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

// Copyright 2019 Marco Napetti
//
// Licensed under the Apache License, Version 2.0, <LICENSE-APACHE or
// http://apache.org/licenses/LICENSE-2.0> or the MIT license <LICENSE-MIT or
// http://opensource.org/licenses/MIT>, at your option. This file may not be
// copied, modified, or distributed except according to those terms.
#![deny(warnings)]
#![deny(missing_docs)]

//! # geo-raycasting
//!
//! Ray Casting algorithm for the geo crate

use geo_types::{Coordinate, CoordinateType, Line, LineString, Point, Polygon};

use num_traits::float::Float;

fn pt_in_polygon<T: CoordinateType + Float>(pt: &Coordinate<T>, poly: &LineString<T>) -> bool {
    let count = poly.lines()
        .filter(|line| ray_intersect_seg(pt, line))
        .count();
 
    count % 2 == 1
}

fn ray_intersect_seg<T: CoordinateType + Float>(p: &Coordinate<T>, line: &Line<T>) -> bool {
    let (pt_x, mut pt_y) = p.x_y();
    let (a, b) = if line.start.y > line.end.y {
        (&line.end, &line.start)
    }
    else {
        (&line.start, &line.end)
    };

    if pt_y == a.y || pt_y == b.y {
        pt_y = pt_y + T::min_positive_value();
    }
 
    if (pt_y > b.y || pt_y < a.y) || pt_x > a.x.max(b.x) {
        false
    } else if pt_x < a.x.min(b.x) {
        true
    } else {
        let m_red = if (a.x - b.x).abs() > T::min_positive_value() {
            (b.y - a.y) / (b.x - a.x)
        } else {
            T::max_value()
        };
        let m_blue = if (a.x - pt_x).abs() > T::min_positive_value() {
            (pt_y - a.y) / (pt_x - a.x)
        } else {
            T::max_value()
        };
        m_blue >= m_red
    }
}

/// Trait implementing Ray Casting algorith
pub trait RayCasting<T: CoordinateType + Float, P: Into<Coordinate<T>>> {
    /// Checks if a point is within a polygonal area
    fn within(&self, pt: &P) -> bool;
}

impl<T: CoordinateType + Float> RayCasting<T, Point<T>> for LineString<T> {
    fn within(&self, pt: &Point<T>) -> bool {
        pt_in_polygon(&pt.x_y().into(), self)
    }
}

impl<T: CoordinateType + Float> RayCasting<T, Coordinate<T>> for LineString<T> {
    fn within(&self, pt: &Coordinate<T>) -> bool {
        pt_in_polygon(&pt, self)
    }
}

impl<T: CoordinateType + Float> RayCasting<T, Point<T>> for Polygon<T> {
    fn within(&self, pt: &Point<T>) -> bool {
        let coord = pt.x_y().into();
        pt_in_polygon(&coord, self.exterior()) &&
            !self.interiors().iter().any(|line| pt_in_polygon(&coord, line))
    }
}

impl<T: CoordinateType + Float> RayCasting<T, Coordinate<T>> for Polygon<T> {
    fn within(&self, pt: &Coordinate<T>) -> bool {
        pt_in_polygon(pt, self.exterior()) &&
            !self.interiors().iter().any(|line| pt_in_polygon(pt, line))
    }
}

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

    use geo_types::{Coordinate, LineString, Polygon, Point};

    fn p(x: f64, y: f64) -> Coordinate<f64> {
        (x, y).into()
    }

    #[test]
    fn poly_square() {
        let poly_square: LineString<f64> = vec![(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0), (0.0, 0.0)].into();
        assert!(poly_square.within(&p(5.0, 5.0)));
        assert!(poly_square.within(&p(5.0, 8.0)));
        assert!(poly_square.within(&p(-10.0, 5.0)) == false);
        assert!(poly_square.within(&p(0.0, 5.0)) == false);
        assert!(poly_square.within(&p(8.0, 5.0)));
        assert!(poly_square.within(&p(10.0, 10.0)) == false);
    }

    #[test]
    fn poly_square_hole() {
        let poly_square_hole: Polygon<f64> = Polygon::new(
            LineString::from(vec![(0.0, 0.0), (10.0, 0.0), (10.0, 10.0), (0.0, 10.0), (0.0, 0.0)]),
            vec![LineString::from(vec![(2.5, 2.5), (7.5, 2.5), (7.5, 7.5), (2.5, 7.5), (2.5, 2.5)])]
        );
        assert!(poly_square_hole.within(&p(5.0, 5.0)) == false);
        assert!(poly_square_hole.within(&p(5.0, 8.0)));
        assert!(poly_square_hole.within(&p(-10.0, 5.0)) == false);
        assert!(poly_square_hole.within(&p(0.0, 5.0)) == false);
        assert!(poly_square_hole.within(&p(10.0, 5.0)));
        assert!(poly_square_hole.within(&p(8.0, 5.0)));
        assert!(poly_square_hole.within(&p(10.0, 10.0)) == false);
    }

    #[test]
    fn poly_strange() {
        let poly_strange: LineString<f64> = vec![(0.0, 0.0), (2.5, 2.5), (0.0, 10.0), (2.5, 7.5), (7.5, 7.5), (10.0, 10.0), (10.0, 0.0), (2.5, 2.5)].into();
        assert!(poly_strange.within(&p(5.0, 5.0)));
        assert!(poly_strange.within(&p(5.0, 8.0)) == false);
        assert!(poly_strange.within(&p(-10.0, 5.0)) == false);
        assert!(poly_strange.within(&p(0.0, 5.0)) == false);
        assert!(poly_strange.within(&p(10.0, 5.0)));
        assert!(poly_strange.within(&p(8.0, 5.0)));
        assert!(poly_strange.within(&p(10.0, 10.0)) == false);
    }

    #[test]
    fn poly_hexagon() {
        let poly_hexagon: LineString<f64> = vec![(3.0, 0.0), (7.0, 0.0), (10.0, 5.0), (7.0, 10.0), (3.0, 10.0), (0.0, 5.0), (3.0, 0.0)].into();
        assert!(poly_hexagon.within(&p(5.0, 5.0)) == false);
        assert!(poly_hexagon.within(&p(5.0, 8.0)));
        assert!(poly_hexagon.within(&p(-10.0, 5.0)) == false);
        assert!(poly_hexagon.within(&p(0.0, 5.0)) == false);
        assert!(poly_hexagon.within(&p(10.0, 5.0)) == false);
        assert!(poly_hexagon.within(&p(8.0, 5.0)) == false);
        assert!(poly_hexagon.within(&p(10.0, 10.0)));
    }

    #[test]
    fn real_coords() {
        let cell1 = Polygon::new(LineString(vec![Coordinate { x: 45.3563321662796, y: 11.9147053956319 }, Coordinate { x: 45.4293499926637, y: 11.9455630525467 }, Coordinate { x: 45.4392542159797, y: 11.8515426867682 }, Coordinate { x: 45.3661863570488, y: 11.8209138798751 }]), vec![]);
        let cell2 = Polygon::new(LineString(vec![Coordinate { x: 45.4293499926637, y: 11.9455630525467 }, Coordinate { x: 45.5024707283596, y: 11.9765478474091 }, Coordinate { x: 45.5124252464723, y: 11.8822977972565 }, Coordinate { x: 45.4392542159797, y: 11.8515426867682 }]), vec![]);
        let cell3 = Polygon::new(LineString(vec![Coordinate { x: 45.3661863570488, y: 11.8209138798751 }, Coordinate { x: 45.4392542159797, y: 11.8515426867682 }, Coordinate { x: 45.4490695215551, y: 11.7576024308158 }, Coordinate { x: 45.3759520538385, y: 11.7272026072339 }]), vec![]);
        let point1 = Point(Coordinate { x: 45.429671680421, y: 11.887047957258 });
        let point2 = Point(Coordinate { x: 45.412408636479, y: 11.866946356603 });
        let point3 = Point(Coordinate { x: 45.390711713006, y: 11.868550140008 });
        let point4 = Point(Coordinate { x: 45.421928106575, y: 11.897589742744 });
        let point5 = Point(Coordinate { x: 45.414838131946, y: 11.811773142492 });
        let point6 = Point(Coordinate { x: 45.41341604488, y: 11.802568326636 });
        let point7 = Point(Coordinate { x: 45.395726701315, y: 11.833525908467 });
        assert!(cell1.within(&point1));
        assert!(cell2.within(&point1) == false);
        assert!(cell3.within(&point1) == false);
        assert!(cell1.within(&point2));
        assert!(cell2.within(&point2) == false);
        assert!(cell3.within(&point2) == false);
        assert!(cell1.within(&point3));
        assert!(cell2.within(&point3) == false);
        assert!(cell3.within(&point3) == false);
        assert!(cell1.within(&point4));
        assert!(cell2.within(&point4) == false);
        assert!(cell3.within(&point4) == false);
        assert!(cell1.within(&point5) == false);
        assert!(cell2.within(&point5) == false);
        assert!(cell3.within(&point5));
        assert!(cell1.within(&point6) == false);
        assert!(cell2.within(&point6) == false);
        assert!(cell3.within(&point6));
        assert!(cell1.within(&point7));
        assert!(cell2.within(&point7) == false);
        assert!(cell3.within(&point7) == false);
    }
}