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pub trait Point: Clone {
    fn x(&self) -> f64;
    fn y(&self) -> f64;
}

pub trait SqDistance<Rhs = Self>
where
    Self: Point,
    Rhs: Point,
{
    fn get_sq_distance(&self, rhs: &Rhs) -> f64 {
        let dx = self.x() - rhs.x();
        let dy = self.y() - rhs.y();

        dx * dx + dy * dy
    }
}

pub trait SqSegDistance<L = Self, R = Self>
where
    Self: Point,
    L: Point,
    R: Point,
{
    fn get_sq_seg_distance(&self, l: &L, r: &R) -> f64 {
        let mut x = l.x();
        let mut y = l.y();

        let mut dx = r.x() - x;
        let mut dy = r.y() - y;

        if dx != 0f64 && dy != 0f64 {
            let t = ((self.x() - x) * dx + (self.y() - y) * dy) / (dx * dx + dy * dy);

            if t > 1f64 {
                x = r.x();
                y = r.y();
            } else if t > 0f64 {
                x += dx * t;
                y += dy * t;
            }
        }

        dx = self.x() - x;
        dy = self.y() - y;

        dx * dx + dy * dy
    }
}

impl<T> SqDistance<T> for T where T: Point {}

impl<T> SqSegDistance<T> for T where T: Point {}

pub struct Simplify<'a, T>
where
    T: Point,
{
    highest_quality: bool,
    tolerance: f64,
    points: &'a mut Vec<T>,
}

impl<'a, T> Simplify<'a, T>
where
    T: Point,
{
    pub fn new(points: &'a mut Vec<T>) -> Self {
        Simplify {
            highest_quality: false,
            tolerance: 1f64,
            points,
        }
    }

    pub fn set_highest_quality(&mut self, b: bool) -> &mut Self {
        self.highest_quality = b;
        self
    }

    pub fn set_tolerance(&mut self, t: f64) -> &mut Self {
        self.tolerance = t * t;
        self
    }

    fn simplify_radial_dist(&mut self) -> &mut Self {
        let mut prev = 0;
        let mut index = 1;

        while index < self.points.len() - 1 {
            unsafe {
                if self
                    .points
                    .get_unchecked(index)
                    .get_sq_distance(self.points.get_unchecked(prev))
                    <= self.tolerance
                {
                    self.points.remove(index);
                    index -= 1;
                } else {
                    prev = index;
                }
            }

            index += 1;
        }

        self
    }

    fn simplify_dp_step(
        &mut self,
        first: usize,
        last: usize,
        simplified: &mut Vec<T>,
    ) {
        let mut max_sq_dist = self.tolerance;
        let mut index = 0;

        for i in first + 1..last {
            let sq_dist = unsafe {
                self.points[i].get_sq_seg_distance(self.points.get_unchecked(first), self.points.get_unchecked(last))
            };

            if sq_dist > max_sq_dist {
                index = i;
                max_sq_dist = sq_dist;
            }
        }

        if max_sq_dist > self.tolerance {
            if index - first > 1 {
                self.simplify_dp_step(first, index, simplified);
            }

            simplified.push(unsafe {
                self.points.get_unchecked(index).clone()
            });

            if last - index > 1 {
                self.simplify_dp_step(index, last, simplified);
            }
        }
    }

    fn simplify_douglas_peucker(&mut self, mut simplified: Vec<T>) -> Vec<T> {
        let last = self.points.len() - 1;

        self.simplify_dp_step(0, last, &mut simplified);
        simplified.push(unsafe {
            self.points.get_unchecked(last).clone()    
        });

        simplified
    }

    pub fn run(&mut self) -> Vec<T> {
        if self.points.len() <= 2 {
            return self.points.clone();
        }

        if !self.highest_quality {
            self.simplify_radial_dist();
        }

        let mut simplified = Vec::new();
        simplified.push(unsafe {
            self.points.get_unchecked(0).clone()
        });

        self.simplify_douglas_peucker(simplified)
    }
}

#[cfg(test)]
mod tests {
    use super::{Point as P, Simplify};

    #[derive(Clone, Debug)]
    pub struct Point {
        pub x: f64,
        pub y: f64,
    }

    impl PartialEq for Point {
        fn eq(&self, other: &Self) -> bool {
            self.x == other.x && self.y == other.y
        }
    }

    impl Eq for Point {}

    impl P for Point {
        fn x(&self) -> f64 {
            self.x
        }

        fn y(&self) -> f64 {
            self.y
        }
    }

    #[test]
    fn test_simplify_with_given_tolerance() {
        let mut data = vec![ Point { x: 224.55, y: 250.15, }, Point { x: 226.91, y: 244.19, }, Point { x: 233.31, y: 241.45, }, Point { x: 234.98, y: 236.06, }, Point { x: 244.21, y: 232.76, }, Point { x: 262.59, y: 215.31, }, Point { x: 267.76, y: 213.81, }, Point { x: 273.57, y: 201.84, }, Point { x: 273.12, y: 192.16, }, Point { x: 277.62, y: 189.03, }, Point { x: 280.36, y: 181.41, }, Point { x: 286.51, y: 177.74, }, Point { x: 292.41, y: 159.37, }, Point { x: 296.91, y: 155.64, }, Point { x: 314.95, y: 151.37, }, Point { x: 319.75, y: 145.16, }, Point { x: 330.33, y: 137.57, }, Point { x: 341.48, y: 139.96, }, Point { x: 369.98, y: 137.89, }, Point { x: 387.39, y: 142.51, }, Point { x: 391.28, y: 139.39, }, Point { x: 409.52, y: 141.14, }, Point { x: 414.82, y: 139.75, }, Point { x: 427.72, y: 127.30, }, Point { x: 439.60, y: 119.74, }, Point { x: 474.93, y: 107.87, }, Point { x: 486.51, y: 106.75, }, Point { x: 489.20, y: 109.45, }, Point { x: 493.79, y: 108.63, }, Point { x: 504.74, y: 119.66, }, Point { x: 512.96, y: 122.35, }, Point { x: 518.63, y: 120.89, }, Point { x: 524.09, y: 126.88, }, Point { x: 529.57, y: 127.86, }, Point { x: 534.21, y: 140.93, }, Point { x: 539.27, y: 147.24, }, Point { x: 567.69, y: 148.91, }, Point { x: 575.25, y: 157.26, }, Point { x: 580.62, y: 158.15, }, Point { x: 601.53, y: 156.85, }, Point { x: 617.74, y: 159.86, }, Point { x: 622.00, y: 167.04, }, Point { x: 629.55, y: 194.60, }, Point { x: 638.90, y: 195.61, }, Point { x: 641.26, y: 200.81, }, Point { x: 651.77, y: 204.56, }, Point { x: 671.55, y: 222.55, }, Point { x: 683.68, y: 217.45, }, Point { x: 695.25, y: 219.15, }, Point { x: 700.64, y: 217.98, }, Point { x: 703.12, y: 214.36, }, Point { x: 712.26, y: 215.87, }, Point { x: 721.49, y: 212.81, }, Point { x: 727.81, y: 213.36, }, Point { x: 729.98, y: 208.73, }, Point { x: 735.32, y: 208.20, }, Point { x: 739.94, y: 204.77, }, Point { x: 769.98, y: 208.42, }, Point { x: 779.60, y: 216.87, }, Point { x: 784.20, y: 218.16, }, Point { x: 800.24, y: 214.62, }, Point { x: 810.53, y: 219.73, }, Point { x: 817.19, y: 226.82, }, Point { x: 820.77, y: 236.17, }, Point { x: 827.23, y: 236.16, }, Point { x: 829.89, y: 239.89, }, Point { x: 851.00, y: 248.94, }, Point { x: 859.88, y: 255.49, }, Point { x: 865.21, y: 268.53, }, Point { x: 857.95, y: 280.30, }, Point { x: 865.48, y: 291.45, }, Point { x: 866.81, y: 298.66, }, Point { x: 864.68, y: 302.71, }, Point { x: 867.79, y: 306.17, }, Point { x: 859.87, y: 311.37, }, Point { x: 860.08, y: 314.35, }, Point { x: 858.29, y: 314.94, }, Point { x: 858.10, y: 327.60, }, Point { x: 854.54, y: 335.40, }, Point { x: 860.92, y: 343.00, }, Point { x: 856.43, y: 350.15, }, Point { x: 851.42, y: 352.96, }, Point { x: 849.84, y: 359.59, }, Point { x: 854.56, y: 365.53, }, Point { x: 849.74, y: 370.38, }, Point { x: 844.09, y: 371.89, }, Point { x: 844.75, y: 380.44, }, Point { x: 841.52, y: 383.67, }, Point { x: 839.57, y: 390.40, }, Point { x: 845.59, y: 399.05, }, Point { x: 848.40, y: 407.55, }, Point { x: 843.71, y: 411.30, }, Point { x: 844.09, y: 419.88, }, Point { x: 839.51, y: 432.76, }, Point { x: 841.33, y: 441.04, }, Point { x: 847.62, y: 449.22, }, Point { x: 847.16, y: 458.44, }, Point { x: 851.38, y: 462.79, }, Point { x: 853.97, y: 471.15, }, Point { x: 866.36, y: 480.77, }, ];
        let simplified = vec![ Point { x: 224.55, y: 250.15, }, Point { x: 267.76, y: 213.81, }, Point { x: 296.91, y: 155.64, }, Point { x: 330.33, y: 137.57, }, Point { x: 409.52, y: 141.14, }, Point { x: 439.60, y: 119.74, }, Point { x: 486.51, y: 106.75, }, Point { x: 529.57, y: 127.86, }, Point { x: 539.27, y: 147.24, }, Point { x: 617.74, y: 159.86, }, Point { x: 629.55, y: 194.60, }, Point { x: 671.55, y: 222.55, }, Point { x: 727.81, y: 213.36, }, Point { x: 739.94, y: 204.77, }, Point { x: 769.98, y: 208.42, }, Point { x: 779.60, y: 216.87, }, Point { x: 800.24, y: 214.62, }, Point { x: 820.77, y: 236.17, }, Point { x: 859.88, y: 255.49, }, Point { x: 865.21, y: 268.53, }, Point { x: 857.95, y: 280.30, }, Point { x: 867.79, y: 306.17, }, Point { x: 859.87, y: 311.37, }, Point { x: 854.54, y: 335.40, }, Point { x: 860.92, y: 343.00, }, Point { x: 849.84, y: 359.59, }, Point { x: 854.56, y: 365.53, }, Point { x: 844.09, y: 371.89, }, Point { x: 839.57, y: 390.40, }, Point { x: 848.40, y: 407.55, }, Point { x: 839.51, y: 432.76, }, Point { x: 853.97, y: 471.15, }, Point { x: 866.36, y: 480.77, }, ];

        let mut s = Simplify::new(&mut data);
        s.set_tolerance(5f64);

        assert_eq!(s.run(), simplified);
    }

    #[test]
    fn test_simplify_with_one_element() {
        let mut data = vec![Point { x: 1f64, y: 2f64 }];

        let mut s = Simplify::new(&mut data);

        assert_eq!(s.run(), vec![Point { x: 1f64, y: 2f64 }]);
    }

    #[test]
    fn test_simplify_with_no_element() {
        let mut data: Vec<Point> = vec![];

        let mut s = Simplify::new(&mut data);

        assert_eq!(s.run(), vec![]);
    }
}