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

A template class for an N-dimensional homogeneous coordinate. More...

#include <homogeneous.hpp>

Public Member Functions
constexpr	Homogeneous () noexcept
	Default constructor.
constexpr	Homogeneous (const Point< T, N > &p) noexcept
	Constructs a homogeneous coordinate from a Point.
constexpr	Homogeneous (const Vector< T, N > &v) noexcept
	Constructs a homogeneous coordinate from a Vec (vector).
template<std::convertible_to< T >... Vals> requires (sizeof...(Vals) == N + 1)
constexpr	Homogeneous (Vals... vals) noexcept
	Constructs a homogeneous coordinate from a list of values.
constexpr	Homogeneous (const Vector< T, N+1 > &data) noexcept
	Explicitly constructs from a raw (N+1)-dimensional vector.
constexpr const T &	w () const
	Returns the w-component of the homogeneous coordinate.
constexpr T &	w ()
	Returns a reference to the w-component of the homogeneous coordinate.
constexpr const T &	operator[] (int index) const
	Returns the value of the homogeneous coordinate at the specified index.
constexpr T &	operator[] (int index)
	Returns the value of the homogeneous coordinate at the specified index.
constexpr const T &	at (int index) const
	Returns the value of the homogeneous coordinate at the specified index.
constexpr bool	is_point () const noexcept
	Checks if this homogeneous coordinate represents a point.
constexpr bool	is_vector () const noexcept
	Checks if this homogeneous coordinate represents a vector.
constexpr Point< T, N >	to_point () const
	Converts the homogeneous coordinate back to a Point.
constexpr Vector< T, N >	to_vector () const
	Converts the homogeneous coordinate back to a Vec.
constexpr const Vector< T, N+1 > &	raw () const noexcept
	Provides read-only access to the underlying raw (N+1)-dimensional vector.
constexpr Vector< T, N+1 > &	raw () noexcept
	Provides mutable access to the underlying raw (N+1)-dimensional vector.

Friends
std::ostream &	operator<< (std::ostream &os, const Homogeneous &h)
	Stream insertion operator for printing the homogeneous coordinate.
Homogeneous	operator* (const Matrix< T, N+1, N+1 > &mat, const Homogeneous &h)
	Multiplication operator for a matrix and a homogeneous coordinate.

Detailed Description

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

A template class for an N-dimensional homogeneous coordinate.

This class unifies the mathematical treatment of points and vectors for use in projective geometry, particularly for 3D transformations. It internally stores an (N+1)-dimensional vector.

The distinction between a point and a vector is encoded in the last component, w:

• A Point (x, y, z) is represented in homogeneous coordinates as (x, y, z, 1).
• A Vector (vx, vy, vz) is represented as (vx, vy, vz, 0).

This class provides a type-safe way to create these coordinates from Point and Vec objects, and to convert them back, including performing the necessary perspective divide for points.

Template Parameters

T	The underlying floating-point type of the coordinate's components.
N	The original number of dimensions (e.g., 3 for 3D space). The internal storage will have N+1 dimensions.

See also

Point

Vec

Matrix

Constructor & Destructor Documentation

Homogeneous() [1/5]

template<typename T, int N>

pbpt::math::Homogeneous< T, N >::Homogeneous ( )

inlineconstexprnoexcept

Default constructor.

Initializes a homogeneous coordinate representing the origin POINT (0, ..., 0, 1).

Homogeneous() [2/5]

template<typename T, int N>

pbpt::math::Homogeneous< T, N >::Homogeneous ( const Point< T, N > & p )

inlineexplicitconstexprnoexcept

Constructs a homogeneous coordinate from a Point.

Copies the point's coordinates and sets the w-component to 1.

Parameters

p	The point to convert.

Homogeneous() [3/5]

template<typename T, int N>

pbpt::math::Homogeneous< T, N >::Homogeneous ( const Vector< T, N > & v )

inlineexplicitconstexprnoexcept

Constructs a homogeneous coordinate from a Vec (vector).

Copies the vector's components and sets the w-component to 0.

Parameters

v	The vector to convert.

Homogeneous() [4/5]

template<typename T, int N>

template<std::convertible_to< T >... Vals>
requires (sizeof...(Vals) == N + 1)

pbpt::math::Homogeneous< T, N >::Homogeneous ( Vals... vals )

inlineexplicitconstexprnoexcept

Constructs a homogeneous coordinate from a list of values.

The number of values must match the number of dimensions (N + 1).

Template Parameters

Vals	The types of the values, must be convertible to T.

Parameters

vals	The values to initialize the homogeneous coordinate.

Homogeneous() [5/5]

template<typename T, int N>

pbpt::math::Homogeneous< T, N >::Homogeneous ( const Vector< T, N+1 > & data )

inlineexplicitconstexprnoexcept

Explicitly constructs from a raw (N+1)-dimensional vector.

This is an advanced constructor, primarily used internally after a matrix transformation has produced a new raw homogeneous coordinate vector.

Parameters

data	The raw Vec<T, N + 1> of homogeneous coordinates.

Member Function Documentation

is_point()

template<typename T, int N>

bool pbpt::math::Homogeneous< T, N >::is_point ( ) const

inlineconstexprnoexcept

Checks if this homogeneous coordinate represents a point.

Returns

true if the w-component is not zero, false otherwise.

Note

For floating-point types, a check against a small epsilon might be more robust in some runtime applications, but w != 0 is standard.

is_vector()

template<typename T, int N>

bool pbpt::math::Homogeneous< T, N >::is_vector ( ) const

inlineconstexprnoexcept

Checks if this homogeneous coordinate represents a vector.

Returns

true if the w-component is exactly zero, false otherwise.

raw() [1/2]

template<typename T, int N>

const Vector< T, N+1 > & pbpt::math::Homogeneous< T, N >::raw ( ) const

inlineconstexprnoexcept

Provides read-only access to the underlying raw (N+1)-dimensional vector.

Returns

A const reference to the internal Vec<T, N + 1>.

raw() [2/2]

template<typename T, int N>

Vector< T, N+1 > & pbpt::math::Homogeneous< T, N >::raw ( )

inlineconstexprnoexcept

Provides mutable access to the underlying raw (N+1)-dimensional vector.

Returns

A mutable reference to the internal Vec<T, N + 1>.

to_point()

template<typename T, int N>

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

inlineconstexpr

Converts the homogeneous coordinate back to a Point.

This method performs the crucial "perspective divide" operation by dividing the x, y, z components by the w component.

Returns

The resulting Point<T, N> in Cartesian space.

Exceptions

std::runtime_error

Throws at runtime if this coordinate represents a vector (w=0), as this conversion is mathematically undefined.

Note

In a constexpr context, an invalid conversion will result in a compile-time error.

to_vector()

template<typename T, int N>

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

inlineconstexpr

Converts the homogeneous coordinate back to a Vec.

This method returns the first N components, assuming w is 0.

Returns

The resulting Vec<T, N> in Cartesian space.

Exceptions

std::runtime_error

Throws at runtime if this coordinate represents a point (w!=0), as this usually indicates a logical error in a transformation pipeline.

Note

In a constexpr context, an invalid conversion will result in a compile-time error.

w() [1/2]

template<typename T, int N>

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

inlineconstexpr

Returns a reference to the w-component of the homogeneous coordinate.

Returns

A reference to the w-component, which can be used to modify it.

w() [2/2]

template<typename T, int N>

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

inlineconstexpr

Returns the w-component of the homogeneous coordinate.

Returns

The w-component, which is 1 for points and 0 for vectors.

Friends And Related Symbol Documentation

operator*

template<typename T, int N>

Homogeneous operator* ( const Matrix< T, N+1, N+1 > & mat, const Homogeneous< T, N > & h )

friend

Multiplication operator for a matrix and a homogeneous coordinate.

This operator performs matrix-vector multiplication, where the matrix is of size (N+1)x(N+1) and the homogeneous coordinate is of size (N+1).

Parameters

mat	The matrix to multiply.
h	The homogeneous coordinate to multiply.

Returns

The result of the matrix-vector multiplication.

operator<<

template<typename T, int N>

std::ostream & operator<< ( std::ostream & os, const Homogeneous< T, N > & h )

friend

Stream insertion operator for printing the homogeneous coordinate.

Prints a [P] or [V] tag to distinguish points from vectors, followed by the raw underlying vector data.

Parameters

os	The output stream.
h	The Homo object 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/homogeneous.hpp