Struct Matrix3 

#[repr(C)]
pub struct Matrix3<T: Scalar> {
    pub col: [Vector3<T>; 3],
}

A 3x3 matrix stored in column-major order.

Commonly used for 2D transformations (with homogeneous coordinates) and 3D rotations.

Layout

[m₀₀ m₀₁ m₀₂]
[m₁₀ m₁₁ m₁₂]
[m₂₀ m₂₁ m₂₂]

Fields

col: [Vector3<T>; 3]

Column vectors of the matrix

Implementations

impl<T: Scalar> Matrix3<T>

pub fn new( m0: T, m1: T, m2: T, m3: T, m4: T, m5: T, m6: T, m7: T, m8: T, ) -> Self

Creates a new 3x3 matrix from column-major elements.

pub fn identity() -> Self

Returns the 3x3 identity matrix.

[1 0 0]
[0 1 0]
[0 0 1]

pub fn determinant(&self) -> T

Computes the determinant of the matrix.

pub fn transpose(&self) -> Self

Returns the transpose of the matrix.

Mᵀ[i,j] = M[j,i]

pub fn inverse(&self) -> Self

Computes the inverse of the matrix.

Uses the adjugate matrix method:

M⁻¹ = (1/det(M)) * adj(M)

Note

Returns NaN or Inf if the matrix is singular (determinant = 0).

pub fn mul_matrix_matrix(l: &Self, r: &Self) -> Self

Multiplies two 3x3 matrices.

Matrix multiplication follows the rule:

C[i,j] = Σₖ A[i,k] * B[k,j]

pub fn mul_matrix_vector(l: &Self, r: &Vector3<T>) -> Vector3<T>

Multiplies a 3x3 matrix by a 3D vector.

Transforms the vector by the matrix:

v' = M * v

pub fn mul_vector_matrix(l: &Vector3<T>, r: &Self) -> Vector3<T>

Multiplies a 3D vector by a 3x3 matrix (row vector).

v' = vᵀ * M

pub fn add_matrix_matrix(l: &Self, r: &Self) -> Self

Adds two matrices element-wise.

C[i,j] = A[i,j] + B[i,j]

pub fn sub_matrix_matrix(l: &Self, r: &Self) -> Self

Subtracts two matrices element-wise.

C[i,j] = A[i,j] - B[i,j]

impl<T: FloatScalar> Matrix3<T>

pub fn of_axis_angle(axis: &Vector3<T>, angle: T, epsilon: T) -> Option<Self>

Creates a 3x3 rotation matrix from an axis and angle.

Uses Rodrigues’ rotation formula:

R = I + sin(θ)K + (1 - cos(θ))K²

where K is the cross-product matrix of the normalized axis.

Parameters

• axis: The rotation axis (will be normalized)
• angle: The rotation angle in radians
• epsilon: Minimum axis length to treat as valid

Returns

• Some(matrix) for a valid axis
• None if the axis length is too small

Trait Implementations

impl<T: Scalar> Add for Matrix3<T>

type Output = Matrix3<T>

The resulting type after applying the + operator.

fn add(self, rhs: Matrix3<T>) -> Matrix3<T>

Performs the + operation.

impl<T: Clone + Scalar> Clone for Matrix3<T>

fn clone(&self) -> Matrix3<T>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + Scalar> Debug for Matrix3<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Scalar> Mul<Matrix3<T>> for Vector3<T>

type Output = Vector3<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix3<T>) -> Vector3<T>

Performs the * operation.

impl<T: Scalar> Mul<Vector3<T>> for Matrix3<T>

type Output = Vector3<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector3<T>) -> Vector3<T>

Performs the * operation.

impl<T: Scalar> Mul for Matrix3<T>

type Output = Matrix3<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix3<T>) -> Matrix3<T>

Performs the * operation.

impl<T: Scalar> Sub for Matrix3<T>

type Output = Matrix3<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix3<T>) -> Matrix3<T>

Performs the - operation.

impl<T: Copy + Scalar> Copy for Matrix3<T>