pbpt::math::Point< T, N > Class Template Reference

A template class for an N-dimensional point in space. More...

#include <point.hpp>

Public Member Functions
constexpr	Point () noexcept
	Default constructor. Initializes the point at the origin.
constexpr	Point (const Vector< T, N > &vec) noexcept
	Constructs a point from a coordinate vector.
template<std::convertible_to< T >... Args> requires (sizeof...(Args) == N)
constexpr	Point (Args &&... args) noexcept
	Constructs a point from a list of individual coordinate values.
constexpr T &	x () noexcept
	Accesses the first coordinate (x-axis).
constexpr T &	y () noexcept
	Accesses the second coordinate (y-axis).
constexpr T &	z () noexcept
	Accesses the third coordinate (z-axis).
constexpr T &	w () noexcept
	Accesses the fourth coordinate (w-axis).
constexpr T	x () const noexcept
	Const access to the first coordinate (x-axis).
constexpr T	y () const noexcept
	Const access to the second coordinate (y-axis).
constexpr T	z () const noexcept
	Const access to the third coordinate (z-axis).
constexpr T	w () const noexcept
	Const access to the fourth coordinate (w-axis).
constexpr int	dims () const noexcept
	Returns the number of dimensions of the point.
constexpr const T &	operator[] (int index) const
	Provides const access to the point's coordinates by index.
constexpr T &	operator[] (int index)
	Provides mutable access to the point's coordinates by index.
constexpr const T &	at (int index) const
	Provides safe const access to the point's coordinates by index.
constexpr Vector< T, N >	to_vector () const noexcept
	Explicitly converts the point to its underlying coordinate vector.
constexpr Point &	operator+= (const Vector< T, N > &rhs) noexcept
	Translates the point by adding a vector.
constexpr bool	operator< (const Point &rhs) const
constexpr bool	operator<= (const Point &rhs) const
constexpr bool	operator> (const Point &rhs) const
	greater than
constexpr bool	operator>= (const Point &rhs) const
	greater than or equal
constexpr bool	operator== (const Point &rhs) const
	equal
constexpr Point &	operator-= (const Vector< T, N > &rhs) noexcept
	Translates the point by subtracting a vector.
constexpr Vector< T, N >	operator- (const Point &rhs) const noexcept
	Rule 1: Calculates the displacement vector between two points (Point - Point = Vector).
constexpr Point	operator+ (const Vector< T, N > &rhs) const noexcept
	Rule 2: Translates a point by a vector, resulting in a new point (Point + Vector = Point).
constexpr Point	operator- (const Vector< T, N > &rhs) const noexcept
	Rule 3: Translates a point by the negative of a vector (Point - Vector = Point).
constexpr Point	mid (const Point< T, N > &rhs) const noexcept
	Calculates the midpoint between two points.

Static Public Member Functions
static constexpr Point	filled (T value) noexcept
	Creates a point filled with a specified value.
static constexpr Point	zeros () noexcept
	Creates a point at the origin (0, 0, ...).
static constexpr Point	ones () noexcept
	Creates a point with all coordinates set to one.

Friends
std::ostream &	operator<< (std::ostream &os, const Point &point)
	Stream insertion operator for printing the point's coordinates.

Detailed Description

template<typename T, int N>
class pbpt::math::Point< T, N >

A template class for an N-dimensional point in space.

Represents a specific location in an N-dimensional affine space. Unlike a Vec, which represents direction and magnitude (a displacement), a Point represents a coordinate.

The class's interface enforces these geometric distinctions through its operator overloads:

• You can subtract two points to get the vector between them (Point - Point = Vec).
• You can add or subtract a vector to a point to get a new, translated point (Point +/- Vec = Point).
• Operations like adding two points are deliberately not defined, as they are geometrically meaningless in most contexts.

Template Parameters

T	The underlying floating-point type of the point's coordinates.
N	The number of dimensions.

See also

Vec

Constructor & Destructor Documentation

Point() [1/2]

template<typename T, int N>

pbpt::math::Point< T, N >::Point ( const Vector< T, N > & vec )

inlineexplicitconstexprnoexcept

Constructs a point from a coordinate vector.

Parameters

vec	The vector representing the point's coordinates from the origin.

Point() [2/2]

template<typename T, int N>

template<std::convertible_to< T >... Args>
requires (sizeof...(Args) == N)

pbpt::math::Point< T, N >::Point ( Args &&... args )

inlineexplicitconstexprnoexcept

Constructs a point from a list of individual coordinate values.

The number of arguments must exactly match the point's dimension N.

Template Parameters

Args	A parameter pack of types convertible to T.

Parameters

args	The coordinate values.

Note

The number of arguments sizeof...(args) must be equal to N.

Member Function Documentation

filled()

template<typename T, int N>

constexpr Point pbpt::math::Point< T, N >::filled ( T value )

inlinestaticconstexprnoexcept

Creates a point filled with a specified value.

Parameters

value

The value to fill all coordinates with.

Returns

A new Point instance filled with the given value.

mid()

template<typename T, int N>

Point pbpt::math::Point< T, N >::mid ( const Point< T, N > & rhs ) const

inlineconstexprnoexcept

Calculates the midpoint between two points.

Parameters

rhs	The second point.

Returns

The point that lies exactly halfway between lhs and rhs.

ones()

template<typename T, int N>

constexpr Point pbpt::math::Point< T, N >::ones ( )

inlinestaticconstexprnoexcept

Creates a point with all coordinates set to one.

Returns

A new Point instance with all coordinates set to 1.0.

operator+()

template<typename T, int N>

Point pbpt::math::Point< T, N >::operator+ ( const Vector< T, N > & rhs ) const

inlineconstexprnoexcept

Rule 2: Translates a point by a vector, resulting in a new point (Point + Vector = Point).

Parameters

rhs	The displacement vector.

Returns

The new, translated point.

operator+=()

template<typename T, int N>

Point & pbpt::math::Point< T, N >::operator+= ( const Vector< T, N > & rhs )

inlineconstexprnoexcept

Translates the point by adding a vector.

Parameters

rhs	The displacement vector to add.

Returns

A reference to the modified point.

operator-() [1/2]

template<typename T, int N>

Vector< T, N > pbpt::math::Point< T, N >::operator- ( const Point< T, N > & rhs ) const

inlineconstexprnoexcept

Rule 1: Calculates the displacement vector between two points (Point - Point = Vector).

Parameters

rhs	The starting point.

Returns

The Vec<T, N> that goes from rhs to lhs.

operator-() [2/2]

template<typename T, int N>

Point pbpt::math::Point< T, N >::operator- ( const Vector< T, N > & rhs ) const

inlineconstexprnoexcept

Rule 3: Translates a point by the negative of a vector (Point - Vector = Point).

Parameters

rhs	The displacement vector to subtract.

Returns

The new, translated point.

operator-=()

template<typename T, int N>

Point & pbpt::math::Point< T, N >::operator-= ( const Vector< T, N > & rhs )

inlineconstexprnoexcept

Translates the point by subtracting a vector.

Parameters

rhs	The displacement vector to subtract.

Returns

A reference to the modified point.

operator==()

template<typename T, int N>

bool pbpt::math::Point< T, N >::operator== ( const Point< T, N > & rhs ) const

inlineconstexpr

equal

Parameters

rhs

Returns

true

false

to_vector()

template<typename T, int N>

Vector< T, N > pbpt::math::Point< T, N >::to_vector ( ) const

inlineconstexprnoexcept

Explicitly converts the point to its underlying coordinate vector.

This allows a point to be treated as a vector from the origin when an explicit cast is used.

Returns

The Vec<T, N> representing the point's coordinates.

w() [1/2]

template<typename T, int N>

T pbpt::math::Point< T, N >::w ( ) const

inlineconstexprnoexcept

Const access to the fourth coordinate (w-axis).

Note

N > 3.

w() [2/2]

template<typename T, int N>

T & pbpt::math::Point< T, N >::w ( )

inlineconstexprnoexcept

Accesses the fourth coordinate (w-axis).

Note

N > 3.

x() [1/2]

template<typename T, int N>

T pbpt::math::Point< T, N >::x ( ) const

inlineconstexprnoexcept

Const access to the first coordinate (x-axis).

Note

N > 0.

x() [2/2]

template<typename T, int N>

T & pbpt::math::Point< T, N >::x ( )

inlineconstexprnoexcept

Accesses the first coordinate (x-axis).

Note

N > 0.

y() [1/2]

template<typename T, int N>

T pbpt::math::Point< T, N >::y ( ) const

inlineconstexprnoexcept

Const access to the second coordinate (y-axis).

Note

N > 1.

y() [2/2]

template<typename T, int N>

T & pbpt::math::Point< T, N >::y ( )

inlineconstexprnoexcept

Accesses the second coordinate (y-axis).

Note

N > 1.

z() [1/2]

template<typename T, int N>

T pbpt::math::Point< T, N >::z ( ) const

inlineconstexprnoexcept

Const access to the third coordinate (z-axis).

Note

N > 2.

z() [2/2]

template<typename T, int N>

T & pbpt::math::Point< T, N >::z ( )

inlineconstexprnoexcept

Accesses the third coordinate (z-axis).

Note

N > 2.

zeros()

template<typename T, int N>

constexpr Point pbpt::math::Point< T, N >::zeros ( )

inlinestaticconstexprnoexcept

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

Returns

A new Point instance at the origin.

Friends And Related Symbol Documentation

operator<<

template<typename T, int N>

std::ostream & operator<< ( std::ostream & os, const Point< T, N > & point )

friend

Stream insertion operator for printing the point's coordinates.

Parameters

os	The output stream.
point	The point to print.

Returns

A reference to the output stream.

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

• /Users/jinceyang/Desktop/codebase/pbpt/engine/math/point.hpp