Implements Ramer-Douglas-Peucker simplification algorithm (TheAlgorit…

…hms#710)

* Implements Ramer-Douglas-Peucker simplification algorithm

* Apply requested changes

* Cargo format

* Cargo clippy

* Apply requested changes

* style: use slice

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

DIRECTORY.md

@@ -115,6 +115,7 @@
     * [Jarvis Scan](https://github.com/TheAlgorithms/Rust/blob/master/src/geometry/jarvis_scan.rs)
     * [Point](https://github.com/TheAlgorithms/Rust/blob/master/src/geometry/point.rs)
     * [Polygon Points](https://github.com/TheAlgorithms/Rust/blob/master/src/geometry/polygon_points.rs)
+    * [Ramer-Douglas-Peucker](https://github.com/TheAlgorithms/Rust/blob/master/src/geometry/ramer_douglas_peucker.rs)
     * [Segment](https://github.com/TheAlgorithms/Rust/blob/master/src/geometry/segment.rs)
   * Graph
     * [Astar](https://github.com/TheAlgorithms/Rust/blob/master/src/graph/astar.rs)

src/geometry/mod.rs

@@ -3,11 +3,13 @@ mod graham_scan;
 mod jarvis_scan;
 mod point;
 mod polygon_points;
+mod ramer_douglas_peucker;
 mod segment;
 
 pub use self::closest_points::closest_points;
 pub use self::graham_scan::graham_scan;
 pub use self::jarvis_scan::jarvis_march;
 pub use self::point::Point;
 pub use self::polygon_points::lattice_points;
+pub use self::ramer_douglas_peucker::ramer_douglas_peucker;
 pub use self::segment::Segment;

src/geometry/ramer_douglas_peucker.rs

@@ -0,0 +1,115 @@
+use crate::geometry::Point;
+
+pub fn ramer_douglas_peucker(points: &[Point], epsilon: f64) -> Vec<Point> {
+    if points.len() < 3 {
+        return points.to_vec();
+    }
+    let mut dmax = 0.0;
+    let mut index = 0;
+    let end = points.len() - 1;
+
+    for i in 1..end {
+        let d = perpendicular_distance(&points[i], &points[0], &points[end]);
+        if d > dmax {
+            index = i;
+            dmax = d;
+        }
+    }
+
+    if dmax > epsilon {
+        let mut results = ramer_douglas_peucker(&points[..=index], epsilon);
+        results.pop();
+        results.extend(ramer_douglas_peucker(&points[index..], epsilon));
+        results
+    } else {
+        vec![points[0].clone(), points[end].clone()]
+    }
+}
+
+fn perpendicular_distance(p: &Point, a: &Point, b: &Point) -> f64 {
+    let num = (b.y - a.y) * p.x - (b.x - a.x) * p.y + b.x * a.y - b.y * a.x;
+    let den = a.euclidean_distance(b);
+    num.abs() / den
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    macro_rules! test_perpendicular_distance {
+        ($($name:ident: $test_case:expr,)*) => {
+            $(
+                #[test]
+                fn $name() {
+                    let (p, a, b, expected) = $test_case;
+                    assert_eq!(perpendicular_distance(&p, &a, &b), expected);
+                    assert_eq!(perpendicular_distance(&p, &b, &a), expected);
+                }
+            )*
+        };
+    }
+
+    test_perpendicular_distance! {
+        basic: (Point::new(4.0, 0.0), Point::new(0.0, 0.0), Point::new(0.0, 3.0), 4.0),
+        basic_shifted_1: (Point::new(4.0, 1.0), Point::new(0.0, 1.0), Point::new(0.0, 4.0), 4.0),
+        basic_shifted_2: (Point::new(2.0, 1.0), Point::new(-2.0, 1.0), Point::new(-2.0, 4.0), 4.0),
+    }
+
+    #[test]
+    fn test_ramer_douglas_peucker_polygon() {
+        let a = Point::new(0.0, 0.0);
+        let b = Point::new(1.0, 0.0);
+        let c = Point::new(2.0, 0.0);
+        let d = Point::new(2.0, 1.0);
+        let e = Point::new(2.0, 2.0);
+        let f = Point::new(1.0, 2.0);
+        let g = Point::new(0.0, 2.0);
+        let h = Point::new(0.0, 1.0);
+        let polygon = vec![
+            a.clone(),
+            b,
+            c.clone(),
+            d,
+            e.clone(),
+            f,
+            g.clone(),
+            h.clone(),
+        ];
+        let epsilon = 0.7;
+        let result = ramer_douglas_peucker(&polygon, epsilon);
+        assert_eq!(result, vec![a, c, e, g, h]);
+    }
+
+    #[test]
+    fn test_ramer_douglas_peucker_polygonal_chain() {
+        let a = Point::new(0., 0.);
+        let b = Point::new(2., 0.5);
+        let c = Point::new(3., 3.);
+        let d = Point::new(6., 3.);
+        let e = Point::new(8., 4.);
+
+        let points = vec![a.clone(), b, c, d, e.clone()];
+
+        let epsilon = 3.; // The epsilon is quite large, so the result will be a single line
+        let result = ramer_douglas_peucker(&points, epsilon);
+        assert_eq!(result, vec![a, e]);
+    }
+
+    #[test]
+    fn test_less_than_three_points() {
+        let a = Point::new(0., 0.);
+        let b = Point::new(1., 1.);
+
+        let epsilon = 0.1;
+
+        assert_eq!(ramer_douglas_peucker(&[], epsilon), vec![]);
+        assert_eq!(
+            ramer_douglas_peucker(&[a.clone()], epsilon),
+            vec![a.clone()]
+        );
+        assert_eq!(
+            ramer_douglas_peucker(&[a.clone(), b.clone()], epsilon),
+            vec![a, b]
+        );
+    }
+}