coord_transforms 1.0.0

A Rust crate use for performing coordinate transformations.
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

use na::Vector3;

/// Converts 3-d spherical coordinates to 3-d cartesian coordinates
/// 
/// # Arguments
/// 
/// * `sphere_vec` - Vector3 reference to the spherical vector (rho, theta, phi) (r, el, az) in radians
/// 
/// # Return Value
/// 
/// * nalgebra::Vector3<f64> - x, y, z
/// 
/// # Formula
/// 
/// * x = rho * sin(theta) * cos(phi)
/// * y = rho * sin(theta) * sin(phi)
/// * z = rho * cos(theta)
pub fn spherical2cartesian(sphere_vec: &Vector3<f64>) -> Vector3<f64> {
    let mut ret_vec: Vector3<f64> = Vector3::new(0.0, 0.0, 0.0);
    ret_vec.x = sphere_vec.x * sphere_vec.y.sin() * sphere_vec.z.cos();
    ret_vec.y = sphere_vec.x * sphere_vec.y.sin() * sphere_vec.z.sin();
    ret_vec.z = sphere_vec.x * sphere_vec.y.cos();
    ret_vec
}

/// Converts 3-d cylindrical coordinates to 3-d cartesian coordinates
/// 
/// # Arguments
/// 
/// * `cyl_vec` - Vector3 reference to the cylindrical vector (rho, theta, z) in radians
/// 
/// # Return Value
/// 
/// * nalgebra::Vector3<f64> - x, y, z
/// 
/// # Formula
/// 
/// * x = rho * cos(theta)
/// * y = rho * sin(theta)
/// * z = z
pub fn cylindrical2cartesian(cyl_vec: &Vector3<f64>) -> Vector3<f64> {
    let mut ret_vec: Vector3<f64> = Vector3::new(0.0, 0.0, 0.0);
    ret_vec.x = cyl_vec.x * cyl_vec.y.cos();
    ret_vec.y = cyl_vec.x * cyl_vec.y.sin();
    ret_vec.z = cyl_vec.z;
    ret_vec
}

/// Converts 3-d cartesian coordinates to 3-d spherical coordinates
/// 
/// # Arguments
/// 
/// * `cart_vec` - Vector3 reference to the cartesian vector (x, y, z)
/// 
/// # Return Value
/// 
/// * nalgebra::Vector3<f64> - rho, theta, phi (in radians)
/// 
/// # Formula
/// 
/// * rho = sqrt( x^2 + y^2 + z^2 )
/// * theta = arctan((sqrt( x2 + y^2 )) / (z))
/// * phi = arctan(y / x)
pub fn cartesian2spherical(cart_vec: &Vector3<f64>) -> Vector3<f64> {
	let mut ret_vec: Vector3<f64> = Vector3::new(0.0, 0.0, 0.0);
	ret_vec.x = (cart_vec.x.powi(2) + cart_vec.y.powi(2) + cart_vec.z.powi(2)).sqrt();
	ret_vec.y = ((cart_vec.x.powi(2) + cart_vec.y.powi(2)).sqrt()).atan2(cart_vec.z); 
	ret_vec.z = cart_vec.y.atan2(cart_vec.x);
	ret_vec
}

/// Converts 3-d cartesian coordinates to 3-d cylindrical coordinates
/// 
/// # Arguments
/// 
/// * `cart_vec` - Vector3 reference to the cartesian vector (x, y, z)
/// 
/// # Return Value
/// 
/// * nalgebra::Vector3<f64> - rho, theta, z (in radians)
/// 
/// # Formula
/// 
/// * rho = sqrt( x^2 + y^2 )
/// * theta = arctan(y / x)
/// * z = z
pub fn cartesian2cylindrical(cart_vec: &Vector3<f64>) -> Vector3<f64> {
    let mut ret_vec: Vector3<f64> = Vector3::new(0.0, 0.0, 0.0);
    ret_vec.x = (cart_vec.x.powi(2) + cart_vec.y.powi(2)).sqrt();
    ret_vec.y = cart_vec.y.atan2(cart_vec.x);
    ret_vec.z = cart_vec.z;
    ret_vec
}

//Unit tests
#[cfg(test)]
mod tests {
	use super::*;
    #[test]
    fn test_spherical2cartesian() {
        let sphere_vec: Vector3<f64> = Vector3::new(3.0, 4.0, 5.0);
        let cart_vec = spherical2cartesian(&sphere_vec);
        assert_approx_eq!(cart_vec.x, -0.6440287493492097);
        assert_approx_eq!(cart_vec.y, 2.177148851629225);
        assert_approx_eq!(cart_vec.z, -1.960930862590836);
    }
    #[test]
    fn test_cylindrical2cartesian() {
        let cyl_vec: Vector3<f64> = Vector3::new(3.0, 4.0, 5.0);
        let cart_vec = cylindrical2cartesian(&cyl_vec);
        assert_approx_eq!(cart_vec.x, -1.960930862590836);
        assert_approx_eq!(cart_vec.y, -2.2704074859237844);
        assert_approx_eq!(cart_vec.z, 5.0);
    }
    #[test]
    fn test_cartesian2spherical() {
        let cart_vec: Vector3<f64> = Vector3::new(3.0, 4.0, 5.0);
        let sphere_vec = cartesian2spherical(&cart_vec);
        assert_approx_eq!(sphere_vec.x, 7.0710678118655);
        assert_approx_eq!(sphere_vec.y, 0.78539816339745);
        assert_approx_eq!(sphere_vec.z, 0.92729521800161);
    }
    #[test]
    fn test_cartesian2cylindrical() {
        let cart_vec: Vector3<f64> = Vector3::new(3.0, 4.0, 5.0);
        let cyl_vec = cartesian2cylindrical(&cart_vec);
        assert_approx_eq!(cyl_vec.x, 5.0);
        assert_approx_eq!(cyl_vec.y, 0.9272952180016122);
        assert_approx_eq!(cyl_vec.z, 5.0);
    }
}