use std::ops::{Add, AddAssign, Sub, SubAssign, Mul, MulAssign, Div, DivAssign, Neg};

////////// POINT ///////////////////////////////////////////////////////////////

#[macro_export]
macro_rules! point {
    ( $x:expr, $y:expr ) => {
        Point { x: $x, y: $y }
    };
}

#[derive(Debug, Default, Copy, Clone, PartialEq)]
pub struct Point<T> {
    pub x: T,
    pub y: T,
}

impl Point<f64> {
    pub fn length(&self) -> f64 {
        ((self.x * self.x) + (self.y * self.y)).sqrt()
    }

    pub fn normalized(&self) -> Self {
	let l = self.length();
	Self {
	    x: self.x / l,
	    y: self.y / l,
	}
    }

    pub fn to_angle(&self) -> Angle {
	self.y.atan2(self.x).radians()
    }

    pub fn to_i32(self) -> Point<i32> {
	Point {
	    x: self.x as i32,
	    y: self.y as i32,
	}
    }
}

macro_rules! impl_point_op {
    ($op:tt, $trait:ident($fn:ident), $trait_assign:ident($fn_assign:ident), $rhs:ident = $Rhs:ty => $x:expr, $y:expr) => {
        impl<T: $trait<Output = T>> $trait<$Rhs> for Point<T> {
            type Output = Self;

            fn $fn(self, $rhs: $Rhs) -> Self {
                Self {
                    x: self.x $op $x,
                    y: self.y $op $y,
                }
            }
        }

        impl<T: $trait<Output = T> + Copy> $trait_assign<$Rhs> for Point<T> {
            fn $fn_assign(&mut self, $rhs: $Rhs) {
                *self = Self {
                    x: self.x $op $x,
                    y: self.y $op $y,
                }
            }
        }
    }
}

impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Point<T> => rhs.x, rhs.y);
impl_point_op!(+, Add(add), AddAssign(add_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(-, Sub(sub), SubAssign(sub_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = (T, T) => rhs.0, rhs.1);
impl_point_op!(*, Mul(mul), MulAssign(mul_assign), rhs = Dimension<T> => rhs.width, rhs.height);
impl_point_op!(/, Div(div), DivAssign(div_assign), rhs = Dimension<T> => rhs.width, rhs.height);

////////// multiply point with scalar //////////////////////////////////////////
impl<T: Mul<Output = T> + Copy> Mul<T> for Point<T> {
    type Output = Self;

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

impl<T: Mul<Output = T> + Copy> MulAssign<T> for Point<T> {
    fn mul_assign(&mut self, rhs: T) {
	*self = Self {
	    x: self.x * rhs,
	    y: self.y * rhs,
	}
    }
}

////////// divide point with scalar ////////////////////////////////////////////
impl<T: Div<Output = T> + Copy> Div<T> for Point<T> {
    type Output = Self;

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

impl<T: Div<Output = T> + Copy> DivAssign<T> for Point<T> {
    fn div_assign(&mut self, rhs: T) {
	*self = Self {
	    x: self.x / rhs,
	    y: self.y / rhs,
	}
    }
}

impl<T: Neg<Output = T>> Neg for Point<T> {
    type Output = Self;

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

impl<T> From<(T, T)> for Point<T> {
    fn from(item: (T, T)) -> Self {
        Point {
            x: item.0,
            y: item.1,
        }
    }
}

impl<T> From<Point<T>> for (T, T) {
    fn from(item: Point<T>) -> Self {
        (item.x, item.y)
    }
}

impl From<Angle> for Point<f64> {
    fn from(item: Angle) -> Self {
	Point {
	    x: item.0.cos(),
	    y: item.0.sin(),
	}
    }
}

////////// ANGLE ///////////////////////////////////////////////////////////////

#[derive(Debug, Default, Clone, Copy)]
pub struct Angle(pub f64);

pub trait ToAngle {
    fn radians(self) -> Angle;
    fn degrees(self) -> Angle;
}

macro_rules! impl_angle {
    ($($type:ty),*) => {
	$(
	    impl ToAngle for $type {
		fn radians(self) -> Angle {
		    Angle(self as f64)
		}

		fn degrees(self) -> Angle {
		    Angle((self as f64).to_radians())
		}
	    }

	    impl Mul<$type> for Angle {
		type Output = Self;

		fn mul(self, rhs: $type) -> Self {
		    Angle(self.0 * (rhs as f64))
		}
	    }

	    impl MulAssign<$type> for Angle {
		fn mul_assign(&mut self, rhs: $type) {
		    self.0 *= rhs as f64;
		}
	    }

	    impl Div<$type> for Angle {
		type Output = Self;

		fn div(self, rhs: $type) -> Self {
		    Angle(self.0 / (rhs as f64))
		}
	    }

	    impl DivAssign<$type> for Angle {
		fn div_assign(&mut self, rhs: $type) {
		    self.0 /= rhs as f64;
		}
	    }
	)*
    }
}

impl_angle!(f32, f64, i8, i16, i32, i64, isize, u8, u16, u32, u64, usize);

impl Angle {
    pub fn to_radians(self) -> f64 {
	self.0
    }

    pub fn to_degrees(self) -> f64 {
	self.0.to_degrees()
    }

    /// Returns the reflection of the incident when mirrored along this angle.
    pub fn mirror(&self, incidence: Angle) -> Angle {
	Angle((std::f64::consts::PI + self.0 * 2.0 - incidence.0) % std::f64::consts::TAU)
    }
}

impl PartialEq for Angle {
    fn eq(&self, rhs: &Angle) -> bool {
	self.0 % std::f64::consts::TAU == rhs.0 % std::f64::consts::TAU
    }
}

// addition and subtraction of angles

impl Add<Angle> for Angle {
    type Output = Self;

    fn add(self, rhs: Angle) -> Self {
	Angle(self.0 + rhs.0)
    }
}

impl AddAssign<Angle> for Angle {
    fn add_assign(&mut self, rhs: Angle) {
	self.0 += rhs.0;
    }
}

impl Sub<Angle> for Angle {
    type Output = Self;

    fn sub(self, rhs: Angle) -> Self {
	Angle(self.0 - rhs.0)
    }
}

impl SubAssign<Angle> for Angle {
    fn sub_assign(&mut self, rhs: Angle) {
	self.0 -= rhs.0;
    }
}

////////// INTERSECTION ////////////////////////////////////////////////////////

#[derive(Debug)]
pub enum Intersection {
    Point(Point<f64>),
    //Line(Point<f64>, Point<f64>), // TODO: overlapping collinear
    None,
}

impl Intersection {
    pub fn lines(p1: Point<f64>, p2: Point<f64>, p3: Point<f64>, p4: Point<f64>) -> Intersection {
	let s1 = p2 - p1;
	let s2 = p4 - p3;

	let denomimator = -s2.x * s1.y + s1.x * s2.y;
	if denomimator != 0.0 {
	    let s = (-s1.y * (p1.x - p3.x) + s1.x * (p1.y - p3.y)) / denomimator;
	    let t = ( s2.x * (p1.y - p3.y) - s2.y * (p1.x - p3.x)) / denomimator;

	    if (0.0..=1.0).contains(&s) && (0.0..=1.0).contains(&t) {
		return Intersection::Point(p1 + (s1 * t))
	    }
	}

	Intersection::None
    }
}

////////// DIMENSION ///////////////////////////////////////////////////////////

#[macro_export]
macro_rules! dimen {
    ( $w:expr, $h:expr ) => {
        Dimension { width: $w, height: $h }
    };
}

#[derive(Debug, Default, Copy, Clone, PartialEq)]
pub struct Dimension<T> {
    pub width: T,
    pub height: T,
}

impl<T: Mul<Output = T> + Copy> Dimension<T> {
    #[allow(dead_code)]
    pub fn area(&self) -> T {
        self.width * self.height
    }
}

impl<T> From<(T, T)> for Dimension<T> {
    fn from(item: (T, T)) -> Self {
        Dimension {
            width: item.0,
            height: item.1,
        }
    }
}

impl<T> From<Dimension<T>> for (T, T) {
    fn from(item: Dimension<T>) -> Self {
        (item.width, item.height)
    }
}

////////////////////////////////////////////////////////////////////////////////

#[allow(dead_code)]
pub fn supercover_line_int(p1: Point<isize>, p2: Point<isize>) -> Vec<Point<isize>> {
    let d = p2 - p1;
    let n = point!(d.x.abs(), d.y.abs());
    let step = point!(
	if d.x > 0 { 1 } else { -1 },
	if d.y > 0 { 1 } else { -1 }
    );

    let mut p = p1;
    let mut points = vec!(point!(p.x as isize, p.y as isize));
    let mut i = point!(0, 0);
    while i.x < n.x || i.y < n.y {
        let decision = (1 + 2 * i.x) * n.y - (1 + 2 * i.y) * n.x;
        if decision == 0 { // next step is diagonal
            p.x += step.x;
            p.y += step.y;
            i.x += 1;
            i.y += 1;
        } else if decision < 0 { // next step is horizontal
            p.x += step.x;
	    i.x += 1;
        } else { // next step is vertical
            p.y += step.y;
            i.y += 1;
        }
        points.push(point!(p.x as isize, p.y as isize));
    }

    points
}

/// Calculates all points a line crosses, unlike Bresenham's line algorithm.
/// There might be room for a lot of improvement here.
pub fn supercover_line(mut p1: Point<f64>, mut p2: Point<f64>) -> Vec<Point<isize>> {
    let mut delta = p2 - p1;
    if (delta.x.abs() > delta.y.abs() && delta.x.is_sign_negative()) || (delta.x.abs() <= delta.y.abs() && delta.y.is_sign_negative()) {
	std::mem::swap(&mut p1, &mut p2);
	delta = -delta;
    }

    let mut last = point!(p1.x as isize, p1.y as isize);
    let mut coords: Vec<Point<isize>> = vec!();
    coords.push(last);

    if delta.x.abs() > delta.y.abs() {
	let k = delta.y / delta.x;
	let m = p1.y as f64 - p1.x as f64 * k;
	for x in (p1.x as isize + 1)..=(p2.x as isize) {
	    let y = (k * x as f64 + m).floor();
	    let next = point!(x as isize - 1, y as isize);
	    if next != last {
		coords.push(next);
	    }
	    let next = point!(x as isize, y as isize);
	    coords.push(next);
	    last = next;
	}
    } else {
	let k = delta.x / delta.y;
	let m = p1.x as f64 - p1.y as f64 * k;
	for y in (p1.y as isize + 1)..=(p2.y as isize) {
	    let x = (k * y as f64 + m).floor();
	    let next = point!(x as isize, y as isize - 1);
	    if next != last {
		coords.push(next);
	    }
	    let next = point!(x as isize, y as isize);
	    coords.push(next);
	    last = next;
	}
    }

    let next = point!(p2.x as isize, p2.y as isize);
    if next != last {
	coords.push(next);
    }

    coords
}

////////// TESTS ///////////////////////////////////////////////////////////////

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn immutable_copy_of_point() {
        let a = point!(0, 0);
        let mut b = a; // Copy
        assert_eq!(a, b); // PartialEq
        b.x = 1;
        assert_ne!(a, b); // PartialEq
    }

    #[test]
    fn add_points() {
        let mut a = point!(1, 0);
        assert_eq!(a + point!(2, 2), point!(3, 2)); // Add
        a += point!(2, 2); // AddAssign
        assert_eq!(a, point!(3, 2));
        assert_eq!(point!(1, 0) + (2, 3), point!(3, 3));
    }

    #[test]
    fn sub_points() {
        let mut a = point!(1, 0);
        assert_eq!(a - point!(2, 2), point!(-1, -2));
        a -= point!(2, 2);
        assert_eq!(a, point!(-1, -2));
        assert_eq!(point!(1, 0) - (2, 3), point!(-1, -3));
    }

    #[test]
    fn mul_points() {
        let mut a = point!(1, 2);
        assert_eq!(a * 2, point!(2, 4));
        assert_eq!(a * point!(2, 3), point!(2, 6));
        a *= 2;
        assert_eq!(a, point!(2, 4));
        a *= point!(3, 1);
        assert_eq!(a, point!(6, 4));
        assert_eq!(point!(1, 0) * (2, 3), point!(2, 0));
    }

    #[test]
    fn div_points() {
        let mut a = point!(4, 8);
        assert_eq!(a / 2, point!(2, 4));
        assert_eq!(a / point!(2, 4), point!(2, 2));
        a /= 2;
        assert_eq!(a, point!(2, 4));
        a /= point!(2, 4);
        assert_eq!(a, point!(1, 1));
        assert_eq!(point!(6, 3) / (2, 3), point!(3, 1));
    }

    #[test]
    fn neg_point() {
        assert_eq!(point!(1, 1), -point!(-1, -1));
    }

    #[test]
    fn angles() {
	assert_eq!(0.radians(), 0.degrees());
	assert_eq!(0.degrees(), 360.degrees());
	assert_eq!(180.degrees(), std::f64::consts::PI.radians());
	assert_eq!(std::f64::consts::PI.radians().to_degrees(), 180.0);
	assert!((Point::from(90.degrees()) - point!(0.0, 1.0)).length() < 0.001);
	assert!((Point::from(std::f64::consts::FRAC_PI_2.radians()) - point!(0.0, 1.0)).length() < 0.001);
    }

    #[test]
    fn area_for_dimension_of_multipliable_type() {
        let r: Dimension<_> = (30, 20).into(); // the Into trait uses the From trait
        assert_eq!(r.area(), 30 * 20);
        // let a = Dimension::from(("a".to_string(), "b".to_string())).area(); // this doesn't work, because area() is not implemented for String
    }

    #[test]
    fn intersection_of_lines() {
        let p1 = point!(0.0, 0.0);
        let p2 = point!(2.0, 2.0);
        let p3 = point!(0.0, 2.0);
        let p4 = point!(2.0, 0.0);
	let r = Intersection::lines(p1, p2, p3, p4);
	if let Intersection::Point(p) = r {
            assert_eq!(p, point!(1.0, 1.0));
	} else {
	    panic!();
	}
    }

    #[test]
    fn some_coordinates_on_line() {
	// horizontally up
	let coords = supercover_line(point!(0.0, 0.0), point!(3.3, 2.2));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(1, 1), point!(2, 1), point!(2, 2), point!(3, 2)]);

	// horizontally down
	let coords = supercover_line(point!(0.0, 5.0), point!(3.3, 2.2));
	assert_eq!(coords.as_slice(), &[point!(0, 5), point!(0, 4), point!(1, 4), point!(1, 3), point!(2, 3), point!(2, 2), point!(3, 2)]);

	// vertically right
	let coords = supercover_line(point!(0.0, 0.0), point!(2.2, 3.3));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(0, 1), point!(1, 1), point!(1, 2), point!(2, 2), point!(2, 3)]);

	// vertically left
	let coords = supercover_line(point!(5.0, 0.0), point!(3.0, 3.0));
	assert_eq!(coords.as_slice(), &[point!(5, 0), point!(4, 0), point!(4, 1), point!(3, 1), point!(3, 2), point!(3, 3)]);

	// negative
	let coords = supercover_line(point!(0.0, 0.0), point!(-3.0, -2.0));
	assert_eq!(coords.as_slice(), &[point!(-3, -2), point!(-2, -2), point!(-2, -1), point!(-1, -1), point!(-1, 0), point!(0, 0)]);

	// 
	let coords = supercover_line(point!(0.0, 0.0), point!(2.3, 1.1));
	assert_eq!(coords.as_slice(), &[point!(0, 0), point!(1, 0), point!(2, 0), point!(2, 1)]);
    }
}