3D operator*(const QVector3D &* v1*, const QVector3D &* v2*)

Multiplies the components of *v1* by the corresponding components in *v2*.

Note: this is not the same as the crossProduct() of *v1* and *v2*.

**See also **QVector3D::crossProduct().

### const QVector3D operator+(const QVector3D &* v1*, const 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+=().

### const QVector3D operator-(const QVector3D &* v1*, const QVector3D &* v2*)

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

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

### const QVector3D operator-(const QVector3D &* vector*)

This is an overloaded function.

Returns a QVector3D object that is formed by changing the sign of all three components of the given *vector*.

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

.

### const QVector3D operator/(const QVector3D &* vector*, float* divisor*)

Returns the QVector3D object formed by dividing all three components of the given *vector* by the given *divisor*.

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

### const QVector3D operator/(const QVector3D &* vector*, const QVector3D &* divisor*)

Returns the QVector3D object formed by dividing components of the given *vector* by a respective components of the given *divisor*.

This function was introduced in Qt 5.5.

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

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

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

**See also **Serializing Qt Data Types.

### bool operator==(const QVector3D &* v1*, const 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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