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use crate::CoordinateType;
#[derive(Clone, Hash, PartialEq, Eq, Debug)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
pub struct Matrix3d<T: CoordinateType> {
pub m11: T,
pub m12: T,
pub m13: T,
pub m21: T,
pub m22: T,
pub m23: T,
pub m31: T,
pub m32: T,
pub m33: T,
}
impl<T> Matrix3d<T>
where T: CoordinateType
{
pub fn new(m11: T, m12: T, m13: T, m21: T, m22: T, m23: T, m31: T, m32: T, m33: T) -> Self {
Matrix3d {
m11,
m12,
m13,
m21,
m22,
m23,
m31,
m32,
m33,
}
}
pub fn identity() -> Self {
let _0 = T::zero();
let _1 = T::one();
Self::new(_1, _0, _0,
_0, _1, _0,
_0, _0, _1)
}
pub fn mul_scalar(&self, rhs: T) -> Self {
Matrix3d::new(
self.m11 * rhs, self.m12 * rhs, self.m13 * rhs,
self.m21 * rhs, self.m22 * rhs, self.m23 * rhs,
self.m31 * rhs, self.m32 * rhs, self.m33 * rhs,
)
}
pub fn add(&self, rhs: &Self) -> Self {
Matrix3d::new(
self.m11 + rhs.m11, self.m12 + rhs.m12, self.m13 + rhs.m13,
self.m21 + rhs.m21, self.m22 + rhs.m22, self.m23 + rhs.m23,
self.m31 + rhs.m31, self.m32 + rhs.m32, self.m33 + rhs.m33,
)
}
pub fn mul_column_vector(&self, rhs: &(T, T, T)) -> (T, T, T) {
(
self.m11 * rhs.0 + self.m12 * rhs.1 + self.m13 * rhs.2,
self.m21 * rhs.0 + self.m22 * rhs.1 + self.m23 * rhs.2,
self.m31 * rhs.0 + self.m32 * rhs.1 + self.m33 * rhs.2,
)
}
pub fn mul_matrix(&self, rhs: &Self) -> Self {
let a = self;
let b = rhs;
let c11 = a.m11 * b.m11 + a.m12 * b.m21 + a.m13 * b.m31;
let c12 = a.m11 * b.m12 + a.m12 * b.m22 + a.m13 * b.m32;
let c13 = a.m11 * b.m13 + a.m12 * b.m23 + a.m13 * b.m33;
let c21 = a.m21 * b.m11 + a.m22 * b.m21 + a.m23 * b.m31;
let c22 = a.m21 * b.m12 + a.m22 * b.m22 + a.m23 * b.m32;
let c23 = a.m21 * b.m13 + a.m22 * b.m23 + a.m23 * b.m33;
let c31 = a.m31 * b.m11 + a.m32 * b.m21 + a.m33 * b.m31;
let c32 = a.m31 * b.m12 + a.m32 * b.m22 + a.m33 * b.m32;
let c33 = a.m31 * b.m13 + a.m32 * b.m23 + a.m33 * b.m33;
Self::new(
c11, c12, c13,
c21, c22, c23,
c31, c32, c33,
)
}
pub fn transpose(&self) -> Self {
Self::new(
self.m11, self.m21, self.m31,
self.m12, self.m22, self.m32,
self.m13, self.m23, self.m33,
)
}
pub fn is_identity(&self) -> bool {
self == &Self::identity()
}
pub fn is_unitary(&self) -> bool {
self.mul_matrix(&self.transpose()).is_identity()
}
pub fn determinant(&self) -> T {
let a = self;
a.m11 * a.m22 * a.m33 - a.m11 * a.m23 * a.m32 - a.m12 * a.m21 * a.m33
+ a.m12 * a.m23 * a.m31 + a.m13 * a.m21 * a.m32 - a.m13 * a.m22 * a.m31
}
pub fn try_inverse(&self) -> Option<Self> {
let a = self;
let det = a.determinant();
if !det.is_zero() {
Some(Self::new(
(a.m22 * a.m33 - a.m23 * a.m32) / det, (a.m13 * a.m32 - a.m12 * a.m33) / det, (a.m12 * a.m23 - a.m13 * a.m22) / det,
(a.m23 * a.m31 - a.m21 * a.m33) / det, (a.m11 * a.m33 - a.m13 * a.m31) / det, (a.m13 * a.m21 - a.m11 * a.m23) / det,
(a.m21 * a.m32 - a.m22 * a.m31) / det, (a.m12 * a.m31 - a.m11 * a.m32) / det, (a.m11 * a.m22 - a.m12 * a.m21) / det,
))
} else {
None
}
}
}
impl<T: CoordinateType> Default for Matrix3d<T> {
fn default() -> Self {
Self::identity()
}
}
#[test]
fn test_matrix_multiplication() {
let id: Matrix3d<i32> = Matrix3d::identity();
assert_eq!(id.mul_matrix(&id), id);
}
#[test]
fn test_mul_column_vector() {
let id: Matrix3d<i32> = Matrix3d::identity();
let v = (1, 2, 3);
assert_eq!(id.mul_column_vector(&v), v);
}
#[test]
fn test_inverse() {
let m = Matrix3d::new(1.0, 4.0, 2.0,
1.0, 2.0, 4.0,
2.0, 0.0, 4.0);
let i = m.try_inverse().unwrap();
assert_eq!(m.mul_matrix(&i), Matrix3d::identity());
assert_eq!(i.mul_matrix(&m), Matrix3d::identity());
}