cgmath/tests/matrix.rs

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// Copyright 2013-2014 The CGMath Developers. For a full listing of the authors,
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// refer to the Cargo.toml file at the top-level directory of this distribution.
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//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
extern crate approx;
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extern crate cgmath;
pub mod matrix2 {
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use std::f64;
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use cgmath::*;
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const A: Matrix2<f64> = Matrix2 {
x: Vector2 {
x: 1.0f64,
y: 3.0f64,
},
y: Vector2 {
x: 2.0f64,
y: 4.0f64,
},
};
const B: Matrix2<f64> = Matrix2 {
x: Vector2 {
x: 2.0f64,
y: 4.0f64,
},
y: Vector2 {
x: 3.0f64,
y: 5.0f64,
},
};
const C: Matrix2<f64> = Matrix2 {
x: Vector2 {
x: 2.0f64,
y: 1.0f64,
},
y: Vector2 {
x: 1.0f64,
y: 2.0f64,
},
};
const V: Vector2<f64> = Vector2 {
x: 1.0f64,
y: 2.0f64,
};
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const F: f64 = 0.5;
#[test]
fn test_neg() {
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assert_eq!(-A, Matrix2::new(-1.0f64, -3.0f64, -2.0f64, -4.0f64));
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}
#[test]
fn test_mul_scalar() {
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let result = Matrix2::new(0.5f64, 1.5f64, 1.0f64, 2.0f64);
assert_eq!(A * F, result);
assert_eq!(F * A, result);
}
#[test]
fn test_div_scalar() {
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assert_eq!(A / F, Matrix2::new(2.0f64, 6.0f64, 4.0f64, 8.0f64));
assert_eq!(4.0f64 / C, Matrix2::new(2.0f64, 4.0f64, 4.0f64, 2.0f64));
}
#[test]
fn test_rem_scalar() {
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assert_eq!(A % 3.0f64, Matrix2::new(1.0f64, 0.0f64, 2.0f64, 1.0f64));
assert_eq!(3.0f64 % A, Matrix2::new(0.0f64, 0.0f64, 1.0f64, 3.0f64));
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}
#[test]
fn test_add_matrix() {
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assert_eq!(A + B, Matrix2::new(3.0f64, 7.0f64, 5.0f64, 9.0f64));
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}
#[test]
fn test_sub_matrix() {
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assert_eq!(A - B, Matrix2::new(-1.0f64, -1.0f64, -1.0f64, -1.0f64));
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}
#[test]
fn test_mul_vector() {
assert_eq!(A * V, Vector2::new(5.0f64, 11.0f64));
}
#[test]
fn test_mul_matrix() {
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assert_eq!(A * B, Matrix2::new(10.0f64, 22.0f64, 13.0f64, 29.0f64));
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assert_eq!(A * B, &A * &B);
}
#[test]
fn test_sum_matrix() {
assert_eq!(A + B + C, [A, B, C].iter().sum());
assert_eq!(A + B + C, [A, B, C].iter().cloned().sum());
}
#[test]
fn test_product_matrix() {
assert_eq!(A * B * C, [A, B, C].iter().product());
assert_eq!(A * B * C, [A, B, C].iter().cloned().product());
}
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#[test]
fn test_determinant() {
assert_eq!(A.determinant(), -2.0f64)
}
#[test]
fn test_trace() {
assert_eq!(A.trace(), 5.0f64);
}
#[test]
fn test_transpose() {
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assert_eq!(
A.transpose(),
Matrix2::<f64>::new(1.0f64, 2.0f64, 3.0f64, 4.0f64)
);
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}
#[test]
fn test_transpose_self() {
let mut mut_a = A;
mut_a.transpose_self();
assert_eq!(mut_a, A.transpose());
}
#[test]
fn test_invert() {
assert!(Matrix2::<f64>::identity().invert().unwrap().is_identity());
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assert_eq!(
A.invert().unwrap(),
Matrix2::new(-2.0f64, 1.5f64, 1.0f64, -0.5f64)
);
assert!(Matrix2::new(0.0f64, 2.0f64, 0.0f64, 5.0f64)
.invert()
.is_none());
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}
#[test]
fn test_predicates() {
assert!(Matrix2::<f64>::identity().is_identity());
assert!(Matrix2::<f64>::identity().is_symmetric());
assert!(Matrix2::<f64>::identity().is_diagonal());
assert!(Matrix2::<f64>::identity().is_invertible());
assert!(!A.is_identity());
assert!(!A.is_symmetric());
assert!(!A.is_diagonal());
assert!(A.is_invertible());
assert!(!C.is_identity());
assert!(C.is_symmetric());
assert!(!C.is_diagonal());
assert!(C.is_invertible());
assert!(Matrix2::from_value(6.0f64).is_diagonal());
}
#[test]
fn test_from_angle() {
// Rotate the vector (1, 0) by π/2 radians to the vector (0, 1)
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let rot1 = Matrix2::from_angle(Rad(0.5f64 * f64::consts::PI));
assert_ulps_eq!(rot1 * Vector2::unit_x(), &Vector2::unit_y());
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// Rotate the vector (-1, 0) by -π/2 radians to the vector (0, 1)
let rot2 = -rot1;
assert_ulps_eq!(rot2 * -Vector2::unit_x(), &Vector2::unit_y());
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// Rotate the vector (1, 1) by π radians to the vector (-1, -1)
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let rot3: Matrix2<f64> = Matrix2::from_angle(Rad(f64::consts::PI));
assert_ulps_eq!(rot3 * Vector2::new(1.0, 1.0), &Vector2::new(-1.0, -1.0));
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}
#[test]
fn test_look_at() {
// rot should rotate unit_x() to look at the input vector
let rot = Matrix2::look_at(V, Vector2::unit_y());
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assert_eq!(rot * Vector2::unit_x(), V.normalize());
let new_up = Vector2::new(-V.y, V.x).normalize();
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assert_eq!(rot * Vector2::unit_y(), new_up);
let rot_down = Matrix2::look_at(V, -1.0 * Vector2::unit_y());
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assert_eq!(rot_down * Vector2::unit_x(), V.normalize());
assert_eq!(rot_down * Vector2::unit_y(), -1.0 * new_up);
let rot2 = Matrix2::look_at(-V, Vector2::unit_y());
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assert_eq!(rot2 * Vector2::unit_x(), (-V).normalize());
}
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}
pub mod matrix3 {
use cgmath::*;
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const A: Matrix3<f64> = Matrix3 {
x: Vector3 {
x: 1.0f64,
y: 4.0f64,
z: 7.0f64,
},
y: Vector3 {
x: 2.0f64,
y: 5.0f64,
z: 8.0f64,
},
z: Vector3 {
x: 3.0f64,
y: 6.0f64,
z: 9.0f64,
},
};
const B: Matrix3<f64> = Matrix3 {
x: Vector3 {
x: 2.0f64,
y: 5.0f64,
z: 8.0f64,
},
y: Vector3 {
x: 3.0f64,
y: 6.0f64,
z: 9.0f64,
},
z: Vector3 {
x: 4.0f64,
y: 7.0f64,
z: 10.0f64,
},
};
const C: Matrix3<f64> = Matrix3 {
x: Vector3 {
x: 2.0f64,
y: 4.0f64,
z: 6.0f64,
},
y: Vector3 {
x: 0.0f64,
y: 2.0f64,
z: 4.0f64,
},
z: Vector3 {
x: 0.0f64,
y: 0.0f64,
z: 1.0f64,
},
};
const D: Matrix3<f64> = Matrix3 {
x: Vector3 {
x: 3.0f64,
y: 2.0f64,
z: 1.0f64,
},
y: Vector3 {
x: 2.0f64,
y: 3.0f64,
z: 2.0f64,
},
z: Vector3 {
x: 1.0f64,
y: 2.0f64,
z: 3.0f64,
},
};
const V: Vector3<f64> = Vector3 {
x: 1.0f64,
y: 2.0f64,
z: 3.0f64,
};
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const F: f64 = 0.5;
#[test]
fn test_neg() {
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assert_eq!(
-A,
Matrix3::new(
-1.0f64, -4.0f64, -7.0f64, -2.0f64, -5.0f64, -8.0f64, -3.0f64, -6.0f64, -9.0f64
)
);
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}
#[test]
fn test_mul_scalar() {
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let result = Matrix3::new(
0.5f64, 2.0f64, 3.5f64, 1.0f64, 2.5f64, 4.0f64, 1.5f64, 3.0f64, 4.5f64,
);
assert_eq!(A * F, result);
assert_eq!(F * A, result);
}
#[test]
fn test_div_scalar() {
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assert_eq!(
A / F,
Matrix3::new(
2.0f64, 8.0f64, 14.0f64, 4.0f64, 10.0f64, 16.0f64, 6.0f64, 12.0f64, 18.0f64
)
);
assert_eq!(
6.0f64 / D,
Matrix3::new(2.0f64, 3.0f64, 6.0f64, 3.0f64, 2.0f64, 3.0f64, 6.0f64, 3.0f64, 2.0f64)
);
}
#[test]
fn test_rem_scalar() {
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assert_eq!(
A % 3.0f64,
Matrix3::new(1.0f64, 1.0f64, 1.0f64, 2.0f64, 2.0f64, 2.0f64, 0.0f64, 0.0f64, 0.0f64)
);
assert_eq!(
9.0f64 % A,
Matrix3::new(0.0f64, 1.0f64, 2.0f64, 1.0f64, 4.0f64, 1.0f64, 0.0f64, 3.0f64, 0.0f64)
);
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}
#[test]
fn test_add_matrix() {
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assert_eq!(
A + B,
Matrix3::new(
3.0f64, 9.0f64, 15.0f64, 5.0f64, 11.0f64, 17.0f64, 7.0f64, 13.0f64, 19.0f64
)
);
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}
#[test]
fn test_sub_matrix() {
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assert_eq!(
A - B,
Matrix3::new(
-1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64
)
);
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}
#[test]
fn test_mul_vector() {
assert_eq!(A * V, Vector3::new(14.0f64, 32.0f64, 50.0f64));
}
#[test]
fn test_mul_matrix() {
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assert_eq!(
A * B,
Matrix3::new(
36.0f64, 81.0f64, 126.0f64, 42.0f64, 96.0f64, 150.0f64, 48.0f64, 111.0f64, 174.0f64
)
);
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assert_eq!(A * B, &A * &B);
}
#[test]
fn test_sum_matrix() {
assert_eq!(A + B + C + D, [A, B, C, D].iter().sum());
assert_eq!(A + B + C + D, [A, B, C, D].iter().cloned().sum());
}
#[test]
fn test_product_matrix() {
assert_eq!(A * B * C * D, [A, B, C, D].iter().product());
assert_eq!(A * B * C * D, [A, B, C, D].iter().cloned().product());
}
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#[test]
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fn test_determinant() {
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assert_eq!(A.determinant(), 0.0f64);
}
#[test]
fn test_trace() {
assert_eq!(A.trace(), 15.0f64);
}
#[test]
fn test_transpose() {
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assert_eq!(
A.transpose(),
Matrix3::<f64>::new(
1.0f64, 2.0f64, 3.0f64, 4.0f64, 5.0f64, 6.0f64, 7.0f64, 8.0f64, 9.0f64
)
);
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}
#[test]
fn test_transpose_self() {
let mut mut_a = A;
mut_a.transpose_self();
assert_eq!(mut_a, A.transpose());
}
#[test]
fn test_invert() {
assert!(Matrix3::<f64>::identity().invert().unwrap().is_identity());
assert_eq!(A.invert(), None);
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assert_eq!(
C.invert().unwrap(),
Matrix3::new(0.5f64, -1.0f64, 1.0f64, 0.0f64, 0.5f64, -2.0f64, 0.0f64, 0.0f64, 1.0f64)
);
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}
#[test]
fn test_predicates() {
assert!(Matrix3::<f64>::identity().is_identity());
assert!(Matrix3::<f64>::identity().is_symmetric());
assert!(Matrix3::<f64>::identity().is_diagonal());
assert!(Matrix3::<f64>::identity().is_invertible());
assert!(!A.is_identity());
assert!(!A.is_symmetric());
assert!(!A.is_diagonal());
assert!(!A.is_invertible());
assert!(!D.is_identity());
assert!(D.is_symmetric());
assert!(!D.is_diagonal());
assert!(D.is_invertible());
assert!(Matrix3::from_value(6.0f64).is_diagonal());
}
#[test]
fn test_from_translation() {
let mat = Matrix3::from_translation(Vector2::new(1.0f64, 2.0f64));
let vertex = Vector3::new(0.0f64, 0.0f64, 1.0f64);
let res = mat * vertex;
assert_eq!(res, Vector3::new(1., 2., 1.));
}
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mod from_axis_x {
use cgmath::*;
fn check_from_axis_angle_x(pitch: Rad<f32>) {
let found = Matrix3::from_angle_x(pitch);
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let expected = Matrix3::from(Euler {
x: pitch,
y: Rad(0.0),
z: Rad(0.0),
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_x(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_x(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_x(Rad(-1.0));
}
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}
mod from_axis_y {
use cgmath::*;
fn check_from_axis_angle_y(yaw: Rad<f32>) {
let found = Matrix3::from_angle_y(yaw);
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let expected = Matrix3::from(Euler {
x: Rad(0.0),
y: yaw,
z: Rad(0.0),
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_y(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_y(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_y(Rad(-1.0));
}
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}
mod from_axis_z {
use cgmath::*;
fn check_from_axis_angle_z(roll: Rad<f32>) {
let found = Matrix3::from_angle_z(roll);
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let expected = Matrix3::from(Euler {
x: Rad(0.0),
y: Rad(0.0),
z: roll,
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_z(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_z(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_z(Rad(-1.0));
}
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}
mod from_axis_angle {
mod axis_x {
use cgmath::*;
fn check_from_axis_angle_x(pitch: Rad<f32>) {
let found = Matrix3::from_axis_angle(Vector3::unit_x(), pitch);
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let expected = Matrix3::from(Euler {
x: pitch,
y: Rad(0.0),
z: Rad(0.0),
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_x(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_x(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_x(Rad(-1.0));
}
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}
mod axis_y {
use cgmath::*;
fn check_from_axis_angle_y(yaw: Rad<f32>) {
let found = Matrix3::from_axis_angle(Vector3::unit_y(), yaw);
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let expected = Matrix3::from(Euler {
x: Rad(0.0),
y: yaw,
z: Rad(0.0),
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_y(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_y(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_y(Rad(-1.0));
}
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}
mod axis_z {
use cgmath::*;
fn check_from_axis_angle_z(roll: Rad<f32>) {
let found = Matrix3::from_axis_angle(Vector3::unit_z(), roll);
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let expected = Matrix3::from(Euler {
x: Rad(0.0),
y: Rad(0.0),
z: roll,
});
assert_relative_eq!(found, expected, epsilon = 0.001);
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}
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#[test]
fn test_zero() {
check_from_axis_angle_z(Rad(0.0));
}
#[test]
fn test_pos_1() {
check_from_axis_angle_z(Rad(1.0));
}
#[test]
fn test_neg_1() {
check_from_axis_angle_z(Rad(-1.0));
}
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}
}
mod rotate_from_euler {
use cgmath::*;
#[test]
fn test_x() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from(Euler::new(Deg(90.0), Deg(0.0), Deg(0.0)));
assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);
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let rot = Matrix3::from(Euler::new(Deg(-90.0), Deg(0.0), Deg(0.0)));
assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);
}
#[test]
fn test_y() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(90.0), Deg(0.0)));
assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);
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let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(-90.0), Deg(0.0)));
assert_ulps_eq!(vec3(-1.0, 0.0, 0.0), rot * vec);
}
#[test]
fn test_z() {
let vec = vec3(1.0, 0.0, 0.0);
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let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(0.0), Deg(90.0)));
assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);
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let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(0.0), Deg(-90.0)));
assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);
}
// tests that the Y rotation is done after the X
#[test]
fn test_x_then_y() {
let vec = vec3(0.0, 1.0, 0.0);
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let rot = Matrix3::from(Euler::new(Deg(90.0), Deg(90.0), Deg(0.0)));
assert_ulps_eq!(vec3(0.0, 0.0, 1.0), rot * vec);
}
// tests that the Z rotation is done after the Y
#[test]
fn test_y_then_z() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from(Euler::new(Deg(0.0), Deg(90.0), Deg(90.0)));
assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);
}
}
mod rotate_from_axis_angle {
use cgmath::*;
#[test]
fn test_x() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from_angle_x(Deg(90.0));
println!("x mat: {:?}", rot);
assert_ulps_eq!(vec3(0.0, -1.0, 0.0), rot * vec);
}
#[test]
fn test_y() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from_angle_y(Deg(90.0));
assert_ulps_eq!(vec3(1.0, 0.0, 0.0), rot * vec);
}
#[test]
fn test_z() {
let vec = vec3(1.0, 0.0, 0.0);
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let rot = Matrix3::from_angle_z(Deg(90.0));
assert_ulps_eq!(vec3(0.0, 1.0, 0.0), rot * vec);
}
#[test]
fn test_xy() {
let vec = vec3(0.0, 0.0, 1.0);
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let rot = Matrix3::from_axis_angle(vec3(1.0, 1.0, 0.0).normalize(), Deg(90.0));
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assert_ulps_eq!(
vec3(2.0f32.sqrt() / 2.0, -2.0f32.sqrt() / 2.0, 0.0),
rot * vec
);
}
#[test]
fn test_yz() {
let vec = vec3(1.0, 0.0, 0.0);
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let rot = Matrix3::from_axis_angle(vec3(0.0, 1.0, 1.0).normalize(), Deg(-90.0));
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assert_ulps_eq!(
vec3(0.0, -2.0f32.sqrt() / 2.0, 2.0f32.sqrt() / 2.0),
rot * vec
);
}
#[test]
fn test_xz() {
let vec = vec3(0.0, 1.0, 0.0);
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let rot = Matrix3::from_axis_angle(vec3(1.0, 0.0, 1.0).normalize(), Deg(90.0));
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assert_ulps_eq!(
vec3(-2.0f32.sqrt() / 2.0, 0.0, 2.0f32.sqrt() / 2.0),
rot * vec
);
}
}
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#[test]
fn test_look_to_lh() {
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let dir = Vector3::new(1.0, 2.0, 3.0).normalize();
let up = Vector3::unit_y();
let m = Matrix3::look_to_lh(dir, up);
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assert_ulps_eq!(
m,
Matrix3::from([
[0.9486833, -0.16903085, 0.26726127],
[0.0, 0.8451542, 0.53452253],
[-0.31622776, -0.50709254, 0.8017838_f32]
])
);
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#[allow(deprecated)]
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{
assert_ulps_eq!(m, Matrix3::look_at(dir, up));
}
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}
#[test]
fn test_look_to_rh() {
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let dir = Vector3::new(1.0, 2.0, 3.0).normalize();
let up = Vector3::unit_y();
let m = Matrix3::look_to_rh(dir, up);
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assert_ulps_eq!(
m,
Matrix3::from([
[-0.9486833, -0.16903085, -0.26726127],
[0.0, 0.8451542, -0.53452253],
[0.31622776, -0.50709254, -0.8017838_f32]
])
);
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}
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}
pub mod matrix4 {
use cgmath::*;
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const A: Matrix4<f64> = Matrix4 {
x: Vector4 {
x: 1.0f64,
y: 5.0f64,
z: 9.0f64,
w: 13.0f64,
},
y: Vector4 {
x: 2.0f64,
y: 6.0f64,
z: 10.0f64,
w: 14.0f64,
},
z: Vector4 {
x: 3.0f64,
y: 7.0f64,
z: 11.0f64,
w: 15.0f64,
},
w: Vector4 {
x: 4.0f64,
y: 8.0f64,
z: 12.0f64,
w: 16.0f64,
},
};
const B: Matrix4<f64> = Matrix4 {
x: Vector4 {
x: 2.0f64,
y: 6.0f64,
z: 10.0f64,
w: 14.0f64,
},
y: Vector4 {
x: 3.0f64,
y: 7.0f64,
z: 11.0f64,
w: 15.0f64,
},
z: Vector4 {
x: 4.0f64,
y: 8.0f64,
z: 12.0f64,
w: 16.0f64,
},
w: Vector4 {
x: 5.0f64,
y: 9.0f64,
z: 13.0f64,
w: 17.0f64,
},
};
const C: Matrix4<f64> = Matrix4 {
x: Vector4 {
x: 3.0f64,
y: 2.0f64,
z: 1.0f64,
w: 1.0f64,
},
y: Vector4 {
x: 2.0f64,
y: 3.0f64,
z: 2.0f64,
w: 2.0f64,
},
z: Vector4 {
x: 1.0f64,
y: 2.0f64,
z: 3.0f64,
w: 3.0f64,
},
w: Vector4 {
x: 0.0f64,
y: 1.0f64,
z: 1.0f64,
w: 0.0f64,
},
};
const D: Matrix4<f64> = Matrix4 {
x: Vector4 {
x: 4.0f64,
y: 3.0f64,
z: 2.0f64,
w: 1.0f64,
},
y: Vector4 {
x: 3.0f64,
y: 4.0f64,
z: 3.0f64,
w: 2.0f64,
},
z: Vector4 {
x: 2.0f64,
y: 3.0f64,
z: 4.0f64,
w: 3.0f64,
},
w: Vector4 {
x: 1.0f64,
y: 2.0f64,
z: 3.0f64,
w: 4.0f64,
},
};
const V: Vector4<f64> = Vector4 {
x: 1.0f64,
y: 2.0f64,
z: 3.0f64,
w: 4.0f64,
};
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const F: f64 = 0.5;
#[test]
fn test_neg() {
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assert_eq!(
-A,
Matrix4::new(
-1.0f64, -5.0f64, -9.0f64, -13.0f64, -2.0f64, -6.0f64, -10.0f64, -14.0f64, -3.0f64,
-7.0f64, -11.0f64, -15.0f64, -4.0f64, -8.0f64, -12.0f64, -16.0f64
)
);
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}
#[test]
fn test_mul_scalar() {
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let result = Matrix4::new(
0.5f64, 2.5f64, 4.5f64, 6.5f64, 1.0f64, 3.0f64, 5.0f64, 7.0f64, 1.5f64, 3.5f64, 5.5f64,
7.5f64, 2.0f64, 4.0f64, 6.0f64, 8.0f64,
);
assert_eq!(A * F, result);
assert_eq!(F * A, result);
}
#[test]
fn test_div_scalar() {
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assert_eq!(
A / F,
Matrix4::new(
2.0f64, 10.0f64, 18.0f64, 26.0f64, 4.0f64, 12.0f64, 20.0f64, 28.0f64, 6.0f64,
14.0f64, 22.0f64, 30.0f64, 8.0f64, 16.0f64, 24.0f64, 32.0f64
)
);
assert_eq!(
12.0f64 / D,
Matrix4::new(
3.0f64, 4.0f64, 6.0f64, 12.0f64, 4.0f64, 3.0f64, 4.0f64, 6.0f64, 6.0f64, 4.0f64,
3.0f64, 4.0f64, 12.0f64, 6.0f64, 4.0f64, 3.0f64
)
);
}
#[test]
fn test_rem_scalar() {
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assert_eq!(
A % 4.0f64,
Matrix4::new(
1.0f64, 1.0f64, 1.0f64, 1.0f64, 2.0f64, 2.0f64, 2.0f64, 2.0f64, 3.0f64, 3.0f64,
3.0f64, 3.0f64, 0.0f64, 0.0f64, 0.0f64, 0.0f64
)
);
assert_eq!(
16.0f64 % A,
Matrix4::new(
0.0f64, 1.0f64, 7.0f64, 3.0f64, 0.0f64, 4.0f64, 6.0f64, 2.0f64, 1.0f64, 2.0f64,
5.0f64, 1.0f64, 0.0f64, 0.0f64, 4.0f64, 0.0f64
)
);
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}
#[test]
fn test_add_matrix() {
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assert_eq!(
A + B,
Matrix4::new(
3.0f64, 11.0f64, 19.0f64, 27.0f64, 5.0f64, 13.0f64, 21.0f64, 29.0f64, 7.0f64,
15.0f64, 23.0f64, 31.0f64, 9.0f64, 17.0f64, 25.0f64, 33.0f64
)
);
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}
#[test]
fn test_sub_matrix() {
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assert_eq!(
A - B,
Matrix4::new(
-1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64,
-1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64, -1.0f64
)
);
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}
#[test]
fn test_mul_vector() {
assert_eq!(A * V, Vector4::new(30.0f64, 70.0f64, 110.0f64, 150.0f64));
}
#[test]
fn test_mul_matrix() {
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assert_eq!(
A * B,
Matrix4::new(
100.0f64, 228.0f64, 356.0f64, 484.0f64, 110.0f64, 254.0f64, 398.0f64, 542.0f64,
120.0f64, 280.0f64, 440.0f64, 600.0f64, 130.0f64, 306.0f64, 482.0f64, 658.0f64
)
);
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assert_eq!(A * B, &A * &B);
}
#[test]
fn test_sum_matrix() {
assert_eq!(A + B + C + D, [A, B, C, D].iter().sum());
assert_eq!(A + B + C + D, [A, B, C, D].iter().cloned().sum());
}
#[test]
fn test_product_matrix() {
assert_eq!(A * B * C * D, [A, B, C, D].iter().product());
assert_eq!(A * B * C * D, [A, B, C, D].iter().cloned().product());
}
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#[test]
fn test_determinant() {
assert_eq!(A.determinant(), 0.0f64);
}
#[test]
fn test_trace() {
assert_eq!(A.trace(), 34.0f64);
}
#[test]
fn test_transpose() {
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assert_eq!(
A.transpose(),
Matrix4::<f64>::new(
1.0f64, 2.0f64, 3.0f64, 4.0f64, 5.0f64, 6.0f64, 7.0f64, 8.0f64, 9.0f64, 10.0f64,
11.0f64, 12.0f64, 13.0f64, 14.0f64, 15.0f64, 16.0f64
)
);
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}
#[test]
fn test_transpose_self() {
let mut mut_a = A;
mut_a.transpose_self();
assert_eq!(mut_a, A.transpose());
}
#[test]
fn test_invert() {
assert!(Matrix4::<f64>::identity().invert().unwrap().is_identity());
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assert_ulps_eq!(
&C.invert().unwrap(),
&(Matrix4::new(
5.0f64, -4.0f64, 1.0f64, 0.0f64, -4.0f64, 8.0f64, -4.0f64, 0.0f64, 4.0f64, -8.0f64,
4.0f64, 8.0f64, -3.0f64, 4.0f64, 1.0f64, -8.0f64
) * 0.125f64)
);
let mat_c = Matrix4::new(
-0.131917f64,
-0.76871f64,
0.625846f64,
0.0f64,
-0.,
0.631364f64,
0.775487f64,
0.0f64,
-0.991261f64,
0.1023f64,
-0.083287f64,
0.0f64,
0.,
-1.262728f64,
-1.550973f64,
1.0f64,
);
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assert!((mat_c.invert().unwrap() * mat_c).is_identity());
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let mat_d = Matrix4::new(
0.065455f64,
-0.720002f64,
0.690879f64,
0.0f64,
-0.,
0.692364f64,
0.721549f64,
0.0f64,
-0.997856f64,
-0.047229f64,
0.045318f64,
0.0f64,
0.,
-1.384727f64,
-1.443098f64,
1.0f64,
);
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assert!((mat_d.invert().unwrap() * mat_d).is_identity());
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let mat_e = Matrix4::new(
0.409936f64,
0.683812f64,
-0.603617f64,
0.0f64,
0.,
0.661778f64,
0.7497f64,
0.0f64,
0.912114f64,
-0.307329f64,
0.271286f64,
0.0f64,
-0.,
-1.323555f64,
-1.499401f64,
1.0f64,
);
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assert!((mat_e.invert().unwrap() * mat_e).is_identity());
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let mat_f = Matrix4::new(
-0.160691f64,
-0.772608f64,
0.614211f64,
0.0f64,
-0.,
0.622298f64,
0.78278f64,
0.0f64,
-0.987005f64,
0.125786f64,
-0.099998f64,
0.0f64,
0.,
-1.244597f64,
-1.565561f64,
1.0f64,
);
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assert!((mat_f.invert().unwrap() * mat_f).is_identity());
}
#[test]
fn test_predicates() {
assert!(Matrix4::<f64>::identity().is_identity());
assert!(Matrix4::<f64>::identity().is_symmetric());
assert!(Matrix4::<f64>::identity().is_diagonal());
assert!(Matrix4::<f64>::identity().is_invertible());
assert!(!A.is_identity());
assert!(!A.is_symmetric());
assert!(!A.is_diagonal());
assert!(!A.is_invertible());
assert!(!D.is_identity());
assert!(D.is_symmetric());
assert!(!D.is_diagonal());
assert!(D.is_invertible());
assert!(Matrix4::from_value(6.0f64).is_diagonal());
}
#[test]
fn test_from_translation() {
let mat = Matrix4::from_translation(Vector3::new(1.0f64, 2.0f64, 3.0f64));
let vertex = Vector4::new(0.0f64, 0.0f64, 0.0f64, 1.0f64);
let res = mat * vertex;
assert_eq!(res, Vector4::new(1., 2., 3., 1.));
}
#[test]
fn test_cast() {
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assert_ulps_eq!(
Matrix2::new(0.2f64, 1.5, 4.7, 2.3).cast().unwrap(),
Matrix2::new(0.2f32, 1.5, 4.7, 2.3)
);
assert_ulps_eq!(
Matrix3::new(0.2f64, 1.5, 4.7, 2.3, 5.7, 2.1, 4.6, 5.2, 6.6,)
.cast()
.unwrap(),
Matrix3::new(0.2f32, 1.5, 4.7, 2.3, 5.7, 2.1, 4.6, 5.2, 6.6,)
);
assert_ulps_eq!(
Matrix4::new(
0.2f64, 1.5, 4.7, 2.5, 2.3, 5.7, 2.1, 1.1, 4.6, 5.2, 6.6, 0.2, 3.2, 1.8, 0.4, 2.9,
)
.cast()
.unwrap(),
Matrix4::new(
0.2f32, 1.5, 4.7, 2.5, 2.3, 5.7, 2.1, 1.1, 4.6, 5.2, 6.6, 0.2, 3.2, 1.8, 0.4, 2.9,
)
);
}
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#[test]
fn test_look_to_rh() {
let eye = Point3::new(10.0, 15.0, 20.0);
let dir = Vector3::new(1.0, 2.0, 3.0).normalize();
let up = Vector3::unit_y();
let m = Matrix4::look_to_rh(eye, dir, up);
#[allow(deprecated)]
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{
assert_ulps_eq!(m, Matrix4::look_at_dir(eye, dir, up));
}
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let expected = Matrix4::from([
[-0.9486833, -0.16903086, -0.26726127, 0.0],
[0.0, 0.84515435, -0.53452253, 0.0],
[0.31622776, -0.5070926, -0.8017838, 0.0],
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[3.1622782, -0.84515476, 26.726126, 1.0_f32],
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]);
assert_ulps_eq!(expected, m);
let m = Matrix4::look_at_rh(eye, eye + dir, up);
assert_abs_diff_eq!(expected, m, epsilon = 1.0e-4);
}
#[test]
fn test_look_to_lh() {
let eye = Point3::new(10.0, 15.0, 20.0);
let dir = Vector3::new(1.0, 2.0, 3.0).normalize();
let up = Vector3::unit_y();
let m = Matrix4::look_to_lh(eye, dir, up);
let expected = Matrix4::from([
[0.9486833, -0.16903086, 0.26726127, 0.0],
[0.0, 0.84515435, 0.53452253, 0.0],
[-0.31622776, -0.5070926, 0.8017838, 0.0],
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[-3.1622782, -0.84515476, -26.726126, 1.0_f32],
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]);
assert_ulps_eq!(expected, m);
let m = Matrix4::look_at_lh(eye, eye + dir, up);
assert_abs_diff_eq!(expected, m, epsilon = 1.0e-4);
}
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mod from {
use cgmath::*;
#[test]
fn test_quaternion() {
let quaternion = Quaternion::new(2f32, 3f32, 4f32, 5f32);
let matrix_short = Matrix4::from(quaternion);
let matrix_long = Matrix3::from(quaternion);
let matrix_long = Matrix4::from(matrix_long);
assert_ulps_eq!(matrix_short, matrix_long);
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}
}
}