geo-buffer 0.2.0

use core::ops::{Add, Sub, Div, Mul};

use crate::util::{feq, Ray};

/// This structure conceptually represents a point or a vector on 
/// the 2-dimensional Cartesian plane.
/// 
/// It may be vary on the context which represents which.
#[derive(Clone, Default, Debug, Copy, PartialEq, PartialOrd)]
pub struct Coordinate(
    /// x-component of the Cartesian coordinates.
    pub f64, 
    /// y-component of the Cartesian coordinates.
    pub f64,
);

impl From<Coordinate> for (f64, f64){
    fn from(item: Coordinate) -> (f64, f64){
        (item.0, item.1)
    }
}

impl From<(f64, f64)> for Coordinate {
    fn from(item: (f64, f64)) -> Coordinate {
        Coordinate(item.0, item.1)
    }
}

impl From<geo_types::Coord<f64>> for Coordinate{
    fn from(value: geo_types::Coord<f64>) -> Self {
        Coordinate(value.x, value.y)
    }
}

impl From<Coordinate> for geo_types::Coord<f64>{
    fn from(value: Coordinate) -> geo_types::Coord<f64> {
        geo_types::geometry::Coord{x: value.0, y: value.1}
    }
}

impl Add for Coordinate{
    type Output = Self;
    fn add(self, rhs: Self) -> Self{
        Self(self.0+rhs.0, self.1+rhs.1)
    }
}

impl Sub for Coordinate{
    type Output = Self;
    fn sub(self, rhs: Self) -> Self{
        Self(self.0-rhs.0, self.1-rhs.1)
    }
}

impl Mul<f64> for Coordinate{
    type Output = Self;
    fn mul(self, rhs: f64) -> Self::Output {
        Self(self.0*rhs, self.1*rhs)
    }
}

impl Div<f64> for Coordinate{
    type Output = Self;
    fn div(self, rhs: f64) -> Self::Output {
        if rhs == 0. {return self;}
        Self(self.0/rhs, self.1/rhs)
    }
}

impl Div<Coordinate> for Coordinate{
    type Output = f64;
    fn div(self, rhs: Self) -> Self::Output{
        if rhs.0 == 0. && rhs.1 == 0. {return 0.;}
        else if rhs.1 == 0. {return self.0/rhs.0;}
        else {return self.1/rhs.1;}
    }
}

impl Coordinate{
    /// Creates and returns a [Coordinate] w.r.t. the given argument.
    /// 
    /// # Argument
    /// 
    /// + `x`: x-component of the `Coordinate`.
    /// + `y`: y-component of the `Coordinate`.
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(3., 4.);
    /// assert_eq!(c1, (3., 4.).into());
    /// ```
    pub fn new(x: f64, y: f64) -> Self{
        Self{0: x, 1: y}
    }

    /// Returns a tuple wihch has values of each component.
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(3., 4.);
    /// let t1 = c1.get_val();
    /// assert_eq!(t1, (3., 4.));
    /// ```
    pub fn get_val(&self) -> (f64, f64){
        (self.0, self.1)
    }

    /// Returns a value of inner product (i.e. dot product) of the Cartesian coordinates of
    /// two vectors.
    /// 
    /// # Argument
    /// 
    /// + `self`: The Cartesian coordinates of the first vector, **a**.
    /// + `rhs`: The Cartesian coordinates of the second vector, **b**.
    /// 
    /// # Return
    /// 
    /// **a** · **b**
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(1., 2.);
    /// let c2 = geo_buffer::Coordinate::new(3., 4.);
    /// let ip = c1.inner_product(&c2);
    /// assert_eq!(ip, 11.);
    /// ``` 
    /// 
    /// # Notes
    /// 
    /// + This operation is linear.
    /// + This operation is commutative.
    /// 
    pub fn inner_product(&self, rhs: &Self) -> f64{
        self.0*rhs.0 + self.1*rhs.1
    }

    /// Returns a value of the magnitude of cross product of the Cartesian coordinates of
    /// two vectors.
    /// 
    /// # Argument
    /// 
    /// + `self`: The Cartesian coordinates of the first vector, **a**.
    /// + `rhs`: The Cartesian coordinates of the second vector, **b**.
    /// 
    /// # Return
    /// 
    /// **a** × **b**
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(1., 2.);
    /// let c2 = geo_buffer::Coordinate::new(3., 4.);
    /// let op = c1.outer_product(&c2);
    /// assert_eq!(op, -2.);
    /// ``` 
    /// 
    /// # Notes
    /// 
    /// + This operation is linear.
    /// + This operation is *not* commutative. (More precisely, it is anti-commutative.)
    /// + The sign of cross product indicates the orientation of **a** and **b**. If **a** lies before **b** in
    /// the counter-clockwise (CCW for short) ordering, the sign of the result will be positive. If **a** lies after **b** in CCW ordering,
    /// the sign will be negative. The result will be zero if two vectors are colinear. (I.e. lay on the same line.)
    /// 
    pub fn outer_product(&self, rhs: &Self) -> f64{
        self.0*rhs.1-self.1*rhs.0
    }

    /// Returns the Euclidean norm (i.e. magnitude, or L2 norm) of the given vector.
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(3., 4.);
    /// assert_eq!(c1.norm(), 5.);
    /// ```
    pub fn norm(&self) -> f64{
        self.inner_product(self).sqrt()
    }

    /// Returns the distance between two Cartesian coordinates.
    ///
    /// # Example
    ///
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(3., 4.);
    /// let c2 = geo_buffer::Coordinate::new(7., 7.);
    /// assert_eq!(c1.dist_coord(&c2), 5.);
    /// ```
    pub fn dist_coord(&self, rhs: &Coordinate) -> f64{
        f64::sqrt((self.0-rhs.0)*(self.0-rhs.0) + (self.1-rhs.1)*(self.1-rhs.1))
    }
    
    /// Returns the distance from `self` to the given ray.
    /// 
    /// Note that this function considers the given ray as a open-ended line.
    /// That is, the foot of perpendicular may lay on the extended line of the given ray.
    /// 
    /// # Example
    /// 
    /// ```
    /// use geo_buffer::{Coordinate, Ray};
    /// 
    /// let r1 = Ray::new((0., 3.).into(), (4., 0.).into());
    /// let c1 = Coordinate::new(0., 0.);
    /// assert_eq!(c1.dist_ray(&r1), 2.4);
    /// ```
    /// 
    pub fn dist_ray(&self, rhs: &Ray) -> f64{
        if rhs.is_degenerated() {return self.dist_coord(&rhs.origin);}
        return f64::abs((*self-rhs.origin).outer_product(&rhs.angle)) / rhs.angle.norm();
    }

    /// Checks whether the given two Cartesian coordinates are the same (by the equality test with a small epsilon).
    /// 
    /// # Result
    /// 
    /// + `true` if the given coordinates are the same.
    /// + `false` otherwise.
    /// 
    /// # Example
    /// 
    /// ```
    /// let c1 = geo_buffer::Coordinate::new(0.1, 0.2);
    /// let c2 = geo_buffer::Coordinate::new(0.2, 0.3);
    /// let c3 = geo_buffer::Coordinate::new(0.3, 0.5);
    /// let c4 = c1 + c2;
    /// assert!(c3.eq(&c4));
    /// ```
    /// 
    /// # Example (this example panics)
    /// 
    /// ```should_panic
    /// let c1 = geo_buffer::Coordinate::new(0.1, 0.2);
    /// let c2 = geo_buffer::Coordinate::new(0.2, 0.3);
    /// let c3 = geo_buffer::Coordinate::new(0.3, 0.5);
    /// let c4 = c1 + c2;
    /// assert_eq!(c3, c4); // should panic since 0.1 + 0.2 != 0.3 due to floating point errors
    /// ```
    pub fn eq(&self, rhs: &Self) -> bool{
        feq(self.0, rhs.0) && feq(self.1, rhs.1)
    }
}