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# QVector3D Class Reference

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

     #include <QVector3D>

This class was introduced in Qt 4.6.

- List of all members, including inherited members

## Public Functions

| QVector3D ()
| QVector3D ( qreal xpos, qreal ypos, qreal zpos )
| QVector3D ( const QPoint & point )
| QVector3D ( const QPointF & point )
| QVector3D ( const QVector2D & vector )
| QVector3D ( const QVector2D & vector, qreal zpos )
| QVector3D ( const QVector4D & vector )
qreal | distanceToLine ( const QVector3D & point, const QVector3D & direction ) const
qreal | distanceToPlane ( const QVector3D & plane, const QVector3D & normal ) const
qreal | distanceToPlane ( const QVector3D & plane1, const QVector3D & plane2, const QVector3D & plane3 ) const
bool | isNull () const
qreal | length () const
qreal | lengthSquared () const
void | normalize ()
QVector3D | normalized () const
void | setX ( qreal x )
void | setY ( qreal y )
void | setZ ( qreal z )
QPoint | toPoint () const
QPointF | toPointF () const
QVector2D | toVector2D () const
QVector4D | toVector4D () const
qreal | x () const
qreal | y () const
qreal | z () const
| operator QVariant () const
QVector3D & | operator*= ( qreal factor )
QVector3D & | operator*= ( const QVector3D & vector )
QVector3D & | operator+= ( const QVector3D & vector )
QVector3D & | operator-= ( const QVector3D & vector )
QVector3D & | operator/= ( qreal divisor )

## Static Public Members

QVector3D | crossProduct ( const QVector3D & v1, const QVector3D & v2 )
qreal | 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* ( qreal factor, const QVector3D & vector )
const QVector3D | operator* ( const QVector3D & vector, qreal 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, qreal 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.

Note: By design values in the QVector3D instance are stored as `float`. This means that on platforms where the `qreal` arguments to QVector3D functions are represented by `double` values, it is possible to lose precision.

See also QVector2D, QVector4D, and QQuaternion.

## Member Function Documentation

### QVector3D::QVector3D ()

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

### QVector3D::QVector3D ( qreal xpos, qreal ypos, qreal 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, qreal 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().

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

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().

### qreal 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().

### qreal 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().

### qreal 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().

### qreal QVector3D::dotProduct ( const QVector3D & v1, const QVector3D & v2 )`[static]`

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.

### qreal QVector3D::length () const

Returns the length of the vector from the origin.

See also lengthSquared() and normalized().

### qreal 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().

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

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().

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

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().

### void QVector3D::setX ( qreal x )

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

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

### void QVector3D::setY ( qreal y )

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

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

### void QVector3D::setZ ( qreal 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().

### qreal QVector3D::x () const

Returns the x coordinate of this point.

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

### qreal QVector3D::y () const

Returns the y coordinate of this point.

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

### qreal 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*= ( qreal 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/= ( qreal divisor )

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

See also operator*=().

## 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* ( qreal 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, qreal 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, qreal divisor )

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

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.