Struct Mat2 

#[repr(C)]
pub struct Mat2<T> {
    pub a11: T,
    pub a12: T,
    pub a21: T,
    pub a22: T,
}

2D transformation matrix.

Each field a_ij represents the i-th row and j-th column of the matrix.

Row-major storage with column-major semantics.

Stored in row-major order (fields appear in reading order), but interpreted as column-major: each column is a transformed basis vector, and matrices are applied to column vectors via mat * vec.

Fields

a11: T

a12: T

a21: T

a22: T

Implementations

impl<T> Mat2<T>

pub const fn new(a11: T, a12: T, a21: T, a22: T) -> Mat2<T>

Constructs a new matrix from components.

impl<T: Zero> Mat2<T>

pub const ZERO: Mat2<T>

Zero matrix.

impl<T: Zero + One> Mat2<T>

pub const IDENTITY: Mat2<T>

Identity matrix.

impl<T: Float> Mat2<T>

pub fn scaling(scale: Vec2<T>) -> Mat2<T>

Scaling matrix.

Scales around the origin.

let mat = cvmath::Mat2::scaling(cvmath::Vec2(2.0, 3.0));
let value = mat * cvmath::Vec2(4.0, 5.0);
let expected = cvmath::Vec2(8.0, 15.0);
assert_eq!(expected, value);

pub fn rotation(angle: Angle<T>) -> Mat2<T>

Rotation matrix.

Rotates around the origin.

let mat = cvmath::Mat2::rotation(cvmath::Angle::deg(90.0));
let value = (mat * cvmath::Vec2(1.0f64, 1.0)).cast::<f32>();
let expected = cvmath::Vec2(-1.0f32, 1.0);
assert_eq!(expected, value);

pub fn rotation_between(from: Vec2<T>, to: Vec2<T>) -> Mat2<T>

Returns the shortest rotation that aligns vector from with vector to.

The resulting matrix R satisfies:

R * from = to

Both vectors are expected to be normalized. The implementation avoids trigonometric functions.

The 2D rotation is uniquely defined even when the vectors are opposite, so this returns a 180° rotation in that case.

This is useful for constructing an orientation matrix that points one direction vector toward another.

let from = cvmath::Vec2(1.0, 1.0).norm();
let to = cvmath::Vec2(-1.0, 1.0).norm();
let mat = cvmath::Mat2::rotation_between(from, to);

let expected = to.cast::<f32>();
let value = (mat * from).cast::<f32>();
assert_eq!(expected, value);

pub fn skewing(skew: Vec2<T>) -> Mat2<T>

Skewing matrix.

pub fn reflection(axis: Vec2<T>) -> Mat2<T>

Reflection matrix.

Reflects around the given axis. If axis is the zero vector, returns a point reflection around the origin.

let mat = cvmath::Mat2::reflection(cvmath::Vec2d::Y);
let value = mat * cvmath::Vec2(2.0, 3.0);
let expected = cvmath::Vec2(-2.0, 3.0);
assert_eq!(expected, value);

pub fn projection(axis: Vec2<T>) -> Mat2<T>

Projection matrix.

Projects onto the given axis. If axis is the zero vector, returns the zero matrix.

let mat = cvmath::Mat2::projection(cvmath::Vec2d::X);
let value = mat * cvmath::Vec2(2.0, 3.0);
let expected = cvmath::Vec2(2.0, 0.0);
assert_eq!(expected, value);

impl<T> Mat2<T>

pub fn transform2(self) -> Transform2<T>

where T: Zero,

Converts to a Transform2 matrix.

let mat = cvmath::Mat2(1, 2, 3, 4).transform2();
let value = mat.into_row_major();
let expected = [[1, 2, 0], [3, 4, 0]];
assert_eq!(expected, value);

pub fn translate(self, trans: Vec2<T>) -> Transform2<T>

Adds a translation to the matrix.

let mat = cvmath::Mat2::IDENTITY.translate(cvmath::Vec2(5, 6));
let value = mat.into_row_major();
let expected = [[1, 0, 5], [0, 1, 6]];
assert_eq!(expected, value);

impl<T> Mat2<T>

pub fn from_row_major(mat: [[T; 2]; 2]) -> Mat2<T>

Imports the matrix from a row-major layout.

let mat = cvmath::Mat2::from_row_major([[1, 2], [3, 4]]);
let expected = cvmath::Mat2(1, 2, 3, 4);
assert_eq!(expected, mat);

pub fn from_column_major(mat: [[T; 2]; 2]) -> Mat2<T>

Imports the matrix from a column-major layout.

let mat = cvmath::Mat2::from_column_major([[1, 3], [2, 4]]);
let expected = cvmath::Mat2(1, 2, 3, 4);
assert_eq!(expected, mat);

pub fn into_row_major(self) -> [[T; 2]; 2]

Exports the matrix as a row-major array.

let mat = cvmath::Mat2(1, 2, 3, 4).into_row_major();
let expected = [[1, 2], [3, 4]];
assert_eq!(expected, mat);

pub fn into_column_major(self) -> [[T; 2]; 2]

Exports the matrix as a column-major array.

let mat = cvmath::Mat2(1, 2, 3, 4).into_column_major();
let expected = [[1, 3], [2, 4]];
assert_eq!(expected, mat);

impl<T> Mat2<T>

pub fn compose(x: Vec2<T>, y: Vec2<T>) -> Mat2<T>

Composes the matrix from basis vectors.

let mat = cvmath::Mat2::compose(cvmath::Vec2(1, 2), cvmath::Vec2(3, 4));
let value = mat.into_row_major();
let expected = [[1, 3], [2, 4]];
assert_eq!(expected, value);

pub fn x(self) -> Vec2<T>

Gets the transformed X basis vector.

let value = cvmath::Mat2(1, 2, 3, 4).x();
let expected = cvmath::Vec2(1, 3);
assert_eq!(expected, value);

pub fn y(self) -> Vec2<T>

Gets the transformed Y basis vector.

let value = cvmath::Mat2(1, 2, 3, 4).y();
let expected = cvmath::Vec2(2, 4);
assert_eq!(expected, value);

impl<T: Scalar> Mat2<T>

pub fn det(self) -> T

Computes the determinant.

let value = cvmath::Mat2(1, 2, 3, 4).det();
assert_eq!(-2, value);

pub fn trace(self) -> T

Computes the trace.

let value = cvmath::Mat2(1, 2, 3, 4).trace();
assert_eq!(5, value);

pub fn flat_norm_sqr(self) -> T

Computes the squared Frobenius norm (sum of squares of all matrix elements).

This measure is useful for quickly checking matrix magnitude or comparing matrices without the cost of a square root operation.

To check if a matrix is effectively zero, test if flat_norm_sqr() is below a small epsilon threshold.

let value = cvmath::Mat2(1, 2, 3, 4).flat_norm_sqr();
assert_eq!(30, value);

pub fn try_invert(self) -> Option<Mat2<T>>

where T: Float,

Attempts to invert the matrix.

let mat = cvmath::Mat2(1.0, 2.0, 3.0, 4.0);
let value = mat.try_invert();
let expected = Some(cvmath::Mat2(-2.0, 1.0, 1.5, -0.5));
assert_eq!(expected, value);

pub fn inverse(self) -> Mat2<T>

where T: Float,

Computes the inverse matrix.

Returns the zero matrix if the determinant is exactly zero.

let mat = cvmath::Mat2(1.0, 2.0, 3.0, 4.0);
let value = mat.inverse();
let expected = cvmath::Mat2(-2.0, 1.0, 1.5, -0.5);
assert_eq!(expected, value);

pub fn transpose(self) -> Mat2<T>

Returns the transposed matrix.

let mat = cvmath::Mat2(1, 2, 3, 4);
assert_eq!(cvmath::Mat2(1, 3, 2, 4), mat.transpose());

pub fn adjugate(self) -> Mat2<T>

Computes the adjugate matrix.

let value = cvmath::Mat2(1, 2, 3, 4).adjugate();
let expected = cvmath::Mat2(4, -2, -3, 1);
assert_eq!(expected, value);

pub fn lerp(self, rhs: Mat2<T>, t: T) -> Mat2<T>

where T: Float,

Linear interpolation between the matrix elements.

let source = cvmath::Mat2::IDENTITY;
let target = cvmath::Mat2::scaling(cvmath::Vec2(3.0, 5.0));
let value = source.lerp(target, 0.5);
let expected = cvmath::Mat2(2.0, 0.0, 0.0, 3.0);
assert_eq!(expected, value);

pub fn around(self, origin: Vec2<T>) -> Transform2<T>

where T: Float,

Applies the transformation around a given origin.

let rotation = cvmath::Mat2::rotation(cvmath::Angle::deg(90.0));
let mat = rotation.around(cvmath::Vec2(2.0f64, 3.0));
let value = (mat * cvmath::Vec2(3.0, 3.0)).cast::<f32>();
let expected = cvmath::Vec2(2.0f32, 4.0);
assert_eq!(expected, value);

Trait Implementations

impl<T> Add<&Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Add<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the + operator.

fn add(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the + operation.

impl<T> Add<&Mat2<T>> for Mat2<T>

where Mat2<T>: Add<Mat2<T>, Output = Mat2<T>> + Copy,

type Output = Mat2<T>

The resulting type after applying the + operator.

fn add(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the + operation.

impl<T> Add<Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Add<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the + operator.

fn add(self, rhs: Mat2<T>) -> Mat2<T>

Performs the + operation.

impl<T: Copy + Add<Output = T>> Add for Mat2<T>

type Output = Mat2<T>

The resulting type after applying the + operator.

fn add(self, rhs: Mat2<T>) -> Mat2<T>

Performs the + operation.

impl<T> AddAssign<&Mat2<T>> for Mat2<T>

where Mat2<T>: AddAssign<Mat2<T>> + Copy,

fn add_assign(&mut self, rhs: &Mat2<T>)

Performs the += operation.

impl<T: Copy + AddAssign> AddAssign for Mat2<T>

fn add_assign(&mut self, rhs: Mat2<T>)

Performs the += operation.

impl<T: Clone> Clone for Mat2<T>

fn clone(&self) -> Mat2<T>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Debug> Debug for Mat2<T>

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

Formats the value using the given formatter.

impl<T: Default> Default for Mat2<T>

fn default() -> Mat2<T>

Returns the “default value” for a type.

impl<T: Display> Display for Mat2<T>

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

Formats the value using the given formatter.

impl<T> Mul<&Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Mul<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the * operation.

impl<T> Mul<&Mat2<T>> for Mat2<T>

where Mat2<T>: Mul<Mat2<T>, Output = Mat2<T>> + Copy,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the * operation.

impl<T> Mul<&T> for &Mat2<T>

where Mat2<T>: Copy + Mul<T, Output = Mat2<T>>, T: Copy,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> Mat2<T>

Performs the * operation.

impl<T> Mul<&T> for Mat2<T>

where Mat2<T>: Mul<T, Output = Mat2<T>>, T: Copy,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &T) -> Mat2<T>

Performs the * operation.

impl<T> Mul<&Vec2<T>> for &Mat2<T>

where Mat2<T>: Copy + Mul<Vec2<T>, Output = Vec2<T>>, Vec2<T>: Copy,

type Output = Vec2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Vec2<T>) -> Vec2<T>

Performs the * operation.

impl<T> Mul<&Vec2<T>> for Mat2<T>

where Mat2<T>: Mul<Vec2<T>, Output = Vec2<T>>, Vec2<T>: Copy,

type Output = Vec2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: &Vec2<T>) -> Vec2<T>

Performs the * operation.

impl<T> Mul<Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Mul<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Mat2<T>) -> Mat2<T>

Performs the * operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> Mul<Mat2<T>> for Transform2<T>

type Output = Transform2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Mat2<T>) -> Transform2<T>

Performs the * operation.

impl<T> Mul<T> for &Mat2<T>

where Mat2<T>: Copy + Mul<T, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Mat2<T>

Performs the * operation.

impl<T: Copy + Mul<Output = T>> Mul<T> for Mat2<T>

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: T) -> Mat2<T>

Performs the * operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> Mul<Transform2<T>> for Mat2<T>

type Output = Transform2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform2<T>) -> Transform2<T>

Performs the * operation.

impl<T> Mul<Vec2<T>> for &Mat2<T>

where Mat2<T>: Copy + Mul<Vec2<T>, Output = Vec2<T>>,

type Output = Vec2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Vec2<T>) -> Vec2<T>

Performs the * operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> Mul<Vec2<T>> for Mat2<T>

type Output = Vec2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Vec2<T>) -> Vec2<T>

Performs the * operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> Mul for Mat2<T>

type Output = Mat2<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Mat2<T>) -> Mat2<T>

Performs the * operation.

impl<T> MulAssign<&Mat2<T>> for Mat2<T>

where Mat2<T>: MulAssign<Mat2<T>> + Copy,

fn mul_assign(&mut self, rhs: &Mat2<T>)

Performs the *= operation.

impl<T> MulAssign<&T> for Mat2<T>

where Mat2<T>: MulAssign<T>, T: Copy,

fn mul_assign(&mut self, rhs: &T)

Performs the *= operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> MulAssign<Mat2<T>> for Transform2<T>

fn mul_assign(&mut self, rhs: Mat2<T>)

Performs the *= operation.

impl<T: Copy + MulAssign> MulAssign<T> for Mat2<T>

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T: Copy + Add<Output = T> + Mul<Output = T>> MulAssign for Mat2<T>

fn mul_assign(&mut self, rhs: Mat2<T>)

Performs the *= operation.

impl<T> Neg for &Mat2<T>

where Mat2<T>: Copy + Neg<Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the - operator.

fn neg(self) -> Mat2<T>

Performs the unary - operation.

impl<T: Neg<Output = T>> Neg for Mat2<T>

type Output = Mat2<T>

The resulting type after applying the - operator.

fn neg(self) -> Mat2<T>

Performs the unary - operation.

impl<T: PartialEq> PartialEq for Mat2<T>

fn eq(&self, other: &Mat2<T>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T> Sub<&Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Sub<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the - operator.

fn sub(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the - operation.

impl<T> Sub<&Mat2<T>> for Mat2<T>

where Mat2<T>: Sub<Mat2<T>, Output = Mat2<T>> + Copy,

type Output = Mat2<T>

The resulting type after applying the - operator.

fn sub(self, rhs: &Mat2<T>) -> Mat2<T>

Performs the - operation.

impl<T> Sub<Mat2<T>> for &Mat2<T>

where Mat2<T>: Copy + Sub<Mat2<T>, Output = Mat2<T>>,

type Output = Mat2<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Mat2<T>) -> Mat2<T>

Performs the - operation.

impl<T: Copy + Sub<Output = T>> Sub for Mat2<T>

type Output = Mat2<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Mat2<T>) -> Mat2<T>

Performs the - operation.

impl<T> SubAssign<&Mat2<T>> for Mat2<T>

where Mat2<T>: SubAssign<Mat2<T>> + Copy,

fn sub_assign(&mut self, rhs: &Mat2<T>)

Performs the -= operation.

impl<T: Copy + SubAssign> SubAssign for Mat2<T>

fn sub_assign(&mut self, rhs: Mat2<T>)

Performs the -= operation.

impl<T: Copy> Copy for Mat2<T>

impl<T> StructuralPartialEq for Mat2<T>