del-geo 0.1.24

2D/3D geometry utility codes
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

//! methods for 2D edge (line segment)

use num_traits::AsPrimitive;

pub fn culling_intersection_<T>(
    po_s0: &[T; 2],
    po_e0: &[T; 2],
    po_s1: &[T; 2],
    po_e1: &[T; 2]) -> bool
    where T: num_traits::Float + 'static + Copy,
          f64: num_traits::AsPrimitive<T>
{
    let min0x = if po_s0[0] < po_e0[0] { po_s0[0] } else { po_e0[0] };
    let max0x = if po_s0[0] > po_e0[0] { po_s0[0] } else { po_e0[0] };
    let max1x = if po_s1[0] > po_e1[0] { po_s1[0] } else { po_e1[0] };
    let min1x = if po_s1[0] < po_e1[0] { po_s1[0] } else { po_e1[0] };
    let min0y = if po_s0[1] < po_e0[1] { po_s0[1] } else { po_e0[1] };
    let max0y = if po_s0[1] > po_e0[1] { po_s0[1] } else { po_e0[1] };
    let max1y = if po_s1[1] > po_e1[1] { po_s1[1] } else { po_e1[1] };
    let min1y = if po_s1[1] < po_e1[1] { po_s1[1] } else { po_e1[1] };
    let len = ((max0x - min0x) + (max0y - min0y) + (max1x - min1x) + (max1y - min1y)) * 0.0001_f64.as_();
    if max1x + len < min0x { return false; }
    if max0x + len < min1x { return false; }
    if max1y + len < min0y { return false; }
    if max0y + len < min1y { return false; }
    true
}


pub fn intersection_edge2_<T>(
    po_s0: &[T; 2],
    po_e0: &[T; 2],
    po_s1: &[T; 2],
    po_e1: &[T; 2]) -> Option<(T, T)>
    where T: num_traits::Float + 'static + Copy,
          f64: num_traits::AsPrimitive<T>
{
    let area1 = crate::tri2::area_(po_s0, po_e0, po_s1);
    let area2 = crate::tri2::area_(po_s0, po_e0, po_e1);
    let area3 = crate::tri2::area_(po_s1, po_e1, po_s0);
    let area4 = crate::tri2::area_(po_s1, po_e1, po_e0);
    if area1 * area2 > 0_f64.as_() { return None; }
    if area3 * area4 > 0_f64.as_() { return None; }
    let r1 = area1 / (area1 - area2);
    let r0 = area3 / (area3 - area4);
    Some((r0, r1))
}

pub fn winding_number_<T>(
    ps: &[T; 2],
    pe: &[T; 2],
    po: &[T; 2]) -> T
    where T: num_traits::Float + num_traits::FloatConst,
{
    let half = T::one() / (T::one() + T::one());
    let p0 = crate::vec2::sub_(ps, po);
    let p1 = crate::vec2::sub_(pe, po);
    let y: T = p1[1] * p0[0] - p1[0] * p0[1];
    let x: T = p0[0] * p1[0] + p0[1] * p1[1];
    y.atan2(x) * T::FRAC_1_PI() * half
}

// -----------------------------
// below: use nalgebra

pub fn length_squared<T>(
    p0: &nalgebra::Vector2<T>,
    p1: &nalgebra::Vector2<T>) -> T
    where T: std::ops::Sub<Output=T> + std::ops::Mul<Output=T> + std::ops::Add<Output=T> + Copy
{
    let x = p0[0] - p1[0];
    let y = p0[1] - p1[1];
    x * x + y * y
}

pub fn intersect_edge2(
    po_s0: &nalgebra::Vector2<f32>,
    po_e0: &nalgebra::Vector2<f32>,
    po_s1: &nalgebra::Vector2<f32>,
    po_e1: &nalgebra::Vector2<f32>) -> bool {
    let area1 = crate::tri2::area_(po_s0.as_ref(), po_e0.as_ref(), po_s1.as_ref());
    let area2 = crate::tri2::area_(po_s0.as_ref(), po_e0.as_ref(), po_e1.as_ref());
    let area3 = crate::tri2::area_(po_s1.as_ref(), po_e1.as_ref(), po_s0.as_ref());
    let area4 = crate::tri2::area_(po_s1.as_ref(), po_e1.as_ref(), po_e0.as_ref());
    let a12 = area1 * area2;
    if a12 > 0_f32 {
        return false;
    }
    let a34 = area3 * area4;
    if a34 > 0_f32 {
        return false;
    }
    true
}

pub fn distance_to_edge2<T>(
    po_s0: &nalgebra::Vector2<T>,
    po_e0: &nalgebra::Vector2<T>,
    po_s1: &nalgebra::Vector2<T>,
    po_e1: &nalgebra::Vector2<T>) -> T
    where T: num_traits::Float + nalgebra::RealField + 'static + Copy + std::fmt::Debug,
          f64: num_traits::AsPrimitive<T>
{
    if intersection_edge2_(po_s0.as_ref(), po_e0.as_ref(), po_s1.as_ref(), po_e1.as_ref()).is_some() {
        return (-1_f64).as_();
    }
    let ds1 = crate::edge::distance_to_point(po_s0, po_s1, po_e1);
    let de1 = crate::edge::distance_to_point(po_e0, po_s1, po_e1);
    let ds0 = crate::edge::distance_to_point(po_s1, po_s0, po_e0);
    let de0 = crate::edge::distance_to_point(po_e1, po_s0, po_e0);
    let mut min_dist = ds1;
    min_dist = if de1 < min_dist { de1 } else { min_dist };
    min_dist = if ds0 < min_dist { ds0 } else { min_dist };
    min_dist = if de0 < min_dist { de0 } else { min_dist };
    min_dist
}

pub fn winding_number<T>(
    ps: &nalgebra::Vector2<T>,
    pe: &nalgebra::Vector2<T>,
    po: &nalgebra::Vector2<T>) -> T
    where T: nalgebra::RealField + Copy,
          f64: AsPrimitive<T>
{
    let p0 = ps - po;
    let p1 = pe - po;
    let y: T = p1[1] * p0[0] - p1[0] * p0[1];
    let x: T = p0[0] * p1[0] + p0[1] * p1[1];
    y.atan2(x) * std::f64::consts::FRAC_1_PI.as_() * 0.5.as_()
}