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

use nalgebra::{
    geometry::Quaternion, geometry::UnitQuaternion, linalg::SymmetricEigen, Matrix4, RealField,
};

/// A quaternion averager.
/// Implemented as discussed [here](https://stackoverflow.com/questions/12374087/average-of-multiple-quaternions)
pub struct QuaternionAverager<T: RealField + Copy + PartialEq> {
    matrix: Matrix4<T>,
    weight_sum: T,
}

impl<T: RealField + Copy + PartialEq> Default for QuaternionAverager<T> {
    fn default() -> Self {
        Self::new()
    }
}

impl<T: RealField + Copy + PartialEq> QuaternionAverager<T> {
    /// Creates and returns a new quaternion averager
    ///
    /// # Example
    ///
    /// ```
    /// use quaternion_averager::QuaternionAverager;
    ///
    /// let mut qa = QuaternionAverager::<f64>::new();
    /// ```
    pub fn new() -> QuaternionAverager<T> {
        QuaternionAverager {
            matrix: Matrix4::zeros(),
            weight_sum: T::from_f32(0f32).unwrap(),
        }
    }

    /// Add a new unit quaternion with weight 1 to the averager
    ///
    /// # Example
    /// ```
    /// use quaternion_averager::QuaternionAverager;
    /// use nalgebra::{
    ///     geometry::Quaternion,
    ///     geometry::UnitQuaternion,
    /// };
    ///
    /// let mut qa = QuaternionAverager::new();
    /// let q1 = Quaternion::new(0.9961947f32, 0.0871557f32, 0f32, 0f32);
    /// let q1 = UnitQuaternion::from_quaternion(q1);
    /// qa.add_quaternion(&q1);
    /// ```
    pub fn add_quaternion(&mut self, quaternion: &UnitQuaternion<T>) {
        let q = quaternion.coords * quaternion.coords.transpose();
        self.matrix += q;
        let w = T::from_f32(1f32).unwrap();
        self.weight_sum += w;
    }

    /// Add a new unit quaternion with custom weight to the averager
    ///
    /// # Example
    /// ```
    /// use quaternion_averager::QuaternionAverager;
    /// use nalgebra::{
    ///     geometry::Quaternion,
    ///     geometry::UnitQuaternion,
    /// };
    ///
    /// let mut qa = QuaternionAverager::new();
    /// let q1 = Quaternion::new(0.9961947f32, 0.0871557f32, 0f32, 0f32);
    /// let q1 = UnitQuaternion::from_quaternion(q1);
    /// qa.add_quaternion_weighted(&q1, 0.25f32);
    /// ```
    pub fn add_quaternion_weighted(&mut self, quaternion: &UnitQuaternion<T>, weight: T) {
        let q = quaternion.coords * quaternion.coords.transpose();
        let q = q / weight;
        self.matrix += q;
        self.weight_sum += weight;
    }

    /// Calculates and returns the quaternion average
    ///
    /// # Example
    /// ```
    /// use quaternion_averager::QuaternionAverager;
    /// use nalgebra::{
    ///     geometry::Quaternion,
    ///     geometry::UnitQuaternion,
    /// };
    ///
    /// let mut qa = QuaternionAverager::new();
    /// let q1 = Quaternion::new(0.9961947f32, 0.0871557f32, 0f32, 0f32);
    /// let q1 = UnitQuaternion::from_quaternion(q1);
    /// let q2 = Quaternion::new(0.9848078f32, 0.1736482f32, 0f32, 0f32);
    /// let q2 = UnitQuaternion::from_quaternion(q2);
    /// qa.add_quaternion(&q1);
    /// qa.add_quaternion(&q2);
    /// let qavg = qa.calc_average();
    /// println!("The average of {} and {} is {}", q1, q2, qavg);
    /// ```
    pub fn calc_average(&self) -> UnitQuaternion<T> {
        let m = self.matrix / self.weight_sum;
        let decomp = SymmetricEigen::new(m);
        let i = decomp.eigenvalues.imax();
        let q = decomp.eigenvectors.column(i);
        let q = Quaternion::new(q[3], q[0], q[1], q[2]);

        UnitQuaternion::from_quaternion(q)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use approx::*;

    #[test]
    fn avg2_32() {
        let mut avg = QuaternionAverager::new();
        let q1 = Quaternion::new(0.9961947f32, 0.0871557f32, 0f32, 0f32);
        let q1 = UnitQuaternion::from_quaternion(q1);
        let q2 = Quaternion::new(0.9848078f32, 0.1736482f32, 0f32, 0f32);
        let q2 = UnitQuaternion::from_quaternion(q2);
        avg.add_quaternion(&q1);
        avg.add_quaternion(&q2);

        let qr = Quaternion::new(0.9914449f32, 0.1305262f32, 0f32, 0f32);
        let qr = UnitQuaternion::from_quaternion(qr);
        let q = avg.calc_average();

        assert_relative_eq!(q, qr, max_relative = 0.00001);
    }

    #[test]
    fn avg2_64() {
        let mut avg = QuaternionAverager::new();
        let q1 = Quaternion::new(0.9961947f64, 0.0871557f64, 0f64, 0f64);
        let q1 = UnitQuaternion::from_quaternion(q1);
        let q2 = Quaternion::new(0.9848078f64, 0.1736482f64, 0f64, 0f64);
        let q2 = UnitQuaternion::from_quaternion(q2);
        avg.add_quaternion(&q1);
        avg.add_quaternion(&q2);

        let qr = Quaternion::new(0.9914449f64, 0.1305262f64, 0f64, 0f64);
        let qr = UnitQuaternion::from_quaternion(qr);
        let q = avg.calc_average();

        assert_relative_eq!(q, qr, max_relative = 0.000001);
    }
}