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

#include <polygon.H>

Inheritance diagram for Regular_Polygon:

Collaboration diagram for 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. Creates an invalid empty polygon.

	Regular_Polygon (const 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
	Check if the polygon is closed.

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

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

const 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 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.

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)

Regular_Polygon::beta

double beta

Central angle between adjacent vertices (2π/n)

Definition polygon.H:835

Regular_Polygon::side_size

double side_size

Length of each side.

Definition polygon.H:831

Regular_Polygon::r

double r

Circumradius (distance from center to vertices)

Definition polygon.H:834

sin

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

Definition gmpfrxx.h:4070

Aleph::maps

DynList< T > maps(const C &c, Op op)

Classic map operation.

Definition ahFunctional.H:693

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);

See also: Polygon

Definition at line 828 of file polygon.H.

Constructor & Destructor Documentation

◆ Regular_Polygon() [1/2]

Regular_Polygon::Regular_Polygon ( )

inline

Default constructor. Creates an invalid empty polygon.

Definition at line 839 of file polygon.H.

◆ Regular_Polygon() [2/2]

Regular_Polygon::Regular_Polygon	(	const 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 < 3.

Definition at line 851 of file polygon.H.

References ah_domain_error_if, beta, Aleph::maps(), PI, r, side_size, and sin().

Member Function Documentation

◆ get_center()

const Point & Regular_Polygon::get_center ( ) const

inline

Get the center point.

Returns: Reference to the center point.

Definition at line 872 of file polygon.H.

References center.

Referenced by TEST_F().

◆ get_first_segment()

Segment Regular_Polygon::get_first_segment ( ) const

inline

Get the first segment (edge).

Returns: Segment from vertex 0 to vertex 1.

Definition at line 920 of file polygon.H.

References get_vertex().

◆ get_first_vertex()

const Point Regular_Polygon::get_first_vertex ( ) const

inline

Get the first vertex (index 0).

Returns: The first vertex point.

Definition at line 912 of file polygon.H.

References get_vertex().

◆ get_last_segment()

Segment Regular_Polygon::get_last_segment ( ) const

inline

Get the last segment (closing edge).

Returns: Segment from vertex 0 to last vertex.

Definition at line 927 of file polygon.H.

References get_vertex(), and num_vertex.

◆ get_last_vertex()

const Point Regular_Polygon::get_last_vertex ( ) const

inline

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

Returns: The last vertex point.

Definition at line 916 of file polygon.H.

References get_vertex(), and num_vertex.

◆ get_side_size()

const double & Regular_Polygon::get_side_size ( ) const

inline

Get the side length.

Returns: Length of each side.

Definition at line 868 of file polygon.H.

References side_size.

Referenced by TEST_F(), and TEST_F().

◆ get_vertex()

const Point 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 895 of file polygon.H.

References ah_out_of_range_error_if, angle, beta, center, Segment::get_tgt_point(), num_vertex, r, and Segment::rotate().

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

◆ highest_point()

Point 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 1070 of file polygon.H.

References center, and r.

◆ is_closed()

bool Regular_Polygon::is_closed ( ) const

inline

Check if the polygon is closed.

Returns: Always true for regular polygons.

Definition at line 884 of file polygon.H.

◆ leftmost_point()

Point 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 1074 of file polygon.H.

References center, and r.

◆ lowest_point()

Point 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 1066 of file polygon.H.

References center, and r.

◆ radius()

const double & Regular_Polygon::radius ( ) const

inline

Get the circumradius.

Returns: Distance from center to each vertex.

Definition at line 880 of file polygon.H.

References r.

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

◆ rightmost_point()

Point 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 1078 of file polygon.H.

References center, and r.

◆ size()

const size_t & Regular_Polygon::size ( ) const

inline

Get the number of vertices.

Returns: Number of vertices (and sides).

Definition at line 876 of file polygon.H.

References num_vertex.

Referenced by Polygon::copy_regular_polygon(), Regular_Polygon::Segment_Iterator::get_current_segment(), Regular_Polygon::Vertex_Iterator::has_curr(), Regular_Polygon::Segment_Iterator::has_curr(), TEST(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

Member Data Documentation

◆ angle

double Regular_Polygon::angle

private

Rotation angle in radians.

Definition at line 833 of file polygon.H.

Referenced by get_vertex().

◆ beta

double Regular_Polygon::beta

private

Central angle between adjacent vertices (2π/n)

Definition at line 835 of file polygon.H.

Referenced by Regular_Polygon(), and get_vertex().

◆ center

Point Regular_Polygon::center

private

Center point of the polygon.

Definition at line 830 of file polygon.H.

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

◆ num_vertex

size_t Regular_Polygon::num_vertex

private

Number of vertices (sides)

Definition at line 832 of file polygon.H.

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

◆ r

double Regular_Polygon::r

private

Circumradius (distance from center to vertices)

Definition at line 834 of file polygon.H.

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

◆ side_size

double Regular_Polygon::side_size

private

Length of each side.

Definition at line 831 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