An ellipse with arbitrary rotation. More...

#include <point.H>

Inheritance diagram for Aleph::RotatedEllipse:

Collaboration diagram for Aleph::RotatedEllipse:

Classes
struct	ExtremalPoints
	Holds the four axis-extremal points of a rotated ellipse. More...

Public Member Functions
	RotatedEllipse (Point center, const Geom_Number &a, const Geom_Number &b, const Geom_Number &cos_theta, const Geom_Number &sin_theta)
	Constructs a rotated ellipse.

	RotatedEllipse (Point center, const Geom_Number &a, const Geom_Number &b)
	Constructs an axis-aligned ellipse (rotation angle is 0).

	RotatedEllipse ()
	Default constructor.

	RotatedEllipse (const RotatedEllipse &)=default

RotatedEllipse &	operator= (const RotatedEllipse &)=default

bool	operator== (const RotatedEllipse &e) const noexcept
	Checks for exact equality between two rotated ellipses.

bool	operator!= (const RotatedEllipse &e) const noexcept
	Checks for inequality between two rotated ellipses.

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

const Geom_Number &	get_a () const
	Gets the semi-axis 'a' (local x-axis radius).

const Geom_Number &	get_b () const
	Gets the semi-axis 'b' (local y-axis radius).

const Geom_Number &	get_cos () const
	Gets the cosine of the rotation angle.

const Geom_Number &	get_sin () const
	Gets the sine of the rotation angle.

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

Geom_Number	radius_value (const Point &p) const
	Evaluates the ellipse equation for a given point.

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

bool	strictly_contains (const Point &p) const
	Checks if a point lies strictly inside the ellipse.

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

Point	sample (const Geom_Number &cos_t, const Geom_Number &sin_t) const
	Samples a point on the ellipse boundary from a parametric angle.

Point	sample (const Geom_Number &t) const
	Samples a point on the ellipse boundary for a parameter `t`.

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

Segment	intersection_with (const Segment &s) const
	Computes the intersection segment between `s` and this ellipse.

std::string	to_string () const

ExtremalPoints	extremal_points () const
	Computes the four axis-extremal points of the rotated ellipse.

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

virtual	~Geom_Object ()=default

Private Member Functions
Point	to_local (const Point &p) const
	Transforms a world point to the ellipse's local, unrotated frame.

Point	to_world (const Point &p) const
	Transforms a point from the ellipse's local frame back to world coordinates.

void	validate_positive_radii () const
	Validates that semi-axes are positive.

void	normalize_rotation ()
	Normalizes the rotation (cos, sin) vector to ensure it's a unit vector.

Private Attributes
Point	center_

Geom_Number	a_

Geom_Number	b_

Geom_Number	cos_th_

Geom_Number	sin_th_

Detailed Description

An ellipse with arbitrary rotation.

Extends the axis-aligned Ellipse by adding a rotation angle. The implicit equation in the rotated frame is:

`((x' - cx)² / a²) + ((y' - cy)² / b²) = 1`

where ‘(x’, y')are coordinates rotated by-θ` around the center.

Since exact trigonometry is often not possible with rational numbers, the rotation is specified by its cosine and sine as exact Geom_Number values. The user is responsible for providing these values.

Definition at line 2472 of file point.H.

Constructor & Destructor Documentation

◆ RotatedEllipse() [1/4]

Aleph::RotatedEllipse::RotatedEllipse	(	Point	center,
		const Geom_Number &	a,
		const Geom_Number &	b,
		const Geom_Number &	cos_theta,
		const Geom_Number &	sin_theta
	)

inline

Constructs a rotated ellipse.

Parameters

center	The center point.
a	The semi-axis length along the ellipse's local x-axis.
b	The semi-axis length along the ellipse's local y-axis.
cos_theta	The cosine of the rotation angle.
sin_theta	The sine of the rotation angle.

Definition at line 2537 of file point.H.

References normalize_rotation(), and validate_positive_radii().

◆ RotatedEllipse() [2/4]

Aleph::RotatedEllipse::RotatedEllipse	(	Point	center,
		const Geom_Number &	a,
		const Geom_Number &	b
	)

inline

Constructs an axis-aligned ellipse (rotation angle is 0).

Parameters

center	The center point.
a	The semi-axis length (horizontal radius).
b	The semi-axis length (vertical radius).

Definition at line 2551 of file point.H.

References validate_positive_radii().

◆ RotatedEllipse() [3/4]

Aleph::RotatedEllipse::RotatedEllipse ( )

inline

Default constructor.

Note: Creates a unit circle at the origin with no rotation.

Definition at line 2561 of file point.H.

◆ RotatedEllipse() [4/4]

Aleph::RotatedEllipse::RotatedEllipse ( const RotatedEllipse & )

default

Member Function Documentation

◆ area()

Geom_Number Aleph::RotatedEllipse::area ( ) const

inline

Calculates the area of the ellipse.

Returns: The area (pi * a * b).

Definition at line 2621 of file point.H.

References a_, b_, Aleph::geom_pi(), and validate_positive_radii().

◆ contains()

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

inline

Checks if a point lies inside or on the ellipse.

Parameters

p	The point to check.

Returns: true if the point is contained.

Definition at line 2646 of file point.H.

References radius_value().

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

◆ extremal_points()

ExtremalPoints Aleph::RotatedEllipse::extremal_points ( ) const

inline

Computes the four axis-extremal points of the rotated ellipse.

Note: These are the points on the ellipse that are most to the right, top, left, and bottom in the world coordinate system.

Returns: An ExtremalPoints struct.

Definition at line 2743 of file point.H.

References a_, b_, Aleph::blossom_maximum_cardinality_matching(), center_, cos_th_, Aleph::Point::get_x(), Aleph::Point::get_y(), sin_th_, Aleph::square_root(), and validate_positive_radii().

Referenced by Aleph::Tikz_Plane::bbox_of(), TEST_F(), and TEST_F().

◆ get_a()

const Geom_Number & Aleph::RotatedEllipse::get_a ( ) const

inline

Gets the semi-axis 'a' (local x-axis radius).

Definition at line 2597 of file point.H.

References a_.

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

◆ get_b()

const Geom_Number & Aleph::RotatedEllipse::get_b ( ) const

inline

Gets the semi-axis 'b' (local y-axis radius).

Definition at line 2602 of file point.H.

References b_.

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

◆ get_center()

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

inline

Gets the center point.

Definition at line 2592 of file point.H.

References center_.

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

◆ get_cos()

const Geom_Number & Aleph::RotatedEllipse::get_cos ( ) const

inline

Gets the cosine of the rotation angle.

Definition at line 2607 of file point.H.

References cos_th_.

Referenced by Aleph::Tikz_Plane::draw_rotated_ellipse(), and TEST_F().

◆ get_sin()

const Geom_Number & Aleph::RotatedEllipse::get_sin ( ) const

inline

Gets the sine of the rotation angle.

Definition at line 2612 of file point.H.

References sin_th_.

Referenced by Aleph::Tikz_Plane::draw_rotated_ellipse(), and TEST_F().

◆ intersection_with()

Segment Aleph::RotatedEllipse::intersection_with ( const Segment & s ) const

inline

Computes the intersection segment between s and this ellipse.

Parameters

s	The segment to intersect with.

Returns: The intersection Segment. Can be a point for tangency.

Exceptions

std::domain_error if there is no intersection.

Definition at line 2714 of file point.H.

References a_, b_, Aleph::blossom_maximum_cardinality_matching(), Aleph::Segment::get_src_point(), Aleph::Segment::get_tgt_point(), Aleph::Ellipse::intersection_with(), to_local(), to_world(), and validate_positive_radii().

Referenced by TEST_F().

◆ intersects_with()

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

inline

Checks if a segment intersects this rotated ellipse.

Parameters

s	The segment to check.

Returns: true if they share at least one point.

Definition at line 2701 of file point.H.

References a_, b_, Aleph::blossom_maximum_cardinality_matching(), Aleph::Segment::get_src_point(), Aleph::Segment::get_tgt_point(), Aleph::Ellipse::intersects_with(), to_local(), and validate_positive_radii().

Referenced by TEST_F().

◆ normalize_rotation()

void Aleph::RotatedEllipse::normalize_rotation ( )

inlineprivate

Normalizes the rotation (cos, sin) vector to ensure it's a unit vector.

Exceptions

std::domain_error if the rotation vector is (0,0).

Definition at line 2516 of file point.H.

References ah_domain_error_if, cos_th_, sin_th_, and Aleph::square_root().

Referenced by RotatedEllipse().

◆ on_boundary()

bool Aleph::RotatedEllipse::on_boundary ( 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 2666 of file point.H.

References radius_value().

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

◆ operator!=()

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

inlinenoexcept

Checks for inequality between two rotated ellipses.

Parameters

e	The other ellipse.

Returns: true if any parameter is different.

Definition at line 2586 of file point.H.

References Aleph::blossom_maximum_cardinality_matching().

◆ operator=()

RotatedEllipse & Aleph::RotatedEllipse::operator= ( const RotatedEllipse & )

default

◆ operator==()

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

inlinenoexcept

Checks for exact equality between two rotated ellipses.

Parameters

e	The other ellipse.

Returns: true if all parameters (center, axes, rotation) are identical.

Definition at line 2575 of file point.H.

References a_, Aleph::and, b_, center_, cos_th_, and sin_th_.

◆ radius_value()

Geom_Number Aleph::RotatedEllipse::radius_value ( const Point & p ) const

inline

Evaluates the ellipse equation for a given point.

Parameters

p	The point in world coordinates.

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

Definition at line 2633 of file point.H.

References a_, b_, Aleph::blossom_maximum_cardinality_matching(), to_local(), and validate_positive_radii().

Referenced by contains(), on_boundary(), strictly_contains(), and TEST_F().

◆ sample() [1/2]

Point Aleph::RotatedEllipse::sample	(	const Geom_Number &	cos_t,
		const Geom_Number &	sin_t
	)		const

inline

Samples a point on the ellipse boundary from a parametric angle.

Parameters

cos_t	The cosine of the parameter angle `t`.
sin_t	The sine of the parameter angle `t`.

Returns: The corresponding Point on the ellipse in world coordinates.

Definition at line 2677 of file point.H.

References a_, b_, Aleph::blossom_maximum_cardinality_matching(), to_world(), and validate_positive_radii().

Referenced by sample(), and TEST_F().

◆ sample() [2/2]

Point Aleph::RotatedEllipse::sample ( const Geom_Number & t ) const

inline

Samples a point on the ellipse boundary for a parameter t.

Parameters

t	A parameter in [0, 1], which maps to an angle in [0, 2π).

Returns: The corresponding Point on the ellipse.

Definition at line 2690 of file point.H.

References Aleph::blossom_maximum_cardinality_matching(), Aleph::cosinus(), Aleph::geom_pi(), sample(), and Aleph::sinus().

◆ strictly_contains()

bool Aleph::RotatedEllipse::strictly_contains ( const Point & p ) const

inline

Checks if a point lies strictly inside the ellipse.

Parameters

p	The point to check.

Returns: true if the point is strictly inside.

Definition at line 2656 of file point.H.

References radius_value().

Referenced by TEST_F().

◆ to_local()

Point Aleph::RotatedEllipse::to_local ( const Point & p ) const

inlineprivate

Transforms a world point to the ellipse's local, unrotated frame.

Parameters

p	A point in world coordinates.

Returns: The corresponding point in the ellipse's local coordinate system.

Definition at line 2485 of file point.H.

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

Referenced by intersection_with(), intersects_with(), and radius_value().

◆ to_string()

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

inline

Definition at line 2722 of file point.H.

References a_, b_, center_, cos_th_, Aleph::geom_number_to_double(), sin_th_, and Aleph::Point::to_string().

Referenced by Aleph::operator<<().

◆ to_world()

Point Aleph::RotatedEllipse::to_world ( const Point & p ) const

inlineprivate

Transforms a point from the ellipse's local frame back to world coordinates.

Parameters

p	A point in the ellipse's local coordinate system.

Returns: The corresponding point in world coordinates.

Definition at line 2497 of file point.H.

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

Referenced by intersection_with(), and sample().

◆ validate_positive_radii()

void Aleph::RotatedEllipse::validate_positive_radii ( ) const

inlineprivate

Validates that semi-axes are positive.

Exceptions

std::domain_error if either a_ or b_ is not > 0.

Definition at line 2507 of file point.H.

References a_, ah_domain_error_if, b_, and Aleph::blossom_maximum_cardinality_matching().

Referenced by RotatedEllipse(), RotatedEllipse(), area(), extremal_points(), intersection_with(), intersects_with(), radius_value(), and sample().

Member Data Documentation

◆ a_

Geom_Number Aleph::RotatedEllipse::a_

private

Definition at line 2475 of file point.H.

Referenced by area(), extremal_points(), get_a(), intersection_with(), intersects_with(), operator==(), radius_value(), sample(), to_string(), and validate_positive_radii().

◆ b_

Geom_Number Aleph::RotatedEllipse::b_

private

Definition at line 2476 of file point.H.

Referenced by area(), extremal_points(), get_b(), intersection_with(), intersects_with(), operator==(), radius_value(), sample(), to_string(), and validate_positive_radii().

◆ center_

Point Aleph::RotatedEllipse::center_

private

Definition at line 2474 of file point.H.

Referenced by extremal_points(), get_center(), operator==(), to_local(), to_string(), and to_world().

◆ cos_th_

Geom_Number Aleph::RotatedEllipse::cos_th_

private

Definition at line 2477 of file point.H.

Referenced by extremal_points(), get_cos(), normalize_rotation(), operator==(), to_local(), to_string(), and to_world().

◆ sin_th_

Geom_Number Aleph::RotatedEllipse::sin_th_

private

Definition at line 2478 of file point.H.

Referenced by extremal_points(), get_sin(), normalize_rotation(), operator==(), to_local(), to_string(), and to_world().

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

point.H

Classes

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RotatedEllipse() [1/4]

◆ RotatedEllipse() [2/4]

◆ RotatedEllipse() [3/4]

◆ RotatedEllipse() [4/4]

Member Function Documentation

◆ area()

◆ contains()

◆ extremal_points()

◆ get_a()

◆ get_b()

◆ get_center()

◆ get_cos()

◆ get_sin()

◆ intersection_with()

◆ intersects_with()

◆ normalize_rotation()

◆ on_boundary()

◆ operator!=()

◆ operator=()

◆ operator==()

◆ radius_value()

◆ sample() [1/2]

◆ sample() [2/2]

◆ strictly_contains()

◆ to_local()

◆ to_string()

◆ to_world()

◆ validate_positive_radii()

Member Data Documentation

◆ a_

◆ b_

◆ center_

◆ cos_th_

◆ sin_th_