Aleph::Triangle3D Class Reference

Represents a triangle in 3D space defined by three points. More...

#include <point.H>

Collaboration diagram for Aleph::Triangle3D:

Classes
struct	BaryCoords
	Structure to hold barycentric coordinates. More...

Public Member Functions
	Triangle3D ()=default
	Default constructor.
	Triangle3D (const Point3D &p1, const Point3D &p2, const Point3D &p3)
	Constructs a 3D triangle from three vertices.
const Point3D &	get_p1 () const
	Gets the first vertex of the triangle.
const Point3D &	get_p2 () const
	Gets the second vertex of the triangle.
const Point3D &	get_p3 () const
	Gets the third vertex of the triangle.
Point3D	normal () const
	Computes the normal vector of the triangle's plane.
Geom_Number	double_area_squared () const
	Calculates twice the squared area of the triangle.
Point3D	centroid () const
	Computes the centroid (center of mass) of the triangle.
bool	is_degenerate () const
	Checks if the triangle is degenerate (i.e., its vertices are collinear).
BaryCoords	barycentric (const Point3D &p) const
	Computes the barycentric coordinates of a point p with respect to this triangle.

Private Attributes
Point3D	p1_
Point3D	p2_
Point3D	p3_

Detailed Description

Represents a triangle in 3D space defined by three points.

Definition at line 3358 of file point.H.

Constructor & Destructor Documentation

Triangle3D() [1/2]

Aleph::Triangle3D::Triangle3D ( )

default

Default constructor.

Initializes a degenerate triangle at the origin.

Triangle3D() [2/2]

Aleph::Triangle3D::Triangle3D ( const Point3D &  p1, const Point3D &  p2, const Point3D &  p3  )

inline

Constructs a 3D triangle from three vertices.

Parameters

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

Definition at line 3372 of file point.H.

Member Function Documentation

barycentric()

BaryCoords Aleph::Triangle3D::barycentric ( const Point3D &  p ) const

inline

Computes the barycentric coordinates of a point p with respect to this triangle.

Parameters

p	The point to find coordinates for.

Returns

A BaryCoords struct containing the coordinates (u, v, w).

Exceptions

std::domain_error

if the triangle is degenerate.

Definition at line 3438 of file point.H.

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

Referenced by TEST_F(), and TEST_F().

centroid()

Point3D Aleph::Triangle3D::centroid ( ) const

inline

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

Returns

A Point3D representing the centroid.

Definition at line 3407 of file point.H.

References p1_, p2_, and p3_.

Referenced by TEST_F().

double_area_squared()

Geom_Number Aleph::Triangle3D::double_area_squared ( ) const

inline

Calculates twice the squared area of the triangle.

Returns

2 * area^2, which is equal to normal().norm_squared() / 2.

Definition at line 3398 of file point.H.

References Aleph::Point3D::norm_squared(), and normal().

Referenced by TEST_F().

get_p1()

const Point3D & Aleph::Triangle3D::get_p1 ( ) const

inline

Gets the first vertex of the triangle.

Definition at line 3376 of file point.H.

References p1_.

Referenced by Aleph::operator<<().

get_p2()

const Point3D & Aleph::Triangle3D::get_p2 ( ) const

inline

Gets the second vertex of the triangle.

Definition at line 3378 of file point.H.

References p2_.

Referenced by Aleph::operator<<().

get_p3()

const Point3D & Aleph::Triangle3D::get_p3 ( ) const

inline

Gets the third vertex of the triangle.

Definition at line 3380 of file point.H.

References p3_.

Referenced by Aleph::operator<<().

is_degenerate()

bool Aleph::Triangle3D::is_degenerate ( ) const

inline

Checks if the triangle is degenerate (i.e., its vertices are collinear).

Returns

true if the area is zero, false otherwise.

Definition at line 3416 of file point.H.

References Aleph::Point3D::norm_squared(), and normal().

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

normal()

Point3D Aleph::Triangle3D::normal ( ) const

inline

Computes the normal vector of the triangle's plane.

The normal is calculated as (p2-p1) x (p3-p1). Its magnitude is twice the triangle's area. The direction depends on the winding order of the vertices.

Returns

A Point3D representing the normal vector (not normalized).

Definition at line 3389 of file point.H.

References Aleph::Point3D::cross(), p1_, p2_, and p3_.

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

Member Data Documentation

p1_

Point3D Aleph::Triangle3D::p1_

private

Definition at line 3360 of file point.H.

Referenced by barycentric(), centroid(), get_p1(), and normal().

p2_

Point3D Aleph::Triangle3D::p2_

private

Definition at line 3360 of file point.H.

Referenced by barycentric(), centroid(), get_p2(), and normal().

p3_

Point3D Aleph::Triangle3D::p3_

private

Definition at line 3360 of file point.H.

Referenced by barycentric(), centroid(), get_p3(), and normal().

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

• point.H