Inkscape: Geom::Line Class Reference

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Infinite line on a plane. More...

#include <line.h>

Inheritance diagram for Geom::Line:

Public Member Functions
std::vector< ShapeIntersection >	intersect (Line const &other) const

std::vector< ShapeIntersection >	intersect (Ray const &r) const

std::vector< ShapeIntersection >	intersect (LineSegment const &ls) const

template<typename T >
Line &	operator*= (T const &tr)

bool	operator== (Line const &other) const

Retrieve and set the line's parameters.
Point	origin () const
	Get the line's origin point.

Point	vector () const
	Get the line's raw direction vector.

Point	versor () const
	Get the line's normalized direction vector.

Coord	angle () const
	Angle the line makes with the X axis, in mathematical convention.

void	setOrigin (Point const &p)
	Set the point at zero time.

void	setVector (Point const &v)
	Set the speed of the line.

void	setAngle (Coord angle)
	Set the angle the line makes with the X axis.

void	setPoints (Point const &a, Point const &b)
	Set a line based on two points it should pass through.

void	setCoefficients (double a, double b, double c)
	Set the coefficients of the line equation.

std::vector< double >	coefficients () const
	Get the coefficients of the line equation as a vector.

void	coefficients (Coord &a, Coord &b, Coord &c) const
	Get the coefficients of the line equation by reference.

bool	isDegenerate () const
	Check if the line has more than one point.

bool	isHorizontal () const
	Check if the line is horizontal (y is constant).

bool	isVertical () const
	Check if the line is vertical (x is constant).

void	normalize ()
	Reparametrize the line so that it has unit speed.

Line	normalized () const
	Return a new line reparametrized for unit speed.

Evaluate the line as a function.
Point	initialPoint () const

Point	finalPoint () const

Point	pointAt (Coord t) const

Coord	valueAt (Coord t, Dim2 d) const

Coord	timeAt (Point const &p) const
	Get a time value corresponding to a point.

Coord	timeAtProjection (Point const &p) const
	Get a time value corresponding to a projection of a point on the line.

Coord	nearestTime (Point const &p) const
	Find a point on the line closest to the query point.

std::vector< Coord >	roots (Coord v, Dim2 d) const
	Find intersection with an axis-aligned line.

Coord	root (Coord v, Dim2 d) const

Create other objects based on this line.
void	reverse ()

Line	reversed () const
	Create a line containing the same points, but in opposite direction.

Curve *	portion (Coord f, Coord t) const
	Same as segment(), but allocate the line segment dynamically.

LineSegment	segment (Coord f, Coord t) const
	Create a segment of this line.

std::optional< LineSegment >	clip (Rect const &r) const
	Return the portion of the line that is inside the given rectangle.

Ray	ray (Coord t)
	Create a ray starting at the specified time value.

Line	derivative () const
	Create a derivative of the line.

Line	transformed (Affine const &m) const
	Create a line transformed by an affine transformation.

Point	normal () const
	Get a unit vector normal to the line.

Point	normalAndDist (double &dist) const

Affine	reflection () const
	Compute an affine matrix representing a reflection about the line.

Affine	rotationToZero (Dim2 d) const
	Compute an affine which transforms all points on the line to zero X or Y coordinate.

Affine	rotationToAxis (Dim2 d) const
	Compute a rotation affine which transforms the line to one of the axes.

Affine	transformTo (Line const &other) const
	Create a transformation that maps one line to another.

Private Attributes
Point	_initial

Point	_final

Friends
template<typename T >
Line	operator* (Line const &l, T const &tr)

Related Symbols
(Note that these are not member symbols.)
double	distance (Point const &p, Line const &line)
	Compute distance from point to line.

bool	are_same (Line const &l1, Line const &l2, double eps=EPSILON)
	Test whether two lines are approximately the same.

bool	are_orthogonal (Line const &l1, Line const &l2, double eps=EPSILON)
	Test whether two lines are perpendicular.

Creating lines.
	Line ()
	Create a default horizontal line.

	Line (Point const &origin, Coord angle)
	Create a line with the specified inclination.

	Line (Point const &a, Point const &b)
	Create a line going through two points.

	Line (double a, double b, double c)
	Create a line based on the coefficients of its equation.

	Line (LineSegment const &seg)
	Create a line by extending a line segment.

	Line (Ray const &r)
	Create a line by extending a ray.

Line *	duplicate () const

static Line	from_normal_distance (Point const &n, Coord c)
	Create a line normal to a vector at a specified distance from origin.

static Line	from_origin_and_vector (Point const &o, Point const &v)
	Create a line from origin and unit vector.

Detailed Description

Infinite line on a plane.

A line is specified as two points through which it passes. Lines can be interpreted as functions \( f: (-\infty, \infty) \to \mathbb{R}^2\). Zero corresponds to the first (origin) point, one corresponds to the second (final) point. All other points are computed as a linear interpolation between those two: \(p = (1-t) a + t b\). Many such functions have the same image and therefore represent the same lines; for example, adding \(b-a\) to both points yields the same line.

2Geom can represent the same line in many ways by design: using a different representation would lead to precision loss. For example, a line from (1e30, 1e30) to (10,0) would actually evaluate to (0,0) at time 1 if it was stored as origin and normalized versor, or origin and angle.

Definition at line 51 of file line.h.

Constructor & Destructor Documentation

◆ Line() [1/6]

Geom::Line::Line ( )

inline

Create a default horizontal line.

Creates a line with unit speed going in +X direction.

Definition at line 62 of file line.h.

Referenced by duplicate().

◆ Line() [2/6]

Geom::Line::Line	(	Point const &	origin,
		Coord	angle
	)

inline

Create a line with the specified inclination.

Parameters

origin	One of the points on the line
angle	Angle of the line in mathematical convention

Definition at line 68 of file line.h.

References _final, _initial, angle(), Geom::sincos(), Geom::X, and Geom::Y.

◆ Line() [3/6]

Geom::Line::Line	(	Point const &	a,
		Point const &	b
	)

inline

Create a line going through two points.

The first point will be at time 0, while the second one will be at time 1.

Parameters

a	Initial point
b	First point

Definition at line 81 of file line.h.

◆ Line() [4/6]

Geom::Line::Line	(	double	a,
		double	b,
		double	c
	)

inline

Create a line based on the coefficients of its equation.

See also: Line::setCoefficients()

Definition at line 88 of file line.h.

References c, and setCoefficients().

◆ Line() [5/6]

Geom::Line::Line ( LineSegment const & seg )

inlineexplicit

Create a line by extending a line segment.

Definition at line 93 of file line.h.

◆ Line() [6/6]

Geom::Line::Line ( Ray const & r )

inlineexplicit

Create a line by extending a ray.

Definition at line 99 of file line.h.

Member Function Documentation

◆ angle()

Coord Geom::Line::angle ( ) const

inline

Angle the line makes with the X axis, in mathematical convention.

Definition at line 137 of file line.h.

References _final, _initial, Geom::X, and Geom::Y.

Referenced by Geom::xAx::axis_angle(), Inkscape::LivePathEffect::LPEMirrorSymmetry::doEffect_path(), Line(), setAngle(), sp_gradient_reset_to_userspace(), Inkscape::LivePathEffect::LPESlice::splititem(), and TEST().

◆ clip()

std::optional< LineSegment > Geom::Line::clip ( Rect const & r ) const

Return the portion of the line that is inside the given rectangle.

Definition at line 151 of file line.cpp.

References _initial, Geom::GenericRect< C >::clamp(), Geom::contains(), Geom::Interval::isFinite(), Geom::GenericRect< C >::max(), Geom::max(), Geom::GenericRect< C >::min(), Geom::min(), Geom::other_dimension(), pointAt(), result, root, vector(), Geom::X, and Geom::Y.

Referenced by Geom::clip(), Inkscape::LivePathEffect::LPELineSegment::doEffect_path(), draw_line(), and Geom::intersection().

◆ coefficients() [1/2]

std::vector< Coord > Geom::Line::coefficients ( ) const

Get the coefficients of the line equation as a vector.

Get the implicit line equation coefficients.

Returns: STL vector v such that v[0] contains \(a\), v[1] contains \(b\), and v[2] contains \(c\).

Note that conversion to implicit form always causes loss of precision when dealing with lines that start far from the origin and end very close to it. It is recommended to normalize the line before converting it to implicit form.

Returns: Vector with three values corresponding to the A, B and C coefficients of the line equation for this line.

Definition at line 120 of file line.cpp.

References c, and coefficients().

Referenced by coefficients(), draw_line(), Geom::Ellipse::intersect(), Geom::xAx::set(), Geom::xAx::set(), Geom::detail::bezier_clipping::signed_distance(), and TEST().

◆ coefficients() [2/2]

void Geom::Line::coefficients	(	Coord &	a,
		Coord &	b,
		Coord &	c
	)		const

Get the coefficients of the line equation by reference.

Definition at line 105 of file line.cpp.

References _final, _initial, c, Geom::cross(), Geom::Point::cw(), vector(), Geom::X, and Geom::Y.

◆ derivative()

Line Geom::Line::derivative ( ) const

inline

Create a derivative of the line.

The new line will always be degenerate. Its origin will be equal to this line's vector.

Definition at line 305 of file line.h.

References result, and vector().

Referenced by wrap_line().

◆ duplicate()

Line * Geom::Line::duplicate ( ) const

inline

Definition at line 119 of file line.h.

References Line().

◆ finalPoint()

Point Geom::Line::finalPoint ( ) const

inline

Definition at line 228 of file line.h.

References _final.

Referenced by Geom::bezier_line_intersections(), Geom::Circle::intersect(), Geom::Circle::intersects(), Inkscape::UI::Widget::line_angle(), and Inkscape::LivePathEffect::LPESlice::splititem().

◆ from_normal_distance()

static Line Geom::Line::from_normal_distance	(	Point const &	n,
		Coord	c
	)

inlinestatic

Create a line normal to a vector at a specified distance from origin.

Definition at line 105 of file line.h.

References c, Geom::rot90(), and start.

◆ from_origin_and_vector()

static Line Geom::Line::from_origin_and_vector	(	Point const &	o,
		Point const &	v
	)

inlinestatic

Create a line from origin and unit vector.

Note that each line direction has two possible unit vectors.

Parameters

o	Point through which the line will pass
v	Unit vector of the line's direction

Definition at line 114 of file line.h.

Referenced by Inkscape::CanvasItemGridXY::_render(), Inkscape::CanvasItemGuideLine::_render(), Inkscape::CanvasItemGuideLine::closest_distance_to(), Geom::decompose_degenerate(), Geom::PlanarGraph< EdgeLabel >::deviatesLeft(), Geom::RatQuad::fromPointsTangents(), Inkscape::Extension::Internal::PdfBuilder::Document::get_radial_pattern(), and Geom::xAx::toCurve().

◆ initialPoint()

Point Geom::Line::initialPoint ( ) const

inline

Definition at line 225 of file line.h.

References _initial.

Referenced by Geom::bezier_line_intersections(), distance(), Geom::Circle::intersect(), intersect(), Geom::Circle::intersects(), is_straight_curve(), Inkscape::UI::Widget::line_angle(), Inkscape::signed_distance(), and Inkscape::LivePathEffect::LPESlice::splititem().

◆ intersect() [1/3]

std::vector< ShapeIntersection > Geom::Line::intersect ( Line const & other ) const

Definition at line 253 of file line.cpp.

References Geom::cross(), initialPoint(), result, and vector().

Referenced by Geom::Ellipse::intersect(), intersect(), intersect(), and TEST().

◆ intersect() [2/3]

std::vector< ShapeIntersection > Geom::Line::intersect ( LineSegment const & ls ) const

Definition at line 277 of file line.cpp.

References Geom::filter_line_segment_intersections(), intersect(), and result.

◆ intersect() [3/3]

std::vector< ShapeIntersection > Geom::Line::intersect ( Ray const & r ) const

Definition at line 269 of file line.cpp.

References Geom::filter_ray_intersections(), intersect(), and result.

◆ isDegenerate()

bool Geom::Line::isDegenerate ( ) const

inline

Check if the line has more than one point.

A degenerate line can be created if the line is created from a line equation that has no solutions.

Returns: True if the line has no points or exactly one point

Definition at line 190 of file line.h.

References _final, and _initial.

Referenced by distance(), Geom::Ellipse::intersect(), timeAtProjection(), and wrap_line().

◆ isHorizontal()

bool Geom::Line::isHorizontal ( ) const

inline

Check if the line is horizontal (y is constant).

Definition at line 194 of file line.h.

References _final, _initial, and Geom::Y.

◆ isVertical()

bool Geom::Line::isVertical ( ) const

inline

Check if the line is vertical (x is constant).

Definition at line 198 of file line.h.

References _final, _initial, and Geom::X.

◆ nearestTime()

Coord Geom::Line::nearestTime ( Point const & p ) const

inline

Find a point on the line closest to the query point.

This is an alias for timeAtProjection().

Definition at line 252 of file line.h.

References timeAtProjection().

Referenced by distance(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::doBeforeEffect(), Inkscape::UI::Handle::dragged(), Inkscape::LivePathEffect::LPELattice2::horizontal(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::horizontal(), operator==(), Geom::projection(), Geom::projection(), Inkscape::UI::Widget::ColorWheelHSLuv::updateGeometry(), Inkscape::LivePathEffect::LPELattice2::vertical(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::vertical(), and wrap_line().

◆ normal()

Point Geom::Line::normal ( ) const

inline

Get a unit vector normal to the line.

If Y grows upwards, then this is the left normal. If Y grows downwards, then this is the right normal.

Definition at line 320 of file line.h.

References Geom::Point::normalized(), Geom::rot90(), and vector().

Referenced by normalAndDist(), and wrap_line().

◆ normalAndDist()

Point Geom::Line::normalAndDist ( double & dist ) const

inline

Definition at line 325 of file line.h.

References _initial, Geom::dot(), and normal().

Referenced by Geom::xAx::fromLine(), and wrap_line().

◆ normalize()

void Geom::Line::normalize ( )

inline

Reparametrize the line so that it has unit speed.

Note that the direction of the line may also change.

Definition at line 204 of file line.h.

References _final, and _initial.

Referenced by Geom::detail::bezier_clipping::clip< intersection_point_tag >().

◆ normalized()

Line Geom::Line::normalized ( ) const

inline

Return a new line reparametrized for unit speed.

Definition at line 215 of file line.h.

References _final, and _initial.

◆ operator*=()

template<typename T >

Line & Geom::Line::operator*= ( T const & tr )

inline

Definition at line 375 of file line.h.

References _final, and _initial.

◆ operator==()

bool Geom::Line::operator== ( Line const & other ) const

inline

Definition at line 382 of file line.h.

References _final, _initial, distance(), nearestTime(), and pointAt().

◆ origin()

Point Geom::Line::origin ( ) const

inline

Get the line's origin point.

Definition at line 128 of file line.h.

References _initial.

Referenced by are_same(), avoid_item_poly(), Geom::intersection(), Geom::detail::intersection_impl(), Geom::detail::intersection_impl(), and Geom::xAx::roots().

◆ pointAt()

Point Geom::Line::pointAt ( Coord t ) const

inline

Definition at line 231 of file line.h.

References _final, _initial, and Geom::lerp().

Referenced by Inkscape::CanvasItemGuideLine::_render(), Geom::xAx::arc_bound(), Geom::CLIPPER_CLASS::are_paired(), box3d_half_line_crosses_joining_line(), clip(), Geom::CLIPPER_CLASS::clip(), Inkscape::LineSnapper::constrainedSnap(), curvature(), Geom::decompose_degenerate(), distance(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::doBeforeEffect(), Inkscape::UI::Handle::dragged(), Geom::CLIPPER_CLASS::find_inner_point(), Geom::CLIPPER_CLASS::find_inner_point_by_bisector_line(), Geom::RatQuad::fromPointsTangents(), Inkscape::GridSnapper::getSnapLinesAxonom(), Inkscape::LivePathEffect::LPELattice2::horizontal(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::horizontal(), Inkscape::intersect_line_rectangle(), Geom::make_angle_bisector_line(), operator==(), portion(), Geom::projection(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::projectPoint(), ray(), segment(), Geom::xAx::set(), TEST(), Geom::xAx::toCurve(), Inkscape::UI::Widget::ColorWheelHSLuv::updateGeometry(), Inkscape::LivePathEffect::LPELattice2::vertical(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::vertical(), and wrap_line().

◆ portion()

Curve * Geom::Line::portion	(	Coord	f,
		Coord	t
	)		const

inline

Same as segment(), but allocate the line segment dynamically.

Definition at line 274 of file line.h.

References pointAt().

◆ ray()

Ray Geom::Line::ray ( Coord t )

inline

Create a ray starting at the specified time value.

The created ray will go in the direction of the line's vector (in the direction of increasing time values).

Parameters

t	Time value where the ray should start

Returns: Ray starting at t and going in the direction of the vector

Definition at line 295 of file line.h.

References pointAt(), result, Geom::Ray::setOrigin(), and vector().

Referenced by sp_gradient_reset_to_userspace(), and Inkscape::LivePathEffect::LPESlice::splititem().

◆ reflection()

Affine Geom::Line::reflection ( ) const

inline

Compute an affine matrix representing a reflection about the line.

Definition at line 332 of file line.h.

References _initial, versor(), Geom::X, and Geom::Y.

Referenced by TEST().

◆ reverse()

void Geom::Line::reverse ( )

inline

Definition at line 262 of file line.h.

References _final, and _initial.

Referenced by wrap_line().

◆ reversed()

Line Geom::Line::reversed ( ) const

inline

Create a line containing the same points, but in opposite direction.

Returns: Line \(g\) such that \(g(t) = f(1-t)\)

Definition at line 267 of file line.h.

References _final, _initial, and result.

◆ root()

Coord Geom::Line::root	(	Coord	v,
		Dim2	d
	)		const

Definition at line 140 of file line.cpp.

References _initial, vector(), Geom::X, and Geom::Y.

◆ roots()

std::vector< Coord > Geom::Line::roots	(	Coord	v,
		Dim2	d
	)		const

Find intersection with an axis-aligned line.

Parameters

v	Coordinate of the axis-aligned line
d	Which axis the coordinate is on. X means a vertical line, Y means a horizontal line.

Returns: Time values at which this line intersects the query line.

Definition at line 131 of file line.cpp.

References result, and root.

Referenced by wrap_line().

◆ rotationToAxis()

Affine Geom::Line::rotationToAxis ( Dim2 d ) const

inline

Compute a rotation affine which transforms the line to one of the axes.

Parameters

d	Which line should be the axis

Definition at line 362 of file line.h.

References Geom::other_dimension(), and rotationToZero().

◆ rotationToZero()

Affine Geom::Line::rotationToZero ( Dim2 d ) const

inline

Compute an affine which transforms all points on the line to zero X or Y coordinate.

This operation is useful in reducing intersection problems to root-finding problems. There are many affines which do this transformation. This function returns one that preserves angles, areas and distances - a rotation combined with a translation, and additionally moves the initial point of the line to (0,0). This way it works without problems even for lines perpendicular to the target, though may in some cases have lower precision than e.g. a shear transform.

Parameters

d	Which coordinate of points on the line should be zero after the transformation

Definition at line 350 of file line.h.

References _initial, vector(), Geom::X, and Geom::Y.

Referenced by Geom::bezier_line_intersections(), rotationToAxis(), and TEST().

◆ segment()

LineSegment Geom::Line::segment	(	Coord	f,
		Coord	t
	)		const

inline

Create a segment of this line.

Parameters

f	Time value for the initial point of the segment
t	Time value for the final point of the segment

Returns: Created line segment

Definition at line 283 of file line.h.

References pointAt().

Referenced by Inkscape::SnappedCurve::intersect(), Geom::projection(), and Geom::rect_line_intersect().

◆ setAngle()

void Geom::Line::setAngle ( Coord angle )

inline

Set the angle the line makes with the X axis.

Origin remains unchanged.

Definition at line 160 of file line.h.

References _final, _initial, angle(), distance(), Geom::sincos(), Geom::X, and Geom::Y.

◆ setCoefficients()

void Geom::Line::setCoefficients	(	double	a,
		double	b,
		double	c
	)

Set the coefficients of the line equation.

Set the line by solving the line equation.

The line equation is: \(ax + by = c\). Points that satisfy the equation are on the line.

A line is a set of points that satisfies the line equation \(Ax + By + C = 0\). This function changes the line so that its points satisfy the line equation with the given coefficients.

Definition at line 62 of file line.cpp.

References _final, _initial, c, offset, Geom::X, and Geom::Y.

Referenced by Geom::xAx::arc_bound(), Geom::xAx::decompose(), Line(), and wrap_line().

◆ setOrigin()

void Geom::Line::setOrigin ( Point const & p )

inline

Set the point at zero time.

The orientation remains unchanged, modulo numeric errors during addition.

Definition at line 147 of file line.h.

References _final, and _initial.

Referenced by avoid_item_poly().

◆ setPoints()

void Geom::Line::setPoints	(	Point const &	a,
		Point const &	b
	)

inline

Set a line based on two points it should pass through.

Definition at line 168 of file line.h.

References _final, and _initial.

Referenced by avoid_item_poly(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::doBeforeEffect(), Geom::CLIPPER_CLASS::find_inner_point(), Inkscape::LivePathEffect::LPEPerspectiveEnvelope::projectPoint(), and wrap_line().

◆ setVector()

void Geom::Line::setVector ( Point const & v )

inline

Set the speed of the line.

Origin remains unchanged.

Definition at line 154 of file line.h.

References _final, and _initial.

Referenced by avoid_item_poly().

◆ timeAt()

Coord Geom::Line::timeAt ( Point const & p ) const

Get a time value corresponding to a point.

Parameters

p	Point on the line. If the point is not on the line, the returned value will be meaningless.

Returns: Time value t such that \(f(t) = p\).

See also: timeAtProjection

Definition at line 223 of file line.cpp.

References _initial, vector(), Geom::X, and Geom::Y.

Referenced by Geom::Ellipse::intersect(), Geom::Circle::intersect(), and Geom::xAx::set().

◆ timeAtProjection()

Coord Geom::Line::timeAtProjection ( Point const & p ) const

inline

Get a time value corresponding to a projection of a point on the line.

Parameters

p	Arbitrary point.

Returns: Time value corresponding to a point closest to p.

Definition at line 244 of file line.h.

References _initial, Geom::dot(), isDegenerate(), and vector().

Referenced by nearestTime(), and Geom::xAx::set().

◆ transformed()

Line Geom::Line::transformed ( Affine const & m ) const

inline

Create a line transformed by an affine transformation.

Definition at line 312 of file line.h.

References _final, and _initial.

Referenced by Inkscape::SnappedCurve::intersect(), and wrap_line().

◆ transformTo()

Affine Geom::Line::transformTo ( Line const & other ) const

Create a transformation that maps one line to another.

This will return a transformation \(A\) such that \(L_1(t) \cdot A = L_2(t)\), where \(L_1\) is this line and \(L_2\) is the line passed as the parameter. The returned transformation will preserve angles.

Definition at line 244 of file line.cpp.

References _initial, Geom::angle_between(), Geom::Point::length(), Geom::length(), result, and vector().

◆ valueAt()

Coord Geom::Line::valueAt	(	Coord	t,
		Dim2	d
	)		const

inline

Definition at line 235 of file line.h.

References _final, _initial, and Geom::lerp().

Referenced by wrap_line().

◆ vector()

Point Geom::Line::vector ( ) const

inline

Get the line's raw direction vector.

The length of the retrieved vector is equal to the length of a segment parametrized by a time interval of length 1.

Definition at line 132 of file line.h.

References _final, and _initial.

Referenced by Inkscape::CanvasItemGridXY::_render(), Geom::angle_between(), are_orthogonal(), Geom::are_parallel(), clip(), coefficients(), derivative(), Inkscape::LivePathEffect::LPEMirrorSymmetry::doAfterEffect(), Inkscape::LivePathEffect::LPEMirrorSymmetry::doEffect_path(), Geom::Ellipse::intersect(), Geom::Circle::intersect(), intersect(), Geom::intersection(), Geom::detail::intersection_impl(), Geom::detail::intersection_impl(), Geom::Circle::intersects(), Geom::make_angle_bisector_line(), Geom::make_orthogonal_line(), normal(), ray(), root(), rotationToZero(), TEST(), timeAt(), timeAtProjection(), and transformTo().

◆ versor()

Point Geom::Line::versor ( ) const

inline

Get the line's normalized direction vector.

The retrieved vector is normalized to unit length.

Definition at line 135 of file line.h.

References _final, _initial, and Geom::Point::normalized().

Referenced by avoid_item_poly(), Inkscape::LineSnapper::constrainedSnap(), reflection(), Geom::xAx::roots(), Inkscape::signed_distance(), and TEST().

Friends And Related Symbol Documentation

◆ are_orthogonal()

bool are_orthogonal	(	Line const &	l1,
		Line const &	l2,
		double	eps = `EPSILON`
	)

Test whether two lines are perpendicular.

Definition at line 447 of file line.h.

References Geom::are_near(), Geom::dot(), and vector().

◆ are_same()

bool are_same	(	Line const &	l1,
		Line const &	l2,
		double	eps = `EPSILON`
	)

Test whether two lines are approximately the same.

This tests for being parallel and the origin of one line being close to the other, so it tests whether the images of the lines are similar, not whether the same time values correspond to similar points. For example a line from (1,1) to (2,2) and a line from (-1,-1) to (0,0) will be the same, because their images match, even though there is no time value for which the lines give similar points.

Definition at line 439 of file line.h.

References Geom::are_near(), Geom::are_parallel(), and origin().

◆ distance()

double distance	(	Point const &	p,
		Line const &	line
	)

Compute distance from point to line.

Definition at line 409 of file line.h.

References initialPoint(), isDegenerate(), nearestTime(), and pointAt().

Referenced by operator==(), and setAngle().

◆ operator*

template<typename T >

Line operator*	(	Line const &	l,
		T const &	tr
	)

friend

Definition at line 389 of file line.h.

Member Data Documentation

◆ _final

Point Geom::Line::_final

private

Definition at line 56 of file line.h.

Referenced by angle(), coefficients(), finalPoint(), isDegenerate(), isHorizontal(), isVertical(), Line(), normalize(), normalized(), operator*=(), operator==(), pointAt(), reverse(), reversed(), setAngle(), setCoefficients(), setOrigin(), setPoints(), setVector(), transformed(), valueAt(), vector(), and versor().

◆ _initial

Point Geom::Line::_initial

private

Definition at line 55 of file line.h.

Referenced by angle(), clip(), coefficients(), initialPoint(), isDegenerate(), isHorizontal(), isVertical(), Line(), normalAndDist(), normalize(), normalized(), operator*=(), operator==(), origin(), pointAt(), reflection(), reverse(), reversed(), root(), rotationToZero(), setAngle(), setCoefficients(), setOrigin(), setPoints(), setVector(), timeAt(), timeAtProjection(), transformed(), transformTo(), valueAt(), vector(), and versor().

The documentation for this class was generated from the following files:

/builds/inkscape/inkscape/src/3rdparty/2geom/include/2geom/line.h
/builds/inkscape/inkscape/src/3rdparty/2geom/src/2geom/line.cpp

Public Member Functions

Private Attributes

Friends

Related Symbols

Creating lines.

Detailed Description

Constructor & Destructor Documentation

◆ Line() [1/6]

◆ Line() [2/6]

◆ Line() [3/6]

◆ Line() [4/6]

◆ Line() [5/6]

◆ Line() [6/6]

Member Function Documentation

◆ angle()

◆ clip()

◆ coefficients() [1/2]

◆ coefficients() [2/2]

◆ derivative()

◆ duplicate()

◆ finalPoint()

◆ from_normal_distance()

◆ from_origin_and_vector()

◆ initialPoint()

◆ intersect() [1/3]

◆ intersect() [2/3]

◆ intersect() [3/3]

◆ isDegenerate()

◆ isHorizontal()

◆ isVertical()

◆ nearestTime()

◆ normal()

◆ normalAndDist()

◆ normalize()

◆ normalized()

◆ operator*=()

◆ operator==()

◆ origin()

◆ pointAt()

◆ portion()

◆ ray()

◆ reflection()

◆ reverse()

◆ reversed()

◆ root()

◆ roots()

◆ rotationToAxis()

◆ rotationToZero()

◆ segment()

◆ setAngle()

◆ setCoefficients()

◆ setOrigin()

◆ setPoints()

◆ setVector()

◆ timeAt()

◆ timeAtProjection()

◆ transformed()

◆ transformTo()

◆ valueAt()

◆ vector()

◆ versor()

Friends And Related Symbol Documentation

◆ are_orthogonal()

◆ are_same()

◆ distance()

◆ operator*

Member Data Documentation

◆ _final

◆ _initial