pub trait VectorSpace:
Mul<f32, Output = Self>
+ Div<f32, Output = Self>
+ Add<Self, Output = Self>
+ Sub<Self, Output = Self>
+ Neg
+ Default
+ Debug
+ Clone
+ Copy {
const ZERO: Self;
// Provided method
fn lerp(&self, rhs: Self, t: f32) -> 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
f32
- 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: f32
,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: f32
,u, v: Self
,(u + v) * a == u * a + v * a
. - (Distributivity for scalar addition) For all
a, b: f32
,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§
Provided Methods§
Sourcefn lerp(&self, rhs: Self, t: f32) -> Self
fn lerp(&self, rhs: Self, t: f32) -> 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 interpolating 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.