inner-space 0.1.0

# Inner Space

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A Rust crate providing essential traits for vector operations, building on [`vector-space`](https://crates.io/crates/vector-space).

## Features

- **`DotProduct` trait**: Defines dot product with flexible output type
- **`InnerSpace` trait**: Provides common vector operations like normalize, project, reflect...
- **Free functions**: `distance` and `distance2` for point operations
- **Zero-cost abstractions**: All operations are inlined and allocation-free

## Example

```rust
use std::ops::{Add, Div, Mul, Neg, Sub};

use inner_space::{DotProduct, VectorSpace, distance};
use num_traits::Zero;

#[derive(Clone, Copy, PartialEq, Debug)]
struct Vector {
    x: f32,
    y: f32,
}

impl Vector {
    fn new(x: f32, y: f32) -> Self {
        Self { x, y }
    }
}

impl Add for Vector {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        Self {
            x: self.x + other.x,
            y: self.y + other.y,
        }
    }
}

impl Sub for Vector {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        Self {
            x: self.x - other.x,
            y: self.y - other.y,
        }
    }
}

impl Mul<f32> for Vector {
    type Output = Self;

    fn mul(self, other: f32) -> Self {
        Self {
            x: self.x * other,
            y: self.y * other,
        }
    }
}

impl Div<f32> for Vector {
    type Output = Self;

    fn div(self, other: f32) -> Self {
        Self {
            x: self.x / other,
            y: self.y / other,
        }
    }
}

impl Neg for Vector {
    type Output = Self;

    fn neg(self) -> Self {
        Self {
            x: -self.x,
            y: -self.y,
        }
    }
}

impl Zero for Vector {
    fn zero() -> Self {
        Self { x: 0.0, y: 0.0 }
    }

    fn is_zero(&self) -> bool {
        self.x == 0.0 && self.y == 0.0
    }
}

impl VectorSpace for Vector {
    type Scalar = f32;
}

impl DotProduct for Vector {
    type Output = f32;

    fn dot(&self, other: &Self) -> f32 {
        self.x * other.x + self.y * other.y
    }
}

// distance

let a = Vector::new(-1.0, 2.0);
let b = Vector::new(2.0, 6.0);

assert_eq!(distance(a, b), 5.0);

// projection, rejection, reflection

let a = Vector::new(-1.0, 3.0);
let b = Vector::new(0.0, 6.0);

assert_eq!(a.project(b), Vector::new(0.0, 3.0));
assert_eq!(a.reject(b), Vector::new(-1.0, 0.0));
assert_eq!(a.reflect(b), Vector::new(1.0, 3.0));
```

## Core Components

### `DotProduct` Trait

```rust
pub trait DotProduct<T = Self>: VectorSpace {
    type Output;

    fn dot(&self, other: &T) -> Self::Output;
}
```

### `InnerSpace` Trait

Automatically implemented for types that implement `DotProduct<Output = Scalar>`. Provides:
- `magnitude()` and `magnitude2()`
- `normalize()`
- `project()` and `reject()`
- `reflect()`
- `angle()`
- `with_magnitude()` and `with_direction()`

### Free Functions

- `distance(a, b)`: Distance between two points
- `distance2(a, b)`: Squared distance between two points

## Example: Vector Operations

```rust
let v = Vec2(3.0, 4.0);
let unit = v.normalize();
assert_eq!(unit, Vec2(0.6, 0.8));

let reflected = v.reflect(Vec2(1.0, 0.0));  // Reflect over x-axis
assert_eq!(reflected, Vec2(3.0, -4.0));
```

## Implementation Guide

1. Implement `VectorSpace` from `vector-space` crate (also reexported here)
2. Implement `DotProduct` with `Output = VectorSpace::Scalar`
3. Get all `InnerSpace` methods automatically

## Compatibility

Works with any type that implements `VectorSpace` and the required operations. Perfect for:
- Custom vector types
- Game development
- Physics simulations
- Graphics programming