Aleph::Tetrahedron Class Reference

Represents a tetrahedron in 3D space defined by four points. More...

#include <point.H>

Collaboration diagram for Aleph::Tetrahedron:

Classes
struct	Faces
	A struct holding the four faces of the tetrahedron. More...

Public Member Functions
	Tetrahedron ()=default
	Default constructor.
	Tetrahedron (const Point3D &p1, const Point3D &p2, const Point3D &p3, const Point3D &p4)
	Constructs a tetrahedron from four vertices.
const Point3D &	get_p1 () const
	Gets the first vertex.
const Point3D &	get_p2 () const
	Gets the second vertex.
const Point3D &	get_p3 () const
	Gets the third vertex.
const Point3D &	get_p4 () const
	Gets the fourth vertex.
Geom_Number	signed_volume_x6 () const
	Calculates 6 times the signed volume of the tetrahedron.
Geom_Number	volume () const
	Calculates the unsigned volume of the tetrahedron.
bool	is_degenerate () const
	Checks if the tetrahedron is degenerate (i.e., its vertices are coplanar).
Point3D	centroid () const
	Computes the centroid (center of mass) of the tetrahedron.
bool	contains (const Point3D &p) const
	Checks if a point lies inside the tetrahedron.
Faces	faces () const
	Gets the four faces of the tetrahedron.

Private Attributes
Point3D	p1_
Point3D	p2_
Point3D	p3_
Point3D	p4_

Detailed Description

Represents a tetrahedron in 3D space defined by four points.

Definition at line 3462 of file point.H.

Constructor & Destructor Documentation

Tetrahedron() [1/2]

Aleph::Tetrahedron::Tetrahedron ( )

default

Default constructor.

Initializes a degenerate tetrahedron at the origin.

Tetrahedron() [2/2]

Aleph::Tetrahedron::Tetrahedron ( const Point3D &  p1, const Point3D &  p2, const Point3D &  p3, const Point3D &  p4  )

inline

Constructs a tetrahedron from four vertices.

Parameters

p1	The first vertex.
p2	The second vertex.
p3	The third vertex.
p4	The fourth vertex.

Definition at line 3477 of file point.H.

Member Function Documentation

centroid()

Point3D Aleph::Tetrahedron::centroid ( ) const

inline

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

Returns

A Point3D representing the centroid.

Definition at line 3526 of file point.H.

References p1_, p2_, p3_, and p4_.

contains()

bool Aleph::Tetrahedron::contains ( const Point3D &  p ) const

inline

Checks if a point lies inside the tetrahedron.

This test is based on checking the sign of the volumes of the four sub-tetrahedra formed by the point and each face.

Parameters

p	The point to check.

Returns

true if the point is inside or on the boundary of the tetrahedron.

Definition at line 3538 of file point.H.

References Aleph::and, Aleph::divide_and_conquer_partition_dp(), p1_, p2_, p3_, p4_, Aleph::scalar_triple_product(), and signed_volume_x6().

faces()

Faces Aleph::Tetrahedron::faces ( ) const

inline

Gets the four faces of the tetrahedron.

Returns

A Faces struct containing four Triangle3D objects.

Definition at line 3573 of file point.H.

References p1_, p2_, p3_, and p4_.

get_p1()

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

inline

Gets the first vertex.

Definition at line 3482 of file point.H.

References p1_.

Referenced by Aleph::operator<<().

get_p2()

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

inline

Gets the second vertex.

Definition at line 3484 of file point.H.

References p2_.

Referenced by Aleph::operator<<().

get_p3()

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

inline

Gets the third vertex.

Definition at line 3486 of file point.H.

References p3_.

Referenced by Aleph::operator<<().

get_p4()

const Point3D & Aleph::Tetrahedron::get_p4 ( ) const

inline

Gets the fourth vertex.

Definition at line 3488 of file point.H.

References p4_.

Referenced by Aleph::operator<<().

is_degenerate()

bool Aleph::Tetrahedron::is_degenerate ( ) const

inline

Checks if the tetrahedron is degenerate (i.e., its vertices are coplanar).

Returns

true if the volume is zero, false otherwise.

Definition at line 3517 of file point.H.

References signed_volume_x6().

signed_volume_x6()

Geom_Number Aleph::Tetrahedron::signed_volume_x6 ( ) const

inline

Calculates 6 times the signed volume of the tetrahedron.

The value is computed using the scalar triple product: (p2-p1) . ((p3-p1) x (p4-p1)). The sign indicates the orientation of the vertices.

Returns

6 times the signed volume.

Definition at line 3497 of file point.H.

References p1_, p2_, p3_, p4_, and Aleph::scalar_triple_product().

Referenced by contains(), is_degenerate(), and volume().

volume()

Geom_Number Aleph::Tetrahedron::volume ( ) const

inline

Calculates the unsigned volume of the tetrahedron.

Returns

The absolute volume.

Definition at line 3506 of file point.H.

References signed_volume_x6().

Member Data Documentation

p1_

Point3D Aleph::Tetrahedron::p1_

private

Definition at line 3464 of file point.H.

Referenced by centroid(), contains(), faces(), get_p1(), and signed_volume_x6().

p2_

Point3D Aleph::Tetrahedron::p2_

private

Definition at line 3464 of file point.H.

Referenced by centroid(), contains(), faces(), get_p2(), and signed_volume_x6().

p3_

Point3D Aleph::Tetrahedron::p3_

private

Definition at line 3464 of file point.H.

Referenced by centroid(), contains(), faces(), get_p3(), and signed_volume_x6().

p4_

Point3D Aleph::Tetrahedron::p4_

private

Definition at line 3464 of file point.H.

Referenced by centroid(), contains(), faces(), get_p4(), and signed_volume_x6().

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

• point.H