Represents a point in 3D space with exact rational coordinates. More...

#include <point.H>

Collaboration diagram for Aleph::Point3D:

Public Member Functions
	Point3D ()
	Default constructor.

	Point3D (const Geom_Number &x, const Geom_Number &y, const Geom_Number &z)
	Constructs a 3D point from x, y, and z coordinates.

	Point3D (const Point3D &)=default

Point3D &	operator= (const Point3D &)=default

const Geom_Number &	get_x () const
	Gets the x-coordinate.

const Geom_Number &	get_y () const
	Gets the y-coordinate.

const Geom_Number &	get_z () const
	Gets the z-coordinate.

bool	operator== (const Point3D &p) const
	Checks for exact equality between two 3D points.

bool	operator!= (const Point3D &p) const
	Checks for inequality between two 3D points.

Point3D	operator+ (const Point3D &p) const
	Vector addition.

Point3D	operator- (const Point3D &p) const
	Vector subtraction.

Point3D &	operator+= (const Point3D &p)
	Vector addition and assignment.

Point3D &	operator-= (const Point3D &p)
	Vector subtraction and assignment.

Point3D	operator- () const
	Unary negation.

Point3D	operator* (const Geom_Number &s) const
	Scalar multiplication.

Point3D	operator/ (const Geom_Number &s) const
	Scalar division.

Geom_Number	dot (const Point3D &p) const
	Dot product.

Point3D	cross (const Point3D &p) const
	Cross product.

Geom_Number	distance_squared_to (const Point3D &p) const
	Squared Euclidean distance to another point.

Geom_Number	norm_squared () const
	Squared Euclidean norm (magnitude).

Geom_Number	norm () const
	Euclidean norm (magnitude).

Geom_Number	distance_to (const Point3D &p) const
	Euclidean distance to another point.

Point3D	normalize () const
	Returns a normalized copy of this vector (unit vector).

Point	to_2d () const
	Projects this 3D point to a 2D point by dropping the z-coordinate.

Static Public Member Functions
static Point3D	from_2d (const Point &p)
	Lifts a 2D point to 3D, setting its z-coordinate to 0.

static Point3D	from_2d (const Point &p, const Geom_Number &z)
	Lifts a 2D point to 3D with a specified z-coordinate.

Private Attributes
Geom_Number	x_

Geom_Number	y_

Geom_Number	z_

Detailed Description

Represents a point in 3D space with exact rational coordinates.

Extends the 2D geometry module with a basic 3D point type. All operations use exact Geom_Number arithmetic.

Definition at line 2972 of file point.H.

Constructor & Destructor Documentation

◆ Point3D() [1/3]

Aleph::Point3D::Point3D ( )

inline

Default constructor.

Initializes a point at the origin (0,0,0).

Definition at line 2980 of file point.H.

◆ Point3D() [2/3]

Aleph::Point3D::Point3D	(	const Geom_Number &	x,
		const Geom_Number &	y,
		const Geom_Number &	z
	)

inline

Constructs a 3D point from x, y, and z coordinates.

Parameters

x	The x-coordinate.
y	The y-coordinate.
z	The z-coordinate.

Definition at line 2988 of file point.H.

◆ Point3D() [3/3]

Aleph::Point3D::Point3D ( const Point3D & )

default

Member Function Documentation

◆ cross()

Point3D Aleph::Point3D::cross ( const Point3D & p ) const

inline

Cross product.

Parameters

p	The other vector.

Returns: A new Point3D representing the cross product vector.

Definition at line 3112 of file point.H.

References x_, y_, and z_.

Referenced by Aleph::Segment3D::contains(), Aleph::Triangle3D::normal(), Aleph::scalar_triple_product(), and TEST_F().

◆ distance_squared_to()

Geom_Number Aleph::Point3D::distance_squared_to ( const Point3D & p ) const

inline

Squared Euclidean distance to another point.

Parameters

p	The other point.

Returns: The squared distance.

Definition at line 3126 of file point.H.

References Aleph::divide_and_conquer_partition_dp(), x_, y_, and z_.

Referenced by distance_to(), Aleph::Segment3D::length_squared(), and TEST_F().

◆ distance_to()

Geom_Number Aleph::Point3D::distance_to ( const Point3D & p ) const

inline

Euclidean distance to another point.

Parameters

p	The other point.

Returns: The distance.

Definition at line 3157 of file point.H.

References distance_squared_to(), and Aleph::square_root().

Referenced by Aleph::Segment3D::distance_to(), and Aleph::Segment3D::length().

◆ dot()

Geom_Number Aleph::Point3D::dot ( const Point3D & p ) const

inline

Dot product.

Parameters

p	The other vector.

Returns: The scalar result of the dot product.

Definition at line 3102 of file point.H.

References x_, y_, and z_.

Referenced by Aleph::Segment3D::contains(), Aleph::Segment3D::distance_to(), Aleph::scalar_triple_product(), and TEST_F().

◆ from_2d() [1/2]

static Point3D Aleph::Point3D::from_2d ( const Point & p )

inlinestatic

Lifts a 2D point to 3D, setting its z-coordinate to 0.

Parameters

p	The 2D point.

Returns: A new Point3D.

Definition at line 3185 of file point.H.

References Aleph::Point::get_x(), and Aleph::Point::get_y().

Referenced by TEST_F().

◆ from_2d() [2/2]

static Point3D Aleph::Point3D::from_2d	(	const Point &	p,
		const Geom_Number &	z
	)

inlinestatic

Lifts a 2D point to 3D with a specified z-coordinate.

Parameters

p	The 2D point.
z	The value for the z-coordinate.

Returns: A new Point3D.

Definition at line 3196 of file point.H.

References Aleph::Point::get_x(), and Aleph::Point::get_y().

◆ get_x()

const Geom_Number & Aleph::Point3D::get_x ( ) const

inline

Gets the x-coordinate.

Definition at line 2996 of file point.H.

References x_.

Referenced by Aleph::operator<<(), Aleph::GeomSerializer::to_geojson(), and Aleph::GeomSerializer::to_wkt().

◆ get_y()

const Geom_Number & Aleph::Point3D::get_y ( ) const

inline

Gets the y-coordinate.

Definition at line 2998 of file point.H.

References y_.

Referenced by Aleph::operator<<(), Aleph::GeomSerializer::to_geojson(), and Aleph::GeomSerializer::to_wkt().

◆ get_z()

const Geom_Number & Aleph::Point3D::get_z ( ) const

inline

Gets the z-coordinate.

Definition at line 3000 of file point.H.

References z_.

Referenced by Aleph::operator<<(), Aleph::GeomSerializer::to_geojson(), and Aleph::GeomSerializer::to_wkt().

◆ norm()

Geom_Number Aleph::Point3D::norm ( ) const

inline

Euclidean norm (magnitude).

Returns: The length of the vector from the origin.

Definition at line 3147 of file point.H.

References norm_squared(), and Aleph::square_root().

Referenced by normalize().

◆ norm_squared()

Geom_Number Aleph::Point3D::norm_squared ( ) const

inline

Squared Euclidean norm (magnitude).

Returns: The squared length of the vector from the origin.

Definition at line 3138 of file point.H.

References x_, y_, and z_.

Referenced by Aleph::Triangle3D::double_area_squared(), Aleph::Triangle3D::is_degenerate(), norm(), and TEST_F().

◆ normalize()

Point3D Aleph::Point3D::normalize ( ) const

inline

Returns a normalized copy of this vector (unit vector).

Returns: A Point3D with a magnitude of 1.

Exceptions

std::domain_error if normalizing the zero vector is attempted.

Definition at line 3167 of file point.H.

References ah_domain_error_if, and norm().

◆ operator!=()

bool Aleph::Point3D::operator!= ( const Point3D & p ) const

inline

Checks for inequality between two 3D points.

Parameters

p	The other point.

Returns: true if any coordinate is different.

Definition at line 3017 of file point.H.

◆ operator*()

Point3D Aleph::Point3D::operator* ( const Geom_Number & s ) const

inline

Scalar multiplication.

Parameters

s	The scalar value.

Returns: A new Point3D with each coordinate multiplied by s.

Definition at line 3082 of file point.H.

References x_, y_, and z_.

◆ operator+()

Point3D Aleph::Point3D::operator+ ( const Point3D & p ) const

inline

Vector addition.

Parameters

p	The other point to add.

Returns: A new Point3D representing the component-wise sum.

Definition at line 3027 of file point.H.

References x_, y_, and z_.

◆ operator+=()

Point3D & Aleph::Point3D::operator+= ( const Point3D & p )

inline

Vector addition and assignment.

Parameters

p	The other point to add.

Returns: A reference to this modified point.

Definition at line 3047 of file point.H.

References x_, y_, and z_.

◆ operator-() [1/2]

Point3D Aleph::Point3D::operator- ( ) const

inline

Unary negation.

Returns: A new Point3D with all coordinates negated.

Definition at line 3072 of file point.H.

References x_, y_, and z_.

◆ operator-() [2/2]

Point3D Aleph::Point3D::operator- ( const Point3D & p ) const

inline

Vector subtraction.

Parameters

p	The other point to subtract.

Returns: A new Point3D representing the component-wise difference.

Definition at line 3037 of file point.H.

References x_, y_, and z_.

◆ operator-=()

Point3D & Aleph::Point3D::operator-= ( const Point3D & p )

inline

Vector subtraction and assignment.

Parameters

p	The other point to subtract.

Returns: A reference to this modified point.

Definition at line 3060 of file point.H.

References x_, y_, and z_.

◆ operator/()

Point3D Aleph::Point3D::operator/ ( const Geom_Number & s ) const

inline

Scalar division.

Parameters

s	The scalar value.

Returns: A new Point3D with each coordinate divided by s.

Definition at line 3092 of file point.H.

References x_, y_, and z_.

◆ operator=()

Point3D & Aleph::Point3D::operator= ( const Point3D & )

default

◆ operator==()

bool Aleph::Point3D::operator== ( const Point3D & p ) const

inline

Checks for exact equality between two 3D points.

Parameters

p	The other point.

Returns: true if all three coordinates are identical.

Definition at line 3007 of file point.H.

References Aleph::and, x_, y_, and z_.

◆ to_2d()

Point Aleph::Point3D::to_2d ( ) const

inline

Projects this 3D point to a 2D point by dropping the z-coordinate.

Returns: A Point with the x and y coordinates of this point.

Definition at line 3178 of file point.H.

References x_, and y_.

Referenced by TEST_F().

Member Data Documentation

◆ x_

Geom_Number Aleph::Point3D::x_

private

Definition at line 2974 of file point.H.

Referenced by cross(), distance_squared_to(), dot(), get_x(), norm_squared(), operator*(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator==(), and to_2d().

◆ y_

Geom_Number Aleph::Point3D::y_

private

Definition at line 2974 of file point.H.

Referenced by cross(), distance_squared_to(), dot(), get_y(), norm_squared(), operator*(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), operator==(), and to_2d().

◆ z_

Geom_Number Aleph::Point3D::z_

private

Definition at line 2974 of file point.H.

Referenced by cross(), distance_squared_to(), dot(), get_z(), norm_squared(), operator*(), operator+(), operator+=(), operator-(), operator-(), operator-=(), operator/(), and operator==().

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

point.H

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Point3D() [1/3]

◆ Point3D() [2/3]

◆ Point3D() [3/3]

Member Function Documentation

◆ cross()

◆ distance_squared_to()

◆ distance_to()

◆ dot()

◆ from_2d() [1/2]

◆ from_2d() [2/2]

◆ get_x()

◆ get_y()

◆ get_z()

◆ norm()

◆ norm_squared()

◆ normalize()

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator=()

◆ operator==()

◆ to_2d()

Member Data Documentation

◆ x_

◆ y_

◆ z_