Struct Matrix3 

pub struct Matrix3 {
    pub rows: [[f64; 3]; 3],
}

A 3×3 matrix, row-major.

Fields

rows: [[f64; 3]; 3]

Rows, each [m[i][0], m[i][1], m[i][2]].

Implementations

impl Matrix3

pub const IDENTITY: Self

The identity.

pub const ZERO: Self

All zeros.

pub const fn new(rows: [[f64; 3]; 3]) -> Self

From rows.

pub const fn from_columns(a: Vector, b: Vector, c: Vector) -> Self

From column vectors.

pub const fn from_rows(a: Vector, b: Vector, c: Vector) -> Self

From row vectors.

pub const fn scaling(s: f64) -> Self

A uniform scaling.

pub const fn scaling_xyz(x: f64, y: f64, z: f64) -> Self

A non-uniform scaling along the coordinate axes.

pub fn rotation(axis: Direction, angle: f64) -> Self

A right-handed rotation of angle radians about axis.

Rodrigues’ formula. Orthonormal to within rounding for any unit axis, which Direction guarantees.

pub fn reflection(n: Direction) -> Self

Reflection in the plane through the origin with normal n.

pub fn get(&self, row: usize, col: usize) -> OgeomResult<f64>

Element at (row, col).

Errors

OgeomError::Range if either index exceeds 2.

pub fn column(&self, i: usize) -> OgeomResult<Vector>

Column i as a vector.

Errors

OgeomError::Range if i > 2.

pub fn row(&self, i: usize) -> OgeomResult<Vector>

Row i as a vector.

Errors

OgeomError::Range if i > 2.

pub const fn transposed(&self) -> Self

The transpose.

pub fn determinant(&self) -> f64

The determinant.

pub fn trace(&self) -> f64

The trace.

pub fn inverse(&self) -> OgeomResult<Self>

The inverse.

Errors

OgeomError::Numeric if the matrix is singular.

Singularity is a question of numerical conditioning, not of modelling tolerance, so this takes no Tolerances. The determinant is compared against the rounding error incurred computing it: for an n x n matrix with entries bounded by s, that is on the order of n * n! * eps * s^n. The bound scales with the entries and has no absolute floor, because a matrix scaled by 1e-3 has a determinant scaled by 1e-9 and is no less invertible for it.

pub fn is_orthonormal(&self, eps: f64) -> bool

Whether the matrix is orthonormal: its rows form an orthonormal basis, so it represents a rotation or a reflection and its inverse is its transpose.

pub fn is_equal(&self, other: &Self, eps: f64) -> bool

Whether every element agrees with other within eps.

Takes a bare epsilon rather than Tolerances: matrix entries are dimensionless ratios, and a length tolerance does not apply to them.

pub fn is_finite(&self) -> bool

Whether every element is finite.

Trait Implementations

impl Add for Matrix3

type Output = Matrix3

The resulting type after applying the + operator.

fn add(self, o: Self) -> Self

Performs the + operation.

impl Clone for Matrix3

fn clone(&self) -> Matrix3

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Matrix3

impl Debug for Matrix3

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

Formats the value using the given formatter.

impl Default for Matrix3

fn default() -> Self

Returns the “default value” for a type.

impl Mul for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

fn mul(self, o: Self) -> Self

Performs the * operation.

impl Mul<Vector> for Matrix3

type Output = Vector

The resulting type after applying the * operator.

fn mul(self, v: Vector) -> Vector

Performs the * operation.

impl Mul<f64> for Matrix3

type Output = Matrix3

The resulting type after applying the * operator.

fn mul(self, s: f64) -> Self

Performs the * operation.

impl Neg for Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Matrix3

fn eq(&self, other: &Matrix3) -> 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 StructuralPartialEq for Matrix3

impl Sub for Matrix3

type Output = Matrix3

The resulting type after applying the - operator.

fn sub(self, o: Self) -> Self

Performs the - operation.