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
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248

//! Path simplification algorithms adapted from https://github.com/mourner/simplify-js

use std::ops::*;
use crate::Point2;

type Float = f64;

/// square distance between 2 points
fn get_sq_dist<T>(p1: Point2<T>, p2: Point2<T>) -> Float
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy + Into<Float> {

    let dx = p1.x - p2.x;
    let dy = p1.y - p2.y;

    (dx * dx + dy * dy).into()
}

/// square distance from a point to a segment
fn get_sq_seg_dist<T>(p: Point2<T>, p1: Point2<T>, p2: Point2<T>) -> Float
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy + Into<Float> {

    let mut x = p1.x.into();
    let mut y = p1.y.into();
    let mut dx = p2.x.into() - x;
    let mut dy = p2.y.into() - y;

    if dx != 0.0 || dy != 0.0 {

        let t = ((p.x.into() - x) * dx + (p.y.into() - y) * dy) / (dx * dx + dy * dy);

        if t > 1.0 {
            x = p2.x.into();
            y = p2.y.into();
        } else if t > 0.0 {
            x += dx * t;
            y += dy * t;
        }
    }

    dx = p.x.into() - x;
    dy = p.y.into() - y;

    dx * dx + dy * dy
}

// rest of the code doesn't care about point format

/// basic distance-based simplification
pub fn simplify_radial_dist<T>(points: &[Point2<T>], sq_tolerance: Float) -> Vec<Point2<T>>
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + std::cmp::PartialEq + Copy + Into<Float> {

    if points.len() <= 2 { return points.to_vec(); }

    let mut prev_point = points[0];
    let mut new_points = vec![prev_point];

    for point in points.iter().skip(1) {
        if get_sq_dist(*point, prev_point) > sq_tolerance {
            new_points.push(*point);
            prev_point = *point;
        }
    }

    if prev_point != *points.last().unwrap() { new_points.push(*points.last().unwrap()); }

    new_points
}

fn simplify_dp_step<T>(points: &[Point2<T>], first: usize, last: usize, sq_tolerance: Float, simplified: &mut Vec<Point2<T>>)
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + std::cmp::PartialEq + Copy + Into<Float> {
    let mut max_sq_dist = sq_tolerance;
    let mut index = 0;

    for i in first+1..last {
        let sq_dist = get_sq_seg_dist(points[i], points[first], points[last]);

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

    if max_sq_dist > sq_tolerance {
        if index - first > 1 { simplify_dp_step(points, first, index, sq_tolerance, simplified); }
        simplified.push(points[index]);
        if last - index > 1 { simplify_dp_step(points, index, last, sq_tolerance, simplified); }
    }
}

/// simplification using Ramer-Douglas-Peucker algorithm
pub fn simplify_douglas_peucker<T>(points: &[Point2<T>], sq_tolerance: Float) -> Vec<Point2<T>>
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + std::cmp::PartialEq + Copy + Into<Float> {
    let last = points.len() - 1;

    let mut simplified = vec![points[0]];
    simplify_dp_step(points, 0, last, sq_tolerance, &mut simplified);
    simplified.push(points[last]);

    simplified
}

/// both algorithms combined for awesome performance
///
/// this is the original implementation from mourner/simplify-js
#[allow(dead_code)]
fn simplify<T>(original: &[Point2<T>], tolerance: Float, highest_quality: bool) -> Vec<Point2<T>>
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + std::cmp::PartialEq + Copy + Into<Float> {

    if original.len() <= 2 { return original.to_vec(); }

    let sq_tolerance = tolerance * tolerance;

    let radial;
    let points = if highest_quality {
        original
    } else {
        radial = simplify_radial_dist(original, sq_tolerance);
        &radial
    };

    simplify_douglas_peucker(points, sq_tolerance)
}

/// Reduce points from a path
///
/// The larger the tolerance, the fewer points will be left in output path
pub fn reduce<T>(original: &[Point2<T>], tolerance: Float) -> Vec<Point2<T>>
where T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + std::cmp::PartialEq + Copy + Into<Float> {

    if original.len() <= 2 { return original.to_vec(); }
    if tolerance == 0.0 { return original.to_vec(); }

    let sq_tolerance = tolerance * tolerance;

    let radial = simplify_radial_dist(original, sq_tolerance * 0.5);

    simplify_douglas_peucker(&radial, sq_tolerance)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{PointI32, PointF64};

    #[test]
    fn simplify_i32() {

        let points = vec![
            PointI32 { x: 22455, y: 25015 }, PointI32 { x: 22691, y: 24419 }, PointI32 { x: 23331, y: 24145 }, PointI32 {x: 23498, y: 23606 },
            PointI32 { x: 24421, y: 23276 }, PointI32 { x: 26259, y: 21531 }, PointI32 { x: 26776, y: 21381 }, PointI32 {x: 27357, y: 20184 },
            PointI32 { x: 27312, y: 19216 }, PointI32 { x: 27762, y: 18903 }, PointI32 { x: 28036, y: 18141 }, PointI32 {x: 28651, y: 17774 },
            PointI32 { x: 29241, y: 15937 }, PointI32 { x: 29691, y: 15564 }, PointI32 { x: 31495, y: 15137 }, PointI32 {x: 31975, y: 14516 },
            PointI32 { x: 33033, y: 13757 }, PointI32 { x: 34148, y: 13996 }, PointI32 { x: 36998, y: 13789 }, PointI32 {x: 38739, y: 14251 },
            PointI32 { x: 39128, y: 13939 }, PointI32 { x: 40952, y: 14114 }, PointI32 { x: 41482, y: 13975 }, PointI32 {x: 42772, y: 12730 },
            PointI32 { x: 43960, y: 11974 }, PointI32 { x: 47493, y: 10787 }, PointI32 { x: 48651, y: 10675 }, PointI32 {x: 48920, y: 10945 },
            PointI32 { x: 49379, y: 10863 }, PointI32 { x: 50474, y: 11966 }, PointI32 { x: 51296, y: 12235 }, PointI32 {x: 51863, y: 12089 },
            PointI32 { x: 52409, y: 12688 }, PointI32 { x: 52957, y: 12786 }, PointI32 { x: 53421, y: 14093 }, PointI32 {x: 53927, y: 14724 },
            PointI32 { x: 56769, y: 14891 }, PointI32 { x: 57525, y: 15726 }, PointI32 { x: 58062, y: 15815 }, PointI32 {x: 60153, y: 15685 },
            PointI32 { x: 61774, y: 15986 }, PointI32 { x: 62200, y: 16704 }, PointI32 { x: 62955, y: 19460 }, PointI32 {x: 63890, y: 19561 },
            PointI32 { x: 64126, y: 20081 }, PointI32 { x: 65177, y: 20456 }, PointI32 { x: 67155, y: 22255 }, PointI32 {x: 68368, y: 21745 },
            PointI32 { x: 69525, y: 21915 }, PointI32 { x: 70064, y: 21798 }, PointI32 { x: 70312, y: 21436 }, PointI32 {x: 71226, y: 21587 },
            PointI32 { x: 72149, y: 21281 }, PointI32 { x: 72781, y: 21336 }, PointI32 { x: 72998, y: 20873 }, PointI32 {x: 73532, y: 20820 },
            PointI32 { x: 73994, y: 20477 }, PointI32 { x: 76998, y: 20842 }, PointI32 { x: 77960, y: 21687 }, PointI32 {x: 78420, y: 21816 },
            PointI32 { x: 80024, y: 21462 }, PointI32 { x: 81053, y: 21973 }, PointI32 { x: 81719, y: 22682 }, PointI32 {x: 82077, y: 23617 },
            PointI32 { x: 82723, y: 23616 }, PointI32 { x: 82989, y: 23989 }, PointI32 { x: 85100, y: 24894 }, PointI32 {x: 85988, y: 25549 },
            PointI32 { x: 86521, y: 26853 }, PointI32 { x: 85795, y: 28030 }, PointI32 { x: 86548, y: 29145 }, PointI32 {x: 86681, y: 29866 },
            PointI32 { x: 86468, y: 30271 }, PointI32 { x: 86779, y: 30617 }, PointI32 { x: 85987, y: 31137 }, PointI32 {x: 86008, y: 31435 },
            PointI32 { x: 85829, y: 31494 }, PointI32 { x: 85810, y: 32760 }, PointI32 { x: 85454, y: 33540 }, PointI32 {x: 86092, y: 34300 },
            PointI32 { x: 85643, y: 35015 }, PointI32 { x: 85142, y: 35296 }, PointI32 { x: 84984, y: 35959 }, PointI32 {x: 85456, y: 36553 },
            PointI32 { x: 84974, y: 37038 }, PointI32 { x: 84409, y: 37189 }, PointI32 { x: 84475, y: 38044 }, PointI32 {x: 84152, y: 38367 },
            PointI32 { x: 83957, y: 39040 }, PointI32 { x: 84559, y: 39905 }, PointI32 { x: 84840, y: 40755 }, PointI32 {x: 84371, y: 41130 },
            PointI32 { x: 84409, y: 41988 }, PointI32 { x: 83951, y: 43276 }, PointI32 { x: 84133, y: 44104 }, PointI32 {x: 84762, y: 44922 },
            PointI32 { x: 84716, y: 45844 }, PointI32 { x: 85138, y: 46279 }, PointI32 { x: 85397, y: 47115 }, PointI32 {x: 86636, y: 48077 }
        ];

        let simplified = vec![
            PointI32 { x: 22455, y: 25015 }, PointI32 { x: 26776, y: 21381 }, PointI32 { x: 29691, y: 15564 }, PointI32 { x: 33033, y: 13757 },
            PointI32 { x: 40952, y: 14114 }, PointI32 { x: 43960, y: 11974 }, PointI32 { x: 48651, y: 10675 }, PointI32 { x: 52957, y: 12786 },
            PointI32 { x: 53927, y: 14724 }, PointI32 { x: 61774, y: 15986 }, PointI32 { x: 62955, y: 19460 }, PointI32 { x: 67155, y: 22255 },
            PointI32 { x: 72781, y: 21336 }, PointI32 { x: 73994, y: 20477 }, PointI32 { x: 76998, y: 20842 }, PointI32 { x: 77960, y: 21687 },
            PointI32 { x: 80024, y: 21462 }, PointI32 { x: 82077, y: 23617 }, PointI32 { x: 85988, y: 25549 }, PointI32 { x: 86521, y: 26853 },
            PointI32 { x: 85795, y: 28030 }, PointI32 { x: 86779, y: 30617 }, PointI32 { x: 85987, y: 31137 }, PointI32 { x: 85454, y: 33540 },
            PointI32 { x: 86092, y: 34300 }, PointI32 { x: 84984, y: 35959 }, PointI32 { x: 85456, y: 36553 }, PointI32 { x: 84409, y: 37189 },
            PointI32 { x: 83957, y: 39040 }, PointI32 { x: 84840, y: 40755 }, PointI32 { x: 83951, y: 43276 }, PointI32 { x: 85397, y: 47115 },
            PointI32 { x: 86636, y: 48077 }
        ];

        assert_eq!(simplify(&points, 500.0, false), simplified);
    }

    #[test]
    fn simplify_f64() {

        let points = vec![
            PointF64 { x: 224.55, y: 250.15 }, PointF64 { x: 226.91, y: 244.19 }, PointF64 { x: 233.31, y: 241.45 }, PointF64 {x: 234.98, y: 236.06 },
            PointF64 { x: 244.21, y: 232.76 }, PointF64 { x: 262.59, y: 215.31 }, PointF64 { x: 267.76, y: 213.81 }, PointF64 {x: 273.57, y: 201.84 },
            PointF64 { x: 273.12, y: 192.16 }, PointF64 { x: 277.62, y: 189.03 }, PointF64 { x: 280.36, y: 181.41 }, PointF64 {x: 286.51, y: 177.74 },
            PointF64 { x: 292.41, y: 159.37 }, PointF64 { x: 296.91, y: 155.64 }, PointF64 { x: 314.95, y: 151.37 }, PointF64 {x: 319.75, y: 145.16 },
            PointF64 { x: 330.33, y: 137.57 }, PointF64 { x: 341.48, y: 139.96 }, PointF64 { x: 369.98, y: 137.89 }, PointF64 {x: 387.39, y: 142.51 },
            PointF64 { x: 391.28, y: 139.39 }, PointF64 { x: 409.52, y: 141.14 }, PointF64 { x: 414.82, y: 139.75 }, PointF64 {x: 427.72, y: 127.30 },
            PointF64 { x: 439.60, y: 119.74 }, PointF64 { x: 474.93, y: 107.87 }, PointF64 { x: 486.51, y: 106.75 }, PointF64 {x: 489.20, y: 109.45 },
            PointF64 { x: 493.79, y: 108.63 }, PointF64 { x: 504.74, y: 119.66 }, PointF64 { x: 512.96, y: 122.35 }, PointF64 {x: 518.63, y: 120.89 },
            PointF64 { x: 524.09, y: 126.88 }, PointF64 { x: 529.57, y: 127.86 }, PointF64 { x: 534.21, y: 140.93 }, PointF64 {x: 539.27, y: 147.24 },
            PointF64 { x: 567.69, y: 148.91 }, PointF64 { x: 575.25, y: 157.26 }, PointF64 { x: 580.62, y: 158.15 }, PointF64 {x: 601.53, y: 156.85 },
            PointF64 { x: 617.74, y: 159.86 }, PointF64 { x: 622.00, y: 167.04 }, PointF64 { x: 629.55, y: 194.60 }, PointF64 {x: 638.90, y: 195.61 },
            PointF64 { x: 641.26, y: 200.81 }, PointF64 { x: 651.77, y: 204.56 }, PointF64 { x: 671.55, y: 222.55 }, PointF64 {x: 683.68, y: 217.45 },
            PointF64 { x: 695.25, y: 219.15 }, PointF64 { x: 700.64, y: 217.98 }, PointF64 { x: 703.12, y: 214.36 }, PointF64 {x: 712.26, y: 215.87 },
            PointF64 { x: 721.49, y: 212.81 }, PointF64 { x: 727.81, y: 213.36 }, PointF64 { x: 729.98, y: 208.73 }, PointF64 {x: 735.32, y: 208.20 },
            PointF64 { x: 739.94, y: 204.77 }, PointF64 { x: 769.98, y: 208.42 }, PointF64 { x: 779.60, y: 216.87 }, PointF64 {x: 784.20, y: 218.16 },
            PointF64 { x: 800.24, y: 214.62 }, PointF64 { x: 810.53, y: 219.73 }, PointF64 { x: 817.19, y: 226.82 }, PointF64 {x: 820.77, y: 236.17 },
            PointF64 { x: 827.23, y: 236.16 }, PointF64 { x: 829.89, y: 239.89 }, PointF64 { x: 851.00, y: 248.94 }, PointF64 {x: 859.88, y: 255.49 },
            PointF64 { x: 865.21, y: 268.53 }, PointF64 { x: 857.95, y: 280.30 }, PointF64 { x: 865.48, y: 291.45 }, PointF64 {x: 866.81, y: 298.66 },
            PointF64 { x: 864.68, y: 302.71 }, PointF64 { x: 867.79, y: 306.17 }, PointF64 { x: 859.87, y: 311.37 }, PointF64 {x: 860.08, y: 314.35 },
            PointF64 { x: 858.29, y: 314.94 }, PointF64 { x: 858.10, y: 327.60 }, PointF64 { x: 854.54, y: 335.40 }, PointF64 {x: 860.92, y: 343.00 },
            PointF64 { x: 856.43, y: 350.15 }, PointF64 { x: 851.42, y: 352.96 }, PointF64 { x: 849.84, y: 359.59 }, PointF64 {x: 854.56, y: 365.53 },
            PointF64 { x: 849.74, y: 370.38 }, PointF64 { x: 844.09, y: 371.89 }, PointF64 { x: 844.75, y: 380.44 }, PointF64 {x: 841.52, y: 383.67 },
            PointF64 { x: 839.57, y: 390.40 }, PointF64 { x: 845.59, y: 399.05 }, PointF64 { x: 848.40, y: 407.55 }, PointF64 {x: 843.71, y: 411.30 },
            PointF64 { x: 844.09, y: 419.88 }, PointF64 { x: 839.51, y: 432.76 }, PointF64 { x: 841.33, y: 441.04 }, PointF64 {x: 847.62, y: 449.22 },
            PointF64 { x: 847.16, y: 458.44 }, PointF64 { x: 851.38, y: 462.79 }, PointF64 { x: 853.97, y: 471.15 }, PointF64 {x: 866.36, y: 480.77 }
        ];

        let simplified = vec![
            PointF64 { x: 224.55, y: 250.15 }, PointF64 { x: 267.76, y: 213.81 }, PointF64 { x: 296.91, y: 155.64 }, PointF64 { x: 330.33, y: 137.57 },
            PointF64 { x: 409.52, y: 141.14 }, PointF64 { x: 439.60, y: 119.74 }, PointF64 { x: 486.51, y: 106.75 }, PointF64 { x: 529.57, y: 127.86 },
            PointF64 { x: 539.27, y: 147.24 }, PointF64 { x: 617.74, y: 159.86 }, PointF64 { x: 629.55, y: 194.60 }, PointF64 { x: 671.55, y: 222.55 },
            PointF64 { x: 727.81, y: 213.36 }, PointF64 { x: 739.94, y: 204.77 }, PointF64 { x: 769.98, y: 208.42 }, PointF64 { x: 779.60, y: 216.87 },
            PointF64 { x: 800.24, y: 214.62 }, PointF64 { x: 820.77, y: 236.17 }, PointF64 { x: 859.88, y: 255.49 }, PointF64 { x: 865.21, y: 268.53 },
            PointF64 { x: 857.95, y: 280.30 }, PointF64 { x: 867.79, y: 306.17 }, PointF64 { x: 859.87, y: 311.37 }, PointF64 { x: 854.54, y: 335.40 },
            PointF64 { x: 860.92, y: 343.00 }, PointF64 { x: 849.84, y: 359.59 }, PointF64 { x: 854.56, y: 365.53 }, PointF64 { x: 844.09, y: 371.89 },
            PointF64 { x: 839.57, y: 390.40 }, PointF64 { x: 848.40, y: 407.55 }, PointF64 { x: 839.51, y: 432.76 }, PointF64 { x: 853.97, y: 471.15 },
            PointF64 { x: 866.36, y: 480.77 }
        ];

        assert_eq!(simplify(&points, 5.0, false), simplified);
    }

    #[test]
    fn simplify_one() {
        let points = vec![ PointI32 {x: 22455, y: 25015 } ];
        assert_eq!(simplify(&points, 5.0, false), points);
    }

    #[test]
    fn simplify_zero() {
        let points = Vec::<PointI32>::new();
        assert_eq!(simplify(&points, 5.0, false), points);
    }
}