liealg 0.4.1

lie group and lie algebra in rust
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

use core::{fmt::Display, ops::Mul};

use super::SO3;
use crate::{
    utils::{approx_zero, axis_angle, hat, length},
    Algebra, Real, Vec3,
};
use nalgebra::{Matrix3, Vector3};

/// so3 group
/// ```ignore
/// so3 = [
///    0 -z  y
///    z  0 -x
///   -y  x  0
/// ]
/// ```
#[allow(non_camel_case_types)]
#[derive(Debug)]
pub struct so3<T> {
    pub(crate) val: Vector3<T>,
}

impl<T> Display for so3<T>
where
    T: Display + Real,
{
    fn fmt(&self, f: &mut core::fmt::Formatter<'_>) -> core::fmt::Result {
        hat(&self.val).fmt(f)
    }
}

impl<T> so3<T>
where
    T: Real,
{
    /// Create a new so3 group element
    /// ```ignore
    /// so3 = [
    ///    0 -z  y
    ///    z  0 -x
    ///   -y  x  0
    /// ]
    /// ```
    pub fn new(x: T, y: T, z: T) -> Self {
        Self {
            val: Vector3::new(x, y, z),
        }
    }
}

impl<T> Mul<T> for so3<T>
where
    T: Real,
{
    type Output = Self;

    fn mul(self, rhs: T) -> Self::Output {
        Self {
            val: self.val * rhs,
        }
    }
}

impl<T> Algebra for so3<T>
where
    T: Real,
{
    type Group = SO3<T>;

    type Vector = Vec3<T>;

    fn exp(&self) -> Self::Group {
        if approx_zero(length(&self.val)) {
            SO3 {
                val: Matrix3::identity(),
            }
        } else {
            let (w, angle) = axis_angle(&self.val);
            let w_so3 = hat(&w);
            SO3 {
                val: Matrix3::identity()
                    + w_so3 * angle.sin()
                    + w_so3 * w_so3 * (T::one() - angle.cos()),
            }
        }
    }

    fn vee(&self) -> Self::Vector {
        Vec3 { val: self.val }
    }
}

#[cfg(test)]
mod test {
    use super::*;
    use approx::assert_relative_eq;
    use core::f64::consts::FRAC_PI_2;

    #[test]
    fn so3_exp() {
        let so3 = so3 {
            val: Vector3::new(0., 0., FRAC_PI_2),
        };
        let rot_mat = so3.exp();
        assert_relative_eq!(
            rot_mat.val,
            &Matrix3::new(0., -1., 0., 1., 0., 0., 0., 0., 1.,)
        );
    }

    #[test]
    fn so3_vee() {
        let so3 = so3 {
            val: Vector3::new(0., 0., FRAC_PI_2),
        };
        let v = so3.vee();
        assert_relative_eq!(v.val, Vector3::new(0., 0., FRAC_PI_2));
    }
}