VectorSpace

bevy::math::common_traits

Trait VectorSpace 

Source 
pub trait VectorSpace:
    Mul<Self::Scalar, Output = Self>
    + Div<Self::Scalar, Output = Self>
    + Add<Output = Self>
    + Sub<Output = Self>
    + Neg<Output = Self>
    + Default
    + Debug
    + Clone
    + Copy {
    type Scalar: ScalarField;

    const ZERO: Self;

    // Provided method
    fn lerp(self, rhs: Self, t: Self::Scalar) -> Self { ... }
}
Expand description

A type that supports the mathematical operations of a real vector space, irrespective of dimension. In particular, this means that the implementing type supports:

  • Scalar multiplication and division on the right by elements of Self::Scalar
  • Negation
  • Addition and subtraction
  • Zero

Within the limitations of floating point arithmetic, all the following are required to hold:

  • (Associativity of addition) For all u, v, w: Self, (u + v) + w == u + (v + w).
  • (Commutativity of addition) For all u, v: Self, u + v == v + u.
  • (Additive identity) For all v: Self, v + Self::ZERO == v.
  • (Additive inverse) For all v: Self, v - v == v + (-v) == Self::ZERO.
  • (Compatibility of multiplication) For all a, b: Self::Scalar, v: Self, v * (a * b) == (v * a) * b.
  • (Multiplicative identity) For all v: Self, v * 1.0 == v.
  • (Distributivity for vector addition) For all a: Self::Scalar, u, v: Self, (u + v) * a == u * a + v * a.
  • (Distributivity for scalar addition) For all a, b: Self::Scalar, v: Self, v * (a + b) == v * a + v * b.

Note that, because implementing types use floating point arithmetic, they are not required to actually implement PartialEq or Eq.

Required Associated Constants§

Source

const ZERO: Self

The zero vector, which is the identity of addition for the vector space type.

Required Associated Types§

Source

type Scalar: ScalarField

The scalar type of this vector space.

Provided Methods§

Source

fn lerp(self, rhs: Self, t: Self::Scalar) -> Self

Perform vector space linear interpolation between this element and another, based on the parameter t. When t is 0, self is recovered. When t is 1, rhs is recovered.

Note that the value of t is not clamped by this function, so extrapolating outside of the interval [0,1] is allowed.

Dyn Compatibility§

This trait is not dyn compatible.

In older versions of Rust, dyn compatibility was called "object safety", so this trait is not object safe.

Implementors§