fp::vec3< Real > Class Template Reference

Internal implementation of a 3D vector. More...

#include <vec3.hpp>

Collaboration diagram for fp::vec3< Real >:

Public Member Functions
void	add (vec3< Real > const &v)
	In place addition method.
void	subtract (vec3< Real > const &v)
	In place subtraction method.
void	scale (Real s)
	Scale the vector by a real number s.
Real	dot (vec3< Real > const &v) const
	Calculate dot product with another vector.
constexpr std::size_t	size () const
	Always returns 3.
vec3< Real >	cross (vec3< Real > const &other) const
	Calculate cross product with another vector.
Real	norm () const
	Returns the norm of the vector.
Real	norm_square () const
	Returns the square of the norm of the vector.
vec3< Real > const &	normalize ()
	Normalize the vector in place. And return a reference to the new normalized vector.
bool	operator== (vec3< Real > const &other) const =default
	default equality operator.
template<typename Index > requires std::is_integral_v<Index>
Real &	operator[] (Index idx)
	element access operator.
template<typename Index > requires std::is_integral_v<Index>
const Real &	operator[] (Index idx) const
	element access operator for constant environments.

Static Public Member Functions
static vec3< Real >	cross (vec3< Real > const &a, vec3< Real > const &b)
	Calculate cross product between two vectors.

Public Attributes
Real	x
	The x component of the vector.
Real	y
	The y component of the vector.
Real	z
	The z component of the vector.

Friends
std::ostream &	operator<< (std::ostream &os, const vec3< Real > &obj)
	Streaming operator for easy printing of the vector.
vec3< Real >	operator+ (vec3< Real > lhs, vec3< Real > const &rhs)
	Overloaded operator defined in terms of vec2::add.
void	operator+= (vec3< Real > &lhs, vec3< Real > const &rhs)
	Overloaded operator defined in terms of vec3::add.
vec3< Real >	operator- (vec3< Real > lhs, vec3< Real > const &rhs)
	Overloaded operator defined in terms of vec3::subtract.
void	operator-= (vec3< Real > &lhs, vec3< Real > const &rhs)
	Overloaded operator defined in terms of vec3::subtract.
vec3< Real >	operator* (Real const &lhs, vec3< Real > rhs)
	Overloaded operator defined in terms of vec3::scale.
vec3< Real >	operator* (vec3< Real > lhs, Real const &rhs)
	Overloaded operator defined in terms of vec3::scale.
void	operator/= (vec3< Real > &lhs, Real const &rhs)
	Overloaded operator defined in terms of vec3::scale.
vec3< Real >	operator/ (vec3< Real > lhs, Real const &rhs)
	Overloaded operator defined in terms of vec3::scale.
vec3< Real >	operator- (vec3< Real > v)
	Unary minus operator.

Detailed Description

template<floating_point_number Real>
class fp::vec3< Real >

Internal implementation of a 3D vector.

!!! vec3 does not throw !!! This means that if you ask vec3 to divide a vector by 0 or more realistically if you normalize a zero length vector vec3 will not check for the division by zero and will return a nan result! Since vec3 is used everywhere in flippy, including in very expensive calculations, I decided to omit the security check for the sake of speed.

To keep the external dependencies low, flippy implements it's own 3D vector class with basic functionality like dot product and cross product

Example:

 ++
fp::vec3<double> v1{1,0,0};
fp::vec3<double> v2{0,0,1};
 
 assert(v1.dot(v2)==0);
 assert(v1.cross(v2).norm()==1);
 assert(((v1-v2)==fp::vec3<double>{1.,0.,-1.}));

Template Parameters

Real	type that will be used for all floating point numbers inside this class/struct. Any data type that satisfies the floating_point_number concept is allowed, for example, float.

Member Function Documentation

add()

template<floating_point_number Real>

void fp::vec3< Real >::add ( vec3< Real > const & v )

inline

In place addition method.

Example:

 ++
fp::vec3<double> v1{1,0,0};
fp::vec3<double> v2{0,0,1};
v1.add(v2);  // v1 will contain {1, 0, 1}

Parameters

v	add this vector elementwise to the vector that is calling the add method.

subtract()

template<floating_point_number Real>

void fp::vec3< Real >::subtract ( vec3< Real > const & v )

inline

In place subtraction method.

Example:

 ++
fp::vec3<double> v1{2,0,0};
fp::vec3<double> v2{1,0,1};
v1.subtract(v2);  // v1 will contain {1, 0, -1}

Parameters

v	subtract this vector elementwise from the vector that is calling the subtract method.

scale()

template<floating_point_number Real>

void fp::vec3< Real >::scale ( Real s )

inline

Scale the vector by a real number s.

This function scales the vector in-place by the provided number s.

Parameters

s	multiplicative prefactor.

dot()

template<floating_point_number Real>

Real fp::vec3< Real >::dot ( vec3< Real > const & v ) const

inline

Calculate dot product with another vector.

Example:

{c++} 
fp::vec3<double> v1{1,0,0};
fp::vec3<double> v2{2,0,1};
double res = v1.dot(v2);  // res will contain 2*1 + 0*0 + 0*1=2

Parameters

v	the other vec3 vector

Returns

result of the dot product between the original vector and v.

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size()

template<floating_point_number Real>

std::size_t fp::vec3< Real >::size ( ) const

inlinenodiscardconstexpr

Always returns 3.

This function always returns 3 since vec3 can only have three elements. It was implemented for completeness, to make it more easy for vec3 to be used as a drop-in replacement for other vector types.

Returns

Size (number of elements) of vec3.

cross() [1/2]

template<floating_point_number Real>

static vec3< Real > fp::vec3< Real >::cross ( vec3< Real > const & a, vec3< Real > const & b )

inlinestatic

Calculate cross product between two vectors.

A static method to calculate cross product between two vectors. Example:

{c++} 
fp::vec3<double> v1{1,0,0};
fp::vec3<double> v2{0,1,0};
fp::vec3<double> v3 = cross(v1, v2);  // v3 will contain {0,0,1}

Parameters

a	first vector of the cross product
b	second vector of the cross product

Returns

result of the cross product between the original vector and v.

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cross() [2/2]

template<floating_point_number Real>

vec3< Real > fp::vec3< Real >::cross ( vec3< Real > const & other ) const

inline

Calculate cross product with another vector.

Example:

{c++} 
fp::vec3<double> v1{1,0,0};
fp::vec3<double> v2{0,1,0};
fp::vec3<double> v3 = v1.cross(v2);  // v3 will contain {0,0,1}

Parameters

other

the other vec3 vector.

Returns

result of the cross product between the original vector and other.

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norm()

template<floating_point_number Real>

Real fp::vec3< Real >::norm ( ) const

inline

Returns the norm of the vector.

Example:

{c++} 
fp::vec3<double> v{1,0,1};
double res = v.norm();  // res will contain 1,4142135624... i.e. sqrt(2)

Returns

The euclidian norm of the vector.

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norm_square()

template<floating_point_number Real>

Real fp::vec3< Real >::norm_square ( ) const

inline

Returns the square of the norm of the vector.

Example:

{c++} 
fp::vec3<double> v{1,0,1};
double res = v.norm_square();  // res will contain 2

Returns

Square of the euclidian norm of the vector.

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normalize()

template<floating_point_number Real>

vec3< Real > const & fp::vec3< Real >::normalize ( )

inline

Normalize the vector in place. And return a reference to the new normalized vector.

Warning

If you normalize a zero length vector, you effectively demand to divide by zero! this function will not do a security check for you and will just return nan!

Returns

Reference to the normalized vector.

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operator==()

template<floating_point_number Real>

bool fp::vec3< Real >::operator== ( vec3< Real > const & other ) const

default

default equality operator.

Parameters

other

vec3 on the right hand side of the comparison operator.

Returns

true if all elements of the compared vectors are equal and to false otherwise.

operator[]() [1/2]

template<floating_point_number Real>

template<typename Index >
requires std::is_integral_v<Index>

Real & fp::vec3< Real >::operator[] ( Index idx )

inline

element access operator.

Template Parameters

Index

automatically deduced type of the index.

Parameters

idx	can only be 0 1 or 2. Any other number will cause the program to exit with an error.

Returns

for a vec3 v: v[1] returns v.x, v[2] returns v.y and v[3] returns v.z.

Note

: The use of the subscription operator might be slower than the direct access of the data member.

operator[]() [2/2]

template<floating_point_number Real>

template<typename Index >
requires std::is_integral_v<Index>

const Real & fp::vec3< Real >::operator[] ( Index idx ) const

inline

element access operator for constant environments.

Template Parameters

Index

automatically deduced type of the index.

Parameters

idx	can only be 0 1 or 2. Any other number will cause the program to exit with an error.

Returns

for a vec3 v: v[1] returns a constant reference to v.x, v[2] returns a constant reference to v.y and v[3] returns a constant reference to v.z.

Note

: The use of the subscription operator might be slower than the direct access of the data member.

Friends And Related Symbol Documentation

operator+

template<floating_point_number Real>

vec3< Real > operator+ ( vec3< Real > lhs, vec3< Real > const & rhs )

friend

Overloaded operator defined in terms of vec2::add.

Parameters

lhs	left hand side of the + operator
rhs	right hand side oif the + operator

Returns

equivalent to a new copy of lhs.add(rhs).

operator+=

template<floating_point_number Real>

void operator+= ( vec3< Real > & lhs, vec3< Real > const & rhs )

friend

Overloaded operator defined in terms of vec3::add.

Equivalent to lhs.add(rhs).

Parameters

lhs	left hand side of the += operator
rhs	right hand side oif the += operator

operator- [1/2]

template<floating_point_number Real>

vec3< Real > operator- ( vec3< Real > lhs, vec3< Real > const & rhs )

friend

Overloaded operator defined in terms of vec3::subtract.

Parameters

lhs	left hand side of the - operator
rhs	right hand side oif the - operator

Returns

equivalent to a new copy of lhs.subtract(rhs).

operator-=

template<floating_point_number Real>

void operator-= ( vec3< Real > & lhs, vec3< Real > const & rhs )

friend

Overloaded operator defined in terms of vec3::subtract.

Equivalent to lhs.subtract(rhs).

Parameters

lhs	left hand side of the -= operator
rhs	right hand side oif the -= operator

operator* [1/2]

template<floating_point_number Real>

vec3< Real > operator* ( Real const & lhs, vec3< Real > rhs )

friend

Overloaded operator defined in terms of vec3::scale.

Left multiplication by a scalar s*v.

Parameters

lhs	left hand side of the * operator
rhs	right hand side oif the * operator

Returns

equivalent to a new copy of rhs.scale(lhs).

operator* [2/2]

template<floating_point_number Real>

vec3< Real > operator* ( vec3< Real > lhs, Real const & rhs )

friend

Overloaded operator defined in terms of vec3::scale.

Right multiplication by a scalar v*s.

Parameters

lhs	left hand side of the * operator
rhs	right hand side oif the * operator

Returns

equivalent to a new copy of lhs.scale(rhs).

operator/=

template<floating_point_number Real>

void operator/= ( vec3< Real > & lhs, Real const & rhs )

friend

Overloaded operator defined in terms of vec3::scale.

In place division by a scalar v/s, equivalent to lhs.scale(1/rhs).

Parameters

lhs	left hand side of the /= operator
rhs	right hand side oif the /= operator

Warning

for performance reasons, this function will not check for zero division!

operator/

template<floating_point_number Real>

vec3< Real > operator/ ( vec3< Real > lhs, Real const & rhs )

friend

Overloaded operator defined in terms of vec3::scale.

Division by a scalar v/s.

Parameters

lhs	left hand side of the / operator
rhs	right hand side oif the / operator

Returns

equivalent to a new copu of lhs.scale(1/rhs).

Warning

for performance reasons, this function will not check for zero division!

operator- [2/2]

template<floating_point_number Real>

vec3< Real > operator- ( vec3< Real > v )

friend

Unary minus operator.

Parameters

v	original vector.

Returns

A copy of -v the vector v itself stays unaffected.

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

• flippy/vec3.hpp