Struct Bivector 

pub struct Bivector<const D: usize> { /* private fields */ }

A bivector in D-dimensional space (grade-2 element of the geometric algebra).

Bivectors represent oriented planes. In 3D they are dual to pseudovectors. In ND they properly represent rotations: a rotation happens IN a plane.

Stack-allocated: uses [f64; 6] fixed array (max for D=4). Zero heap allocation — safe for physics hot loops at 60+ Hz.

Component ordering: lexicographic (i,j) with i < j. For D=4: [e01, e02, e03, e12, e13, e23].

Implementations

impl<const D: usize> Bivector<D>

pub const fn num_components() -> usize

Number of independent components: D*(D-1)/2.

pub fn zero() -> Self

Zero bivector.

pub fn unit_plane(i: usize, j: usize) -> Self

Unit bivector in the plane spanned by axes i and j (i < j).

pub fn get(&self, i: usize, j: usize) -> f64

Get the component for the (i, j) plane (i < j).

pub fn set(&mut self, i: usize, j: usize, value: f64)

Set the component for the (i, j) plane (i < j).

pub fn to_matrix(&self) -> SMatrix<f64, D, D>

Convert to antisymmetric matrix representation.

pub fn from_matrix(mat: &SMatrix<f64, D, D>) -> Self

Construct from an antisymmetric matrix.

pub fn is_finite(&self) -> bool

Returns true if all components are finite (not NaN or infinite).

pub fn norm_squared(&self) -> f64

Squared norm.

pub fn norm(&self) -> f64

Norm.

pub fn normalized(&self) -> Option<Self>

Normalize to unit bivector. Returns None if zero.

pub fn scale(&self, s: f64) -> Self

Scale all components by a scalar.

pub fn add(&self, other: &Self) -> Self

Add two bivectors.

pub fn apply_to_vector(&self, v: &SVector<f64, D>) -> SVector<f64, D>

Apply this bivector (as angular velocity) to a vector. Returns B · v (antisymmetric matrix × vector).

Trait Implementations

impl<const D: usize> Clone for Bivector<D>

fn clone(&self) -> Bivector<D>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const D: usize> Debug for Bivector<D>

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

Formats the value using the given formatter.

impl<const D: usize> Default for Bivector<D>

fn default() -> Self

Returns the “default value” for a type.

impl<const D: usize> PartialEq for Bivector<D>

fn eq(&self, other: &Self) -> 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<const D: usize> Copy for Bivector<D>