2D infinite line in slope-intercept form. More...

#include <line.H>

Public Member Functions
constexpr	LineEq () noexcept=default
	Default constructor creates line y = x.

constexpr	LineEq (double __y0, double __m) noexcept
	Construct line from y-intercept and slope.

constexpr	LineEq (double x1, double y1, double __m) noexcept
	Construct line through a point with given slope.

	LineEq (double x1, double y1, double x2, double y2)
	Construct line through two points.

constexpr double	operator() (double x) const noexcept
	Evaluate line at given x-coordinate.

constexpr double	slope () const noexcept
	Get the slope of the line.

constexpr double	y_intercept () const noexcept
	Get the y-intercept of the line.

constexpr bool	is_horizontal (double epsilon=LINE_EPSILON) const noexcept
	Check if the line is horizontal (slope = 0).

constexpr bool	is_parallel_to (const LineEq &l, double epsilon=LINE_EPSILON) const noexcept
	Check if this line is parallel to another.

constexpr bool	is_perpendicular_to (const LineEq &l, double epsilon=LINE_EPSILON) const noexcept
	Check if this line is perpendicular to another.

double	x_at (double y) const
	Compute x-coordinate for a given y-coordinate.

std::pair< double, double >	intersection (const LineEq &l, double epsilon=LINE_EPSILON) const
	Compute intersection point with another line.

LineEq	perpendicular_through (double px, double py) const
	Compute perpendicular line through a point.

double	distance_to (double px, double py) const noexcept
	Compute distance from a point to this line.

bool	contains_point (double px, double py, double epsilon=LINE_EPSILON) const noexcept
	Check if a point lies on this line.

bool	operator== (const LineEq &l) const noexcept
	Test equality of two lines.

bool	operator!= (const LineEq &l) const noexcept
	Test inequality of two lines.

std::string	to_string () const
	Convert line to string representation.

Public Attributes
double	y0 = 0
	Y-intercept (where line crosses y-axis)

double	m = 1
	Slope (dy/dx)

Friends
std::ostream &	operator<< (std::ostream &out, const LineEq &l)
	Output stream operator.

Detailed Description

2D infinite line in slope-intercept form.

Represents an infinite line using the equation y = y0 + m*x where:

y0 is the y-intercept (value of y when x = 0)
m is the slope (dy/dx)

Note: This representation cannot handle vertical lines (infinite slope). For vertical lines, use parametric or implicit form.

Definition at line 120 of file line.H.

Constructor & Destructor Documentation

◆ LineEq() [1/4]

constexpr Aleph::LineEq::LineEq ( )

constexprdefaultnoexcept

Default constructor creates line y = x.

The default line passes through origin with slope 1.

Referenced by perpendicular_through().

◆ LineEq() [2/4]

constexpr Aleph::LineEq::LineEq	(	double	__y0,
		double	__m
	)

inlineconstexprnoexcept

Construct line from y-intercept and slope.

Creates line: y = y0 + m*x

Parameters

__y0	Y-intercept (value of y when x = 0)
__m	Slope of the line

Example: LineEq line(5.0, 2.0); // y = 5 + 2x

Aleph::LineEq
2D infinite line in slope-intercept form.
Definition line.H:121

Definition at line 145 of file line.H.

◆ LineEq() [3/4]

constexpr Aleph::LineEq::LineEq	(	double	x1,
		double	y1,
		double	__m
	)

inlineconstexprnoexcept

Construct line through a point with given slope.

Computes y-intercept from point and slope using: y0 = y1 - m*x1

Parameters

x1	X-coordinate of point on the line
y1	Y-coordinate of point on the line
__m	Slope of the line

Example: // Line through (2, 4) with slope 3

LineEq line(2.0, 4.0, 3.0); // y = -2 + 3x

Definition at line 163 of file line.H.

◆ LineEq() [4/4]

Aleph::LineEq::LineEq	(	double	x1,
		double	y1,
		double	x2,
		double	y2
	)

inline

Construct line through two points.

Computes slope and y-intercept from the two points. The slope is: m = (y2 - y1) / (x2 - x1)

Parameters

x1	X-coordinate of first point
y1	Y-coordinate of first point
x2	X-coordinate of second point
y2	Y-coordinate of second point

Exceptions

std::domain_error if x1 == x2 (vertical line, undefined slope)

Note: Horizontal lines (y1 == y2) are valid and result in slope = 0.

Example: LineEq line(0.0, 0.0, 2.0, 6.0); // y = 3x

LineEq horizontal(0.0, 5.0, 10.0, 5.0); // y = 5 (horizontal)

Definition at line 187 of file line.H.

References ah_domain_error_if, Aleph::LINE_EPSILON, m, y0, and y1().

Member Function Documentation

◆ contains_point()

bool Aleph::LineEq::contains_point	(	double	px,
		double	py,
		double	epsilon = `LINE_EPSILON`
	)		const

inlinenoexcept

Check if a point lies on this line.

Parameters

px	X-coordinate of point
py	Y-coordinate of point
epsilon	Tolerance for floating-point comparison

Returns: True if point is on the line

Definition at line 359 of file line.H.

References Aleph::maps().

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

◆ distance_to()

double Aleph::LineEq::distance_to	(	double	px,
		double	py
	)		const

inlinenoexcept

Compute distance from a point to this line.

Uses the formula: d = |y_point - (y0 + m*x_point)| / sqrt(1 + m^2)

Parameters

px	X-coordinate of point
py	Y-coordinate of point

Returns: Perpendicular distance from point to line

Definition at line 345 of file line.H.

References Aleph::diff(), m, Aleph::maps(), and y0.

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

◆ intersection()

std::pair< double, double > Aleph::LineEq::intersection	(	const LineEq &	l,
		double	epsilon = `LINE_EPSILON`
	)		const

inline

Compute intersection point with another line.

Solves the system of equations to find where lines cross:

y = y0_1 + m_1 * x
y = y0_2 + m_2 * x

Solution: x = (y0_1 - y0_2) / (m_2 - m_1)

Parameters

l	The other line
epsilon	Tolerance for parallel line detection

Returns: Pair (x, y) of intersection coordinates

Exceptions

std::domain_error if lines are parallel (no unique intersection)

Example: LineEq l1(0.0, 1.0); // y = x

LineEq l2(2.0, -1.0); // y = 2 - x

auto [x, y] = l1.intersection(l2); // (1, 1)

y
static mpfr_t y
Definition mpfr_mul_d.c:3

Definition at line 305 of file line.H.

References ah_domain_error_if, is_parallel_to(), l, m, and y0.

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

◆ is_horizontal()

constexpr bool Aleph::LineEq::is_horizontal ( double epsilon = LINE_EPSILON ) const

inlineconstexprnoexcept

Check if the line is horizontal (slope = 0).

Parameters

epsilon Tolerance for floating-point comparison

Returns: True if the line is horizontal

Definition at line 233 of file line.H.

References m.

Referenced by perpendicular_through(), TEST(), TEST_F(), TEST_F(), TEST_F(), and x_at().

◆ is_parallel_to()

constexpr bool Aleph::LineEq::is_parallel_to	(	const LineEq &	l,
		double	epsilon = `LINE_EPSILON`
	)		const

inlineconstexprnoexcept

Check if this line is parallel to another.

Two lines are parallel if they have the same slope.

Parameters

l	The other line
epsilon	Tolerance for floating-point comparison

Returns: True if lines are parallel

Definition at line 247 of file line.H.

References l, and m.

Referenced by intersection(), and TEST_F().

◆ is_perpendicular_to()

constexpr bool Aleph::LineEq::is_perpendicular_to	(	const LineEq &	l,
		double	epsilon = `LINE_EPSILON`
	)		const

inlineconstexprnoexcept

Check if this line is perpendicular to another.

Two lines are perpendicular if m1 * m2 = -1

Parameters

l	The other line
epsilon	Tolerance for floating-point comparison

Returns: True if lines are perpendicular

Definition at line 262 of file line.H.

References l, and m.

Referenced by TEST_F(), and TEST_F().

◆ operator!=()

bool Aleph::LineEq::operator!= ( const LineEq & l ) const

inlinenoexcept

Test inequality of two lines.

Parameters

l	Line to compare with

Returns: True if lines differ

Definition at line 386 of file line.H.

References l, and Aleph::maps().

◆ operator()()

constexpr double Aleph::LineEq::operator() ( double x ) const

inlineconstexprnoexcept

Evaluate line at given x-coordinate.

Computes y = y0 + m*x

Parameters

x	X-coordinate to evaluate

Returns: Y-coordinate on the line

Example: LineEq line(1.0, 2.0); // y = 1 + 2x

double y = line(3.0); // y = 7

Definition at line 211 of file line.H.

References m, and y0.

◆ operator==()

bool Aleph::LineEq::operator== ( const LineEq & l ) const

inlinenoexcept

Test equality of two lines.

Lines are equal if they have the same slope and y-intercept (within epsilon tolerance).

Parameters

l	Line to compare with

Returns: True if lines are identical

Definition at line 374 of file line.H.

References l, Aleph::LINE_EPSILON, m, Aleph::maps(), and y0.

◆ perpendicular_through()

LineEq Aleph::LineEq::perpendicular_through	(	double	px,
		double	py
	)		const

inline

Compute perpendicular line through a point.

Returns the line perpendicular to this one that passes through the given point. The perpendicular slope is -1/m.

Parameters

px	X-coordinate of point
py	Y-coordinate of point

Returns: Perpendicular line through (px, py)

Exceptions

std::domain_error if this line is horizontal (perpendicular would be vertical)

Definition at line 327 of file line.H.

References LineEq(), ah_domain_error_if, is_horizontal(), m, and Aleph::maps().

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

◆ slope()

constexpr double Aleph::LineEq::slope ( ) const

inlineconstexprnoexcept

Get the slope of the line.

Returns: The slope (m)

Definition at line 220 of file line.H.

References m.

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

◆ to_string()

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

inline

Convert line to string representation.

Returns: String in format "y = y0 + m * x"

Definition at line 396 of file line.H.

References m, and y0.

Referenced by TEST(), and TEST_F().

◆ x_at()

double Aleph::LineEq::x_at ( double y ) const

inline

Compute x-coordinate for a given y-coordinate.

Solves x = (y - y0) / m

Parameters

y	Y-coordinate

Returns: X-coordinate on the line

Exceptions

std::domain_error if line is horizontal (undefined x)

Definition at line 277 of file line.H.

References ah_domain_error_if, is_horizontal(), m, y, and y0.

Referenced by TEST_F(), and TEST_F().

◆ y_intercept()

constexpr double Aleph::LineEq::y_intercept ( ) const

inlineconstexprnoexcept

Get the y-intercept of the line.

Returns: The y-intercept (y0)

Definition at line 226 of file line.H.

References y0.

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

Friends And Related Symbol Documentation

◆ operator<<

std::ostream & operator<<	(	std::ostream &	out,
		const LineEq &	l
	)

friend

Output stream operator.

Parameters

out	Output stream
l	Line to output

Returns: Reference to output stream

Definition at line 410 of file line.H.

Member Data Documentation

◆ m

double Aleph::LineEq::m = 1

Slope (dy/dx)

Definition at line 123 of file line.H.

Referenced by LineEq(), distance_to(), intersection(), is_horizontal(), is_parallel_to(), is_perpendicular_to(), operator()(), operator==(), perpendicular_through(), slope(), TEST_F(), TEST_F(), TEST_F(), to_string(), and x_at().

◆ y0

double Aleph::LineEq::y0 = 0

Y-intercept (where line crosses y-axis)

Definition at line 122 of file line.H.

Referenced by LineEq(), distance_to(), intersection(), operator()(), operator==(), TEST_F(), TEST_F(), TEST_F(), to_string(), x_at(), and y_intercept().

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

line.H

Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ LineEq() [1/4]

◆ LineEq() [2/4]

◆ LineEq() [3/4]

◆ LineEq() [4/4]

Member Function Documentation

◆ contains_point()

◆ distance_to()

◆ intersection()

◆ is_horizontal()

◆ is_parallel_to()

◆ is_perpendicular_to()

◆ operator!=()

◆ operator()()

◆ operator==()

◆ perpendicular_through()

◆ slope()

◆ to_string()

◆ x_at()

◆ y_intercept()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ m

◆ y0