ga2 0.3.0

use crate::*;

use derive_more::{Add, AddAssign, Neg, Sub, SubAssign};
use num_traits::{real::Real, Zero};
use std::ops::{Div, DivAssign, Mul, MulAssign};
use vector_basis::Basis;
use vector_space::{DotProduct, InnerSpace, VectorSpace};

/// The 2D vector type.
#[derive(Copy, Clone, Debug, PartialEq, Eq, Add, AddAssign, Sub, SubAssign, Neg)]
pub struct Vector<T> {
    /// The component representing the x axis.
    pub x: T,
    /// The component representing the y axis.
    pub y: T,
}

impl<T> Vector<T> {
    /// Creates a new vector from its components.
    pub fn new(x: T, y: T) -> Self {
        Self { x, y }
    }
}

impl<T: Zero> Vector<T> {
    /// Creates a new vector along the x axis.
    pub fn x(x: T) -> Self {
        Self { x, y: T::zero() }
    }

    /// Creates a new vector along the y axis.
    pub fn y(y: T) -> Self {
        Self { x: T::zero(), y }
    }
}

impl<T: Real> Basis<0> for Vector<T> {
    fn unit_basis() -> Self {
        Self {
            x: T::one(),
            y: T::zero(),
        }
    }

    fn basis_of(x: T) -> Self {
        Self { x, y: T::zero() }
    }

    fn basis(&self) -> Self::Scalar {
        self.x
    }

    fn basis_mut(&mut self) -> &mut Self::Scalar {
        &mut self.x
    }

    fn with_basis(self, x: T) -> Self {
        Self { x, ..self }
    }
}

impl<T: Real> Basis<1> for Vector<T> {
    fn unit_basis() -> Self {
        Self {
            x: T::zero(),
            y: T::one(),
        }
    }

    fn basis_of(y: T) -> Self {
        Self { x: T::zero(), y }
    }

    fn basis(&self) -> Self::Scalar {
        self.y
    }

    fn basis_mut(&mut self) -> &mut Self::Scalar {
        &mut self.y
    }

    fn with_basis(self, y: T) -> Self {
        Self { y, ..self }
    }
}

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

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

impl<T> Mul<T> for Vector<T>
where
    T: Mul<Output = T> + Copy,
{
    type Output = Self;
    fn mul(self, other: T) -> Self {
        Self {
            x: self.x * other,
            y: self.y * other,
        }
    }
}

impl<T> MulAssign<T> for Vector<T>
where
    T: MulAssign + Copy,
{
    fn mul_assign(&mut self, other: T) {
        self.x *= other;
        self.y *= other;
    }
}

impl<T> Div<T> for Vector<T>
where
    T: Div<Output = T> + Copy,
{
    type Output = Self;
    fn div(self, other: T) -> Self {
        Self {
            x: self.x / other,
            y: self.y / other,
        }
    }
}

impl<T> DivAssign<T> for Vector<T>
where
    T: DivAssign + Copy,
{
    fn div_assign(&mut self, other: T) {
        self.x /= other;
        self.y /= other;
    }
}

impl<T: Real> VectorSpace for Vector<T> {
    type Scalar = T;
}

impl<T: Real> DotProduct for Vector<T> {
    type Output = Self::Scalar;
    fn dot(self, other: Self) -> T {
        self.x * other.x + self.y * other.y
    }
}

impl<T: Real> DotProduct<Bivector<T>> for Vector<T> {
    type Output = Self;
    fn dot(self, other: Bivector<T>) -> Self {
        Self {
            x: -self.y * other.xy,
            y: self.x * other.xy,
        }
    }
}

impl<T: Real> DotProduct<Rotor<T>> for Vector<T> {
    type Output = Self;
    fn dot(self, other: Rotor<T>) -> Self {
        self * other.scalar
            + Self {
                x: -self.y * other.xy,
                y: self.x * other.xy,
            }
    }
}

impl<T: Real> InnerSpace for Vector<T> {
    fn scalar(self, other: Self) -> T {
        self.dot(other)
    }
}

impl<T: Real> Mul for Vector<T> {
    type Output = Rotor<T>;
    fn mul(self, other: Self) -> Rotor<T> {
        Rotor {
            scalar: self.dot(other),
            xy: self.x * other.y + self.y * other.x,
        }
    }
}