nalgebra/tests/geometry/quaternion.rs

#![cfg(feature = "arbitrary")]
#![allow(non_snake_case)]

use na::{Point3, Quaternion, Rotation3, Unit, UnitQuaternion, Vector3};

quickcheck!(
    /*
     *
     * Euler angles.
     *
     */
    fn from_euler_angles(r: f64, p: f64, y: f64) -> bool {
        let roll  = UnitQuaternion::from_euler_angles(r, 0.0, 0.0);
        let pitch = UnitQuaternion::from_euler_angles(0.0, p, 0.0);
        let yaw   = UnitQuaternion::from_euler_angles(0.0, 0.0, y);

        let rpy = UnitQuaternion::from_euler_angles(r, p, y);

        let rroll  = roll.to_rotation_matrix();
        let rpitch = pitch.to_rotation_matrix();
        let ryaw   = yaw.to_rotation_matrix();

        relative_eq!(rroll[(0, 0)],  1.0, epsilon = 1.0e-7) && // rotation wrt. x axis.
        relative_eq!(rpitch[(1, 1)], 1.0, epsilon = 1.0e-7) && // rotation wrt. y axis.
        relative_eq!(ryaw[(2, 2)],   1.0, epsilon = 1.0e-7) && // rotation wrt. z axis.
        relative_eq!(yaw * pitch * roll, rpy, epsilon = 1.0e-7)
    }

    fn to_euler_angles(r: f64, p: f64, y: f64) -> bool {
        let rpy = UnitQuaternion::from_euler_angles(r, p, y);
        let (roll, pitch, yaw) = rpy.to_euler_angles();
        relative_eq!(UnitQuaternion::from_euler_angles(roll, pitch, yaw), rpy, epsilon = 1.0e-7)
    }


    /*
     *
     * From/to rotation matrix.
     *
     */
    fn unit_quaternion_rotation_conversion(q: UnitQuaternion<f64>) -> bool {
        let r  = q.to_rotation_matrix();
        let qq = UnitQuaternion::from_rotation_matrix(&r);
        let rr = qq.to_rotation_matrix();

        relative_eq!(q, qq, epsilon = 1.0e-7) &&
        relative_eq!(r, rr, epsilon = 1.0e-7)
    }

    /*
     *
     * Point/Vector transformation.
     *
     */
    fn unit_quaternion_transformation(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
        let r = q.to_rotation_matrix();
        let rv = r * v;
        let rp = r * p;

        relative_eq!( q *  v, rv, epsilon = 1.0e-7) &&
        relative_eq!( q * &v, rv, epsilon = 1.0e-7) &&
        relative_eq!(&q *  v, rv, epsilon = 1.0e-7) &&
        relative_eq!(&q * &v, rv, epsilon = 1.0e-7) &&

        relative_eq!( q *  p, rp, epsilon = 1.0e-7) &&
        relative_eq!( q * &p, rp, epsilon = 1.0e-7) &&
        relative_eq!(&q *  p, rp, epsilon = 1.0e-7) &&
        relative_eq!(&q * &p, rp, epsilon = 1.0e-7)
    }


    /*
     *
     * Inversion.
     *
     */
    fn unit_quaternion_inv(q: UnitQuaternion<f64>) -> bool {
        let iq = q.inverse();
        relative_eq!(&iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!( iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!(&iq *  q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!( iq *  q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&

        relative_eq!(&q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!( q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!(&q *  iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
        relative_eq!( q *  iq, UnitQuaternion::identity(), epsilon = 1.0e-7)
    }

    /*
     *
     * Quaterion * Vector == Rotation * Vector
     *
     */
    fn unit_quaternion_mul_vector(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
        let r = q.to_rotation_matrix();

        relative_eq!(q * v, r * v, epsilon = 1.0e-7) &&
        relative_eq!(q * p, r * p, epsilon = 1.0e-7) &&
        // Equivalence q = -q
        relative_eq!((-q) * v, r * v, epsilon = 1.0e-7) &&
        relative_eq!((-q) * p, r * p, epsilon = 1.0e-7)
    }

    /*
     *
     * Unit quaternion double-covering.
     *
     */
    fn unit_quaternion_double_covering(q: UnitQuaternion<f64>) -> bool {
        let mq = -q;

        mq == q && mq.angle() == q.angle() && mq.axis() == q.axis()
    }

    // Test that all operators (incl. all combinations of references) work.
    // See the top comment on `geometry/quaternion_ops.rs` for details on which operations are
    // supported.
    fn all_op_exist(q: Quaternion<f64>, uq: UnitQuaternion<f64>,
                   v: Vector3<f64>, p: Point3<f64>, r: Rotation3<f64>,
                   s: f64) -> bool {
        let uv = Unit::new_normalize(v);

        let qpq = q + q;
        let qmq = q - q;
        let qMq = q * q;
        let mq  = -q;
        let qMs = q * s;
        let qDs = q / s;
        let sMq = s * q;

        let uqMuq = uq * uq;
        let uqMr  = uq * r;
        let rMuq  = r * uq;
        let uqDuq = uq / uq;
        let uqDr  = uq / r;
        let rDuq  = r / uq;

        let uqMp  = uq * p;
        let uqMv  = uq * v;
        let uqMuv = uq * uv;

        let mut qMs1 = q;

        let mut qMq1 = q;
        let mut qMq2 = q;

        let mut qpq1 = q;
        let mut qpq2 = q;

        let mut qmq1 = q;
        let mut qmq2 = q;

        let mut uqMuq1 = uq;
        let mut uqMuq2 = uq;

        let mut uqMr1 = uq;
        let mut uqMr2 = uq;

        let mut uqDuq1 = uq;
        let mut uqDuq2 = uq;

        let mut uqDr1 = uq;
        let mut uqDr2 = uq;

        qMs1 *= s;

        qMq1 *= q;
        qMq2 *= &q;

        qpq1 += q;
        qpq2 += &q;

        qmq1 -= q;
        qmq2 -= &q;

        uqMuq1 *= uq;
        uqMuq2 *= &uq;

        uqMr1 *= r;
        uqMr2 *= &r;

        uqDuq1 /= uq;
        uqDuq2 /= &uq;

        uqDr1 /= r;
        uqDr2 /= &r;

        qMs1 == qMs  &&

        qMq1 == qMq  &&
        qMq1 == qMq2 &&

        qpq1 == qpq  &&
        qpq1 == qpq2 &&

        qmq1 == qmq  &&
        qmq1 == qmq2 &&

        uqMuq1 == uqMuq  &&
        uqMuq1 == uqMuq2 &&

        uqMr1  == uqMr   &&
        uqMr1  == uqMr2  &&

        uqDuq1 == uqDuq  &&
        uqDuq1 == uqDuq2 &&

        uqDr1  == uqDr   &&
        uqDr1  == uqDr2  &&

        qpq == &q + &q &&
        qpq ==  q + &q &&
        qpq == &q +  q &&

        qmq == &q - &q &&
        qmq ==  q - &q &&
        qmq == &q -  q &&

        qMq == &q * &q &&
        qMq ==  q * &q &&
        qMq == &q *  q &&

        mq == -&q &&

        qMs == &q * s &&
        qDs == &q / s &&
        sMq == s * &q &&

        uqMuq == &uq * &uq &&
        uqMuq ==  uq * &uq &&
        uqMuq == &uq *  uq &&

        uqMr == &uq * &r &&
        uqMr ==  uq * &r &&
        uqMr == &uq *  r &&

        rMuq == &r * &uq &&
        rMuq ==  r * &uq &&
        rMuq == &r *  uq &&

        uqDuq == &uq / &uq &&
        uqDuq ==  uq / &uq &&
        uqDuq == &uq /  uq &&

        uqDr == &uq / &r &&
        uqDr ==  uq / &r &&
        uqDr == &uq /  r &&

        rDuq == &r / &uq &&
        rDuq ==  r / &uq &&
        rDuq == &r /  uq &&

        uqMp == &uq * &p &&
        uqMp ==  uq * &p &&
        uqMp == &uq *  p &&

        uqMv == &uq * &v &&
        uqMv ==  uq * &v &&
        uqMv == &uq *  v &&

        uqMuv == &uq * &uv &&
        uqMuv ==  uq * &uv &&
        uqMuv == &uq *  uv
    }
);