A regular polygon defined by center, side length, and vertex count. More...

#include <polygon.H>

Inheritance diagram for Aleph::Regular_Polygon:

Collaboration diagram for Aleph::Regular_Polygon:

Classes
class	Segment_Iterator
	Iterator over the edges (segments) of a regular polygon. More...

class	Vertex_Iterator
	Iterator over the vertices of a regular polygon. More...

Public Member Functions
	Regular_Polygon ()
	Default constructor.

	Regular_Polygon (Point c, const double &side_sz, const size_t &n, const double &ang=0)
	Construct a regular polygon.

const double &	get_side_size () const
	Get the side length.

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

const size_t &	size () const
	Get the number of vertices.

const double &	radius () const
	Get the circumradius.

bool	is_closed () const noexcept
	Check if the polygon is a valid closed regular polygon.

Point	get_vertex (const size_t &i) const
	Get the i-th vertex of the polygon.

Point	get_first_vertex () const
	Get the first vertex (index 0).

Point	get_last_vertex () const
	Get the last vertex (index size()-1).

Segment	get_first_segment () const
	Get the first segment (edge).

Segment	get_last_segment () const
	Get the last segment (closing edge).

Point	lowest_point () const
	Get the lowest point of the bounding circle.

Point	highest_point () const
	Get the highest point of the bounding circle.

Point	leftmost_point () const
	Get the leftmost point of the bounding circle.

Point	rightmost_point () const
	Get the rightmost point of the bounding circle.

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

virtual	~Geom_Object ()=default

Private Attributes
Point	center_
	Center point of the polygon.

double	side_size_
	Length of each side (double due to trig limitations)

size_t	num_vertex_
	Number of vertices (sides)

double	angle_
	Rotation angle in radians.

double	r_
	Circumradius (distance from center to vertices)

double	beta_
	Central angle between adjacent vertices (2π/n)

Detailed Description

A regular polygon defined by center, side length, and vertex count.

Regular_Polygon represents an n-sided regular polygon (equilateral and equiangular) defined parametrically by its center point, the length of each side, and the number of vertices.

Construction

The polygon is constructed using the law of sines to calculate the circumradius from the side length:

r = side_size * sin(alpha) / sin(beta)

sin

__gmp_expr< T, __gmp_unary_expr< __gmp_expr< T, U >, __gmp_sin_function > > sin(const __gmp_expr< T, U > &expr)

Definition gmpfrxx.h:4081

Aleph::blossom_maximum_cardinality_matching

size_t blossom_maximum_cardinality_matching(const GT &g, DynDlist< typename GT::Arc * > &matching, SA sa=SA())

Alias of compute_maximum_cardinality_general_matching().

Definition Blossom.H:466

r

gsl_rng * r

Definition test_sort_lists.C:45

Where:

beta = 2π/n (central angle)
alpha = (π - beta)/2 (angle between radius and side)

Vertex Numbering

Vertices are numbered 0 to n-1. Vertex 0 is positioned at angle angle from the negative y-axis (i.e., pointing "south" when angle=0).

Example

// Create a regular hexagon centered at (100, 100) with side length 50
Regular_Polygon hexagon(Point(100, 100), 50.0, 6);
 
// Iterate over vertices
for (size_t i = 0; i < hexagon.size(); ++i)
  std::cout << hexagon.get_vertex(i).to_string() << "\n";
 
// Create rotated square (45 degrees = PI/4 radians)
Regular_Polygon diamond(Point(0, 0), 100.0, 4, PI/4);

Note: This class uses double internally for side length, angles, and circumradius because vertex positions require trigonometric functions (sin, cos) whose results are transcendental and cannot be exactly represented in Geom_Number (rational arithmetic). The center point remains exact; vertex coordinates are computed with floating-point precision.

See also: Polygon

Definition at line 1134 of file polygon.H.

Constructor & Destructor Documentation

◆ Regular_Polygon() [1/2]

Aleph::Regular_Polygon::Regular_Polygon ( )

inline

Default constructor.

Creates a completely initialized empty polygon at the origin.

Definition at line 1148 of file polygon.H.

◆ Regular_Polygon() [2/2]

Aleph::Regular_Polygon::Regular_Polygon	(	Point	c,
		const double &	side_sz,
		const size_t &	n,
		const double &	ang = `0`
	)

inline

Construct a regular polygon.

Parameters

c	Center point of the polygon.
side_sz	Length of each side.
n	Number of vertices (must be >= 3).
ang	Rotation angle in radians (default 0).

Exceptions

std::domain_error If n is less than 3, side_sz is not positive and finite, ang is not finite, or the derived circumradius is not representable.

Definition at line 1163 of file polygon.H.

References ah_domain_error_if, beta_, Aleph::blossom_maximum_cardinality_matching(), Aleph::PI, r_, side_size_, and sin().

Member Function Documentation

◆ get_center()

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

inline

Get the center point.

Returns: Reference to the center point.

Definition at line 1192 of file polygon.H.

References center_.

Referenced by Aleph::operator<<(), TEST_F(), and TEST_F().

◆ get_first_segment()

Segment Aleph::Regular_Polygon::get_first_segment ( ) const

inline

Get the first segment (edge).

Returns: Segment from vertex 0 to vertex 1.

Definition at line 1242 of file polygon.H.

References get_vertex().

◆ get_first_vertex()

Point Aleph::Regular_Polygon::get_first_vertex ( ) const

inline

Get the first vertex (index 0).

Returns: The first vertex point.

Definition at line 1234 of file polygon.H.

References get_vertex().

◆ get_last_segment()

Segment Aleph::Regular_Polygon::get_last_segment ( ) const

inline

Get the last segment (closing edge).

Returns: Segment from the last vertex to vertex 0.

Definition at line 1249 of file polygon.H.

References get_vertex(), and num_vertex_.

◆ get_last_vertex()

Point Aleph::Regular_Polygon::get_last_vertex ( ) const

inline

Get the last vertex (index size()-1).

Returns: The last vertex point.

Definition at line 1238 of file polygon.H.

References get_vertex(), and num_vertex_.

◆ get_side_size()

const double & Aleph::Regular_Polygon::get_side_size ( ) const

inline

Get the side length.

Returns: Length of each side.

Definition at line 1188 of file polygon.H.

References side_size_.

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

◆ get_vertex()

Point Aleph::Regular_Polygon::get_vertex ( const size_t & i ) const

inline

Get the i-th vertex of the polygon.

Vertex 0 is at angle angle from the negative y-axis. Subsequent vertices are placed at equal angular intervals counter-clockwise.

Parameters

i	Vertex index (0 to size()-1).

Returns: The vertex point.

Exceptions

std::out_of_range If i >= size().

Definition at line 1218 of file polygon.H.

References ah_out_of_range_error_if, angle_, beta_, center_, Aleph::Segment::get_tgt_point(), num_vertex_, r_, and Aleph::Segment::rotate().

Referenced by Aleph::Tikz_Plane::bbox_of(), build_poly_graph(), Aleph::Polygon::copy_regular_polygon(), Aleph::Tikz_Plane::draw_regular_polygon(), Aleph::Regular_Polygon::Segment_Iterator::get_current_segment(), Aleph::Regular_Polygon::Vertex_Iterator::get_current_vertex(), get_first_segment(), get_first_vertex(), get_last_segment(), get_last_vertex(), Aleph::put_polygon_vertices(), TEST(), TEST_F(), TEST_F(), and TEST_F().

◆ highest_point()

Point Aleph::Regular_Polygon::highest_point ( ) const

inline

Get the highest point of the bounding circle.

Returns: Point at the top of the circumscribed circle.

Definition at line 1385 of file polygon.H.

References center_, and r_.

◆ is_closed()

bool Aleph::Regular_Polygon::is_closed ( ) const

inlinenoexcept

Check if the polygon is a valid closed regular polygon.

Returns: True for constructed polygons and false for the default empty state.

Note: This is an instance query because closure depends on whether the object represents a constructed polygon or the default empty state.

Definition at line 1207 of file polygon.H.

References num_vertex_.

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

◆ leftmost_point()

Point Aleph::Regular_Polygon::leftmost_point ( ) const

inline

Get the leftmost point of the bounding circle.

Returns: Point at the left of the circumscribed circle.

Definition at line 1389 of file polygon.H.

References center_, and r_.

◆ lowest_point()

Point Aleph::Regular_Polygon::lowest_point ( ) const

inline

Get the lowest point of the bounding circle.

Returns: Point at the bottom of the circumscribed circle.

Note: For simplicity, returns cardinal points of the circumcircle, not the actual extreme vertices.

Definition at line 1381 of file polygon.H.

References center_, and r_.

◆ radius()

const double & Aleph::Regular_Polygon::radius ( ) const

inline

Get the circumradius.

Returns: Distance from center to each vertex.

Definition at line 1200 of file polygon.H.

References r_.

Referenced by main(), Aleph::operator<<(), TEST(), TEST_F(), TEST_F(), and TEST_F().

◆ rightmost_point()

Point Aleph::Regular_Polygon::rightmost_point ( ) const

inline

Get the rightmost point of the bounding circle.

Returns: Point at the right of the circumscribed circle.

Definition at line 1393 of file polygon.H.

References center_, and r_.

◆ size()

const size_t & Aleph::Regular_Polygon::size ( ) const

inline

Get the number of vertices.

Returns: Number of vertices (and sides).

Definition at line 1196 of file polygon.H.

References num_vertex_.

Referenced by Aleph::Tikz_Plane::bbox_of(), Aleph::Polygon::copy_regular_polygon(), Aleph::Tikz_Plane::draw_regular_polygon(), Aleph::Regular_Polygon::Segment_Iterator::get_current_segment(), Aleph::Regular_Polygon::Vertex_Iterator::has_curr(), Aleph::Regular_Polygon::Segment_Iterator::has_curr(), main(), Aleph::operator<<(), Aleph::put_polygon_vertices(), TEST(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

Member Data Documentation

◆ angle_

double Aleph::Regular_Polygon::angle_

private

Rotation angle in radians.

Definition at line 1139 of file polygon.H.

Referenced by get_vertex().

◆ beta_

double Aleph::Regular_Polygon::beta_

private

Central angle between adjacent vertices (2π/n)

Definition at line 1141 of file polygon.H.

Referenced by Regular_Polygon(), and get_vertex().

◆ center_

Point Aleph::Regular_Polygon::center_

private

Center point of the polygon.

Definition at line 1136 of file polygon.H.

Referenced by get_center(), get_vertex(), highest_point(), leftmost_point(), lowest_point(), and rightmost_point().

◆ num_vertex_

size_t Aleph::Regular_Polygon::num_vertex_

private

Number of vertices (sides)

Definition at line 1138 of file polygon.H.

Referenced by get_last_segment(), get_last_vertex(), get_vertex(), is_closed(), and size().

◆ r_

double Aleph::Regular_Polygon::r_

private

Circumradius (distance from center to vertices)

Definition at line 1140 of file polygon.H.

Referenced by Regular_Polygon(), get_vertex(), highest_point(), leftmost_point(), lowest_point(), radius(), and rightmost_point().

◆ side_size_

double Aleph::Regular_Polygon::side_size_

private

Length of each side (double due to trig limitations)

Definition at line 1137 of file polygon.H.

Referenced by Regular_Polygon(), and get_side_size().

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

polygon.H

Classes

Public Member Functions

Private Attributes

Detailed Description

Construction

Vertex Numbering

Example

Constructor & Destructor Documentation

◆ Regular_Polygon() [1/2]

◆ Regular_Polygon() [2/2]

Member Function Documentation

◆ get_center()

◆ get_first_segment()

◆ get_first_vertex()

◆ get_last_segment()

◆ get_last_vertex()

◆ get_side_size()

◆ get_vertex()

◆ highest_point()

◆ is_closed()

◆ leftmost_point()

◆ lowest_point()

◆ radius()

◆ rightmost_point()

◆ size()

Member Data Documentation

◆ angle_

◆ beta_

◆ center_

◆ num_vertex_

◆ r_

◆ side_size_