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geometry_kernel/
predicates.rs

1use robust::{orient2d, Coord as RobustCoord};
2
3use crate::precision::PrecisionModel;
4use crate::types::{Coord, LinearRing, Polygon};
5
6#[derive(Debug, Clone, Copy, PartialEq, Eq)]
7pub enum PointLocation {
8    Exterior,
9    Boundary,
10    Interior,
11}
12
13pub fn orientation(a: Coord, b: Coord, c: Coord) -> f64 {
14    orient2d(
15        RobustCoord { x: a.x, y: a.y },
16        RobustCoord { x: b.x, y: b.y },
17        RobustCoord { x: c.x, y: c.y },
18    )
19}
20
21pub fn signed_ring_area(ring: &LinearRing) -> f64 {
22    signed_area_coords(&ring.coords)
23}
24
25pub fn signed_area_coords(coords: &[Coord]) -> f64 {
26    coords
27        .windows(2)
28        .map(|pair| pair[0].x * pair[1].y - pair[1].x * pair[0].y)
29        .sum::<f64>()
30        * 0.5
31}
32
33pub fn polygon_area(polygon: &Polygon) -> f64 {
34    if polygon.is_empty() {
35        return 0.0;
36    }
37    let holes = polygon
38        .holes
39        .iter()
40        .map(|ring| signed_ring_area(ring).abs())
41        .sum::<f64>();
42    signed_ring_area(&polygon.exterior).abs() - holes
43}
44
45pub fn is_ring_ccw(ring: &LinearRing) -> bool {
46    signed_ring_area(ring) > 0.0
47}
48
49pub fn point_on_segment(point: Coord, a: Coord, b: Coord, precision: PrecisionModel) -> bool {
50    if orientation(a, b, point).abs() > orientation_epsilon(a, b, point, precision) {
51        return false;
52    }
53
54    point.x >= a.x.min(b.x) - precision.epsilon()
55        && point.x <= a.x.max(b.x) + precision.epsilon()
56        && point.y >= a.y.min(b.y) - precision.epsilon()
57        && point.y <= a.y.max(b.y) + precision.epsilon()
58}
59
60pub fn point_in_ring(point: Coord, ring: &LinearRing, precision: PrecisionModel) -> PointLocation {
61    if ring.coords.len() < 4 {
62        return PointLocation::Exterior;
63    }
64
65    let mut inside = false;
66    for (a, b) in ring.segments() {
67        if point_on_segment(point, a, b, precision) {
68            return PointLocation::Boundary;
69        }
70
71        let crosses = (a.y > point.y) != (b.y > point.y);
72        if crosses {
73            let x_at_y = (b.x - a.x) * (point.y - a.y) / (b.y - a.y) + a.x;
74            if x_at_y > point.x {
75                inside = !inside;
76            }
77        }
78    }
79
80    if inside {
81        PointLocation::Interior
82    } else {
83        PointLocation::Exterior
84    }
85}
86
87pub fn point_in_polygon(
88    point: Coord,
89    polygon: &Polygon,
90    precision: PrecisionModel,
91) -> PointLocation {
92    match point_in_ring(point, &polygon.exterior, precision) {
93        PointLocation::Exterior => PointLocation::Exterior,
94        PointLocation::Boundary => PointLocation::Boundary,
95        PointLocation::Interior => {
96            for hole in &polygon.holes {
97                match point_in_ring(point, hole, precision) {
98                    PointLocation::Interior => return PointLocation::Exterior,
99                    PointLocation::Boundary => return PointLocation::Boundary,
100                    PointLocation::Exterior => {}
101                }
102            }
103            PointLocation::Interior
104        }
105    }
106}
107
108#[derive(Debug, Clone, PartialEq)]
109pub enum SegmentIntersection {
110    Point(Coord),
111    Overlap(Coord, Coord),
112}
113
114pub fn segment_intersection(
115    a1: Coord,
116    a2: Coord,
117    b1: Coord,
118    b2: Coord,
119    precision: PrecisionModel,
120) -> Option<SegmentIntersection> {
121    if segment_bboxes_disjoint(a1, a2, b1, b2, precision) {
122        return None;
123    }
124
125    let o1 = orientation(a1, a2, b1);
126    let o2 = orientation(a1, a2, b2);
127    let o3 = orientation(b1, b2, a1);
128    let o4 = orientation(b1, b2, a2);
129    let s1 = orientation_sign(o1, orientation_epsilon(a1, a2, b1, precision));
130    let s2 = orientation_sign(o2, orientation_epsilon(a1, a2, b2, precision));
131    let s3 = orientation_sign(o3, orientation_epsilon(b1, b2, a1, precision));
132    let s4 = orientation_sign(o4, orientation_epsilon(b1, b2, a2, precision));
133
134    if s1 == 0 && s2 == 0 && s3 == 0 && s4 == 0 {
135        return collinear_overlap(a1, a2, b1, b2, precision);
136    }
137
138    if s1 != 0 && s1 == s2 {
139        return None;
140    }
141    if s3 != 0 && s3 == s4 {
142        return None;
143    }
144
145    let r = Coord::new(a2.x - a1.x, a2.y - a1.y);
146    let s = Coord::new(b2.x - b1.x, b2.y - b1.y);
147    let denom = cross(r, s);
148    if denom.abs() <= cross_epsilon(r, s, precision) {
149        return None;
150    }
151
152    let q_minus_p = Coord::new(b1.x - a1.x, b1.y - a1.y);
153    let t = cross(q_minus_p, s) / denom;
154    let point = precision.snap_coord(Coord::new(a1.x + t * r.x, a1.y + t * r.y));
155
156    if point_on_segment(point, a1, a2, precision) && point_on_segment(point, b1, b2, precision) {
157        Some(SegmentIntersection::Point(point))
158    } else {
159        None
160    }
161}
162
163fn cross(a: Coord, b: Coord) -> f64 {
164    a.x * b.y - a.y * b.x
165}
166
167fn orientation_epsilon(a: Coord, b: Coord, c: Coord, precision: PrecisionModel) -> f64 {
168    let ab = l1_distance(a, b);
169    let ac = l1_distance(a, c);
170    precision.epsilon() * (ab + ac).max(f64::EPSILON)
171}
172
173fn cross_epsilon(a: Coord, b: Coord, precision: PrecisionModel) -> f64 {
174    precision.epsilon() * (l1_vector_length(a) + l1_vector_length(b)).max(f64::EPSILON)
175}
176
177fn l1_distance(a: Coord, b: Coord) -> f64 {
178    (a.x - b.x).abs() + (a.y - b.y).abs()
179}
180
181fn l1_vector_length(vector: Coord) -> f64 {
182    vector.x.abs() + vector.y.abs()
183}
184
185fn segment_bboxes_disjoint(
186    a1: Coord,
187    a2: Coord,
188    b1: Coord,
189    b2: Coord,
190    precision: PrecisionModel,
191) -> bool {
192    let eps = precision.epsilon();
193    a1.x.min(a2.x) > b1.x.max(b2.x) + eps
194        || b1.x.min(b2.x) > a1.x.max(a2.x) + eps
195        || a1.y.min(a2.y) > b1.y.max(b2.y) + eps
196        || b1.y.min(b2.y) > a1.y.max(a2.y) + eps
197}
198
199fn orientation_sign(value: f64, epsilon: f64) -> i8 {
200    if value > epsilon {
201        1
202    } else if value < -epsilon {
203        -1
204    } else {
205        0
206    }
207}
208
209fn collinear_overlap(
210    a1: Coord,
211    a2: Coord,
212    b1: Coord,
213    b2: Coord,
214    precision: PrecisionModel,
215) -> Option<SegmentIntersection> {
216    let use_x = (a2.x - a1.x).abs() >= (a2.y - a1.y).abs();
217    let mut points = [a1, a2, b1, b2];
218    points.sort_by(|left, right| {
219        let l = if use_x { left.x } else { left.y };
220        let r = if use_x { right.x } else { right.y };
221        l.partial_cmp(&r).unwrap_or(std::cmp::Ordering::Equal)
222    });
223
224    let start = points[1];
225    let end = points[2];
226    if point_on_segment(start, a1, a2, precision)
227        && point_on_segment(start, b1, b2, precision)
228        && point_on_segment(end, a1, a2, precision)
229        && point_on_segment(end, b1, b2, precision)
230    {
231        if precision.same_coord(start, end) {
232            Some(SegmentIntersection::Point(precision.snap_coord(start)))
233        } else {
234            Some(SegmentIntersection::Overlap(
235                precision.snap_coord(start),
236                precision.snap_coord(end),
237            ))
238        }
239    } else {
240        None
241    }
242}
243
244pub fn is_convex_ring(ring: &LinearRing, precision: PrecisionModel) -> bool {
245    let coords = &ring.coords;
246    if coords.len() < 4 {
247        return false;
248    }
249    let mut sign = 0i8;
250    for i in 0..coords.len() - 1 {
251        let a = coords[i];
252        let b = coords[(i + 1) % (coords.len() - 1)];
253        let c = coords[(i + 2) % (coords.len() - 1)];
254        let o = orientation(a, b, c);
255        if o.abs() <= orientation_epsilon(a, b, c, precision) {
256            continue;
257        }
258        let current = if o > 0.0 { 1 } else { -1 };
259        if sign == 0 {
260            sign = current;
261        } else if sign != current {
262            return false;
263        }
264    }
265    true
266}