pointy 0.8.0

Minimal 2D geometry library
Documentation 
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
249
250
251
252
253
254
255
256
257
258

// segment.rs    2D Line Segments
//
// Copyright (c) 2020-2025  Douglas P Lau
//
use crate::bbox::{BBox, Bounded, Bounds};
use crate::float::Float;
use crate::line::Line;
use crate::point::Pt;
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};

/// Segment of a line between two endpoints
///
/// ```rust
/// use pointy::Seg;
///
/// let seg = Seg::new((10.0, 15.0), (0.0, 2.0));
/// ```
#[derive(Clone, Copy, Debug, Eq, PartialEq)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub struct Seg<F>
where
    F: Float,
{
    /// First endpoint
    pub p0: Pt<F>,

    /// Second endpoint
    pub p1: Pt<F>,
}

impl<F> Bounded<F> for Seg<F>
where
    F: Float,
{
    fn bounded_by(self, bbox: BBox<F>) -> bool {
        let p0 = bbox.check(self.p0.x, self.p0.y);
        let p1 = bbox.check(self.p1.x, self.p1.y);
        match (p0, p1) {
            (Bounds::Within, _) | (_, Bounds::Within) => true,
            // both opposite horizontally
            (Bounds::Left, Bounds::Right) => true,
            (Bounds::Right, Bounds::Left) => true,
            // both opposite vertically
            (Bounds::Below, Bounds::Above) => true,
            (Bounds::Above, Bounds::Below) => true,
            (
                Bounds::Left | Bounds::BelowLeft | Bounds::AboveLeft,
                Bounds::Left | Bounds::BelowLeft | Bounds::AboveLeft,
            ) => false,
            (
                Bounds::Right | Bounds::BelowRight | Bounds::AboveRight,
                Bounds::Right | Bounds::BelowRight | Bounds::AboveRight,
            ) => false,
            (
                Bounds::Below | Bounds::BelowLeft | Bounds::BelowRight,
                Bounds::Below | Bounds::BelowLeft | Bounds::BelowRight,
            ) => false,
            (
                Bounds::Above | Bounds::AboveLeft | Bounds::AboveRight,
                Bounds::Above | Bounds::AboveLeft | Bounds::AboveRight,
            ) => false,
            (Bounds::Left, _) | (_, Bounds::Left) => {
                self.intersects(bbox.x_min_edge())
            }
            (Bounds::Right, _) | (_, Bounds::Right) => {
                self.intersects(bbox.x_max_edge())
            }
            (Bounds::BelowLeft, _) | (_, Bounds::BelowLeft) => {
                self.intersects(bbox.x_min_edge())
                    || self.intersects(bbox.y_min_edge())
            }
            (Bounds::AboveLeft, _) | (_, Bounds::AboveLeft) => {
                self.intersects(bbox.x_min_edge())
                    || self.intersects(bbox.y_max_edge())
            }
            (Bounds::BelowRight, _) | (_, Bounds::BelowRight) => {
                self.intersects(bbox.x_max_edge())
                    || self.intersects(bbox.y_min_edge())
            }
            (Bounds::AboveRight, _) | (_, Bounds::AboveRight) => {
                self.intersects(bbox.x_max_edge())
                    || self.intersects(bbox.y_max_edge())
            }
        }
    }
}

impl<F> Seg<F>
where
    F: Float,
{
    /// Create a new line segment
    pub fn new<P0, P1>(p0: P0, p1: P1) -> Self
    where
        P0: Into<Pt<F>>,
        P1: Into<Pt<F>>,
    {
        Self {
            p0: p0.into(),
            p1: p1.into(),
        }
    }

    /// Get the distance from the line segment to a point
    pub fn distance<P>(self, pt: P) -> F
    where
        P: Into<Pt<F>>,
    {
        let pt = pt.into();
        // If the dot product of `v0` and `v1` is greater than zero,
        // then the nearest point on the segment is `p1`
        let v0 = self.p1 - self.p0;
        let v1 = pt - self.p1;
        if v0.dot(v1) > F::zero() {
            return v1.mag();
        }
        // If the dot product of `v2` and `v3` is greater than zero,
        // then the nearest point on the segment is `p0`
        let v2 = self.p0 - self.p1;
        let v3 = pt - self.p0;
        if v2.dot(v3) > F::zero() {
            return v3.mag();
        }
        // Otherwise, the nearest point on the segment is between
        // `p0` and `p1`, so calculate the point-line distance
        (v0 * v3).abs() / v0.mag()
    }

    /// Get the point where two segments intersect
    pub fn intersection(self, rhs: Self) -> Option<Pt<F>> {
        let l0 = Line::new(self.p0, self.p1);
        let l1 = Line::new(rhs.p0, rhs.p1);
        l0.intersection(l1)
            .filter(|p| p.bounded_by(BBox::new([rhs.p0, rhs.p1])))
    }

    /// Check if segment intersects with another segment
    pub fn intersects(self, rhs: Self) -> bool {
        self.intersection(rhs).is_some()
    }

    /// Clip segment with a bounding box
    pub fn clip(mut self, bbox: BBox<F>) -> Option<Self> {
        if !self.bounded_by(bbox) {
            return None;
        }
        if let Some(p) = self.intersection(bbox.x_min_edge()) {
            let xmn = bbox.x_min();
            if self.p0.x < xmn {
                self.p0 = p;
            } else if self.p1.x < xmn {
                self.p1 = p;
            }
        }
        if let Some(p) = self.intersection(bbox.x_max_edge()) {
            let xmx = bbox.x_max();
            if self.p0.x > xmx {
                self.p0 = p;
            } else if self.p1.x > xmx {
                self.p1 = p;
            }
        }
        if let Some(p) = self.intersection(bbox.y_min_edge()) {
            let ymn = bbox.y_min();
            if self.p0.y < ymn {
                self.p0 = p;
            } else if self.p1.y < ymn {
                self.p1 = p;
            }
        }
        if let Some(p) = self.intersection(bbox.y_max_edge()) {
            let ymx = bbox.y_max();
            if self.p0.y > ymx {
                self.p0 = p;
            } else if self.p1.y > ymx {
                self.p1 = p;
            }
        }
        Some(self)
    }
}

// Private BBox helper functions
impl<F> BBox<F>
where
    F: Float,
{
    /// Get edge on X min side
    fn x_min_edge(self) -> Seg<F> {
        let xmn = self.x_min();
        Seg::new((xmn, self.y_min()), (xmn, self.y_max()))
    }

    /// Get edge on X max side
    fn x_max_edge(self) -> Seg<F> {
        let xmx = self.x_max();
        Seg::new((xmx, self.y_min()), (xmx, self.y_max()))
    }

    /// Get edge on Y min side
    fn y_min_edge(self) -> Seg<F> {
        let ymn = self.y_min();
        Seg::new((self.x_min(), ymn), (self.x_max(), ymn))
    }

    /// Get edge on Y max side
    fn y_max_edge(self) -> Seg<F> {
        let ymx = self.y_max();
        Seg::new((self.x_min(), ymx), (self.x_max(), ymx))
    }
}

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

    #[test]
    fn distance() {
        let a = Seg::new((0.0, 0.0), (10.0, 0.0));
        assert_eq!(a.distance((0.0, 5.0)), 5.0);
        assert_eq!(a.distance((5.0, 5.0)), 5.0);
        assert_eq!(a.distance((10.0, 5.0)), 5.0);
        assert_eq!(a.distance((-5.0, 0.0)), 5.0);
        assert_eq!(a.distance((15.0, 0.0)), 5.0);
        assert_eq!(a.distance((0.0, -5.0)), 5.0);
        assert_eq!(a.distance((5.0, -5.0)), 5.0);
        assert_eq!(a.distance((10.0, -5.0)), 5.0);
    }

    #[test]
    fn intersection() {
        let a = Seg::new((0.0, 0.0), (1.0, 0.0));
        assert_eq!(a.intersection(a), None);
        let b = Seg::new((1.0, 1.0), (1.0, 0.0));
        assert_eq!(a.intersection(b), Some(Pt::new(1.0, 0.0)));
        let c = Seg::new((0.5, 1.0), (0.5, 10.0));
        assert_eq!(a.intersection(c), None);
        let d = Seg::new((0.5, 1.0), (0.5, -1.0));
        assert_eq!(a.intersection(d), Some(Pt::new(0.5, 0.0)));
    }

    #[test]
    fn bounded() {
        let b = BBox::new([(0.0, 0.0), (1.0, 1.0)]);
        assert!(Seg::new((0.0, 0.0), (1.0, 1.0)).bounded_by(b));
        assert!(Seg::new((1.0, 1.0), (2.0, 2.0)).bounded_by(b));
        assert!(Seg::new((0.0, 0.0), (-1.0, -1.0)).bounded_by(b));
        assert!(!Seg::new((2.0, 2.0), (3.0, 3.0)).bounded_by(b));
        assert!(!Seg::new((-1.0, -1.0), (-2.0, -2.0)).bounded_by(b));
        assert!(Seg::new((0.5, 0.5), (1.5, 0.5)).bounded_by(b));
        assert!(Seg::new((0.5, 0.5), (0.5, 1.5)).bounded_by(b));
        assert!(Seg::new((0.5, 1.5), (1.5, 0.5)).bounded_by(b));
        assert!(!Seg::new((0.5, 1.6), (1.6, 0.5)).bounded_by(b));
        assert!(Seg::new((-0.5, 0.5), (1.5, 0.5)).bounded_by(b));
        assert!(Seg::new((0.5, -0.5), (0.5, 1.5)).bounded_by(b));
    }
}