1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131

use num_traits::Float;
use types::{Point, LineString};
use algorithm::distance::Distance;

// perpendicular distance from a point to a line
fn point_line_distance<T>(point: &Point<T>, start: &Point<T>, end: &Point<T>) -> T
    where T: Float
{
    if start == end {
        point.distance(start)
    } else {
        let numerator = ((end.x() - start.x()) * (start.y() - point.y()) -
                         (start.x() - point.x()) * (end.y() - start.y()))
            .abs();
        let denominator = start.distance(end);
        numerator / denominator
    }
}

// Ramer–Douglas-Peucker line simplification algorithm
fn rdp<T>(points: &[Point<T>], epsilon: &T) -> Vec<Point<T>>
    where T: Float
{
    if points.is_empty() {
        return points.to_vec();
    }
    let mut dmax = T::zero();
    let mut index: usize = 0;
    let mut distance: T;

    for (i, _) in points.iter().enumerate().take(points.len() - 1).skip(1) {
        distance = point_line_distance(&points[i],
                                       &points[0],
                                       &*points.last().unwrap());
        if distance > dmax {
            index = i;
            dmax = distance;
        }
    }
    if dmax > *epsilon {
        let mut intermediate = rdp(&points[..index + 1], &*epsilon);
        intermediate.pop();
        intermediate.extend_from_slice(&rdp(&points[index..], &*epsilon));
        intermediate
    } else {
        vec![*points.first().unwrap(), *points.last().unwrap()]
    }
}

pub trait Simplify<T, Epsilon = T> {
    /// Returns the simplified representation of a LineString, using the [Ramer–Douglas–Peucker](https://en.wikipedia.org/wiki/Ramer–Douglas–Peucker_algorithm) algorithm
    ///
    /// ```
    /// use geo::{Point, LineString};
    /// use geo::algorithm::simplify::{Simplify};
    ///
    /// let mut vec = Vec::new();
    /// vec.push(Point::new(0.0, 0.0));
    /// vec.push(Point::new(5.0, 4.0));
    /// vec.push(Point::new(11.0, 5.5));
    /// vec.push(Point::new(17.3, 3.2));
    /// vec.push(Point::new(27.8, 0.1));
    /// let linestring = LineString(vec);
    /// let mut compare = Vec::new();
    /// compare.push(Point::new(0.0, 0.0));
    /// compare.push(Point::new(5.0, 4.0));
    /// compare.push(Point::new(11.0, 5.5));
    /// compare.push(Point::new(27.8, 0.1));
    /// let ls_compare = LineString(compare);
    /// let simplified = linestring.simplify(&1.0);
    /// assert_eq!(simplified, ls_compare)
    /// ```
    fn simplify(&self, epsilon: &T) -> Self where T: Float;
}

impl<T> Simplify<T> for LineString<T>
    where T: Float
{
    fn simplify(&self, epsilon: &T) -> LineString<T> {
        LineString(rdp(&self.0, epsilon))
    }
}

#[cfg(test)]
mod test {
    use types::{Point};
    use super::{point_line_distance, rdp};

    #[test]
    fn perpdistance_test() {
        let start = Point::new(1.0, 2.0);
        let end = Point::new(3.0, 4.0);
        let p = Point::new(1.0, 1.0);
        let dist = point_line_distance(&p, &start, &end);
        assert_relative_eq!(dist, 0.7071067811865475);
    }
    #[test]
    fn rdp_test() {
        let mut vec = Vec::new();
        vec.push(Point::new(0.0, 0.0));
        vec.push(Point::new(5.0, 4.0));
        vec.push(Point::new(11.0, 5.5));
        vec.push(Point::new(17.3, 3.2));
        vec.push(Point::new(27.8, 0.1));
        let mut compare = Vec::new();
        compare.push(Point::new(0.0, 0.0));
        compare.push(Point::new(5.0, 4.0));
        compare.push(Point::new(11.0, 5.5));
        compare.push(Point::new(27.8, 0.1));
        let simplified = rdp(&vec, &1.0);
        assert_eq!(simplified, compare);
    }
    #[test]
    fn rdp_test_empty_linestring() {
        let vec = Vec::new();
        let compare = Vec::new();
        let simplified = rdp(&vec, &1.0);
        assert_eq!(simplified, compare);
    }
    #[test]
    fn rdp_test_two_point_linestring() {
        let mut vec = Vec::new();
        vec.push(Point::new(0.0, 0.0));
        vec.push(Point::new(27.8, 0.1));
        let mut compare = Vec::new();
        compare.push(Point::new(0.0, 0.0));
        compare.push(Point::new(27.8, 0.1));
        let simplified = rdp(&vec, &1.0);
        assert_eq!(simplified, compare);
    }
}