An axis-aligned ellipse. More...

#include <point.H>

Inheritance diagram for Aleph::Ellipse:

Collaboration diagram for Aleph::Ellipse:

Public Member Functions
	Ellipse (Point center, const Geom_Number &hr, const Geom_Number &vr)
	Constructs an ellipse.

	Ellipse (const Ellipse &e)=default
	Copy constructor.

	Ellipse ()
	Default constructor.

bool	operator== (const Ellipse &e) const noexcept
	Checks for exact equality.

bool	operator!= (const Ellipse &e) const noexcept
	Checks for inequality.

const Point &	get_center () const
	Gets the center point of the ellipse.

const Geom_Number &	get_hradius () const
	Gets the horizontal radius.

const Geom_Number &	get_vradius () const
	Gets the vertical radius.

Geom_Number	area () const
	Calculates the area of the ellipse.

Geom_Number	perimeter () const
	Approximates the perimeter of the ellipse.

Point	sample (const Geom_Number &angle) const
	Samples a point on the ellipse's boundary at a given angle.

std::string	to_string () const
	Returns a string representation of the ellipse.

Point	highest_point () const
	Gets the highest point on the ellipse boundary.

Point	lowest_point () const
	Gets the lowest point on the ellipse boundary.

Point	leftmost_point () const
	Gets the leftmost point on the ellipse boundary.

Point	rightmost_point () const
	Gets the rightmost point on the ellipse boundary.

void	compute_tangents (Segment &s1, Segment &s2, const Geom_Number &m) const
	Computes the two tangent segments to this ellipse with a given slope.

bool	intersects_with (const Segment &s) const
	Checks if a segment intersects the ellipse.

bool	contains (const Point &p) const
	Checks if a point lies inside or on the boundary of this ellipse.

bool	contains_to (const Point &p) const

bool	intersects_with (const Point &p) const
	Checks if a point lies exactly on the ellipse boundary.

Segment	intersection_with (const Segment &sg) const
	Computes the intersection segment between a line segment and this ellipse.

Public Member Functions inherited from Aleph::Geom_Object
	Geom_Object ()=default

virtual	~Geom_Object ()=default

Static Public Member Functions
static bool	is_clockwise ()
	Returns the orientation of the ellipse.

Private Member Functions
void	validate_positive_radii () const
	Validates that radii are positive.

Geom_Number	compute_radius (const Point &p) const
	Computes the ellipse equation value for a point.

Static Private Member Functions
static bool	in_unit_interval (const Geom_Number &t)
	Helper to check if a parameter `t` is in the [0, 1] interval.

Private Attributes
Point	center_

Geom_Number	hr_

Geom_Number	vr_

Friends
class	Point

Detailed Description

An axis-aligned ellipse.

Represents an axis-aligned ellipse centered at a point with a horizontal and a vertical radius. Provides methods for calculating geometric properties and handling intersections.

Definition at line 2005 of file point.H.

Constructor & Destructor Documentation

◆ Ellipse() [1/3]

Aleph::Ellipse::Ellipse	(	Point	center,
		const Geom_Number &	hr,
		const Geom_Number &	vr
	)

inline

Constructs an ellipse.

Parameters

center	The center point of the ellipse.
hr	The horizontal radius.
vr	The vertical radius.

Exceptions

std::domain_error if either radius is not positive.

Definition at line 2032 of file point.H.

References validate_positive_radii().

◆ Ellipse() [2/3]

Aleph::Ellipse::Ellipse ( const Ellipse & e )

default

Copy constructor.

◆ Ellipse() [3/3]

Aleph::Ellipse::Ellipse ( )

inline

Default constructor.

Note: Creates a unit circle centered at the origin.

Definition at line 2050 of file point.H.

Member Function Documentation

◆ area()

Geom_Number Aleph::Ellipse::area ( ) const

inline

Calculates the area of the ellipse.

Returns: The area (pi * hr * vr).

Definition at line 2086 of file point.H.

References Aleph::geom_pi(), hr_, validate_positive_radii(), and vr_.

◆ compute_radius()

Geom_Number Aleph::Ellipse::compute_radius ( const Point & p ) const

inlineprivate

Computes the ellipse equation value for a point.

Calculates (x-xc)^2/hr^2 + (y-yc)^2/vr^2.

Parameters

p	The point to evaluate.

Returns: A value that is < 1 for interior points, = 1 for boundary points, and > 1 for exterior points.

Definition at line 2266 of file point.H.

References center_, Aleph::Point::get_x(), Aleph::Point::get_y(), hr_, validate_positive_radii(), and vr_.

Referenced by contains(), and intersects_with().

◆ compute_tangents()

void Aleph::Ellipse::compute_tangents	(	Segment &	s1,
		Segment &	s2,
		const Geom_Number &	m
	)		const

inline

Computes the two tangent segments to this ellipse with a given slope.

Parameters

[out]	s1	The first tangent segment.
[out]	s2	The second tangent segment.
[in]	m	The slope of the tangents.

Definition at line 2189 of file point.H.

References ah_domain_error_if, center_, Aleph::divide_and_conquer_partition_dp(), hr_, m, Point, Aleph::square_root(), validate_positive_radii(), and vr_.

◆ contains()

bool Aleph::Ellipse::contains ( const Point & p ) const

inline

Checks if a point lies inside or on the boundary of this ellipse.

Parameters

p	The point to check.

Returns: true if the point is contained within the ellipse.

Definition at line 2285 of file point.H.

References compute_radius().

Referenced by contains_to(), Aleph::Point::is_inside(), TEST_F(), and TEST_F().

◆ contains_to()

bool Aleph::Ellipse::contains_to ( const Point & p ) const

inline

Deprecated:: Use contains() instead.

Definition at line 2292 of file point.H.

References contains().

◆ get_center()

const Point & Aleph::Ellipse::get_center ( ) const

inline

Gets the center point of the ellipse.

Definition at line 2076 of file point.H.

References center_.

Referenced by Aleph::Tikz_Plane::draw_ellipse(), and Eepic_Plane::draw_ellipse().

◆ get_hradius()

const Geom_Number & Aleph::Ellipse::get_hradius ( ) const

inline

Gets the horizontal radius.

Definition at line 2078 of file point.H.

References hr_.

Referenced by Aleph::Tikz_Plane::draw_ellipse(), Eepic_Plane::draw_ellipse(), and TEST_F().

◆ get_vradius()

const Geom_Number & Aleph::Ellipse::get_vradius ( ) const

inline

Gets the vertical radius.

Definition at line 2080 of file point.H.

References vr_.

Referenced by Aleph::Tikz_Plane::draw_ellipse(), Eepic_Plane::draw_ellipse(), and TEST_F().

◆ highest_point()

Point Aleph::Ellipse::highest_point ( ) const

inline

Gets the highest point on the ellipse boundary.

Definition at line 2159 of file point.H.

References center_, Aleph::Point::get_x(), Aleph::Point::get_y(), and vr_.

Referenced by Aleph::Tikz_Plane::bbox_of().

◆ in_unit_interval()

static bool Aleph::Ellipse::in_unit_interval ( const Geom_Number & t )

inlinestaticprivate

Helper to check if a parameter t is in the [0, 1] interval.

Definition at line 2146 of file point.H.

References Aleph::and.

Referenced by intersection_with(), and intersects_with().

◆ intersection_with()

Segment Aleph::Ellipse::intersection_with ( const Segment & sg ) const

inline

Computes the intersection segment between a line segment and this ellipse.

Parameters

sg	The segment to intersect with.

Returns: A Segment representing the portion of sg inside the ellipse. If tangent, the segment is degenerate (a point).

Exceptions

std::domain_error if there is no intersection.

Definition at line 2311 of file point.H.

References ah_domain_error_if, Aleph::and, Aleph::Segment::at(), center_, Aleph::divide_and_conquer_partition_dp(), Aleph::Segment::get_src_point(), Aleph::Segment::get_tgt_point(), Aleph::Point::get_x(), Aleph::Point::get_y(), hr_, in_unit_interval(), root(), Aleph::square_root(), validate_positive_radii(), and vr_.

Referenced by Aleph::Segment::intersection_with(), Aleph::RotatedEllipse::intersection_with(), and TEST_F().

◆ intersects_with() [1/2]

bool Aleph::Ellipse::intersects_with ( const Point & p ) const

inline

Checks if a point lies exactly on the ellipse boundary.

Parameters

p	The point to check.

Returns: true if the point is on the boundary.

Definition at line 2299 of file point.H.

References compute_radius().

◆ intersects_with() [2/2]

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

inline

Checks if a segment intersects the ellipse.

Solves the quadratic equation for the intersection of a line and an ellipse.

Parameters

s	The segment to check.

Returns: true if the segment and ellipse share at least one point.

Definition at line 2224 of file point.H.

References center_, Aleph::divide_and_conquer_partition_dp(), Aleph::Segment::get_src_point(), Aleph::Segment::get_tgt_point(), Aleph::Point::get_x(), Aleph::Point::get_y(), hr_, in_unit_interval(), root(), Aleph::square_root(), validate_positive_radii(), and vr_.

Referenced by Aleph::Point::intersects_with(), Aleph::Segment::intersects_with(), Aleph::RotatedEllipse::intersects_with(), TEST_F(), TEST_F(), and TEST_F().

◆ is_clockwise()

static bool Aleph::Ellipse::is_clockwise ( )

inlinestatic

Returns the orientation of the ellipse.

Always counter-clockwise.

Returns: false, indicating CCW.

Definition at line 2156 of file point.H.

Referenced by TEST_F().

◆ leftmost_point()

Point Aleph::Ellipse::leftmost_point ( ) const

inline

Gets the leftmost point on the ellipse boundary.

Definition at line 2171 of file point.H.

References center_, Aleph::Point::get_x(), Aleph::Point::get_y(), and hr_.

Referenced by Aleph::Tikz_Plane::bbox_of().

◆ lowest_point()

Point Aleph::Ellipse::lowest_point ( ) const

inline

Gets the lowest point on the ellipse boundary.

Definition at line 2165 of file point.H.

References center_, Aleph::Point::get_x(), Aleph::Point::get_y(), and vr_.

Referenced by Aleph::Tikz_Plane::bbox_of().

◆ operator!=()

bool Aleph::Ellipse::operator!= ( const Ellipse & e ) const

inlinenoexcept

Checks for inequality.

Parameters

e	The other ellipse.

Returns: true if center or radii are different.

Definition at line 2070 of file point.H.

References Aleph::divide_and_conquer_partition_dp().

◆ operator==()

bool Aleph::Ellipse::operator== ( const Ellipse & e ) const

inlinenoexcept

Checks for exact equality.

Parameters

e	The other ellipse.

Returns: true if center and radii are identical.

Definition at line 2060 of file point.H.

References Aleph::and, center_, hr_, and vr_.

◆ perimeter()

Geom_Number Aleph::Ellipse::perimeter ( ) const

inline

Approximates the perimeter of the ellipse.

Uses Ramanujan's second approximation formula for the perimeter.

Returns: The approximate perimeter length.

Definition at line 2097 of file point.H.

References Aleph::divide_and_conquer_partition_dp(), Aleph::geom_pi(), h, hr_, Aleph::square_root(), validate_positive_radii(), and vr_.

◆ rightmost_point()

Point Aleph::Ellipse::rightmost_point ( ) const

inline

Gets the rightmost point on the ellipse boundary.

Definition at line 2177 of file point.H.

References center_, Aleph::Point::get_x(), Aleph::Point::get_y(), and hr_.

Referenced by Aleph::Tikz_Plane::bbox_of().

◆ sample()

Point Aleph::Ellipse::sample ( const Geom_Number & angle ) const

inline

Samples a point on the ellipse's boundary at a given angle.

Parameters

angle The parametric angle in radians.

Returns: A Point on the ellipse's boundary.

Definition at line 2113 of file point.H.

References center_, Aleph::cosinus(), Aleph::divide_and_conquer_partition_dp(), Aleph::Point::get_x(), Aleph::Point::get_y(), hr_, Aleph::sinus(), validate_positive_radii(), and vr_.

◆ to_string()

std::string Aleph::Ellipse::to_string ( ) const

inline

Returns a string representation of the ellipse.

Returns: A std::string describing the ellipse's properties.

Definition at line 2126 of file point.H.

References center_, Aleph::geom_number_to_double(), hr_, Aleph::Point::to_string(), and vr_.

Referenced by Aleph::operator<<().

◆ validate_positive_radii()

void Aleph::Ellipse::validate_positive_radii ( ) const

inlineprivate

Validates that radii are positive.

Exceptions

std::domain_error if either radius is not > 0.

Definition at line 2138 of file point.H.

References ah_domain_error_if, Aleph::divide_and_conquer_partition_dp(), hr_, and vr_.

Referenced by Ellipse(), area(), compute_radius(), compute_tangents(), intersection_with(), intersects_with(), perimeter(), and sample().

Friends And Related Symbol Documentation

◆ Point

friend class Point

friend

Definition at line 2007 of file point.H.

Referenced by compute_tangents().

Member Data Documentation

◆ center_

Point Aleph::Ellipse::center_

private

Definition at line 2019 of file point.H.

Referenced by compute_radius(), compute_tangents(), get_center(), highest_point(), intersection_with(), intersects_with(), leftmost_point(), lowest_point(), operator==(), rightmost_point(), sample(), and to_string().

◆ hr_

Geom_Number Aleph::Ellipse::hr_

private

Definition at line 2021 of file point.H.

Referenced by area(), compute_radius(), compute_tangents(), get_hradius(), intersection_with(), intersects_with(), leftmost_point(), operator==(), perimeter(), rightmost_point(), sample(), to_string(), and validate_positive_radii().

◆ vr_

Geom_Number Aleph::Ellipse::vr_

private

Definition at line 2022 of file point.H.

Referenced by area(), compute_radius(), compute_tangents(), get_vradius(), highest_point(), intersection_with(), intersects_with(), lowest_point(), operator==(), perimeter(), sample(), to_string(), and validate_positive_radii().

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

point.H

Public Member Functions

Static Public Member Functions

Private Member Functions

Static Private Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Ellipse() [1/3]

◆ Ellipse() [2/3]

◆ Ellipse() [3/3]

Member Function Documentation

◆ area()

◆ compute_radius()

◆ compute_tangents()

◆ contains()

◆ contains_to()

◆ get_center()

◆ get_hradius()

◆ get_vradius()

◆ highest_point()

◆ in_unit_interval()

◆ intersection_with()

◆ intersects_with() [1/2]

◆ intersects_with() [2/2]

◆ is_clockwise()

◆ leftmost_point()

◆ lowest_point()

◆ operator!=()

◆ operator==()

◆ perimeter()

◆ rightmost_point()

◆ sample()

◆ to_string()

◆ validate_positive_radii()

Friends And Related Symbol Documentation

◆ Point

Member Data Documentation

◆ center_

◆ hr_

◆ vr_