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

// Copyright (c) 2018-2020 Thomas Kramer.
// SPDX-FileCopyrightText: 2018-2022 Thomas Kramer
//
// SPDX-License-Identifier: AGPL-3.0-or-later

//! Compute the convex hull of a list of points.

use crate::prelude::{Point, SimplePolygon, Edge, Side};
use num_traits::Num;

/// Get the convex hull of the polygon.
///
/// Implements Andrew's Monotone Chain algorithm.
/// See: <http://geomalgorithms.com/a10-_hull-1.html>
pub fn convex_hull<T>(points: Vec<Point<T>>) -> SimplePolygon<T>
    where T: Num + Ord + Copy {

    // Sort points by coordinates.
    let p = {
        let mut p = points;
        p.sort();
        p
    };

    assert!(p.len() >= 2);

    // minmin = index of P with min x first and min y second
    let minmin = 0;
    let p_minmin = p[minmin];
    // maxmax = index of P with max x first and max y second
    let maxmax = p.len() - 1;
    let p_maxmax = p[maxmax];
    // minmax = index of P with min x first and max y second
    let minmax = p.iter().enumerate()
        .take_while(|(_, p)| p.x == p_minmin.x)
        .last().unwrap().0;
    let p_minmax = p[minmax];
    // maxmin = index of P with max x first and min y second
    let maxmin = p.iter().enumerate().rev()
        .take_while(|(_, p)| p.x == p_maxmax.x)
        .last().unwrap().0;
    let p_maxmin = p[maxmin];

    debug_assert!(minmin <= minmax);
    debug_assert!(minmax <= maxmin || p_minmax.x == p_maxmin.x);
    debug_assert!(maxmin <= maxmax);

    debug_assert!(p.iter().all(|&p| p_minmin <= p));
    debug_assert!(p.iter().all(|&p| p_maxmax >= p));
    debug_assert!(p.iter().all(|&p|
        p_minmax.x < p.x || (p_minmax.x == p.x && p_minmax.y >= p.y)
    ));
    debug_assert!(p.iter().all(|&p|
        p_maxmin.x > p.x || (p_maxmin.x == p.x && p_maxmin.y <= p.y)
    ));

    // Handle degenerate case where all x coordinates are equal.
    if p_minmin.x == p_maxmax.x {
        if p_minmin.y == p_maxmax.y {
            SimplePolygon::new(vec![p_minmin])
        } else {
            SimplePolygon::new(vec![p_minmin, p_maxmax])
        }
    } else {
        let build_half_hull =
            |l: Edge<T>, points: &[Point<T>]| {
                let mut stack = Vec::new();
                // Push starting point on stack.
                stack.push(l.start);

                for &pi in points {
                    // Skip all points that are not strictly right of `l`.
                    if l.side_of(pi) == Side::Right {
                        while stack.len() >= 2 {
                            let pt1 = stack[stack.len() - 1];
                            let pt2 = stack[stack.len() - 2];

                            if Edge::new(pt2, pt1).side_of(pi) == Side::Left {
                                // `pi` is strictly left of the line defined by the top two elements
                                // on the stack.
                                break;
                            }
                            stack.pop();
                        }
                        stack.push(pi);
                    }
                }

                stack
            };

        // Compute the lower hull.
        let l_min = Edge::new(p_minmin, p_maxmin);
        let mut lower_half_hull = build_half_hull(l_min, &p[minmax + 1..maxmin]);

        // Push p_maxmin on stack if necessary.
        if p_maxmin != p_maxmax {
            lower_half_hull.push(p_maxmin);
        }

        // Compute the upper hull.
        let l_max = Edge::new(p_maxmax, p_minmax);
        let mut upper_half_hull = build_half_hull(l_max, &p[minmax + 1..maxmin]);

        // Push p_minmax on stack if necessary.
        if p_minmax != p_minmin {
            upper_half_hull.push(p_minmax);
        }

        // Join both hulls.
        lower_half_hull.append(&mut upper_half_hull);

        SimplePolygon::new(lower_half_hull)
    }
}