ga2 0.6.2

Common types for 2D geometric algebra
Documentation 
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use crate::*;

use std::ops::{Div, DivAssign, Mul, MulAssign};

use derive_more::{Add, AddAssign, Neg, Sub, SubAssign};
use inner_space::{DotProduct, VectorSpace};
use scalars::{Exp, Real, Zero};

/// The 2D bivector type.
#[derive(Copy, Clone, Debug, PartialEq, Eq, Add, AddAssign, Sub, SubAssign, Neg)]
pub struct Bivector<T> {
    /// The component representing the xy plane.
    pub xy: T,
}

impl<T> Bivector<T> {
    /// Creates a new bivector from its components.
    pub fn new(xy: T) -> Self {
        Self { xy }
    }
}

impl<T: Real> Exp for Bivector<T> {
    type Output = Rotor<T>;

    fn exp(self) -> Rotor<T> {
        let [xy, scalar] = self.xy.sin_cos();
        Rotor { scalar, xy }
    }

    fn exp2(self) -> Rotor<T> {
        self.exp()
    }
}

impl<T: Zero> Bivector<T> {
    /// Creates a new bivector along the xy plane.
    pub fn xy(xy: T) -> Self {
        Self { xy }
    }
}

impl<T: Zero> Zero for Bivector<T> {
    fn zero() -> Self {
        Self { xy: T::zero() }
    }

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

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

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

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

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

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

impl<T: Real> DotProduct for Bivector<T> {
    type Output = Self::Scalar;

    fn dot(&self, other: &Self) -> T {
        -self.xy * other.xy
    }

    fn scalar(&self, other: &Self) -> T {
        self.xy * other.xy
    }
}

impl<T: Real> DotProduct<Vector<T>> for Bivector<T> {
    type Output = Vector<T>;
    #[inline]
    fn dot(&self, other: &Vector<T>) -> Vector<T> {
        other.dot(self)
    }
}

impl<T: Real> DotProduct<Rotor<T>> for Bivector<T> {
    type Output = Rotor<T>;
    fn dot(&self, other: &Rotor<T>) -> Rotor<T> {
        Rotor {
            scalar: -self.xy * other.xy,
            xy: self.xy * other.scalar,
        }
    }
}

impl<T: std::fmt::Display> std::fmt::Display for Bivector<T> {
    fn fmt(&self, formatter: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(formatter, "({})", self.xy)
    }
}

impl<T: std::str::FromStr> std::str::FromStr for Bivector<T> {
    type Err = String;

    fn from_str(source: &str) -> Result<Self, Self::Err> {
        let trimmed = source
            .strip_prefix('(')
            .and_then(|s| s.strip_suffix(')'))
            .ok_or_else(|| format!("expected format (xy), got {source}"))?;
        let xy = trimmed
            .trim()
            .parse::<T>()
            .map_err(|_| "failed to parse xy component".to_string())?;
        Ok(Self { xy })
    }
}