RVector

Class in Math Module
Header: #include <src/core/math/RVector.h>
Inherited by: RRefPoint
Nested classes: RVectorAngleSort, RVectorDistanceSort, RVectorLeftRightTopBottomSort

Description

Represents a 3d vector (x/y/z).

Scriptable: This class is available in script environments.

Copyable: Objects are cleaned up automatically by the garbage collector of the script engine.

Public Functions

	RVector() Constructor for a valid null vector (0/0/0).
	RVector(const QList< double > &tuples) Constructor from a list of up to three doubles (x, y, z).
	RVector(double vx, double vy, double vz=0.0, bool valid_in=true) Constructor for a point with given valid flag.
	~RVector()
RVector	axonometricProjection(RS::IsoProjectionType type) Axonometric projection (isometric, dimetric, trimetric).
double	dot(const RVector &other) const
bool	equalsFuzzy(const RVector &v, double tol=RS::PointTolerance) const
bool	equalsFuzzy2D(const RVector &v, double tol=RS::PointTolerance) const
RVector	flipHorizontal() Mirrors this vector at the Y-axis.
RVector	flipVertical() Mirrors this vector at the X-axis.
RVector	get2D() const
RVector	getAbsolute() const
double	getAngle() const
double	getAngleTo(const RVector &v) const
double	getAngleToPlaneXY() const
RVector	getCeil() const
RVector	getClosest(const QList< RVector > &list) const
RVector	getClosest2D(const QList< RVector > &list) const
double	getClosestDistance(const QList< RVector > &list, int counts)
int	getClosestIndex(const QList< RVector > &list, bool ignoreZ=false) const
int	getClosestIndex2D(const QList< RVector > &list) const
double	getDistanceTo(const RVector &v) const
double	getDistanceTo2D(const RVector &v) const
RVector	getDividedComponents(const RVector &v) const
RVector	getFloor() const
RVector	getLerp(const RVector &v, double t) const Linear interpolation between this and v by fraction ‘t’.
double	getMagnitude() const
double	getMagnitude2D() const
RVector	getMirrored(const RLine &axis) const
RVector	getMultipliedComponents(const RVector &v) const
RVector	getNegated() const
RVector	getNormalized() const
RVector	getRotated(double rotation, const RVector &center) const
RVector	getScaled(const RVector &factors, const RVector &center) const
double	getSquaredMagnitude() const
RVector	getTransformed(const RMatrix &m) const
RVector	getTransformed2D(const QTransform &t) const
RVector	getTransformed2DM(const RMatrix &m) const
RVector	getUnitVector() const
double	getX() const
double	getY() const
double	getZ() const
bool	gteXY(const RVector &v) const
bool	isInside(const RBox &b) const
bool	isInWindow(const RVector &firstCorner, const RVector &secondCorner) const
bool	isNaN() const
RVector	isoProject(RS::IsoProjectionType type) Changes this vector into its isometric projection.
bool	isSane() const
bool	isValid() const
bool	isZero() const
bool	lteXY(const RVector &v) const
RVector	mirror(const RLine &axis) Mirrors this vector at the given axis.
RVector	mirror(const RVector &axis1, const RVector &axis2) Mirrors this vector at the axis defined by two points.
RVector	move(const RVector &offset) Moves this vector by the given offset.
RVector	normalize() Normalizes this vector and returns a reference to this vector.
RVector	obliqueProjection(RS::IsoProjectionType type)
bool	operator!=(const RVector &v) const
RVector	operator*(double s) const binary * operator.
void	operator*=(double s) *= operator
RVector	operator+(const RVector &v) const binary + operator.
void	operator+=(const RVector &v) += operator.
RVector	operator-() const unary - operator.
RVector	operator-(const RVector &v) const binary - operator.
void	operator-=(const RVector &v) -= operator.
RVector	operator/(double s) const binary / operator.
void	operator/=(double s) /= operator
bool	operator==(const RVector &v) const == operator
RVector	rotate(double rotation) Rotates this vector around the origin by the given angle (in rad).
RVector	rotate(double rotation, const RVector &center) Rotates this vector around the given center by the given angle.
RVector	rotate3D(const QQuaternion &quaternion) Rotates this vector by the given quaternion.
RVector	rotate3D(const RLine &axis, double rotation) Rotates this vector around the given 3D axis line by the given angle (in rad).
RVector	scale(const RVector &factors, const RVector &center=nullVector) Scales this vector by the given factors with the given center.
RVector	scale(double factor, const RVector &center=nullVector) Scales this vector by the given factor with the given center.
void	set(double vx, double vy, double vz=0.0) Sets new values for the vector and makes the vector valid.
void	setAngle(double a) Sets the direction of this vector to the given angle (in rad), preserving its magnitude.
void	setMagnitude2D(double m) Sets the vector magnitude without changing the direction.
void	setPolar(double radius, double angle) Sets a new position for the vector in polar coordinates.
void	setX(double x)
void	setY(double y)
void	setZ(double z)
RVector	stretch(const RPolyline &area, const RVector &offset) Moves this vector by offset if it is inside the given area.
RVector	transform(const RMatrix &m) Generic 3d transformation.
RVector	transform2D(const QTransform &t) Transforms this vector with the given transformation matrix.
RVector	transform2DM(const RMatrix &m) Generic 2d transformation.

Static Public Functions

static bool	containsFuzzy(const QList< RVector > &vectors, const RVector &v, double tol=RS::PointTolerance)
static RVector	createPolar(double radius, double angle)
static int	findFirstFuzzy(const QList< RVector > &vectors, const RVector &v, double tol=RS::PointTolerance)
static RVector	getAverage(const QList< RVector > &vectors)
static RVector	getAverage(const RVector &v1, const RVector &v2) Convenience function.
static RVector	getCrossProduct(const RVector &v1, const RVector &v2)
static double	getDotProduct(const RVector &v1, const RVector &v2) Scalarproduct (dot product).
static QList< RVector >	getIntersection(const QList< RVector > &vectorsA, const QList< RVector > &vectorsB, double tol=RS::PointTolerance)
static RVector	getMaximum(const QList< RVector > &vectors)
static RVector	getMaximum(const RVector &v1, const RVector &v2)
static RVector	getMaximumX(const QList< RVector > &vectors)
static RVector	getMaximumY(const QList< RVector > &vectors)
static RVector	getMinimum(const QList< RVector > &vectors)
static RVector	getMinimum(const RVector &v1, const RVector &v2)
static RVector	getMinimumX(const QList< RVector > &vectors)
static RVector	getMinimumY(const QList< RVector > &vectors)
static QList< RVector >	getSortedByAngle(const QList< RVector > &list, const RVector &center, double angle)
static QList< RVector >	getSortedByDistance(const QList< RVector > &list, const RVector &v)
static QList< RVector >	getSortedLeftRightTopBottom(const QList< RVector > &list)
static QList< RVector >	getUnique(const QList< RVector > &vectors, double tol=RS::PointTolerance)
static QList< double >	getXList(const QList< RVector > &vectors)
static QList< double >	getYList(const QList< RVector > &vectors)
static QList< double >	getZList(const QList< RVector > &vectors)
static bool	greaterThanEqualXY(const RVector &v1, const RVector &v2)
static bool	greaterThanX(const RVector &v1, const RVector &v2)
static bool	greaterThanY(const RVector &v1, const RVector &v2)
static bool	lessThanEqualXY(const RVector &v1, const RVector &v2)
static bool	lessThanX(const RVector &v1, const RVector &v2)
static bool	lessThanY(const RVector &v1, const RVector &v2)
static void	moveList(QList< RVector > &list, const RVector &offset) Moves all vectors in the list by the given offset.
static void	rotateList(QList< RVector > &list, double rotation) Rotates all vectors in the list around the origin by the given angle (in rad).
static void	rotateList(QList< RVector > &list, double rotation, const RVector &center) Rotates all vectors in the list around center by the given angle (in rad).
static void	scaleList(QList< RVector > &list, const RVector &factors, const RVector &center=nullVector) Scales all vectors in the list by the given per-axis factors around center.
static void	scaleList(QList< RVector > &list, double factor, const RVector &center=nullVector) Scales all vectors in the list by the given uniform factor around center.

Public Attributes

bool	valid Getter function for this property: isValid.
double	x Getter function for this property: getX.
double	y Getter function for this property: getY.
double	z Getter function for this property: getZ.

Static Public Attributes

static const RVector	invalid invalid vector
static const RVector	nanVector NaN vector.
static const RVector	nullVector null vector
static const RVector	zAxis Z axis vector (default extrusion direction).

Member Documentation

RVector

RVector::RVector()

inline

Constructor for a valid null vector (0/0/0).

RVector

explicit RVector::RVector(const QList< double > &tuples)

explicit

Constructor from a list of up to three doubles (x, y, z).

Missing components default to 0.

RVector

RVector::RVector(double vx, double vy, double vz=0.0, bool valid_in=true)

Constructor for a point with given valid flag.

Parameters:

• v: true: a valid vector with default coordinates is created. false: an invalid vector is created Constructor for a point with given coordinates.

~RVector

RVector::~RVector()

axonometricProjection

RVector RVector::axonometricProjection(RS::IsoProjectionType type)

Axonometric projection (isometric, dimetric, trimetric).

dot

double RVector::dot(const RVector &other) const

inline const

equalsFuzzy

bool RVector::equalsFuzzy(const RVector &v, double tol=RS::PointTolerance) const

const

Returns: True if this vector and the given vector are almost equal (see RS::PointTolerance).

Parameters:

• tol: Tolerance in X, Y and Z.

equalsFuzzy2D

bool RVector::equalsFuzzy2D(const RVector &v, double tol=RS::PointTolerance) const

const

Returns: True if this vector and the given vector are almost equal (see RS::PointTolerance) in 2D space (x,y).

Parameters:

• tol: Tolerance in X, Y.

flipHorizontal

RVector RVector::flipHorizontal()

Mirrors this vector at the Y-axis.

flipVertical

RVector RVector::flipVertical()

Mirrors this vector at the X-axis.

get2D

RVector RVector::get2D() const

inline const

getAbsolute

RVector RVector::getAbsolute() const

const

Returns: A new vector with all components replaced by their absolute values.

getAngle

double RVector::getAngle() const

const

Returns: The angle from zero to this vector (in rad), in range [0, 2*PI).

getAngleTo

double RVector::getAngleTo(const RVector &v) const

const

Returns: The angle from this and the given coordinate (in rad).

getAngleToPlaneXY

double RVector::getAngleToPlaneXY() const

const

Returns: Elevation angle above the XY plane (in rad). Positive above, negative below. Returns PI/2 for zero-length vectors.

getCeil

RVector RVector::getCeil() const

const

Returns: Vector with all components ceiled to the next higher integer.

getClosest

RVector RVector::getClosest(const QList< RVector > &list) const

const

Returns: The vector in list closest to this vector (3D distance), with Z set to 0, or an invalid vector if the list contains no valid vectors.

getClosest2D

RVector RVector::getClosest2D(const QList< RVector > &list) const

const

Returns: The vector in list closest to this vector (2D distance, Z ignored), or an invalid vector if the list contains no valid vectors.

getClosestDistance

double RVector::getClosestDistance(const QList< RVector > &list, int counts)

getClosestIndex

int RVector::getClosestIndex(const QList< RVector > &list, bool ignoreZ=false) const

const

getClosestIndex2D

int RVector::getClosestIndex2D(const QList< RVector > &list) const

inline const

getDistanceTo

double RVector::getDistanceTo(const RVector &v) const

const

Returns: The distance between this and the given coordinate.

getDistanceTo2D

double RVector::getDistanceTo2D(const RVector &v) const

const

Returns: The distance between this and the given coordinate on the XY plane.

getDividedComponents

RVector RVector::getDividedComponents(const RVector &v) const

const

Returns: A new vector with all components divided by the components given in vector v. Note that the division of two vectors is not defined. This is merely a helper function that does what it does.

getFloor

RVector RVector::getFloor() const

const

Returns: Vector with all components floored to the next lower integer.

getLerp

RVector RVector::getLerp(const RVector &v, double t) const

const

Linear interpolation between this and v by fraction ‘t’.

getMagnitude

double RVector::getMagnitude() const

const

Returns: Magnitude (length) of the vector.

getMagnitude2D

double RVector::getMagnitude2D() const

const

Returns: Magnitude (length) of the vector projected to the x/y plane (2d).

getMirrored

RVector RVector::getMirrored(const RLine &axis) const

const

Returns: A new vector equal to this vector mirrored at the given axis line.

getMultipliedComponents

RVector RVector::getMultipliedComponents(const RVector &v) const

const

Returns: A new vector with all components multiplied by the components given in vector v. Note that the multiplication of two vectors is not defined. This is merely a helper function that does what it does.

getNegated

RVector RVector::getNegated() const

const

Returns: New vector with negated components.

getNormalized

RVector RVector::getNormalized() const

const

Returns: A new unit vector with the same direction as this vector.

getRotated

RVector RVector::getRotated(double rotation, const RVector &center) const

const

Returns: A new vector equal to this vector rotated by rotation around center.

getScaled

RVector RVector::getScaled(const RVector &factors, const RVector &center) const

const

Returns: A new vector equal to this vector scaled by factors around center.

getSquaredMagnitude

double RVector::getSquaredMagnitude() const

const

Returns: Square of magnitude (length).

getTransformed

RVector RVector::getTransformed(const RMatrix &m) const

const

Returns: A new vector which is the result of this vector transformed by the given matrix.

getTransformed2D

RVector RVector::getTransformed2D(const QTransform &t) const

const

Returns: A new vector which is the result of this vector transformed by the given transformation matrix.

getTransformed2DM

RVector RVector::getTransformed2DM(const RMatrix &m) const

const

Returns: A new vector which is the result of this vector transformed by the given matrix.

getUnitVector

RVector RVector::getUnitVector() const

const

Returns: Unit vector for this vector.

getX

double RVector::getX() const

const

getY

double RVector::getY() const

const

getZ

double RVector::getZ() const

const

gteXY

bool RVector::gteXY(const RVector &v) const

inline const

isInside

bool RVector::isInside(const RBox &b) const

const

Returns: True if this vector is inside the given box, false otherwise.

isInWindow

bool RVector::isInWindow(const RVector &firstCorner, const RVector &secondCorner) const

const

Returns: true if this vector is within the given range (2d).

isNaN

bool RVector::isNaN() const

const

Returns: True if any component is NaN.

isoProject

RVector RVector::isoProject(RS::IsoProjectionType type)

Changes this vector into its isometric projection.

isSane

bool RVector::isSane() const

const

Returns: True if this vector is valid and all components are finite (not NaN or Inf).

isValid

bool RVector::isValid() const

const

Returns: True if this vector is valid (not explicitly marked invalid).

isZero

bool RVector::isZero() const

const

Returns: True if all components are within PointTolerance of zero.

lteXY

bool RVector::lteXY(const RVector &v) const

inline const

mirror

RVector RVector::mirror(const RLine &axis)

Mirrors this vector at the given axis.

mirror

RVector RVector::mirror(const RVector &axis1, const RVector &axis2)

Mirrors this vector at the axis defined by two points.

move

RVector RVector::move(const RVector &offset)

Moves this vector by the given offset.

Equal to the operator +=.

normalize

RVector RVector::normalize()

Normalizes this vector and returns a reference to this vector.

obliqueProjection

RVector RVector::obliqueProjection(RS::IsoProjectionType type)

operator!=

bool RVector::operator!=(const RVector &v) const

inline const

operator*

RVector RVector::operator*(double s) const

const

binary * operator.

operator*=

void RVector::operator*=(double s)

*= operator

operator+

RVector RVector::operator+(const RVector &v) const

const

binary + operator.

operator+=

void RVector::operator+=(const RVector &v)

+= operator.

The result is only valid if both vectors are valid.

operator-

RVector RVector::operator-() const

const

unary - operator.

operator-

RVector RVector::operator-(const RVector &v) const

const

binary - operator.

operator-=

void RVector::operator-=(const RVector &v)

-= operator.

The result is only valid if both vectors are valid.

operator/

RVector RVector::operator/(double s) const

const

binary / operator.

operator/=

void RVector::operator/=(double s)

/= operator

operator==

bool RVector::operator==(const RVector &v) const

const

== operator

rotate

RVector RVector::rotate(double rotation)

Rotates this vector around the origin by the given angle (in rad).

rotate

RVector RVector::rotate(double rotation, const RVector &center)

Rotates this vector around the given center by the given angle.

rotate3D

RVector RVector::rotate3D(const QQuaternion &quaternion)

Rotates this vector by the given quaternion.

rotate3D

RVector RVector::rotate3D(const RLine &axis, double rotation)

Rotates this vector around the given 3D axis line by the given angle (in rad).

The axis direction is taken as startPoint - endPoint.

scale

RVector RVector::scale(const RVector &factors, const RVector &center=nullVector)

Scales this vector by the given factors with the given center.

scale

RVector RVector::scale(double factor, const RVector &center=nullVector)

Scales this vector by the given factor with the given center.

set

void RVector::set(double vx, double vy, double vz=0.0)

inline

Sets new values for the vector and makes the vector valid.

setAngle

void RVector::setAngle(double a)

Sets the direction of this vector to the given angle (in rad), preserving its magnitude.

setMagnitude2D

void RVector::setMagnitude2D(double m)

Sets the vector magnitude without changing the direction.

setPolar

void RVector::setPolar(double radius, double angle)

Sets a new position for the vector in polar coordinates.

Parameters:

• radius: the radius or the distance
• angle: the angle in rad

setX

void RVector::setX(double x)

setY

void RVector::setY(double y)

setZ

void RVector::setZ(double z)

stretch

RVector RVector::stretch(const RPolyline &area, const RVector &offset)

Moves this vector by offset if it is inside the given area.

transform

RVector RVector::transform(const RMatrix &m)

Generic 3d transformation.

m must be a 3x3 matrix.

transform2D

RVector RVector::transform2D(const QTransform &t)

Transforms this vector with the given transformation matrix.

transform2DM

RVector RVector::transform2DM(const RMatrix &m)

Generic 2d transformation.

m must be a 3x2 matrix.

containsFuzzy

static bool RVector::containsFuzzy(const QList< RVector > &vectors, const RVector &v, double tol=RS::PointTolerance)

static

Returns: True if vectors contains a vector approximately equal to v within tol.

createPolar

static RVector RVector::createPolar(double radius, double angle)

static inline

findFirstFuzzy

static int RVector::findFirstFuzzy(const QList< RVector > &vectors, const RVector &v, double tol=RS::PointTolerance)

static

Returns: Index of the first vector in vectors approximately equal to v within tol, or -1 if not found.

getAverage

static RVector RVector::getAverage(const QList< RVector > &vectors)

static

Returns: The average (centroid) of the given vectors, or an invalid vector if the list is empty.

getAverage

static RVector RVector::getAverage(const RVector &v1, const RVector &v2)

static

Convenience function.

Returns: (v1 + v2) / 2.0

getCrossProduct

static RVector RVector::getCrossProduct(const RVector &v1, const RVector &v2)

static

Returns: Cross product of two vectors.

getDotProduct

static double RVector::getDotProduct(const RVector &v1, const RVector &v2)

static

Scalarproduct (dot product).

getIntersection

static QList< RVector > RVector::getIntersection(const QList< RVector > &vectorsA, const QList< RVector > &vectorsB, double tol=RS::PointTolerance)

static

Returns: Elements of vectorsA that also appear in vectorsB (fuzzy intersection).

getMaximum

static RVector RVector::getMaximum(const QList< RVector > &vectors)

static

Returns: A vector with the maximum components from the given vectors. These might be mixed components from all vectors.

getMaximum

static RVector RVector::getMaximum(const RVector &v1, const RVector &v2)

static

Returns: A vector with the maximum values from the vectors v1 and v2

getMaximumX

static RVector RVector::getMaximumX(const QList< RVector > &vectors)

static

Returns: That one vector from the given vectors with the largest X coordinate.

getMaximumY

static RVector RVector::getMaximumY(const QList< RVector > &vectors)

static

Returns: That one vector from the given vectors with the largest Y coordinate.

getMinimum

static RVector RVector::getMinimum(const QList< RVector > &vectors)

static

Returns: A vector with the minimum components from the given vectors. These might be mixed components from all vectors.

getMinimum

static RVector RVector::getMinimum(const RVector &v1, const RVector &v2)

static

Returns: A vector with the minimum components from the vectors v1 and v2. These might be mixed components from both vectors.

getMinimumX

static RVector RVector::getMinimumX(const QList< RVector > &vectors)

static

Returns: That one vector from the given vectors with the smallest X coordinate.

getMinimumY

static RVector RVector::getMinimumY(const QList< RVector > &vectors)

static

Returns: That one vector from the given vectors with the smallest Y coordinate.

getSortedByAngle

static QList< RVector > RVector::getSortedByAngle(const QList< RVector > &list, const RVector &center, double angle)

static

Returns: List of same vectors as given, ordered by shortest angle difference to given reference angle.

getSortedByDistance

static QList< RVector > RVector::getSortedByDistance(const QList< RVector > &list, const RVector &v)

static

Returns: List of same vectors as given, ordered by shortes distance to given vector v.

getSortedLeftRightTopBottom

static QList< RVector > RVector::getSortedLeftRightTopBottom(const QList< RVector > &list)

static

Returns: List of same vectors as given, ordered from left to right, top to bottom.

getUnique

static QList< RVector > RVector::getUnique(const QList< RVector > &vectors, double tol=RS::PointTolerance)

static

Returns: A copy of vectors with duplicate entries (within tol) removed, preserving the order of first occurrence.

getXList

static QList< double > RVector::getXList(const QList< RVector > &vectors)

static

Returns: All X values of the given list of vectors as a new list.

getYList

static QList< double > RVector::getYList(const QList< RVector > &vectors)

static

Returns: All Y values of the given list of vectors as a new list.

getZList

static QList< double > RVector::getZList(const QList< RVector > &vectors)

static

Returns: All Z values of the given list of vectors as a new list.

greaterThanEqualXY

static bool RVector::greaterThanEqualXY(const RVector &v1, const RVector &v2)

static inline

greaterThanX

static bool RVector::greaterThanX(const RVector &v1, const RVector &v2)

static inline

greaterThanY

static bool RVector::greaterThanY(const RVector &v1, const RVector &v2)

static inline

lessThanEqualXY

static bool RVector::lessThanEqualXY(const RVector &v1, const RVector &v2)

static inline

lessThanX

static bool RVector::lessThanX(const RVector &v1, const RVector &v2)

static inline

lessThanY

static bool RVector::lessThanY(const RVector &v1, const RVector &v2)

static inline

moveList

static void RVector::moveList(QList< RVector > &list, const RVector &offset)

static

Moves all vectors in the list by the given offset.

Non-Scriptable: This function is not available in script environments.

rotateList

static void RVector::rotateList(QList< RVector > &list, double rotation)

static

Rotates all vectors in the list around the origin by the given angle (in rad).

Non-Scriptable: This function is not available in script environments.

rotateList

static void RVector::rotateList(QList< RVector > &list, double rotation, const RVector &center)

static

Rotates all vectors in the list around center by the given angle (in rad).

Non-Scriptable: This function is not available in script environments.

scaleList

static void RVector::scaleList(QList< RVector > &list, const RVector &factors, const RVector &center=nullVector)

static

Scales all vectors in the list by the given per-axis factors around center.

Non-Scriptable: This function is not available in script environments.

scaleList

static void RVector::scaleList(QList< RVector > &list, double factor, const RVector &center=nullVector)

static

Scales all vectors in the list by the given uniform factor around center.

Non-Scriptable: This function is not available in script environments.

valid

bool RVector::valid

Getter function for this property: isValid.

x

double RVector::x

Getter function for this property: getX.

Setter function for this property: setX

y

double RVector::y

Getter function for this property: getY.

Setter function for this property: setY

z

double RVector::z

Getter function for this property: getZ.

Setter function for this property: setZ

invalid

static const RVector RVector::invalid = RVector(0, 0, 0, false)

static

invalid vector

nanVector

static const RVector RVector::nanVector = RVector(RNANDOUBLE, RNANDOUBLE, RNANDOUBLE, true)

static

NaN vector.

nullVector

static const RVector RVector::nullVector = RVector(0, 0, 0, true)

static

null vector

zAxis

static const RVector RVector::zAxis = RVector(0, 0, 1, true)

static

Z axis vector (default extrusion direction).