RArc

Class in Math Module
Header: #include <src/core/math/RArc.h>
Inherits: RShape
Inherited by: RArcData

Description

Low-level mathematical representation of an arc.

Scriptable: This class is available in script environments.

Shared Pointer Support: Objects can be used in QSharedPointer.

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

Stream Operator: Object has a stream operator to present itself as string, for example when using toString() in a script.

Public Functions


	RArc`()` Creates an arc shape with an invalid center.
	RArc`(const RVector &center, double radius, double startAngle, double endAngle, bool reversed=false)` Creates an arc from a center point, radius, start/end angles (in rad) and direction.
	RArc`(double cx, double cy, double radius, double startAngle, double endAngle, bool reversed=false)` Creates an arc from center coordinates, radius, start/end angles (in rad) and direction.
RPolyline	approximateWithLines`(double segmentLength, double angle=0.0) const`
RPolyline	approximateWithLinesTan`(double segmentLength, double angle=0.0) const`
virtual QSharedPointer< RShape >	clone`() const`
QSharedPointer< RArc >	cloneToArc`() const`
virtual double	getAngleAt`(double distance, RS::From from=RS::FromStart) const`
double	getAngleLength`(bool allowForZeroLength=false) const`
virtual QList< RVector >	getArcReferencePoints`() const`
double	getArea`() const`
virtual QList< bool >	getBoolProperties`() const`
virtual RBox	getBoundingBox`() const`
double	getBulge`() const`
RVector	getCenter`() const`
virtual QList< RVector >	getCenterPoints`() const`
double	getChordArea`() const`
double	getDiameter`() const`
virtual double	getDirection1`() const`
virtual double	getDirection2`() const`
virtual double	getDistanceFromStart`(const RVector &p) const`
virtual QList< double >	getDoubleProperties`() const`
double	getEndAngle`() const`
virtual RVector	getEndPoint`() const`
virtual QList< RVector >	getEndPoints`() const`
virtual double	getLength`() const`
virtual RVector	getMiddlePoint`() const`
virtual QList< RVector >	getMiddlePoints`() const`
virtual QList< QSharedPointer< RShape > >	getOffsetShapes`(double distance, int number, RS::Side side, const RVector &position=RVector::invalid)`
RVector	getPointAtAngle`(double a) const`
virtual QList< RVector >	getPointCloud`(double segmentLength) const`
virtual QList< RVector >	getPointsWithDistanceToEnd`(double distance, int from=RS::FromAny) const`
double	getRadius`() const`
virtual RShape::Type	getShapeType`() const`
virtual RS::Side	getSideOfPoint`(const RVector &point) const`
double	getStartAngle`() const`
virtual RVector	getStartPoint`() const`
double	getSweep`() const`
QList< RLine >	getTangents`(const RVector &point) const`
virtual QSharedPointer< RShape >	getTransformed`(const QTransform &transform) const`
virtual RS::Ending	getTrimEnd`(const RVector &trimPoint, const RVector &clickPoint)`
virtual QList< RVector >	getVectorProperties`() const`
virtual RVector	getVectorTo`(const RVector &point, bool limited=true, double strictRange=RMAXDOUBLE) const`
bool	isAngleWithinArc`(double a) const`
virtual bool	isDirected`() const`
bool	isFullCircle`(double tolerance=RS::AngleTolerance) const`
bool	isReversed`() const`
virtual bool	isValid`() const`
virtual bool	mirror`(const RLine &axis)` Mirrors the arc about `axis`.
virtual bool	move`(const RVector &offset)` Moves the arc by `offset`.
void	moveEndPoint`(const RVector &pos, bool keepRadius=true)` Moves the end point of the arc, optionally keeping the radius.
void	moveMiddlePoint`(const RVector &pos)` Moves the midpoint of the arc to `pos` by reconstructing from current start/end and the new middle point.
void	moveStartPoint`(const RVector &pos, bool keepRadius=true)` Moves the start point of the arc, optionally keeping the radius.
virtual bool	reverse`()` Reverses the arc direction by swapping start/end angles and toggling the reversed flag.
virtual bool	rotate`(double rotation, const RVector &center=RDEFAULT_RVECTOR)` Rotates the arc around `c` by `rotation` radians.
virtual bool	scale`(const RVector &scaleFactors, const RVector &center=RDEFAULT_RVECTOR)` Scales the arc by `scaleFactors` relative to `c`.
void	setArea`(double a)` Sets the arc sweep angle by adjusting the end angle to match the given sector area.
void	setCenter`(const RVector &vector)` Sets the center point of the arc.
void	setDiameter`(double d)` Sets the radius from a diameter value.
void	setEndAngle`(double endAngle)` Sets the end angle, normalizing it to [0, 2π).
void	setLength`(double l)` Sets the arc length by adjusting the end angle (keeping start angle and radius).
void	setRadius`(double radius)` Sets the radius of the arc.
void	setReversed`(bool reversed)` Sets the arc direction: true = clockwise, false = counter-clockwise.
void	setStartAngle`(double startAngle)` Sets the start angle, normalizing it to [0, 2π).
void	setSweep`(double s)` Sets the sweep angle (end = start + s); sets reversed if s < 0.
virtual void	setZ`(double z)` Sets the Z coordinate of the center point.
virtual QList< QSharedPointer< RShape > >	splitAt`(const QList< RVector > &points) const` Splits this arc at the given `points` (sorted by angle from start).
QList< RArc >	splitAtQuadrantLines`() const`
virtual bool	stretch`(const RPolyline &area, const RVector &offset)` Stretches the arc by moving endpoint(s) inside `area` by `offset`.
virtual bool	trimEndPoint`(const RVector &trimPoint, const RVector &clickPoint=RVector::invalid, bool extend=false)` Trims the end of the arc to the angle corresponding to `trimPoint`.
virtual bool	trimEndPoint`(double trimDist)`
virtual bool	trimStartPoint`(const RVector &trimPoint, const RVector &clickPoint=RVector::invalid, bool extend=false)` Trims the start of the arc to the angle corresponding to `trimPoint`.
virtual bool	trimStartPoint`(double trimDist)`

Static Public Functions


static QList< RArc >	createBiarc`(const RVector &startPoint, double startDirection, const RVector &endPoint, double endDirection, bool secondTry=false)` Creates a biarc (pair of two arcs) with the given conditions.
static RArc	createFrom2PBulge`(const RVector &startPoint, const RVector &endPoint, double bulge)` Creates an arc from its startpoint, endpoint and bulge (= tan(angle/4)).
static RArc	createFrom3Points`(const RVector &startPoint, const RVector &point, const RVector &endPoint)` Creates an arc from 3 points.
static RArc	createTangential`(const RVector &startPoint, const RVector &pos, double direction, double radius=0.0, double sweep=0.0)` Creates an arc tangent to a given direction at `startPoint`, passing near `pos`.
static RArcProxy *	getArcProxy`()`
static bool	hasProxy`()`
static void	setArcProxy`(RArcProxy *p)`

Public Attributes


RVector	center Getter function for this property: getCenter.
double	endAngle Getter function for this property: getEndAngle.
double	radius Getter function for this property: getRadius.
bool	reversed Getter function for this property: isReversed.
double	startAngle Getter function for this property: getStartAngle.

Protected Functions


virtual void	print`(QDebug dbg) const` Prints arc properties to `dbg` for debugging.

Static Private Attributes


static RArcProxy *	arcProxy

Member Documentation

RArc

RArc::RArc()

Creates an arc shape with an invalid center.

RArc

RArc::RArc(const RVector &center, double radius, double startAngle, double endAngle, bool reversed=false)

Creates an arc from a center point, radius, start/end angles (in rad) and direction.

RArc

RArc::RArc(double cx, double cy, double radius, double startAngle, double endAngle, bool reversed=false)

Creates an arc from center coordinates, radius, start/end angles (in rad) and direction.

approximateWithLines

RPolyline RArc::approximateWithLines(double segmentLength, double angle=0.0) const

const

Returns: Polyline approximation of arc with line segments of given length or (if length is 0) given angle. Polyline is on the inside of the arc.

approximateWithLinesTan

RPolyline RArc::approximateWithLinesTan(double segmentLength, double angle=0.0) const

const

Returns: Polyline approximation of arc with line segments of given length or (if length is 0) given angle. Polyline is on the outside of the arc.

clone

virtual QSharedPointer< RShape > RArc::clone() const

virtual inline const

Reimplemented from clone.

cloneToArc

QSharedPointer< RArc > RArc::cloneToArc() const

inline const

getAngleAt

virtual double RArc::getAngleAt(double distance, RS::From from=RS::FromStart) const

virtual const

Returns: Tangent direction angle at the point on the arc at the given arc-length distance from the start or end. Returns RNANDOUBLE if no such point exists.

Reimplemented from getAngleAt.

getAngleLength

double RArc::getAngleLength(bool allowForZeroLength=false) const

const

Returns: Angle length in rad.

Parameters:

allowForZeroLength: Allow for zero length result if start and end angle are the same. Otherwise 2*PI will be returned for such an arc, assuming it is a full circle.

getArcReferencePoints

virtual QList< RVector > RArc::getArcReferencePoints() const

virtual const

Returns: The quadrant extremes (0°, 90°, 180°, 270° points on the circle) that lie within the arc. Used as snappable reference points.

Reimplemented from getArcReferencePoints.

getArea

double RArc::getArea() const

const

Returns: Area of the circular sector (pie slice) defined by this arc.

getBoolProperties

virtual QList< bool > RArc::getBoolProperties() const

virtual const

Returns: List of boolean properties: reversed.

Reimplemented from getBoolProperties.

getBoundingBox

virtual RBox RArc::getBoundingBox() const

virtual const

Returns: Axis-aligned bounding box of this arc. Checks which of the four quadrant extremes (0°, 90°, 180°, 270°) lie within the arc and expands the box accordingly.

Reimplemented from getBoundingBox.

getBulge

double RArc::getBulge() const

const

Returns: Bulge value (tan(sweep/4)), negative for clockwise arcs. Used in DXF/DWG polyline vertex encoding.

getCenter

RVector RArc::getCenter() const

const

Returns: Center point of the arc.

getCenterPoints

virtual QList< RVector > RArc::getCenterPoints() const

virtual const

Returns: List containing the center point of the arc.

Reimplemented from getCenterPoints.

getChordArea

double RArc::getChordArea() const

const

Returns: Area of the circular segment bounded by the arc and its chord (the region between the arc and the straight line connecting start and end point).

Derivation: segment = sector − isosceles_triangle(center, p1, p2) sector area = r²θ/2 triangle area = r²sin(θ)/2 → segment = r²(θ − sin θ)/2

This formula is correct for all arc angles (minor, major, full circle).

getDiameter

double RArc::getDiameter() const

const

Returns: Diameter (2 * radius).

getDirection1

virtual double RArc::getDirection1() const

virtual const

Returns: Tangent direction at the start point (in rad): perpendicular to the radius, pointing in the direction of travel.

Reimplemented from getDirection1.

Reimplemented in getDirection1.

getDirection2

virtual double RArc::getDirection2() const

virtual const

Returns: Tangent direction at the end point (in rad), pointing away from the arc.

Reimplemented from getDirection2.

Reimplemented in getDirection2.

getDistanceFromStart

virtual double RArc::getDistanceFromStart(const RVector &p) const

virtual const

Returns: Arc-length distance from the start point to the projection of p onto the arc’s circle (i.e. the point at the angle from center to p).

Reimplemented from getDistanceFromStart.

getDoubleProperties

virtual QList< double > RArc::getDoubleProperties() const

virtual const

Returns: List of scalar properties: radius, startAngle, endAngle.

Reimplemented from getDoubleProperties.

getEndAngle

double RArc::getEndAngle() const

const

Returns: End angle in radians (normalized to [0, 2π)).

getEndPoint

virtual RVector RArc::getEndPoint() const

virtual const

Returns: End point of the arc.

Reimplemented from getEndPoint.

getEndPoints

virtual QList< RVector > RArc::getEndPoints() const

virtual const

Returns: List containing the start and end points of the arc.

Reimplemented from getEndPoints.

getLength

virtual double RArc::getLength() const

virtual const

Returns: Arc length (angle length * radius).

Reimplemented from getLength.

Reimplemented in getLength.

getMiddlePoint

virtual RVector RArc::getMiddlePoint() const

virtual const

Returns: Point at the midpoint of the arc (halfway along the sweep).

Reimplemented from getMiddlePoint.

getMiddlePoints

virtual QList< RVector > RArc::getMiddlePoints() const

virtual const

Returns: List containing the midpoint of the arc.

Reimplemented from getMiddlePoints.

getOffsetShapes

virtual QList< QSharedPointer< RShape > > RArc::getOffsetShapes(double distance, int number, RS::Side side, const RVector &position=RVector::invalid)

virtual inline

Returns: Parallels to this shape.

Parameters:

distance: Distance of first parallel or concentric arc or circle.
number: Number of offset shapes to generate.
side: Side, should be RS.LeftHand or RS.RightHand or RS.BothSides.
sidePosition: Position indicating what side of the shape the parallels should be.

Reimplemented from getOffsetShapes.

getPointAtAngle

RVector RArc::getPointAtAngle(double a) const

const

Returns: Point on the arc at the given angle a (in radians).

getPointCloud

virtual QList< RVector > RArc::getPointCloud(double segmentLength) const

virtual const

Returns: Dense set of points sampling the arc. Combines vertices from both the inscribed and circumscribed polyline approximations.

Reimplemented from getPointCloud.

getPointsWithDistanceToEnd

virtual QList< RVector > RArc::getPointsWithDistanceToEnd(double distance, int from=RS::FromAny) const

virtual const

Returns: Point(s) on the arc at arc-length distance from the start and/or end, controlled by the from bitmask (RS::FromStart, RS::FromEnd, RS::FromAny).

Reimplemented from getPointsWithDistanceToEnd.

getRadius

double RArc::getRadius() const

const

Returns: Radius of the arc.

getShapeType

virtual RShape::Type RArc::getShapeType() const

virtual inline const

Reimplemented from getShapeType.

getSideOfPoint

virtual RS::Side RArc::getSideOfPoint(const RVector &point) const

virtual const

Returns: Which side of the arc the given point is on. A point inside the circle is on the left for CCW arcs, right for CW arcs.

Reimplemented from getSideOfPoint.

getStartAngle

double RArc::getStartAngle() const

const

Returns: Start angle in radians (normalized to [0, 2π)).

getStartPoint

virtual RVector RArc::getStartPoint() const

virtual const

Returns: Start point of the arc.

Reimplemented from getStartPoint.

getSweep

double RArc::getSweep() const

const

Returns: Arc sweep in rad. The sweep is the angle covered by this arc. Positive for ccw, negative for cw.

getTangents

QList< RLine > RArc::getTangents(const RVector &point) const

const

Returns: The tangent lines from the external point to this arc’s circle. Delegates to RCircle::getTangents.

getTransformed

virtual QSharedPointer< RShape > RArc::getTransformed(const QTransform &transform) const

virtual const

Reimplemented from getTransformed.

getTrimEnd

virtual RS::Ending RArc::getTrimEnd(const RVector &trimPoint, const RVector &clickPoint)

virtual

Returns: Which end of the arc is closer to clickPoint relative to trimPoint. Used to decide which end to trim when the user clicks near a trim point.

Reimplemented from getTrimEnd.

Reimplemented in getTrimEnd.

getVectorProperties

virtual QList< RVector > RArc::getVectorProperties() const

virtual const

Returns: List containing the center point (used for property-based transformations).

Reimplemented from getVectorProperties.

getVectorTo

virtual RVector RArc::getVectorTo(const RVector &point, bool limited=true, double strictRange=RMAXDOUBLE) const

virtual const

Returns: Vector from the nearest point on the arc to point, or RVector::invalid if limited is true and the projection falls outside the arc span. Note: strictRange is not implemented.

Reimplemented from getVectorTo.

Reimplemented in getVectorTo.

isAngleWithinArc

bool RArc::isAngleWithinArc(double a) const

inline const

isDirected

virtual bool RArc::isDirected() const

virtual inline const

Reimplemented from isDirected.

isFullCircle

bool RArc::isFullCircle(double tolerance=RS::AngleTolerance) const

const

Returns: True if the start and end angles are equal within tolerance, indicating that this arc spans a full circle.

isReversed

bool RArc::isReversed() const

const

Returns: True if the arc is clockwise (reversed).

isValid

virtual bool RArc::isValid() const

virtual const

Returns: True if the center is valid and the radius is positive.

Reimplemented from isValid.

Reimplemented in isValid.

mirror

virtual bool RArc::mirror(const RLine &axis)

virtual

Mirrors the arc about axis.

Reverses the arc direction and reflects the start/end angles. Full circles only need their center mirrored.

Reimplemented from mirror.

Reimplemented in mirror.

move

virtual bool RArc::move(const RVector &offset)

virtual

Moves the arc by offset.

Returns false if the offset is invalid or negligibly small. Uses squared magnitude to avoid a sqrt call; tolerance is squared accordingly.

Reimplemented from move.

Reimplemented in move.

moveEndPoint

void RArc::moveEndPoint(const RVector &pos, bool keepRadius=true)

Moves the end point of the arc, optionally keeping the radius.

If keepRadius is true and the arc is not a full circle, the arc is reconstructed from the current start point and the new end point with the same bulge. If keepRadius is false, the arc is reconstructed from the current start point, the current middle point and the new end point.

moveMiddlePoint

void RArc::moveMiddlePoint(const RVector &pos)

Moves the midpoint of the arc to pos by reconstructing from current start/end and the new middle point.

moveStartPoint

void RArc::moveStartPoint(const RVector &pos, bool keepRadius=true)

Moves the start point of the arc, optionally keeping the radius.

If keepRadius is true and the arc is not a full circle, the arc is reconstructed from the new start point and the current end point with the same bulge. If keepRadius is false, the arc is reconstructed from the new start point, the current middle point and end point.

reverse

virtual bool RArc::reverse()

virtual

Reverses the arc direction by swapping start/end angles and toggling the reversed flag.

Reimplemented from reverse.

Reimplemented in reverse.

rotate

virtual bool RArc::rotate(double rotation, const RVector &center=RDEFAULT_RVECTOR)

virtual

Rotates the arc around c by rotation radians.

Skips angle update for full circles.

Reimplemented from rotate.

Reimplemented in rotate.

scale

virtual bool RArc::scale(const RVector &scaleFactors, const RVector &center=RDEFAULT_RVECTOR)

virtual

Scales the arc by scaleFactors relative to c.

Negative scale factors are decomposed into a mirror plus a positive scale. Only uniform XY scaling is supported for the radius (scaleFactors.x is used).

Reimplemented from scale.

Reimplemented in scale.

setArea

void RArc::setArea(double a)

Sets the arc sweep angle by adjusting the end angle to match the given sector area.

setCenter

void RArc::setCenter(const RVector &vector)

Sets the center point of the arc.

setDiameter

void RArc::setDiameter(double d)

Sets the radius from a diameter value.

setEndAngle

void RArc::setEndAngle(double endAngle)

Sets the end angle, normalizing it to [0, 2π).

setLength

void RArc::setLength(double l)

Sets the arc length by adjusting the end angle (keeping start angle and radius).

setRadius

void RArc::setRadius(double radius)

Sets the radius of the arc.

setReversed

void RArc::setReversed(bool reversed)

Sets the arc direction: true = clockwise, false = counter-clockwise.

setStartAngle

void RArc::setStartAngle(double startAngle)

Sets the start angle, normalizing it to [0, 2π).

setSweep

void RArc::setSweep(double s)

Sets the sweep angle (end = start + s); sets reversed if s < 0.

setZ

virtual void RArc::setZ(double z)

virtual

Sets the Z coordinate of the center point.

Reimplemented from setZ.

Reimplemented in setZ.

splitAt

virtual QList< QSharedPointer< RShape > > RArc::splitAt(const QList< RVector > &points) const

virtual const

Splits this arc at the given points (sorted by angle from start).

Reversed arcs are temporarily flipped, split, then the result list is reversed.

Reimplemented from splitAt.

splitAtQuadrantLines

QList< RArc > RArc::splitAtQuadrantLines() const

const

Returns: This arc split at the quadrant angles (0°, 90°, 180°, 270°) that lie within the arc span. Useful for bounding-box calculations.

stretch

virtual bool RArc::stretch(const RPolyline &area, const RVector &offset)

virtual

Stretches the arc by moving endpoint(s) inside area by offset.

If both endpoints are inside, the whole arc is moved.

Reimplemented from stretch.

Reimplemented in stretch.

trimEndPoint

virtual bool RArc::trimEndPoint(const RVector &trimPoint, const RVector &clickPoint=RVector::invalid, bool extend=false)

virtual

Trims the end of the arc to the angle corresponding to trimPoint.

Reimplemented from trimEndPoint.

Reimplemented in trimEndPoint.

trimEndPoint

virtual bool RArc::trimEndPoint(double trimDist)

virtual inline

Reimplemented from trimEndPoint.

trimStartPoint

virtual bool RArc::trimStartPoint(const RVector &trimPoint, const RVector &clickPoint=RVector::invalid, bool extend=false)

virtual

Trims the start of the arc to the angle corresponding to trimPoint.

Reimplemented from trimStartPoint.

Reimplemented in trimStartPoint.

trimStartPoint

virtual bool RArc::trimStartPoint(double trimDist)

virtual inline

Reimplemented from trimStartPoint.

createBiarc

static QList< RArc > RArc::createBiarc(const RVector &startPoint, double startDirection, const RVector &endPoint, double endDirection, bool secondTry=false)

static

Creates a biarc (pair of two arcs) with the given conditions.

createFrom2PBulge

static RArc RArc::createFrom2PBulge(const RVector &startPoint, const RVector &endPoint, double bulge)

static

Creates an arc from its startpoint, endpoint and bulge (= tan(angle/4)).

createFrom3Points

static RArc RArc::createFrom3Points(const RVector &startPoint, const RVector &point, const RVector &endPoint)

static

Creates an arc from 3 points.

createTangential

static RArc RArc::createTangential(const RVector &startPoint, const RVector &pos, double direction, double radius=0.0, double sweep=0.0)

static

Creates an arc tangent to a given direction at startPoint, passing near pos.

Delegates to the arc proxy if available.

getArcProxy

static RArcProxy * RArc::getArcProxy()

static inline

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

hasProxy

static bool RArc::hasProxy()

static inline

setArcProxy

static void RArc::setArcProxy(RArcProxy *p)

static inline

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

center

RVector RArc::center

Getter function for this property: getCenter.

Setter function for this property: setCenter

endAngle

double RArc::endAngle

Getter function for this property: getEndAngle.

Setter function for this property: setEndAngle

radius

double RArc::radius

Getter function for this property: getRadius.

Setter function for this property: setRadius

reversed

bool RArc::reversed

Getter function for this property: isReversed.

Setter function for this property: setReversed

startAngle

double RArc::startAngle

Getter function for this property: getStartAngle.

Setter function for this property: setStartAngle

print

virtual void RArc::print(QDebug dbg) const

virtual const protected

Prints arc properties to dbg for debugging.

Reimplemented from print.

arcProxy

static RArcProxy * RArc::arcProxy = NULL

static private

This file is part of the QCAD project.

QCAD is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

QCAD is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with QCAD.