The Point class represents an N-dimensional point containing N scalar values. More...

#include <vclib/space/core/point.h>

Inheritance diagram for vcl::Point< Scalar, N >:

[legend]

Public Types
using	BaseMatrixType = Base

using	ScalarType = Scalar
	The Scalar type of the Point.

Public Member Functions
	Point ()
	Constructs a Point object with all components set to zero.

template<typename OtherDerived >
	Point (const Eigen::MatrixBase< OtherDerived > &other)
	Constructs a Point object from an Eigen matrix.

template<typename... Scalars> requires (sizeof...(scalars) == N)
	Point (Scalars... scalars)
	Constructs a Point object from a set of scalar values.

ScalarType &	x ()
	Returns a reference to the x-component of the Point object.

const ScalarType &	x () const
	Returns a const reference to the x-component of the Point object.

ScalarType &	y ()
	Returns a reference to the y-component of the Point object.

const ScalarType &	y () const
	Returns a const reference to the y-component of the Point object.

ScalarType &	z ()
	Returns a reference to the z-component of the Point object.

const ScalarType &	z () const
	Returns a const reference to the z-component of the Point object.

ScalarType &	w ()
	Returns a reference to the w-component of the Point object.

const ScalarType &	w () const
	Returns a const reference to the w-component of the Point object.

ScalarType &	at (uint i)

const ScalarType &	at (uint i) const

template<typename S >
auto	cast () const
	Casts the Point object to a different scalar type.

bool	isDegenerate () const
	Returns true if at least one of its components is NaN or inf.

bool	epsilonEquals (const Point &p1, Scalar epsilon=std::numeric_limits< Scalar >::epsilon()) const
	Checks for the equality of two Point objects within a given epsilon tolerance.

Scalar	angle (const Point &p1) const
	Computes the angle between two Point objects.

Scalar	dist (const Point &p1) const
	Computes the Euclidean distance between two Point objects.

Scalar	squaredDist (const Point &p1) const
	Computes the squared Euclidean distance between two Point objects.

Point	mul (const Point &p1) const
	Multiplies the components of two Point objects.

Point	div (const Point &p1) const
	Divides the components of two Point objects.

constexpr uint	size () const
	Returns the size of the Point object.

template<typename... Scalars> requires (sizeof...(scalars) == N)
void	set (Scalars... scalars)
	Sets all the components of the Point object from a set of scalar values.

auto	outerProduct (const Point &p1) const
	Returns the outer product between this point p and p1, which is p * p1^T.

void	orthoBase (Point &u, Point &v) const
	Computes an Orthonormal Basis starting from this point n.

void	serialize (std::ostream &os) const
	Serializes the point to the given output stream.

void	deserialize (std::istream &is)
	Deserializes the point from the given input stream.

std::size_t	hash () const
	Computes the hash value of the point.

template<typename OtherDerived >
Point &	operator= (const Eigen::MatrixBase< OtherDerived > &other)
	Assigns the point to the given Eigen matrix.

auto	operator<=> (const Point &p1) const
	Compares the point with another point using the spaceship operator.

Point	operator+ (const Scalar &s) const
	Adds a scalar value to each coordinate of the point.

Point	operator- (const Scalar &s) const
	Subtracts a scalar value from each coordinate of the point.

Scalar	operator* (const Point &p1) const
	Computes the dot product of this point with another point.

Point	operator* (const Eigen::Matrix< Scalar, N+1, N+1 > &m) const
	Returns a new 3D point/vector on which has been applied a TRS 4x4 matrix.

Point &	operator+= (const Scalar &s)
	Adds a scalar value to this point.

Point &	operator-= (const Scalar &s)
	Subtracts a scalar value from this point.

Point &	operator*= (const Eigen::Matrix< Scalar, N+1, N+1 > &m)
	Applies a TRS 4x4 matrix transformation to this point.

Static Public Attributes
static const uint	DIM = N
	DIM: the number of dimensions of the Point.

Private Types
using	Base = Eigen::Matrix< Scalar, N, 1 >

Detailed Description

template<typename Scalar, uint N>
class vcl::Point< Scalar, N >

The Point class represents an N-dimensional point containing N scalar values.

The Point class template represents an N-dimensional point containing N scalar values. The scalar type and the number of dimensions are template parameters of the class. The class provides a number of member functions for accessing, manipulating, and comparing points, as well as arithmetic and assignment operators for points.

The Point class is implemented using an Eigen matrix of size Nx1 to store the point components. The class also defines a number of type aliases, static constants and member functions for convenience.

Template Parameters

Scalar	The scalar type of the point components.
N	The number of dimensions of the point.

Constructor & Destructor Documentation

◆ Point() [1/2]

template<typename Scalar , uint N>

template<typename OtherDerived >

vcl::Point< Scalar, N >::Point ( const Eigen::MatrixBase< OtherDerived > & other )

inline

Constructs a Point object from an Eigen matrix.

The constructor initializes the components of the Point object from an Eigen matrix with the same dimensionality as the Point object.

Parameters

[in] other An Eigen matrix with the same dimensionality as the Point object.

◆ Point() [2/2]

template<typename Scalar , uint N>

template<typename... Scalars>
requires (sizeof...(scalars) == N)

vcl::Point< Scalar, N >::Point ( Scalars... scalars )

inline

Constructs a Point object from a set of scalar values.

The constructor takes a variable number of scalar arguments, which are used to initialize the components of the Point object. The number of arguments must be equal to the dimensionality of the Point object, which is determined by the template parameter N.

Template Parameters

Scalars The types of the scalar arguments.

Parameters

[in] scalars The scalar arguments used to initialize the components of the Point object.

Member Function Documentation

◆ angle()

template<typename Scalar , uint N>

Scalar vcl::Point< Scalar, N >::angle ( const Point< Scalar, N > & p1 ) const

inline

Computes the angle between two Point objects.

The function computes the angle between two Point objects, which is defined as the inverse cosine of the dot product of the two Point objects divided by the product of their magnitudes. The two Point objects must have the same dimension.

Parameters

[in] p1 The Point object to compute the angle with.

Returns: The angle between the two Point objects in radians, or -1 if the magnitude of one of the Point objects is 0.

◆ cast()

template<typename Scalar , uint N>

template<typename S >

auto vcl::Point< Scalar, N >::cast ( ) const

inline

Casts the Point object to a different scalar type.

The function returns a new Point object with the same dimension as the original object, but with each scalar value casted to a different type.

Template Parameters

S	The scalar type to cast to.

Returns: A new Point object with the same dimension as the original object, but with each scalar value casted to a different type.

◆ deserialize()

template<typename Scalar , uint N>

void vcl::Point< Scalar, N >::deserialize ( std::istream & is )

inline

Deserializes the point from the given input stream.

Parameters

[in] is The input stream.

◆ dist()

template<typename Scalar , uint N>

Scalar vcl::Point< Scalar, N >::dist ( const Point< Scalar, N > & p1 ) const

inline

Computes the Euclidean distance between two Point objects.

The function computes the Euclidean distance between two Point objects, which is defined as the square root of the sum of the squares of the differences of the corresponding components of the two Point objects. The two Point objects must have the same dimension.

Parameters

[in] p1 The Point object to compute the distance to.

Returns: The Euclidean distance between the two Point objects.

◆ div()

template<typename Scalar , uint N>

Point vcl::Point< Scalar, N >::div ( const Point< Scalar, N > & p1 ) const

inline

Divides the components of two Point objects.

This function divides the components of two Point objects element-wise, and returns the result as a new Point object. The two Point objects must have the same dimension. If any component of the second Point object is zero, the function throws a std::runtime_error exception.

Parameters

[in] p1 The other Point object to divide with.

Returns: A new Point object that contains the resulting quotients of the component-wise division of the two Point objects.

Exceptions

std::runtime_error if any component of the second Point object is zero.

◆ epsilonEquals()

template<typename Scalar , uint N>

bool vcl::Point< Scalar, N >::epsilonEquals	(	const Point< Scalar, N > &	p1,
		Scalar	epsilon = `std::numeric_limits<Scalar>::epsilon()`
	)		const

inline

Checks for the equality of two Point objects within a given epsilon tolerance.

The function compares two Point objects component-wise within a given epsilon tolerance. If the difference between the corresponding components of the two Point objects is less than or equal to the epsilon tolerance, the components are considered equal, and the function returns true. Otherwise, the function returns false.

Parameters

[in]	p1	The Point object to compare against.
[in]	epsilon	The epsilon tolerance to use for the comparison.

Returns: true if the two Point objects are considered equal within the epsilon tolerance, false otherwise.

◆ hash()

template<typename Scalar , uint N>

std::size_t vcl::Point< Scalar, N >::hash ( ) const

inline

Computes the hash value of the point.

This function computes a hash value of the point, which can be used for hashing and comparison purposes.

Returns: The hash value of the point.

◆ isDegenerate()

template<typename Scalar , uint N>

bool vcl::Point< Scalar, N >::isDegenerate ( ) const

inline

Returns true if at least one of its components is NaN or inf.

The function checks whether at least one of the scalar components of the Point object is NaN (Not-a-Number) or inf (Infinity). If any component is NaN or inf, the function returns true, indicating that the Point object is degenerate. Otherwise, the function returns false, indicating that the Point object is not degenerate.

Returns: true if the Point object is degenerate, false otherwise.

◆ mul()

template<typename Scalar , uint N>

Point vcl::Point< Scalar, N >::mul ( const Point< Scalar, N > & p1 ) const

inline

Multiplies the components of two Point objects.

This function multiplies the components of two Point objects element-wise, and returns the result as a new Point object. The two Point objects must have the same dimension.

Parameters

[in] p1 The other Point object to multiply with.

Returns: A new Point object that contains the resulting products of the component-wise multiplication of the two Point objects.

◆ operator*() [1/2]

template<typename Scalar , uint N>

Point vcl::Point< Scalar, N >::operator* ( const Eigen::Matrix< Scalar, N+1, N+1 > & m ) const

inline

Returns a new 3D point/vector on which has been applied a TRS 4x4 matrix.

This operator returns a new 3D point/vector obtained by applying a 4x4 TRS matrix to this point/vector. The TRS matrix is a combination of a translation, rotation, and scaling transformation. This operator is available only for points of size 3.

Parameters

[in] m The TRS matrix to apply.

Returns: The new 3D point/vector obtained by applying the TRS matrix to this point/vector.

Note: This function is available only on Points having size == 3.

◆ operator*() [2/2]

template<typename Scalar , uint N>

Scalar vcl::Point< Scalar, N >::operator* ( const Point< Scalar, N > & p1 ) const

inline

Computes the dot product of this point with another point.

This operator computes the dot product of this point with another point and returns the resulting scalar value. The dot product is computed by taking the component-wise product of the coordinates of the two points and summing the products.

Parameters

[in] p1 The point to compute the dot product with.

Returns: The dot product of this point with the other point.

◆ operator*=()

template<typename Scalar , uint N>

Point & vcl::Point< Scalar, N >::operator*= ( const Eigen::Matrix< Scalar, N+1, N+1 > & m )

inline

Applies a TRS 4x4 matrix transformation to this point.

This operator applies a TRS 4x4 matrix transformation to this point and returns a reference to this point. The transformation is performed by multiplying the TRS 4x4 matrix with the homogeneous coordinate representation of this point.

Parameters

[in] m The TRS 4x4 matrix to apply.

Returns: A reference to this point after the transformation.

Note: This function is available only on Points having size == 3.

◆ operator+()

template<typename Scalar , uint N>

Point vcl::Point< Scalar, N >::operator+ ( const Scalar & s ) const

inline

Adds a scalar value to each coordinate of the point.

This operator adds a scalar value to each coordinate of the point and returns the resulting point. The scalar value is added component-wise to each coordinate of the point.

Parameters

[in] s The scalar value to add.

Returns: The point obtained by adding the scalar value to each coordinate of the point.

◆ operator+=()

template<typename Scalar , uint N>

Point & vcl::Point< Scalar, N >::operator+= ( const Scalar & s )

inline

Adds a scalar value to this point.

This operator adds a scalar value to each coordinate of this point and returns a reference to this point. The addition is performed by adding the scalar value to each coordinate of the point.

Parameters

[in] s The scalar value to add.

Returns: A reference to this point after the addition operation.

◆ operator-()

template<typename Scalar , uint N>

Point vcl::Point< Scalar, N >::operator- ( const Scalar & s ) const

inline

Subtracts a scalar value from each coordinate of the point.

This operator subtracts a scalar value from each coordinate of the point and returns the resulting point. The scalar value is subtracted component-wise from each coordinate of the point.

Parameters

[in] s The scalar value to subtract.

Returns: The point obtained by subtracting the scalar value from each coordinate of the point.

◆ operator-=()

template<typename Scalar , uint N>

Point & vcl::Point< Scalar, N >::operator-= ( const Scalar & s )

inline

Subtracts a scalar value from this point.

This operator subtracts a scalar value from each coordinate of this point and returns a reference to this point. The subtraction is performed by subtracting the scalar value from each coordinate of the point.

Parameters

[in] s The scalar value to subtract.

Returns: A reference to this point after the subtraction operation.

◆ operator<=>()

template<typename Scalar , uint N>

auto vcl::Point< Scalar, N >::operator<=> ( const Point< Scalar, N > & p1 ) const

inline

Compares the point with another point using the spaceship operator.

This operator compares the point with another point using the spaceship operator. The comparison is performed by comparing the coordinates of the two points in lexicographic order. The comparison stops as soon as a pair of coordinates that are not equal is found. If all coordinates are equal, the comparison returns std::strong_ordering::equal.

Parameters

[in] p1 The point to compare with.

Returns: A three-way comparison result indicating the relative order of the two points.

◆ operator=()

template<typename Scalar , uint N>

template<typename OtherDerived >

Point & vcl::Point< Scalar, N >::operator= ( const Eigen::MatrixBase< OtherDerived > & other )

inline

Assigns the point to the given Eigen matrix.

Parameters

[in] other The Eigen matrix to assign to.

Returns: A reference to the assigned point.

◆ orthoBase()

template<typename Scalar , uint N>

void vcl::Point< Scalar, N >::orthoBase	(	Point< Scalar, N > &	u,
		Point< Scalar, N > &	v
	)		const

inline

Computes an Orthonormal Basis starting from this point n.

This function computes an Orthonormal Basis starting from this point n. The orthonormal basis is composed of three vectors: the input vector n and two output vectors u and v. The two output vectors are orthogonal to n and each other, and have unit length.

This function is available only on Points having size == 3.

Parameters

[out]	u	The first output vector of the orthonormal basis, orthogonal to n and v.
[out]	v	The second output vector of the orthonormal basis, orthogonal to n and u.

Note: This function uses the cross product operation, which is only defined for 3D vectors.

◆ outerProduct()

template<typename Scalar , uint N>

auto vcl::Point< Scalar, N >::outerProduct ( const Point< Scalar, N > & p1 ) const

inline

Returns the outer product between this point p and p1, which is p * p1^T.

The returned type is a DIM*DIM Eigen Matrix, where DIM is the number of dimensions of the two points.

Parameters

p1	The Point object to compute the outer product with.

Returns: A DIM*DIM Eigen Matrix representing the outer product between this point p and p1.

◆ serialize()

template<typename Scalar , uint N>

void vcl::Point< Scalar, N >::serialize ( std::ostream & os ) const

inline

Serializes the point to the given output stream.

Parameters

[in] os The output stream.

◆ set()

template<typename Scalar , uint N>

template<typename... Scalars>
requires (sizeof...(scalars) == N)

void vcl::Point< Scalar, N >::set ( Scalars... scalars )

inline

Sets all the components of the Point object from a set of scalar values.

The member function takes a variable number of scalar arguments, which are used to set the components of the Point object. The number of arguments must be equal to the dimensionality of the Point object, which is determined by the template parameter N.

Template Parameters

Scalars The types of the scalar arguments.

Parameters

[in] scalars The scalar arguments used to set the components of the Point object.

◆ size()

template<typename Scalar , uint N>

constexpr uint vcl::Point< Scalar, N >::size ( ) const

inlineconstexpr

Returns the size of the Point object.

This function returns the size (number of components) of the Point object.

Returns: The size of the Point object.

◆ squaredDist()

template<typename Scalar , uint N>

Scalar vcl::Point< Scalar, N >::squaredDist ( const Point< Scalar, N > & p1 ) const

inline

Computes the squared Euclidean distance between two Point objects.

The function computes the squared Euclidean distance between two Point objects, which is defined as the sum of the squares of the differences of the corresponding components of the two Point objects. The two Point objects must have the same dimension.

Parameters

[in] p1 The Point object to compute the squared distance to.

Returns: The squared Euclidean distance between the two Point objects.

◆ w() [1/2]

template<typename Scalar , uint N>

ScalarType & vcl::Point< Scalar, N >::w ( )

inline

Returns a reference to the w-component of the Point object.

The function returns a reference to the fourth component of the Point object. If the Point object has fewer than four components, calling this member function results in a compile-time error.

Returns: A reference to the w-component of the Point object.

◆ w() [2/2]

template<typename Scalar , uint N>

const ScalarType & vcl::Point< Scalar, N >::w ( ) const

inline

Returns a const reference to the w-component of the Point object.

The function returns a const reference to the fourth component of the Point object. If the Point object has fewer than four components, calling this member function results in a compile-time error.

Returns: A const reference to the w-component of the Point object.

◆ x() [1/2]

template<typename Scalar , uint N>

ScalarType & vcl::Point< Scalar, N >::x ( )

inline

Returns a reference to the x-component of the Point object.

The function returns a reference to the first component of the Point object. If the Point object has fewer than one component, calling this member function results in a compile-time error.

Returns: A reference to the x-component of the Point object.

◆ x() [2/2]

template<typename Scalar , uint N>

const ScalarType & vcl::Point< Scalar, N >::x ( ) const

inline

Returns a const reference to the x-component of the Point object.

The function returns a const reference to the first component of the Point object. If the Point object has fewer than one component, calling this member function results in a compile-time error.

Returns: A const reference to the x-component of the Point object.

◆ y() [1/2]

template<typename Scalar , uint N>

ScalarType & vcl::Point< Scalar, N >::y ( )

inline

Returns a reference to the y-component of the Point object.

The function returns a reference to the second component of the Point object. If the Point object has fewer than two components, calling this member function results in a compile-time error.

Returns: A reference to the y-component of the Point object.

◆ y() [2/2]

template<typename Scalar , uint N>

const ScalarType & vcl::Point< Scalar, N >::y ( ) const

inline

Returns a const reference to the y-component of the Point object.

The function returns a const reference to the second component of the Point object. If the Point object has fewer than two components, calling this member function results in a compile-time error.

Returns: A const reference to the y-component of the Point object.

◆ z() [1/2]

template<typename Scalar , uint N>

ScalarType & vcl::Point< Scalar, N >::z ( )

inline

Returns a reference to the z-component of the Point object.

The function returns a reference to the third component of the Point object. If the Point object has fewer than three components, calling this member function results in a compile-time error.

Returns: A reference to the z-component of the Point object.

◆ z() [2/2]

template<typename Scalar , uint N>

const ScalarType & vcl::Point< Scalar, N >::z ( ) const

inline

Returns a const reference to the z-component of the Point object.

The function returns a const reference to the third component of the Point object. If the Point object has fewer than three components, calling this member function results in a compile-time error.

Returns: A const reference to the z-component of the Point object.

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

vclib/core/include/vclib/space/core/point.h

Public Types

Public Member Functions

Static Public Attributes

Private Types

Detailed Description

Constructor & Destructor Documentation

◆ Point() [1/2]

◆ Point() [2/2]

Member Function Documentation

◆ angle()

◆ cast()

◆ deserialize()

◆ dist()

◆ div()

◆ epsilonEquals()

◆ hash()

◆ isDegenerate()

◆ mul()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-()

◆ operator-=()

◆ operator<=>()

◆ operator=()

◆ orthoBase()

◆ outerProduct()

◆ serialize()

◆ set()

◆ size()

◆ squaredDist()

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]