# QVector3D Class

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

## 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)
 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.

## 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.

### QVector3D::QVector3D(const QVector2D & vector, qreal zpos)

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

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

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

### `[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.

### 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.

### 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.

### qreal QVector3D::distanceToPlane(const QVector3D & plane1, const QVector3D & plane2, const QVector3D & plane3) const

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.

### `[static] `qreal 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.

### qreal QVector3D::length() const

Returns the length of the vector from the origin.

### 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.

### `[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.

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

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.

### 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.

### 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.

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

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

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

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

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

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

### QPoint QVector3D::toPoint() const

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

### QPointF QVector3D::toPointF() const

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

### QVector2D QVector3D::toVector2D() const

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

### QVector4D QVector3D::toVector4D() const

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

### qreal QVector3D::x() const

Returns the x coordinate of this point.

### qreal QVector3D::y() const

Returns the y coordinate of this point.

### qreal QVector3D::z() const

Returns the z coordinate of this point.

### 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.

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

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.

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

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

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

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

### QVector3D & QVector3D::operator/=(qreal divisor)

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

## Related Non-Members

### boolqFuzzyCompare(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.

### booloperator!=(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 QVector3Doperator*(qreal factor, const QVector3D & vector)

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

### const QVector3Doperator*(const QVector3D & vector, qreal factor)

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

### const QVector3Doperator*(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.

### const QVector3Doperator+(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.

### const QVector3Doperator-(const QVector3D & v1, const QVector3D & v2)

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

### const QVector3Doperator-(const QVector3D & vector)

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 QVector3Doperator/(const QVector3D & vector, qreal divisor)

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

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

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