versor 0.1.0

A Rust port of versor in D3.js
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
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175

use std::f32::consts::PI;

const RADIANS: f32 = PI / 180f32;

const DEGREES: f32 = 180f32 / PI;

/// Represents a spherical coordinate.
pub type SphericalCoordinate = (f32, f32);

/// Represents a 3-dimensional vector.
pub struct Vec3(f32, f32, f32);

/// Represents a quaternion.
#[derive(Copy, Clone)]
pub struct Quaternion(f32, f32, f32, f32);

fn hypot(a: f32, b: f32, c: f32, d: f32) -> f32 {
    (a * a + b * b + c * c + d * d).sqrt()
}

impl Quaternion {
    /// Computes the quaternion from a cartesian coordinate.
    pub fn from_cartesian(Vec3(x, y, z): Vec3) -> Quaternion {
        Quaternion(0f32, z, -y, x)
    }

    /// Computes the unit quaternion from a Euler rotation angles `(λ, φ, γ)`.
    pub fn from_angles(l: f32, p: f32, g: f32) -> Quaternion {
        let l = l * RADIANS / 2f32;
        let p = p * RADIANS / 2f32;
        let g = g * RADIANS / 2f32;
        let sl = l.sin();
        let cl = l.cos();
        let sp = p.sin();
        let cp = p.cos();
        let sg = g.sin();
        let cg = g.cos();
        Quaternion(
            cl * cp * cg + sl * sp * sg,
            sl * cp * cg - cl * sp * sg,
            cl * sp * cg + sl * cp * sg,
            cl * cp * sg - sl * sp * cg,
        )
    }

    /// Computes the Euler rotation angles `(λ, φ, γ)`.
    pub fn to_angles(&self) -> (f32, f32, f32) {
        let Quaternion(a, b, c, d) = self;
        (
            (2f32 * (a * b + c * d)).atan2(1f32 - 2f32 * (b * b + c * c)) * DEGREES,
            (2f32 * (a * c - d * b)).min(1f32).max(-1f32).asin() * DEGREES,
            (2f32 * (a * d + b * c)).atan2(1f32 - 2f32 * (c * c + d * d)) * DEGREES,
        )
    }

    /// Computes the length of `self`.
    pub fn length(&self) -> f32 {
        hypot(self.0, self.1, self.2, self.3)
    }

    /// Computes the dot product of `self` and `other`.
    pub fn dot(&self, rhs: &Quaternion) -> f32 {
        self.0 * rhs.0 + self.1 * rhs.1 + self.2 * rhs.2 + self.3 * rhs.3
    }

    /// Element-wisely multiplies `self` and `other`.
    pub fn multiply(&self, rhs: &Quaternion) -> Quaternion {
        let Quaternion(a1, b1, c1, d1) = self;
        let Quaternion(a2, b2, c2, d2) = rhs;
        Quaternion(
            a1 * a2 - b1 * b2 - c1 * c2 - d1 * d2,
            a1 * b2 + b1 * a2 + c1 * d2 - d1 * c2,
            a1 * c2 - b1 * d2 + c1 * a2 + d1 * b2,
            a1 * d2 + b1 * c2 - c1 * b2 + d1 * a2,
        )
    }
}

/// The type for interpolation functions.
pub type InterpolationFn = Box<dyn Fn(f32) -> Quaternion>;

/// Interpolate linearly between two quaternions.
pub fn linear_interpolate(a: Quaternion, b: Quaternion) -> InterpolationFn {
    let Quaternion(a1, b1, c1, d1) = a;
    let Quaternion(mut a2, mut b2, mut c2, mut d2) = b;
    a2 -= a1;
    b2 -= b1;
    c2 -= c1;
    d2 -= d1;
    Box::new(move |t: f32| -> Quaternion {
        let mut x = Quaternion(a1 + a2 * t, b1 + b2 * t, c1 + c2 * t, d1 + d2 * t);
        let l = x.length();
        x.0 /= l;
        x.1 /= l;
        x.2 /= l;
        x.3 /= l;
        x
    })
}

/// Interpolate between two quaternions.
pub fn interpolate(a: Quaternion, b: Quaternion) -> InterpolationFn {
    let Quaternion(a1, b1, c1, d1) = a;
    let Quaternion(mut a2, mut b2, mut c2, mut d2) = b;
    let mut dot = a.dot(&b);
    if dot < 0f32 {
        a2 = -a2;
        b2 = -b2;
        c2 = -c2;
        d2 = -d2;
        dot = -dot;
    }
    if dot > 0.9995 {
        return linear_interpolate(a, b);
    }
    let theta0 = dot.min(1f32).max(-1f32).acos();
    a2 -= a1 * dot;
    b2 -= b1 * dot;
    c2 -= c1 * dot;
    d2 -= d1 * dot;
    let l = hypot(a2, b2, c2, d2);
    a2 /= l;
    b2 /= l;
    c2 /= l;
    d2 /= l;
    Box::new(move |t: f32| -> Quaternion {
        let theta = theta0 * t;
        let s = theta.sin();
        let c = theta.cos();
        Quaternion(a1 * c + a2 * s, b1 * c + b2 * s, c1 * c + c2 * s, d1 * c + d2 * s)
    })
}

/// Returns Cartesian coordinates `[x, y, z]` given spherical coordinates `[λ, φ]`.
pub fn cartesian(e: SphericalCoordinate) -> (f32, f32, f32) {
    let l = e.0 * RADIANS;
    let p = e.1 * RADIANS;
    let cp = p.cos();
    (cp * l.cos(), cp * l.sin(), p.sin())
}

/// Returns the quaternion to rotate between two cartesian points on the sphere.
/// The value `alpha`, ranging from 0 to 1, is for tweening.
/// See https://github.com/Fil/versor/issues/8 for more.
pub fn delta(v0: Vec3, v1: Vec3, alpha: f32) -> Quaternion {
    fn cross(v0: &Vec3, v1: &Vec3) -> Vec3 {
        Vec3(
            v0.1 * v1.2 - v0.2 * v1.1,
            v0.2 * v1.0 - v0.0 * v1.2,
            v0.0 * v1.1 - v0.1 * v1.0
        )
    }

    fn dot(v0: &Vec3, v1: &Vec3) -> f32 {
        v0.0 * v1.0 + v0.1 * v1.1 + v0.2 * v1.2
    }
    
    let w = cross(&v0, &v1);
    let l = dot(&w, &w).sqrt();
    if l.is_nan() {
        Quaternion(1f32, 0f32, 0f32, 0f32)
    } else {
        let t = alpha * dot(&v0, &v1).min(1f32).max(-1f32).acos();
        let s = t.sin();
        Quaternion(t.cos(), w.2 / l * s, -w.1 / l * s, w.0 / l * s)
    }
}

#[cfg(test)]
mod tests {
    #[test]
    fn it_works() {
        assert_eq!(2 + 2, 4);
    }
}