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

#include <line.H>

Collaboration diagram for Aleph::LineEq:

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

	LineEq (const Geom_Number &__y0, const Geom_Number &__m) noexcept
	Construct line from y-intercept and slope.

	LineEq (const Geom_Number &x1, const Geom_Number &y1, const Geom_Number &__m) noexcept
	Construct line through a point with given slope.

	LineEq (const Geom_Number &x1, const Geom_Number &y1, const Geom_Number &x2, const Geom_Number &y2)
	Construct a line through two points.

	LineEq (const Point &p, const Geom_Number &__m) noexcept
	Construct a line through a Point with a given slope.

	LineEq (const Point &p1, const Point &p2)
	Construct line through two Points.

Geom_Number	operator() (const Geom_Number &x) const noexcept
	Evaluate line at given x-coordinate.

const Geom_Number &	slope () const noexcept
	Get the slope of the line.

const Geom_Number &	y_intercept () const noexcept
	Get the y-intercept of the line.

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

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

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

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

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

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

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

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

Geom_Number	distance_to (const Point &p) const noexcept
	Compute distance from a Point to this line.

LineEq	perpendicular_through (const Point &p) const
	Compute a perpendicular line through a Point.

bool	contains_point (const Point &p, const Geom_Number &epsilon=LINE_EPSILON) const noexcept
	Check if a Point lies on this line.

Point	intersection_point (const LineEq &l, const Geom_Number &epsilon=LINE_EPSILON) const
	Compute the intersection Point with another 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.

bool	approx_equal (const LineEq &l, const Geom_Number &epsilon) const noexcept
	Test approximate equality of two lines.

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

Public Attributes
Geom_Number	y0 {0}
	Y-intercept (where line crosses y-axis)

Geom_Number	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 125 of file line.H.

Constructor & Destructor Documentation

◆ LineEq() [1/6]

constexpr Aleph::LineEq::LineEq ( )

constexprdefaultnoexcept

Default constructor creates line y = x.

The default line passes through origin with slope 1.

◆ LineEq() [2/6]

Aleph::LineEq::LineEq	(	const Geom_Number &	__y0,
		const Geom_Number &	__m
	)

inlinenoexcept

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(Geom_Number(5), Geom_Number(2)); // y = 5 + 2x

Aleph::Geom_Number
mpq_class Geom_Number
Numeric type used by the geometry module.
Definition point.H:115

Aleph::LineEq
2D infinite line in slope-intercept form.
Definition line.H:126

Definition at line 150 of file line.H.

◆ LineEq() [3/6]

Aleph::LineEq::LineEq	(	const Geom_Number &	x1,
		const Geom_Number &	y1,
		const Geom_Number &	__m
	)

inlinenoexcept

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(Geom_Number(2), Geom_Number(4), Geom_Number(3)); // y = -2 + 3x

Definition at line 168 of file line.H.

◆ LineEq() [4/6]

Aleph::LineEq::LineEq	(	const Geom_Number &	x1,
		const Geom_Number &	y1,
		const Geom_Number &	x2,
		const Geom_Number &	y2
	)

inline

Construct a 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

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

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

Example: LineEq line(Geom_Number(0), Geom_Number(0), Geom_Number(2), Geom_Number(6)); // y = 3x

LineEq horizontal(Geom_Number(0), Geom_Number(5), Geom_Number(10), Geom_Number(5)); // y = 5 (horizontal)

Definition at line 192 of file line.H.

References ah_domain_error_if, m, y0, and y1().

◆ LineEq() [5/6]

Aleph::LineEq::LineEq	(	const Point &	p,
		const Geom_Number &	__m
	)

inlinenoexcept

Construct a line through a Point with a given slope.

Parameters

p	Point on the line
__m	Slope of the line

Example: Point p(Geom_Number(2), Geom_Number(4));

LineEq line(p, Geom_Number(3)); // Line through (2, 4) with slope 3

Aleph::Point
Represents a point with rectangular coordinates in a 2D plane.
Definition point.H:229

Definition at line 215 of file line.H.

◆ LineEq() [6/6]

Aleph::LineEq::LineEq	(	const Point &	p1,
		const Point &	p2
	)

inline

Construct line through two Points.

Parameters

p1	First point
p2	Second point

Exceptions

domain_error if points have the same x-coordinate (vertical line)

Example: Point a(Geom_Number(0), Geom_Number(0));

Point b(Geom_Number(2), Geom_Number(6));

LineEq line(a, b); // y = 3x

Definition at line 232 of file line.H.

Member Function Documentation

◆ approx_equal()

bool Aleph::LineEq::approx_equal	(	const LineEq &	l,
		const Geom_Number &	epsilon
	)		const

inlinenoexcept

Test approximate equality of two lines.

Lines are approximately equal if their slope and y-intercept are within an epsilon tolerance.

Parameters

l	Line to compare with
epsilon	Tolerance for comparison

Returns: True if lines are approximately equal

Definition at line 497 of file line.H.

References abs(), Aleph::and, l, m, and y0.

◆ contains_point() [1/2]

bool Aleph::LineEq::contains_point	(	const Geom_Number &	px,
		const Geom_Number &	py,
		const Geom_Number &	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 comparison (default: exact equality)

Returns: True if point is on the line

Definition at line 399 of file line.H.

References abs(), and Aleph::divide_and_conquer_partition_dp().

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

◆ contains_point() [2/2]

bool Aleph::LineEq::contains_point	(	const Point &	p,
		const Geom_Number &	epsilon = `LINE_EPSILON`
	)		const

inlinenoexcept

Check if a Point lies on this line.

Parameters

p	The point to test
epsilon	Tolerance for comparison (default: exact equality)

Returns: True if the point is on the line

Definition at line 435 of file line.H.

References contains_point().

◆ distance_to() [1/2]

Geom_Number Aleph::LineEq::distance_to	(	const Geom_Number &	px,
		const Geom_Number &	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 383 of file line.H.

References abs(), Aleph::diff(), Aleph::divide_and_conquer_partition_dp(), m, sqrt(), and y0.

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

◆ distance_to() [2/2]

Geom_Number Aleph::LineEq::distance_to ( const Point & p ) const

inlinenoexcept

Compute distance from a Point to this line.

Parameters

p The point

Returns: Perpendicular distance from point to line

Definition at line 411 of file line.H.

References distance_to().

◆ intersection()

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

inline

Compute the 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

domain_error if lines are parallel (no unique intersection)

Example: LineEq l1(Geom_Number(0), Geom_Number(1)); // y = x

LineEq l2(Geom_Number(2), Geom_Number(-1)); // y = 2 - x

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

y
static mpfr_t y
Definition mpfr_mul_d.c:3

l1
DynList< int > l1
Definition test-zip-it.cc:36

l2
DynList< int > l2
Definition test-zip-it.cc:37

Definition at line 343 of file line.H.

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

Referenced by intersection_point(), and TEST_F().

◆ intersection_point()

Point Aleph::LineEq::intersection_point	(	const LineEq &	l,
		const Geom_Number &	epsilon = `LINE_EPSILON`
	)		const

inline

Compute the intersection Point with another line.

Parameters

l	The other line
epsilon	Tolerance for parallel line detection

Returns: Intersection point

Exceptions

domain_error if lines are parallel (no unique intersection)

Example: LineEq l1(Geom_Number(0), Geom_Number(1)); // y = x

LineEq l2(Geom_Number(2), Geom_Number(-1)); // y = 2 - x

Point p = l1.intersection_point(l2); // Point(1, 1)

Definition at line 456 of file line.H.

References intersection(), l, and y.

◆ is_horizontal()

bool Aleph::LineEq::is_horizontal ( const Geom_Number & epsilon = LINE_EPSILON ) const

inlinenoexcept

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

Parameters

epsilon Tolerance for comparison (default: exact equality)

Returns: True if the line is horizontal

Definition at line 271 of file line.H.

References abs(), and m.

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

◆ is_parallel_to()

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

inlinenoexcept

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 comparison (default: exact equality)

Returns: True if lines are parallel

Definition at line 285 of file line.H.

References abs(), l, and m.

Referenced by intersection().

◆ is_perpendicular_to()

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

inlinenoexcept

Check if this line is perpendicular to another.

Two lines are perpendicular if m1 * m2 = -1

Parameters

l	The other line
epsilon	Tolerance for comparison (default: exact equality)

Returns: True if lines are perpendicular

Definition at line 300 of file line.H.

References abs(), l, and m.

◆ 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 482 of file line.H.

References Aleph::divide_and_conquer_partition_dp(), and l.

◆ operator()()

Geom_Number Aleph::LineEq::operator() ( const Geom_Number & x ) const

inlinenoexcept

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(Geom_Number(1), Geom_Number(2)); // y = 1 + 2x

Geom_Number y = line(Geom_Number(3)); // y = 7

__gmp_expr< mpq_t, mpq_t >
Definition gmpfrxx.h:2041

Definition at line 249 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.

Parameters

l	Line to compare with

Returns: True if lines are identical

Definition at line 471 of file line.H.

References Aleph::and, l, m, and y0.

◆ perpendicular_through() [1/2]

LineEq Aleph::LineEq::perpendicular_through	(	const Geom_Number &	px,
		const Geom_Number &	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

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

Definition at line 365 of file line.H.

References ah_domain_error_if, Aleph::divide_and_conquer_partition_dp(), is_horizontal(), and m.

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

◆ perpendicular_through() [2/2]

LineEq Aleph::LineEq::perpendicular_through ( const Point & p ) const

inline

Compute a perpendicular line through a Point.

Parameters

p	Point on the perpendicular line

Returns: Perpendicular line through p

Exceptions

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

Definition at line 423 of file line.H.

References Aleph::Point::get_x(), Aleph::Point::get_y(), and perpendicular_through().

◆ slope()

const Geom_Number & Aleph::LineEq::slope ( ) const

inlinenoexcept

Get the slope of the line.

Returns: The slope (m)

Definition at line 258 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 a string representation.

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

Definition at line 507 of file line.H.

References m, and y0.

Referenced by TEST(), and TEST_F().

◆ x_at()

Geom_Number Aleph::LineEq::x_at ( const Geom_Number & 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

domain_error if line is horizontal (undefined x)

Definition at line 315 of file line.H.

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

Referenced by TEST_F(), and TEST_F().

◆ y_intercept()

const Geom_Number & Aleph::LineEq::y_intercept ( ) const

inlinenoexcept

Get the y-intercept of the line.

Returns: The y-intercept (y0)

Definition at line 264 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	The output stream.
l	The line to output.

Returns: A reference to the output stream.

Definition at line 521 of file line.H.

Member Data Documentation

◆ m

Geom_Number Aleph::LineEq::m {1}

Slope (dy/dx)

Definition at line 128 of file line.H.

Referenced by LineEq(), approx_equal(), 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

Geom_Number Aleph::LineEq::y0 {0}

Y-intercept (where line crosses y-axis)

Definition at line 127 of file line.H.

Referenced by LineEq(), approx_equal(), 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() [1/6]

◆ LineEq() [2/6]

◆ LineEq() [3/6]

◆ LineEq() [4/6]

◆ LineEq() [5/6]

◆ LineEq() [6/6]

Member Function Documentation

◆ approx_equal()

◆ contains_point() [1/2]

◆ contains_point() [2/2]

◆ distance_to() [1/2]

◆ distance_to() [2/2]

◆ intersection()

◆ intersection_point()

◆ is_horizontal()

◆ is_parallel_to()

◆ is_perpendicular_to()

◆ operator!=()

◆ operator()()

◆ operator==()

◆ perpendicular_through() [1/2]

◆ perpendicular_through() [2/2]

◆ slope()

◆ to_string()

◆ x_at()

◆ y_intercept()

Friends And Related Symbol Documentation

◆ operator<<

Member Data Documentation

◆ m

◆ y0