Fundamental segment defined by two points. More...

#include <point.H>

Inheritance diagram for Segment:

Collaboration diagram for Segment:

Public Types
enum	Sense { E , NE , N , NW , W , S , SW , SE }
	Cardinal directions associated with a segment. More...

Public Member Functions
bool	operator== (const Segment &s) const

bool	operator!= (const Segment &s) const

const Point &	highest_point () const

const Point &	lowest_point () const

const Point &	leftmost_point () const

const Point &	rightmost_point () const

const Point &	get_src_point () const

const Point &	get_tgt_point () const

	Segment ()=default

	Segment (Point __src, const Point &__tgt)

	Segment (Point __src, const Geom_Number &m, const Geom_Number &l)
	Builds a new segment given source point, slope and length.

	Segment (const Segment &sg, const Geom_Number &dist)
	Builds a new segment parallel to sg and with a distance dist.

double	slope () const

double	counterclockwise_angle_with (const Segment &s) const
	Compute the counterclockwise wise angle respect another segment s.

double	counterclockwise_angle () const
	Compute the counterclockwise angle of this respect x-axis.

Geom_Number	size () const
	Return the Euclidean length of the segment (distance between endpoints).

bool	is_colinear_with (const Point &p) const
	Return true if `p` is colinear with this segment.

bool	is_to_left_from (const Point &p) const
	Return true if this segment is to the left of point `p`.

bool	is_to_right_from (const Point &p) const
	Return true if this segment is to the right of point `p`.

Point	mid_point () const
	Return the midpoint of this segment.

const Point &	nearest_point (const Point &p) const
	Return whichever endpoint is nearer to `p`.

Segment	get_perpendicular (const Point &p) const
	Construct the segment perpendicular to `this` passing through `p`.

Segment	mid_perpendicular (const Geom_Number &dist) const
	Return the perpendicular chord of length `2*dist` through the midpoint.

bool	intersects_properly_with (const Segment &s) const
	Return true if the segments intersect at interior points only.

bool	contains_to (const Point &p) const
	Return true if `p` lies on this segment.

bool	contains_to (const Segment &s) const
	Return true if `s` lies entirely inside this segment.

bool	intersects_with (const Segment &s) const
	Return true if `s` intersects this segment (including endpoints).

bool	intersects_with (const Triangle &t) const

bool	intersects_with (const Ellipse &e) const

bool	is_parallel_with (const Segment &s) const
	Return true if `s` has the same slope.

Point	intersection_with (const Segment &s) const
	Compute intersection point solving point-slope equations for both lines.

Sense	sense () const

void	enlarge_src (const Geom_Number &__dist)
	Extend the segment by `__dist` from the source endpoint.

void	enlarge_tgt (const Geom_Number &__dist)
	Extend the segment by `__dist` from the target endpoint.

std::string	to_string () const
	Return "(src)(tgt)" textual form.

	operator std::string () const

void	rotate (const double &angle)
	Rotate the segment by `angle` (radians) around the source point.

Segment	intersection_with (const Triangle &t) const

Segment	intersection_with (const Ellipse &e) const

Public Member Functions inherited from Geom_Object
	Geom_Object ()=default

virtual	~Geom_Object ()=default

Private Member Functions
double	compute_slope () const

Static Private Member Functions
static Point	compute_tgt_point (const Point &__src, const Geom_Number &m, const Geom_Number &d)
	Computes the target point of a segment given the source point, slope and length.

Private Attributes
Point	src

Point	tgt

Friends
class	Point

class	Triangle

Detailed Description

Fundamental segment defined by two points.

Definition at line 416 of file point.H.

Member Enumeration Documentation

◆ Sense

enum Segment::Sense

Cardinal directions associated with a segment.

Enumerator
E
NE
N
NW
W
S
SW
SE

Definition at line 756 of file point.H.

Constructor & Destructor Documentation

◆ Segment() [1/4]

Segment::Segment ( )

default

Referenced by intersection_with(), and intersects_with().

◆ Segment() [2/4]

Segment::Segment	(	Point	__src,
		const Point &	__tgt
	)

inline

Definition at line 480 of file point.H.

◆ Segment() [3/4]

Segment::Segment	(	Point	__src,
		const Geom_Number &	m,
		const Geom_Number &	l
	)

inline

Builds a new segment given source point, slope and length.

It computes the source point by usen these equations:

\( d^2 = (x - x_1)^2 + (y - y_1)^2\) (Pythagoras)
\( y - y_1 = m(x - x_1)\) (line equation given point and slope)

Parameters

[in]	__src	Source point
[in]	m	slope (rise over run, dimensionless)
[in]	l	length

Definition at line 523 of file point.H.

◆ Segment() [4/4]

Segment::Segment	(	const Segment &	sg,
		const Geom_Number &	dist
	)

inline

Builds a new segment parallel to sg and with a distance dist.

Definition at line 532 of file point.H.

References get_src_point(), get_tgt_point(), mid_perpendicular(), mid_point(), src, and tgt.

Member Function Documentation

◆ compute_slope()

double Segment::compute_slope ( ) const

inlineprivate

Definition at line 423 of file point.H.

References __gmp_expr< mpq_t, mpq_t >::get_d(), src, tgt, Point::x, and Point::y.

Referenced by slope().

◆ compute_tgt_point()

static Point Segment::compute_tgt_point	(	const Point &	__src,
		const Geom_Number &	m,
		const Geom_Number &	d
	)

inlinestaticprivate

Computes the target point of a segment given the source point, slope and length.

It uses the solution of these equations:

d^2 = (tx-sx)^2 + (ty-sy)^2 (Pythagorean theorem)
ty - sy = m(tx-sx) (line equation)

Returns: The point placed to the east (right).

Definition at line 497 of file point.H.

References square_root(), Point::x, y, and Point::y.

Referenced by enlarge_src(), and enlarge_tgt().

◆ contains_to() [1/2]

bool Segment::contains_to ( const Point & p ) const

inline

Return true if p lies on this segment.

Definition at line 700 of file point.H.

References Point::is_between(), src, and tgt.

Referenced by intersects_with(), and Point::is_inside().

◆ contains_to() [2/2]

bool Segment::contains_to ( const Segment & s ) const

inline

Return true if s lies entirely inside this segment.

Definition at line 706 of file point.H.

References get_src_point(), get_tgt_point(), Point::is_between(), src, and tgt.

◆ counterclockwise_angle()

double Segment::counterclockwise_angle ( ) const

inline

Compute the counterclockwise angle of this respect x-axis.

Definition at line 571 of file point.H.

References counterclockwise_angle_with(), and Point.

Referenced by TEST_F().

◆ counterclockwise_angle_with()

double Segment::counterclockwise_angle_with ( const Segment & s ) const

inline

Compute the counterclockwise wise angle respect another segment s.

Definition at line 550 of file point.H.

References arctan2(), __gmp_expr< mpq_t, mpq_t >::get_d(), PI, src, tgt, Point::x, Point::y, and y1().

Referenced by counterclockwise_angle(), Aleph::GiftWrappingConvexHull::operator()(), and TEST_F().

◆ enlarge_src()

void Segment::enlarge_src ( const Geom_Number & __dist )

inline

Extend the segment by __dist from the source endpoint.

Definition at line 783 of file point.H.

References compute_tgt_point(), size(), slope(), and src.

Referenced by Ellipse::compute_tangents().

◆ enlarge_tgt()

void Segment::enlarge_tgt ( const Geom_Number & __dist )

inline

Extend the segment by __dist from the target endpoint.

Definition at line 796 of file point.H.

References compute_tgt_point(), size(), slope(), and tgt.

Referenced by Ellipse::compute_tangents().

◆ get_perpendicular()

Segment Segment::get_perpendicular ( const Point & p ) const

inline

Construct the segment perpendicular to this passing through p.

Definition at line 618 of file point.H.

References Point::get_x(), Point::get_y(), Point, slope(), src, tgt, y, and y1().

Referenced by Aleph::QuickHull::get_fartest_point().

◆ get_src_point()

const Point & Segment::get_src_point ( ) const

inline

Definition at line 468 of file point.H.

References src.

Referenced by Segment(), Ellipse::compute_tangents(), contains_to(), Aleph::CuttingEarsTriangulation::diagonalie(), Ellipse::intersection_with(), Ellipse::intersects_with(), nearest_point(), Aleph::BruteForceConvexHull::operator()(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ get_tgt_point()

const Point & Segment::get_tgt_point ( ) const

inline

Definition at line 470 of file point.H.

References tgt.

Referenced by Segment(), Ellipse::compute_tangents(), contains_to(), Aleph::CuttingEarsTriangulation::diagonalie(), Regular_Polygon::get_vertex(), Ellipse::intersection_with(), Ellipse::intersects_with(), nearest_point(), Aleph::BruteForceConvexHull::operator()(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ highest_point()

const Point & Segment::highest_point ( ) const

inline

Definition at line 448 of file point.H.

References src, tgt, and Point::y.

Referenced by TEST_F().

◆ intersection_with() [1/3]

Segment Segment::intersection_with ( const Ellipse & e ) const

inline

Definition at line 1473 of file point.H.

References Ellipse::intersection_with().

◆ intersection_with() [2/3]

Point Segment::intersection_with ( const Segment & s ) const

inline

Compute intersection point solving point-slope equations for both lines.

Definition at line 733 of file point.H.

References ah_domain_error_if, is_parallel_with(), slope(), src, Point::x, y, Point::y, and y1().

Referenced by Triangle::intersection_with(), and intersection_with().

◆ intersection_with() [3/3]

Segment Segment::intersection_with ( const Triangle & t ) const

inline

Definition at line 1088 of file point.H.

References Segment(), ah_domain_error_if, Triangle::contains_to(), Triangle::get_p1(), Triangle::get_p2(), Triangle::get_p3(), intersection_with(), and intersects_with().

◆ intersects_properly_with()

bool Segment::intersects_properly_with ( const Segment & s ) const

inline

Return true if the segments intersect at interior points only.

Definition at line 687 of file point.H.

References Point::is_colinear_with(), Point::is_to_left_from(), src, and tgt.

Referenced by intersects_with().

◆ intersects_with() [1/3]

bool Segment::intersects_with ( const Ellipse & e ) const

inline

Definition at line 1466 of file point.H.

References Ellipse::intersects_with().

◆ intersects_with() [2/3]

bool Segment::intersects_with ( const Segment & s ) const

inline

Return true if s intersects this segment (including endpoints).

Definition at line 713 of file point.H.

References contains_to(), intersects_properly_with(), src, and tgt.

Referenced by Aleph::CuttingEarsTriangulation::diagonalie(), intersection_with(), and intersects_with().

◆ intersects_with() [3/3]

bool Segment::intersects_with ( const Triangle & t ) const

inline

Definition at line 1077 of file point.H.

References Segment(), Triangle::get_p1(), Triangle::get_p2(), Triangle::get_p3(), and intersects_with().

◆ is_colinear_with()

bool Segment::is_colinear_with ( const Point & p ) const

inline

Return true if p is colinear with this segment.

Definition at line 584 of file point.H.

References Point::is_colinear_with(), src, and tgt.

Referenced by TEST_F().

◆ is_parallel_with()

bool Segment::is_parallel_with ( const Segment & s ) const

inline

Return true if s has the same slope.

Definition at line 727 of file point.H.

References slope().

Referenced by intersection_with().

◆ is_to_left_from()

bool Segment::is_to_left_from ( const Point & p ) const

inline

Return true if this segment is to the left of point p.

Definition at line 590 of file point.H.

References Point::is_to_right_from().

Referenced by Ellipse::intersects_with(), and TEST_F().

◆ is_to_right_from()

bool Segment::is_to_right_from ( const Point & p ) const

inline

Return true if this segment is to the right of point p.

Definition at line 596 of file point.H.

References Point::is_to_left_from().

Referenced by TEST_F().

◆ leftmost_point()

const Point & Segment::leftmost_point ( ) const

inline

Definition at line 458 of file point.H.

References src, tgt, and Point::x.

Referenced by TEST_F().

◆ lowest_point()

const Point & Segment::lowest_point ( ) const

inline

Definition at line 453 of file point.H.

References src, tgt, and Point::y.

Referenced by TEST_F().

◆ mid_perpendicular()

Segment Segment::mid_perpendicular ( const Geom_Number & dist ) const

inline

Return the perpendicular chord of length 2*dist through the midpoint.

Definition at line 650 of file point.H.

References arctan(), Polar_Point::get_r(), Polar_Point::get_theta(), Point::is_to_right_from(), pitag(), Point, src, and tgt.

Referenced by Segment().

◆ mid_point()

Point Segment::mid_point ( ) const

inline

Return the midpoint of this segment.

Definition at line 602 of file point.H.

References Point::get_x(), Point::get_y(), src, tgt, and y.

Referenced by Segment(), TEST_F(), TEST_F(), and TEST_F().

◆ nearest_point()

const Point & Segment::nearest_point ( const Point & p ) const

inline

Return whichever endpoint is nearer to p.

Definition at line 612 of file point.H.

References get_src_point(), get_tgt_point(), and Point::nearest_point().

◆ operator std::string()

Segment::operator std::string ( ) const

inline

Definition at line 814 of file point.H.

References to_string().

◆ operator!=()

bool Segment::operator!= ( const Segment & s ) const

inline

Definition at line 443 of file point.H.

◆ operator==()

bool Segment::operator== ( const Segment & s ) const

inline

Definition at line 438 of file point.H.

References src, and tgt.

◆ rightmost_point()

const Point & Segment::rightmost_point ( ) const

inline

Definition at line 463 of file point.H.

References src, tgt, and Point::x.

Referenced by TEST_F().

◆ rotate()

void Segment::rotate ( const double & angle )

inline

Rotate the segment by angle (radians) around the source point.

Definition at line 820 of file point.H.

References Polar_Point::get_r(), Polar_Point::get_theta(), src, and tgt.

Referenced by Regular_Polygon::get_vertex().

◆ sense()

Sense Segment::sense ( ) const

inline

Definition at line 758 of file point.H.

References E, N, NE, NW, S, SE, src, SW, tgt, W, Point::x, and Point::y.

◆ size()

Geom_Number Segment::size ( ) const

inline

Return the Euclidean length of the segment (distance between endpoints).

Definition at line 578 of file point.H.

References pitag(), src, tgt, Point::x, and Point::y.

Referenced by enlarge_src(), enlarge_tgt(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ slope()

double Segment::slope ( ) const

inline

Definition at line 544 of file point.H.

References compute_slope().

Referenced by enlarge_src(), enlarge_tgt(), get_perpendicular(), intersection_with(), Ellipse::intersection_with(), Ellipse::intersects_with(), is_parallel_with(), and TEST_F().

◆ to_string()

std::string Segment::to_string ( ) const

inline

Return "(src)(tgt)" textual form.

Definition at line 809 of file point.H.

References src, tgt, and Point::to_string().

Referenced by operator std::string().

Friends And Related Symbol Documentation

◆ Point

friend class Point

friend

Definition at line 418 of file point.H.

Referenced by counterclockwise_angle(), get_perpendicular(), and mid_perpendicular().

◆ Triangle

friend class Triangle

friend

Definition at line 419 of file point.H.

Member Data Documentation

◆ src

Point Segment::src

private

◆ tgt

Point Segment::tgt

private

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

point.H

Public Types

Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Friends

Detailed Description

Member Enumeration Documentation

◆ Sense

Constructor & Destructor Documentation

◆ Segment() [1/4]

◆ Segment() [2/4]

◆ Segment() [3/4]

◆ Segment() [4/4]

Member Function Documentation

◆ compute_slope()

◆ compute_tgt_point()

◆ contains_to() [1/2]

◆ contains_to() [2/2]

◆ counterclockwise_angle()

◆ counterclockwise_angle_with()

◆ enlarge_src()

◆ enlarge_tgt()

◆ get_perpendicular()

◆ get_src_point()

◆ get_tgt_point()

◆ highest_point()

◆ intersection_with() [1/3]

◆ intersection_with() [2/3]

◆ intersection_with() [3/3]

◆ intersects_properly_with()

◆ intersects_with() [1/3]

◆ intersects_with() [2/3]

◆ intersects_with() [3/3]

◆ is_colinear_with()

◆ is_parallel_with()

◆ is_to_left_from()

◆ is_to_right_from()

◆ leftmost_point()

◆ lowest_point()

◆ mid_perpendicular()

◆ mid_point()

◆ nearest_point()

◆ operator std::string()

◆ operator!=()

◆ operator==()

◆ rightmost_point()

◆ rotate()

◆ sense()

◆ size()

◆ slope()

◆ to_string()

Friends And Related Symbol Documentation

◆ Point

◆ Triangle

Member Data Documentation

◆ src

◆ tgt