del-geo 0.1.25

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
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148

//! methods for 3D vector

use num_traits::AsPrimitive;

pub fn squared_norm_<T>(p: &[T; 3]) -> T
where
    T: std::ops::Mul<Output = T> + std::ops::Add<Output = T> + Copy,
{
    assert_eq!(p.len(), 3);
    p[0] * p[0] + p[1] * p[1] + p[2] * p[2]
}

pub fn norm_<T>(v: &[T; 3]) -> T
where
    T: num_traits::Float,
{
    (v[0] * v[0] + v[1] * v[1] + v[2] * v[2]).sqrt()
}

pub fn normalize_<T>(v: &mut [T; 3]) -> T
where
    T: num_traits::Float + std::ops::MulAssign,
{
    let l = norm_(v);
    let linv = T::one() / l;
    v[0] *= linv;
    v[1] *= linv;
    v[2] *= linv;
    l
}

pub fn cross_mut_<T>(vo: &mut [T; 3], v1: &[T; 3], v2: &[T; 3])
where
    T: std::ops::Mul<Output = T> + std::ops::Sub<Output = T> + Copy,
{
    vo[0] = v1[1] * v2[2] - v2[1] * v1[2];
    vo[1] = v1[2] * v2[0] - v2[2] * v1[0];
    vo[2] = v1[0] * v2[1] - v2[0] * v1[1];
}

pub fn cross_<T>(v1: &[T; 3], v2: &[T; 3]) -> [T; 3]
where
    T: std::ops::Mul<Output = T> + std::ops::Sub<Output = T> + Copy,
{
    [
        v1[1] * v2[2] - v2[1] * v1[2],
        v1[2] * v2[0] - v2[2] * v1[0],
        v1[0] * v2[1] - v2[0] * v1[1],
    ]
}

pub fn dot_<T>(a: &[T; 3], b: &[T; 3]) -> T
where
    T: std::ops::Mul<Output = T> + std::ops::Add<Output = T> + Copy,
{
    a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
}

pub fn sub_<T>(a: &[T; 3], b: &[T; 3]) -> [T; 3]
where
    T: std::ops::Sub<Output = T> + Copy,
{
    [a[0] - b[0], a[1] - b[1], a[2] - b[2]]
}

pub fn scale_<T>(a: &[T; 3], s: T) -> [T; 3]
where
    T: Copy + std::ops::Mul<Output = T>,
{
    [s * a[0], s * a[1], s * a[2]]
}

pub fn distance_<T>(p0: &[T; 3], p1: &[T; 3]) -> T
where
    T: num_traits::Float,
{
    let v0 = p1[0] - p0[0];
    let v1 = p1[1] - p0[1];
    let v2 = p1[2] - p0[2];
    (v0 * v0 + v1 * v1 + v2 * v2).sqrt()
}

pub fn scalar_triple_product_<T>(a: &[T; 3], b: &[T; 3], c: &[T; 3]) -> T
where
    T: std::ops::Mul<Output = T> + std::ops::Sub<Output = T> + std::ops::Add<Output = T> + Copy,
{
    let v0: T = a[0] * (b[1] * c[2] - b[2] * c[1]);
    let v1: T = a[1] * (b[2] * c[0] - b[0] * c[2]);
    let v2: T = a[2] * (b[0] * c[1] - b[1] * c[0]);
    v0 + v1 + v2
}

// -------------------

pub fn scalar_triple_product<T>(
    a: &nalgebra::Vector3<T>,
    b: &nalgebra::Vector3<T>,
    c: &nalgebra::Vector3<T>,
) -> T
where
    T: nalgebra::RealField,
{
    b.cross(c).dot(a)
}

pub fn frame_from_z_vector<T>(
    vec_n: nalgebra::Vector3<T>,
) -> (nalgebra::Vector3<T>, nalgebra::Vector3<T>)
where
    T: nalgebra::RealField + 'static + Copy,
    f64: num_traits::AsPrimitive<T>,
{
    let vec_s = nalgebra::Vector3::<T>::new(T::zero(), T::one(), T::zero());
    let mut vec_x = vec_s.cross(&vec_n);
    let len = vec_x.norm();
    if len < 1.0e-10_f64.as_() {
        let vec_t = nalgebra::Vector3::<T>::new(T::one(), T::zero(), T::zero());
        let vec_x = vec_t.cross(&vec_n);
        let vec_y = vec_n.cross(&vec_x);
        (vec_x, vec_y)
    } else {
        let invlen = T::one() / len;
        vec_x *= invlen;
        let vec_y = vec_n.cross(&vec_x);
        (vec_x, vec_y)
    }
}

pub fn sample_unit_cube<T>() -> nalgebra::Vector3<T>
where
    T: nalgebra::RealField + nalgebra::Scalar,
    rand::distributions::Standard: rand::prelude::Distribution<T>,
{
    use rand::Rng;
    let mut p0 = nalgebra::Vector3::<T>::zeros();
    let mut rng = rand::thread_rng();
    for v in p0.iter_mut() {
        *v = rng.gen();
    }
    p0
}

pub fn to_na<T>(vtx2xyz: &[T], i_vtx: usize) -> nalgebra::Vector3<T>
where
    T: Copy + nalgebra::RealField,
{
    nalgebra::Vector3::<T>::from_row_slice(&vtx2xyz[i_vtx * 3..(i_vtx + 1) * 3])
}