A non-degenerate triangle defined by three points. More...

#include <point.H>

Inheritance diagram for Aleph::Triangle:

Collaboration diagram for Aleph::Triangle:

Public Member Functions
	Triangle (Point p1, Point p2, Point p3)
	Constructs a triangle from three points.

	Triangle (Point p, const Segment &s)
	Constructs a triangle from a point and a segment.

	Triangle (const Segment &s, Point p)
	Constructs a triangle from a segment and a point.

Geom_Number	area () const
	Calculates the unsigned area of the triangle.

bool	is_clockwise () const
	Checks if the triangle vertices are ordered clockwise.

const Point &	highest_point () const
	Gets the vertex with the largest y-coordinate.

const Point &	lowest_point () const
	Gets the vertex with the smallest y-coordinate.

const Point &	leftmost_point () const
	Gets the vertex with the smallest x-coordinate.

const Point &	rightmost_point () const
	Gets the vertex with the largest x-coordinate.

const Point &	get_p1 () const
	Gets the first vertex.

const Point &	get_p2 () const
	Gets the second vertex.

const Point &	get_p3 () const
	Gets the third vertex.

bool	operator== (const Triangle &t) const noexcept
	Checks for equality between two triangles.

bool	operator!= (const Triangle &t) const noexcept
	Checks for inequality between two triangles.

Point	centroid () const
	Computes the centroid (center of mass) of the triangle.

Geom_Number	perimeter () const
	Computes the perimeter of the triangle.

Point	circumcenter () const
	Computes the circumcenter of the triangle.

Point	incenter () const
	Computes the incenter of the triangle.

std::array< Segment, 3 >	edges () const
	Gets the three edges of the triangle.

bool	contains (const Point &p) const
	Checks if a point lies strictly inside this triangle.

Segment	intersection_with (const Segment &s) const
	Computes the intersection segment between this triangle and a segment.

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

virtual	~Geom_Object ()=default

Private Attributes
Point	p1_

Point	p2_

Point	p3_

Geom_Number	area_

Friends
class	Point

class	Segment

Detailed Description

A non-degenerate triangle defined by three points.

Provides basic geometric properties and predicates for a triangle, such as area, orientation, and special centers (centroid, circumcenter, incenter). Used by polygon triangulation and other geometric algorithms.

Definition at line 1477 of file point.H.

Constructor & Destructor Documentation

◆ Triangle() [1/3]

Aleph::Triangle::Triangle	(	Point	p1,
		Point	p2,
		Point	p3
	)

inline

Constructs a triangle from three points.

Parameters

p1	The first vertex.
p2	The second vertex.
p3	The third vertex.

Exceptions

std::domain_error if the three points are collinear.

Definition at line 1494 of file point.H.

References ah_domain_error_if, area_, Aleph::area_of_parallelogram(), p1_, p2_, and p3_.

◆ Triangle() [2/3]

Aleph::Triangle::Triangle	(	Point	p,
		const Segment &	s
	)

inline

Constructs a triangle from a point and a segment.

Parameters

p	The first vertex.
s	The segment defining the other two vertices.

Exceptions

std::domain_error if the three points are collinear.

Definition at line 1508 of file point.H.

References ah_domain_error_if, area_, Aleph::area_of_parallelogram(), p1_, p2_, and p3_.

◆ Triangle() [3/3]

Aleph::Triangle::Triangle	(	const Segment &	s,
		Point	p
	)

inline

Constructs a triangle from a segment and a point.

Parameters

s	The segment defining the first two vertices.
p	The third vertex.

Exceptions

std::domain_error if the three points are collinear.

Definition at line 1521 of file point.H.

References ah_domain_error_if, area_, Aleph::area_of_parallelogram(), p1_, p2_, and p3_.

Member Function Documentation

◆ area()

Geom_Number Aleph::Triangle::area ( ) const

inline

Calculates the unsigned area of the triangle.

Returns: The area of the triangle.

Definition at line 1532 of file point.H.

References abs(), and area_.

◆ centroid()

Point Aleph::Triangle::centroid ( ) const

inline

Computes the centroid (center of mass) of the triangle.

Returns: A Point representing the centroid.

Definition at line 1622 of file point.H.

References p1_, p2_, and p3_.

◆ circumcenter()

Point Aleph::Triangle::circumcenter ( ) const

inline

Computes the circumcenter of the triangle.

The circumcenter is the intersection point of the perpendicular bisectors of the edges and is equidistant from the three vertices.

Returns: A Point representing the circumcenter.

Exceptions

std::domain_error if the triangle is degenerate (collinear vertices).

Definition at line 1643 of file point.H.

References ah_domain_error_if, Aleph::divide_and_conquer_partition_dp(), Aleph::Point::get_x(), Aleph::Point::get_y(), p1_, p2_, p3_, and y1().

◆ contains()

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

inline

Checks if a point lies strictly inside this triangle.

This is done by checking if the point is on the same side of all three edges. The result depends on the triangle's orientation.

Parameters

p	The point to check.

Returns: true if the point is strictly inside, false if it is on an edge or outside.

Definition at line 1706 of file point.H.

References Aleph::and, is_clockwise(), Aleph::Point::is_left_of(), Aleph::Point::is_to_right_from(), p1_, p2_, and p3_.

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

◆ edges()

std::array< Segment, 3 > Aleph::Triangle::edges ( ) const

inline

Gets the three edges of the triangle.

Returns: A std::array of 3 Segments in the order (p1,p2), (p2,p3), (p3,p1).

Definition at line 1693 of file point.H.

References p1_, p2_, p3_, and Segment.

◆ get_p1()

const Point & Aleph::Triangle::get_p1 ( ) const

inline

Gets the first vertex.

Definition at line 1587 of file point.H.

References p1_.

Referenced by Aleph::ShortestPathInPolygon::build_tris(), Eepic_Triangle::draw(), Aleph::Tikz_Plane::draw_triangle(), Aleph::Segment::intersection_with(), Aleph::Segment::intersects_with(), Aleph::ConvexPolygonDecomposition::operator()(), Aleph::operator<<(), print_triangle(), Aleph::detail::spp_build_tris(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_wkt(), and triangle_area().

◆ get_p2()

const Point & Aleph::Triangle::get_p2 ( ) const

inline

Gets the second vertex.

Definition at line 1589 of file point.H.

References p2_.

Referenced by Aleph::ShortestPathInPolygon::build_tris(), Eepic_Triangle::draw(), Aleph::Tikz_Plane::draw_triangle(), Aleph::Segment::intersection_with(), Aleph::Segment::intersects_with(), Aleph::ConvexPolygonDecomposition::operator()(), Aleph::operator<<(), print_triangle(), Aleph::detail::spp_build_tris(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_wkt(), and triangle_area().

◆ get_p3()

const Point & Aleph::Triangle::get_p3 ( ) const

inline

Gets the third vertex.

Definition at line 1591 of file point.H.

References p3_.

Referenced by Aleph::ShortestPathInPolygon::build_tris(), Eepic_Triangle::draw(), Aleph::Tikz_Plane::draw_triangle(), Aleph::Segment::intersection_with(), Aleph::Segment::intersects_with(), Aleph::ConvexPolygonDecomposition::operator()(), Aleph::operator<<(), print_triangle(), Aleph::detail::spp_build_tris(), Aleph::GeomSerializer::to_geojson(), Aleph::GeomSerializer::to_wkt(), and triangle_area().

◆ highest_point()

const Point & Aleph::Triangle::highest_point ( ) const

inline

Gets the vertex with the largest y-coordinate.

Returns: A const reference to the highest vertex.

Definition at line 1550 of file point.H.

References Aleph::Point::get_y(), max(), p1_, p2_, and p3_.

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

◆ incenter()

Point Aleph::Triangle::incenter ( ) const

inline

Computes the incenter of the triangle.

The incenter is the intersection point of the angle bisectors and is the center of the triangle's incircle.

Returns: A Point representing the incenter.

Exceptions

std::domain_error if the triangle is degenerate.

Definition at line 1678 of file point.H.

References ah_domain_error_if, Aleph::Point::distance_to(), p1_, p2_, p3_, and Aleph::sum().

◆ intersection_with()

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

inline

Computes the intersection segment between this triangle and a segment.

Parameters

s	The segment to intersect with.

Returns: The intersection Segment.

See also: Segment::intersection_with(const Triangle &)

Definition at line 1723 of file point.H.

References Aleph::Segment::intersection_with().

◆ is_clockwise()

bool Aleph::Triangle::is_clockwise ( ) const

inline

Checks if the triangle vertices are ordered clockwise.

Returns: true if the vertex order (p1, p2, p3) is clockwise, false otherwise.

Definition at line 1541 of file point.H.

References area_.

Referenced by contains().

◆ leftmost_point()

const Point & Aleph::Triangle::leftmost_point ( ) const

inline

Gets the vertex with the smallest x-coordinate.

Returns: A const reference to the leftmost vertex.

Definition at line 1570 of file point.H.

References Aleph::Point::get_x(), min(), p1_, p2_, and p3_.

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

◆ lowest_point()

const Point & Aleph::Triangle::lowest_point ( ) const

inline

Gets the vertex with the smallest y-coordinate.

Returns: A const reference to the lowest vertex.

Definition at line 1560 of file point.H.

References Aleph::Point::get_y(), min(), p1_, p2_, and p3_.

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

◆ operator!=()

bool Aleph::Triangle::operator!= ( const Triangle & t ) const

inlinenoexcept

Checks for inequality between two triangles.

Parameters

t	The other triangle to compare.

Returns: true if the triangles do not share the same three vertices.

Definition at line 1613 of file point.H.

References Aleph::divide_and_conquer_partition_dp().

◆ operator==()

bool Aleph::Triangle::operator== ( const Triangle & t ) const

inlinenoexcept

Checks for equality between two triangles.

Note: Triangles are equal if they have the same set of three vertices, regardless of their order.

Parameters

t	The other triangle to compare.

Returns: true if the triangles are composed of the same three points.

Definition at line 1600 of file point.H.

References Aleph::and, Aleph::divide_and_conquer_partition_dp(), p1_, p2_, and p3_.

◆ perimeter()

Geom_Number Aleph::Triangle::perimeter ( ) const

inline

Computes the perimeter of the triangle.

Returns: The sum of the lengths of the three edges.

Definition at line 1631 of file point.H.

References Aleph::Point::distance_to(), p1_, p2_, and p3_.

◆ rightmost_point()

const Point & Aleph::Triangle::rightmost_point ( ) const

inline

Gets the vertex with the largest x-coordinate.

Returns: A const reference to the rightmost vertex.

Definition at line 1580 of file point.H.

References Aleph::Point::get_x(), max(), p1_, p2_, and p3_.

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

Friends And Related Symbol Documentation

◆ Point

friend class Point

friend

Definition at line 1479 of file point.H.

◆ Segment

friend class Segment

friend

Definition at line 1480 of file point.H.

Referenced by edges().

Member Data Documentation

◆ area_

Geom_Number Aleph::Triangle::area_

private

Definition at line 1484 of file point.H.

Referenced by Triangle(), Triangle(), Triangle(), area(), and is_clockwise().

◆ p1_

Point Aleph::Triangle::p1_

private

Definition at line 1482 of file point.H.

Referenced by Triangle(), Triangle(), Triangle(), centroid(), circumcenter(), contains(), edges(), get_p1(), highest_point(), incenter(), leftmost_point(), lowest_point(), operator==(), perimeter(), and rightmost_point().

◆ p2_

Point Aleph::Triangle::p2_

private

Definition at line 1482 of file point.H.

Referenced by Triangle(), Triangle(), Triangle(), centroid(), circumcenter(), contains(), edges(), get_p2(), highest_point(), incenter(), leftmost_point(), lowest_point(), operator==(), perimeter(), and rightmost_point().

◆ p3_

Point Aleph::Triangle::p3_

private

Definition at line 1482 of file point.H.

Referenced by Triangle(), Triangle(), Triangle(), centroid(), circumcenter(), contains(), edges(), get_p3(), highest_point(), incenter(), leftmost_point(), lowest_point(), operator==(), perimeter(), and rightmost_point().

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

point.H

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Triangle() [1/3]

◆ Triangle() [2/3]

◆ Triangle() [3/3]

Member Function Documentation

◆ area()

◆ centroid()

◆ circumcenter()

◆ contains()

◆ edges()

◆ get_p1()

◆ get_p2()

◆ get_p3()

◆ highest_point()

◆ incenter()

◆ intersection_with()

◆ is_clockwise()

◆ leftmost_point()

◆ lowest_point()

◆ operator!=()

◆ operator==()

◆ perimeter()

◆ rightmost_point()

Friends And Related Symbol Documentation

◆ Point

◆ Segment

Member Data Documentation

◆ area_

◆ p1_

◆ p2_

◆ p3_