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use super::*;
impl<T: Copy> mat3<T> {
/// Get transposed matrix.
///
/// # Examples
/// ```
/// # use batbox_la::*;
/// let matrix = mat3::translate(vec2(1, 2));
/// let matrix_transposed = matrix.transpose();
/// for i in 0..3 {
/// for j in 0..3 {
/// assert_eq!(matrix[(i, j)], matrix_transposed[(j, i)]);
/// }
/// }
/// ```
pub fn transpose(self) -> Self {
let mut result = self;
for i in 0..3 {
for j in 0..3 {
result[(i, j)] = self[(j, i)];
}
}
result
}
}
impl<T: Num> mat3<T> {
/// Construct a transformation matrix with given orts
///
/// # Examples
/// ```
/// # use batbox_la::*;
/// let e1 = vec2(1.0, 2.0);
/// let e2 = vec2(3.0, 4.0);
/// let m = mat3::from_orts(e1, e2);
/// assert_eq!(vec2(1.0, 0.0).transform(m), e1);
/// assert_eq!(vec2(0.0, 1.0).transform(m), e2);
/// let v = vec2(2.0, 3.0);
/// assert_eq!(v.transform(m), e1 * v.x + e2 * v.y);
/// ```
pub fn from_orts(x: vec2<T>, y: vec2<T>) -> Self {
mat3::new([
[x.x, y.x, T::ZERO],
[x.y, y.y, T::ZERO],
[T::ZERO, T::ZERO, T::ONE],
])
}
/// Extend this into a 3d transformation matrix, leaving z coordinate as is
pub fn extend3d(self) -> mat4<T> {
let Self([[a00, a01, a02], [a10, a11, a12], [a20, a21, a22]]) = self;
mat4([
[a00, a01, T::ZERO, a02],
[a10, a11, T::ZERO, a12],
[T::ZERO, T::ZERO, T::ONE, T::ZERO],
[a20, a21, T::ZERO, a22],
])
}
}
impl<T: Float> mat3<T> {
/// Get inverse matrix.
///
/// # Examples
/// ```
/// # use batbox_la::*;
/// let matrix = mat3::<f64>::rotate(Angle::from_radians(0.123));
/// let matrix_inv = matrix.inverse();
/// let mult = matrix * matrix_inv;
/// for i in 0..3 {
/// for j in 0..3 {
/// assert!((mult[(i, j)] - if i == j { 1.0 } else { 0.0 }).abs() < 1e-5);
/// }
/// }
/// ```
pub fn inverse(self) -> Self {
let b01 = self[(2, 2)] * self[(1, 1)] - self[(2, 1)] * self[(1, 2)];
let b11 = -self[(2, 2)] * self[(0, 1)] + self[(2, 1)] * self[(0, 2)];
let b21 = self[(1, 2)] * self[(0, 1)] - self[(1, 1)] * self[(0, 2)];
let det = self[(0, 0)] * b01 + self[(1, 0)] * b11 + self[(2, 0)] * b21;
if det == T::ZERO {
Self::identity()
} else {
mat3::new([
[b01, b11, b21],
[
-self[(2, 2)] * self[(1, 0)] + self[(2, 0)] * self[(1, 2)],
self[(2, 2)] * self[(0, 0)] - self[(2, 0)] * self[(0, 2)],
-self[(1, 2)] * self[(0, 0)] + self[(1, 0)] * self[(0, 2)],
],
[
self[(2, 1)] * self[(1, 0)] - self[(2, 0)] * self[(1, 1)],
-self[(2, 1)] * self[(0, 0)] + self[(2, 0)] * self[(0, 1)],
self[(1, 1)] * self[(0, 0)] - self[(1, 0)] * self[(0, 1)],
],
]) / det
}
}
}
#[test]
fn test_mat_inverse_random() {
fn check(m: mat3<f64>) {
let m_inv = m.inverse();
let mul = m * m_inv;
assert!(mul.approx_eq(&mat3::identity()));
}
// Random generated test cases
check(mat3::new([
[8.7, 3.6, 6.5],
[7.4, 5.8, 8.6],
[1.8, 8.3, 6.6],
]));
check(mat3::new([
[9.6, 0.6, 5.4],
[0.5, 0.1, 5.4],
[2.0, 3.8, 0.0],
]));
check(mat3::new([
[6.1, 1.7, 2.7],
[1.8, 2.5, 7.8],
[2.6, 9.5, 1.5],
]));
check(mat3::new([
[8.4, 1.0, 6.4],
[1.6, 1.1, 1.5],
[5.5, 1.2, 0.6],
]));
check(mat3::new([
[0.6, 5.7, 0.2],
[3.5, 1.7, 6.4],
[2.0, 3.4, 4.1],
]));
check(mat3::new([
[1.9, 1.4, 4.0],
[7.8, 8.2, 9.1],
[3.2, 4.4, 3.9],
]));
check(mat3::new([
[6.0, 7.0, 4.0],
[0.9, 8.7, 6.2],
[0.2, 4.6, 3.7],
]));
check(mat3::new([
[5.1, 9.6, 4.6],
[1.5, 9.2, 2.3],
[5.6, 7.6, 0.4],
]));
check(mat3::new([
[3.0, 5.7, 8.6],
[6.2, 7.2, 0.1],
[5.3, 5.9, 5.8],
]));
check(mat3::new([
[4.3, 8.4, 2.0],
[2.3, 9.0, 4.6],
[5.5, 1.2, 8.8],
]));
}