Struct Blade 

pub struct Blade(pub u32);

Basis blade represented as a bitmask of generator vectors. E.g., scalar = 0b0000, e_1 = 0b0001, e_2 = 0b0010, e_12 = 0b0011, e_123 = 0b0111.

Tuple Fields

0: u32

Implementations

impl Blade

pub const SCALAR: Self

pub const fn new(mask: u32) -> Self

pub const fn generator(i: usize) -> Self

pub const fn grade(self) -> usize

Grade of the blade (number of basis vectors spanning it).

pub const fn reverse_sign(self) -> i8

Reverse sign of the blade: (-1)^{k(k-1)/2}.

pub const fn involution_sign(self) -> i8

Grade involution sign of the blade: (-1)^k.

pub const fn conjugation_sign(self) -> i8

Clifford conjugation sign of the blade: (-1)^{k(k+1)/2}.

pub fn geometric_product<const P: usize, const Q: usize, const R: usize>( self, rhs: Self, ) -> Option<(Self, i8)>

Computes the geometric product of two basis blades e_I * e_J under metric Cl(p, q, r). Returns Some((resulting_blade, sign)) or None if the result is zero (due to degenerate r-generators).

pub fn wedge_product(self, rhs: Self) -> Option<(Self, i8)>

Computes the exterior wedge product e_I ^ e_J. Nonzero if and only if blades share no common generators (I & J == 0).

pub fn left_contraction<const P: usize, const Q: usize, const R: usize>( self, rhs: Self, ) -> Option<(Self, i8)>

Computes the left contraction e_I _| e_J under metric Cl(p, q, r). Nonzero only if grade(result) == grade(J) - grade(I).

pub fn right_contraction<const P: usize, const Q: usize, const R: usize>( self, rhs: Self, ) -> Option<(Self, i8)>

Computes the right contraction e_I |_ e_J under metric Cl(p, q, r). Nonzero only if grade(result) == grade(I) - grade(J).

Trait Implementations

impl Clone for Blade

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Blade

impl Debug for Blade

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

Formats the value using the given formatter.

impl Default for Blade

fn default() -> Self

Returns the “default value” for a type.

impl Eq for Blade

impl Hash for Blade

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Ord for Blade

fn cmp(&self, other: &Self) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

fn clamp_to<R>(self, range: R) -> Self

where Self: Sized, R: ClampBounds<Self>,

🔬This is a nightly-only experimental API. (clamp_to)

Restrict a value to a certain range.

impl PartialEq for Blade

fn eq(&self, other: &Self) -> bool

Equality operator ==.

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

Inequality operator !=.

impl PartialOrd for Blade

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

Tests less than (for self and other) and is used by the < operator.

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

Tests less than or equal to (for self and other) and is used by the <= operator.

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

Tests greater than (for self and other) and is used by the > operator.

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

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl StructuralPartialEq for Blade