- Qt 5.15
- Qt GUI
- C++ Classes
- QVector3D
- Qt 5.15.18 Reference Documentation

# QVector3D Class

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

Header: | #include <QVector3D>
qmake: | QT += gui
Since: | Qt 4.6

This class was introduced in Qt 4.6.

- List of all members, including inherited members

## Public Functions

| QVector3D(const QVector4D &vector)
| QVector3D(const QVector2D &vector, float zpos)
| QVector3D(const QVector2D &vector)
| QVector3D(const QPointF &point)
| QVector3D(const QPoint &point)
| QVector3D(float xpos, float ypos, float zpos)
| QVector3D()
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
QVariant | 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

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(const QVector4D &vector)

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

See also toVector4D().

### 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 QVector2D &vector)

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

See also toVector2D().

### 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 QPoint &point)

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

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

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

### QVector3D::QVector3D()

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

### `[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 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(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().

### QVariant 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.