nalgebra/tests/geometry/rotation.rs
2017-08-15 19:36:38 +02:00

190 lines
5.8 KiB
Rust

use std::f64;
use alga::general::Real;
use na::{self, Vector2, Vector3, Rotation2, Rotation3, Unit};
#[test]
fn angle_2() {
let a = Vector2::new(4.0, 0.0);
let b = Vector2::new(9.0, 0.0);
assert_eq!(a.angle(&b), 0.0);
}
#[test]
fn angle_3() {
let a = Vector3::new(4.0, 0.0, 0.5);
let b = Vector3::new(8.0, 0.0, 1.0);
assert_eq!(a.angle(&b), 0.0);
}
quickcheck!(
/*
*
* Euler angles.
*
*/
fn from_euler_angles(r: f64, p: f64, y: f64) -> bool {
let roll = Rotation3::from_euler_angles(r, 0.0, 0.0);
let pitch = Rotation3::from_euler_angles(0.0, p, 0.0);
let yaw = Rotation3::from_euler_angles(0.0, 0.0, y);
let rpy = Rotation3::from_euler_angles(r, p, y);
roll[(0, 0)] == 1.0 && // rotation wrt. x axis.
pitch[(1, 1)] == 1.0 && // rotation wrt. y axis.
yaw[(2, 2)] == 1.0 && // rotation wrt. z axis.
yaw * pitch * roll == rpy
}
/*
*
* Inversion is transposition.
*
*/
fn rotation_inv_3(a: Rotation3<f64>) -> bool {
let ta = a.transpose();
let ia = a.inverse();
ta == ia &&
relative_eq!(&ta * &a, Rotation3::identity(), epsilon = 1.0e-7) &&
relative_eq!(&ia * a, Rotation3::identity(), epsilon = 1.0e-7) &&
relative_eq!( a * &ta, Rotation3::identity(), epsilon = 1.0e-7) &&
relative_eq!( a * ia, Rotation3::identity(), epsilon = 1.0e-7)
}
fn rotation_inv_2(a: Rotation2<f64>) -> bool {
let ta = a.transpose();
let ia = a.inverse();
ta == ia &&
relative_eq!(&ta * &a, Rotation2::identity(), epsilon = 1.0e-7) &&
relative_eq!(&ia * a, Rotation2::identity(), epsilon = 1.0e-7) &&
relative_eq!( a * &ta, Rotation2::identity(), epsilon = 1.0e-7) &&
relative_eq!( a * ia, Rotation2::identity(), epsilon = 1.0e-7)
}
/*
*
* Angle between vectors.
*
*/
fn angle_is_commutative_2(a: Vector2<f64>, b: Vector2<f64>) -> bool {
a.angle(&b) == b.angle(&a)
}
fn angle_is_commutative_3(a: Vector3<f64>, b: Vector3<f64>) -> bool {
a.angle(&b) == b.angle(&a)
}
/*
*
* Rotation matrix between vectors.
*
*/
fn rotation_between_is_anticommutative_2(a: Vector2<f64>, b: Vector2<f64>) -> bool {
let rab = Rotation2::rotation_between(&a, &b);
let rba = Rotation2::rotation_between(&b, &a);
relative_eq!(rab * rba, Rotation2::identity())
}
fn rotation_between_is_anticommutative_3(a: Vector3<f64>, b: Vector3<f64>) -> bool {
let rots = (Rotation3::rotation_between(&a, &b), Rotation3::rotation_between(&b, &a));
if let (Some(rab), Some(rba)) = rots {
relative_eq!(rab * rba, Rotation3::identity(), epsilon = 1.0e-7)
}
else {
true
}
}
fn rotation_between_is_identity(v2: Vector2<f64>, v3: Vector3<f64>) -> bool {
let vv2 = 3.42 * v2;
let vv3 = 4.23 * v3;
relative_eq!(v2.angle(&vv2), 0.0, epsilon = 1.0e-7) &&
relative_eq!(v3.angle(&vv3), 0.0, epsilon = 1.0e-7) &&
relative_eq!(Rotation2::rotation_between(&v2, &vv2), Rotation2::identity()) &&
Rotation3::rotation_between(&v3, &vv3).unwrap() == Rotation3::identity()
}
fn rotation_between_2(a: Vector2<f64>, b: Vector2<f64>) -> bool {
if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) {
let r = Rotation2::rotation_between(&a, &b);
relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7)
}
else {
true
}
}
fn rotation_between_3(a: Vector3<f64>, b: Vector3<f64>) -> bool {
if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) {
let r = Rotation3::rotation_between(&a, &b).unwrap();
relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7)
}
else {
true
}
}
/*
*
* Rotation construction.
*
*/
fn new_rotation_2(angle: f64) -> bool {
let r = Rotation2::new(angle);
let angle = na::wrap(angle, -f64::pi(), f64::pi());
relative_eq!(r.angle(), angle, epsilon = 1.0e-7)
}
fn new_rotation_3(axisangle: Vector3<f64>) -> bool {
let r = Rotation3::new(axisangle);
if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) {
let angle = na::wrap(angle, -f64::pi(), f64::pi());
(relative_eq!(r.angle(), angle, epsilon = 1.0e-7) &&
relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) ||
(relative_eq!(r.angle(), -angle, epsilon = 1.0e-7) &&
relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7))
}
else {
r == Rotation3::identity()
}
}
/*
*
* Rotation pow.
*
*/
fn powf_rotation_2(angle: f64, pow: f64) -> bool {
let r = Rotation2::new(angle).powf(pow);
let angle = na::wrap(angle, -f64::pi(), f64::pi());
let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi());
relative_eq!(r.angle(), pangle, epsilon = 1.0e-7)
}
fn powf_rotation_3(axisangle: Vector3<f64>, pow: f64) -> bool {
let r = Rotation3::new(axisangle).powf(pow);
if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) {
let angle = na::wrap(angle, -f64::pi(), f64::pi());
let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi());
(relative_eq!(r.angle(), pangle, epsilon = 1.0e-7) &&
relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) ||
(relative_eq!(r.angle(), -pangle, epsilon = 1.0e-7) &&
relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7))
}
else {
r == Rotation3::identity()
}
}
);