toy::math::Vector2< T > Class Template Reference

2D vector with floating-point or fixed-point components for positions, movement, and physics. More...

Collaboration diagram for toy::math::Vector2< T >:

Public Member Functions
constexpr	Vector2 () noexcept
	Default constructor.
constexpr	Vector2 (const T &x, const T &y) noexcept
	Constructs a vector with the given components.
constexpr	Vector2 (const T *values) noexcept
	Constructs a vector from an array.
constexpr T *	c_arr () noexcept
	Pointer to the component array (x, then y).
constexpr const T *	c_arr () const noexcept
	Read-only pointer to the component array (x, then y).
constexpr Vector2 &	operator+= (const Vector2 &vector) noexcept
	Adds vector to this vector.
constexpr Vector2 &	operator-= (const Vector2 &vector) noexcept
	Subtracts vector from this vector.
constexpr Vector2 &	operator*= (const T &scalar) noexcept
	Multiplies both components by scalar.
constexpr Vector2 &	operator/= (const T &scalar) noexcept
	Divides both components by scalar.
constexpr T	sqrMagnitude () const noexcept
	Squared Euclidean length (x² + y²).
constexpr void	setZero () noexcept
	Sets x and y to zero.
constexpr bool	isZero () const noexcept
	Returns whether both components are zero.
constexpr bool	isEqual (const Vector2 &vector, T absEpsilon=8 *numeric_limits< T >::epsilon(), T relEpsilon=64 *numeric_limits< T >::epsilon()) const noexcept
	Equality within absolute and relative epsilon.

Public Attributes
T	x
	X component of the vector.
T	y
	Y component of the vector.

Detailed Description

template<Vector2Component T>
class toy::math::Vector2< T >

2D vector with floating-point or fixed-point components for positions, movement, and physics.

Represents a 2D vector with x and y components. Suited for world/screen coordinates, velocity, forces, and transformations where sub-pixel or fractional precision is needed. For integer pixel coordinates use toy::math::Point.

Key Features

• Precision: Component type T is toy::math::Vector2Component (float, double, or fixed-point).
• Constexpr: Most operations are constexpr.
• Exception safety: All operations are noexcept.
• Small size: Two components; stack-friendly.

Usage Example

#include "math.hpp"
 
toy::math::Vector2 pos(100.5f, 200.3f);
toy::math::Vector2 velocity(50.0f, -25.0f);
auto deltaTime = 0.5f;
pos += velocity * deltaTime;
 
toy::math::Vector2 force(10.0f, 0.0f);
auto mass = 2.0f;
auto acceleration = force / mass;

Performance Characteristics

• Construction, assignment, arithmetic, comparison: O(1).
• Memory: 2 × sizeof(T).

Safety Guarantees

• Contracts: Division by zero is asserted in debug.
• Exception safety: noexcept; no exceptions thrown.

Note

For pixel-aligned UI coordinates use toy::math::Point.

See also

toy::math::Point

Constructor & Destructor Documentation

Vector2() [1/3]

template<Vector2Component T>

toy::math::Vector2< T >::Vector2 ( )

constexprnoexcept

Default constructor.

Vector2() [2/3]

template<Vector2Component T>

toy::math::Vector2< T >::Vector2 ( const T & x, const T & y )

constexprnoexcept

Constructs a vector with the given components.

Parameters

x	X component.
y	Y component.

Vector2() [3/3]

template<Vector2Component T>

toy::math::Vector2< T >::Vector2 ( const T * values )

explicitconstexprnoexcept

Constructs a vector from an array.

Parameters

values

Pointer to at least two elements; values[0] is x, values[1] is y.

Precondition

values != nullptr; array has at least two elements.

Postcondition

x == values[0], y == values[1].

Member Function Documentation

c_arr() [1/2]

template<Vector2Component T>

const T * toy::math::Vector2< T >::c_arr ( ) const

nodiscardconstexprnoexcept

Read-only pointer to the component array (x, then y).

Returns

Pointer to x; y follows contiguously.

c_arr() [2/2]

template<Vector2Component T>

T * toy::math::Vector2< T >::c_arr ( )

nodiscardconstexprnoexcept

Pointer to the component array (x, then y).

Returns

Pointer to x; y follows contiguously.

isEqual()

template<Vector2Component T>

bool toy::math::Vector2< T >::isEqual ( const Vector2< T > & vector, T absEpsilon = 8 * numeric_limits<T>::epsilon(), T relEpsilon = 64 * numeric_limits<T>::epsilon() ) const

nodiscardconstexprnoexcept

Equality within absolute and relative epsilon.

Parameters

vector	Other vector.
absEpsilon	Maximum absolute difference per component (default: 8× numeric_limits<T>::epsilon()).
relEpsilon	Maximum relative difference (default: 64× numeric_limits<T>::epsilon()).

Returns

true if both components are equal within tolerances, false otherwise.

Precondition

absEpsilon ≥ 0 and relEpsilon ≥ 0.

isZero()

template<Vector2Component T>

bool toy::math::Vector2< T >::isZero ( ) const

nodiscardconstexprnoexcept

Returns whether both components are zero.

Returns

true if x and y are zero, false otherwise.

operator*=()

template<Vector2Component T>

Vector2< T > & toy::math::Vector2< T >::operator*= ( const T & scalar )

constexprnoexcept

Multiplies both components by scalar.

Parameters

scalar

Scale factor.

Returns

Reference to *this.

operator+=()

template<Vector2Component T>

Vector2< T > & toy::math::Vector2< T >::operator+= ( const Vector2< T > & vector )

constexprnoexcept

Adds vector to this vector.

Parameters

vector

Vector to add.

Returns

Reference to *this.

Postcondition

Components are the sum of the previous values and vector.

operator-=()

template<Vector2Component T>

Vector2< T > & toy::math::Vector2< T >::operator-= ( const Vector2< T > & vector )

constexprnoexcept

Subtracts vector from this vector.

Parameters

vector

Vector to subtract.

Returns

Reference to *this.

Postcondition

Components are the difference of the previous values and vector.

operator/=()

template<Vector2Component T>

Vector2< T > & toy::math::Vector2< T >::operator/= ( const T & scalar )

constexprnoexcept

Divides both components by scalar.

Parameters

scalar

Divisor.

Returns

Reference to *this.

Precondition

scalar != 0.

setZero()

template<Vector2Component T>

void toy::math::Vector2< T >::setZero ( )

constexprnoexcept

Sets x and y to zero.

Postcondition

Vector is at the origin.

sqrMagnitude()

template<Vector2Component T>

T toy::math::Vector2< T >::sqrMagnitude ( ) const

nodiscardconstexprnoexcept

Squared Euclidean length (x² + y²).

Returns

Squared magnitude; avoids sqrt for comparisons.

Member Data Documentation

x

template<Vector2Component T>

T toy::math::Vector2< T >::x

X component of the vector.

y

template<Vector2Component T>

T toy::math::Vector2< T >::y

Y component of the vector.

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

• include/math/vector2.hpp
• include/math/vector2.inl