vector_space/
lib.rs

1#![no_std]
2#![deny(missing_docs)]
3/*!
4Minimal `VectorSpace` trait for generic vector math.
5
6Defines `Scalar` type and core operation bounds. Use as compatibility layer across vector libraries (math, physics, rendering).
7
8Implement once, use everywhere.
9*/
10
11use core::{
12    cmp::PartialOrd,
13    ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
14};
15use num_traits::{Zero, real::Real};
16
17/// This trait specifies some type to be a vector type.
18/// It specifies the scalar type and is required for other vector types.
19pub trait VectorSpace: Zero + PartialEq
20where
21    Self: Add<Output = Self>
22        + Sub<Output = Self>
23        + Mul<<Self as VectorSpace>::Scalar, Output = Self>
24        + Div<<Self as VectorSpace>::Scalar, Output = Self>
25        + Neg<Output = Self>,
26{
27    /// The scalar type of the vector space.
28    type Scalar: Real + PartialOrd;
29}
30
31impl VectorSpace for f32 {
32    type Scalar = Self;
33}
34impl VectorSpace for f64 {
35    type Scalar = Self;
36}
37
38/// This trait is automatically implemented for vector spaces, which also implement assignment operations.
39pub trait VectorSpaceAssign:
40    VectorSpace + AddAssign + SubAssign + MulAssign<Self::Scalar> + DivAssign<Self::Scalar>
41{
42}
43impl<T> VectorSpaceAssign for T where
44    T: VectorSpace + AddAssign + SubAssign + MulAssign<Self::Scalar> + DivAssign<Self::Scalar>
45{
46}
47
48/// Marker trait for affine spaces, types whose differences are vectors.
49pub trait AffineSpace: Sub<Output = Self::Diff> + Sized {
50    /// The difference type.
51    type Diff: VectorSpace;
52}
53
54impl<T, D> AffineSpace for T
55where
56    T: Sub<Output = D>,
57    D: VectorSpace,
58{
59    type Diff = D;
60}
61
62/// A transformation that maps vectors to vectors.
63///
64/// Math libraries can implement this for their transform types
65/// (matrices, quaternions, rotors, etc.) to enable generic transform support
66/// across libraries that depend on `vector-space`.
67pub trait Transform<V> {
68    /// Applies this transformation to a point.
69    fn apply_point(&self, point: V) -> V;
70}
71
72/// Linear interpolation of two points.
73#[inline]
74pub fn interpolate<T>(a: T, b: T, ratio: <T::Diff as VectorSpace>::Scalar) -> T
75where
76    T: Clone + AffineSpace + Add<T::Diff, Output = T>,
77{
78    a.clone() + (b - a) * ratio
79}
vector_space/lib.rs

vector_space/
lib.rs
