Struct QuaternionPair 

pub struct QuaternionPair<T, const K: i8> { /* private fields */ }

An element a + e*b, where a and b are ordinary quaternions and the central unit satisfies e*e = K.

K must be -1 (complex), 0 (dual), or 1 (split). Different values are different types and cannot accidentally be multiplied together. Both quaternions use scalar-first component order. This is an algebra element, not necessarily a normalized isometry.

Quaternion conjugation, scalar conjugation (e -> -e), and their combination are distinct operations. The quaternion norm is itself a central pair, so ordinary eight-dimensional Euclidean normalization is not appropriate.

Implementations

impl<T, const K: i8> QuaternionPair<T, K>

pub fn new(real: Quaternion<T>, unreal: Quaternion<T>) -> Self

Construct an algebra element. Panics if K is not -1, 0, or 1.

pub fn into_parts(self) -> (Quaternion<T>, Quaternion<T>)

pub fn from_array(values: [T; 8]) -> Self

Construct from [a.w, a.x, a.y, a.z, b.w, b.x, b.y, b.z].

pub fn into_array(self) -> [T; 8]

Return [a.w, a.x, a.y, a.z, b.w, b.x, b.y, b.z].

impl<T: Copy, const K: i8> QuaternionPair<T, K>

pub fn real(&self) -> Quaternion<T>

pub fn unreal(&self) -> Quaternion<T>

impl<T: Neg<Output = T>, const K: i8> QuaternionPair<T, K>

pub fn quaternion_conj(self) -> Self

Quaternion conjugation: (conj(a), conj(b)). Reverses products.

pub fn scalar_conj(self) -> Self

Conjugation of the central unit: (a, -b). Preserves product order.

pub fn combined_conj(self) -> Self

Combined conjugation: (conj(a), -conj(b)). Reverses products.

impl<T: Num + Copy, const K: i8> QuaternionPair<T, K>

pub fn norm_sqr(self) -> (T, T)

The central coefficients (n, m) of self * self.quaternion_conj(): n = |a|² + K |b|², m = 2 dot(a,b).

impl<T: Float, const K: i8> QuaternionPair<T, K>

pub fn is_finite(self) -> bool

pub fn try_inv(self) -> Option<Self>

Invert a nonsingular element. Returns None for singular/nonfinite inputs or when intermediate arithmetic overflows.

pub fn try_normalize(self) -> Option<Self>

Divide by a central square root of the quaternion norm.

The result has norm_sqr() = (1, 0) up to roundoff. Complex pairs use the principal complex square root; dual and split pairs use the positive real branches. Returns None for singular/nonfinite inputs or when intermediate arithmetic overflows. This selects a normalization branch, not a canonical sign for the double cover.

Trait Implementations

impl<T: Add<Output = T>, const K: i8> Add for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Clone, const K: i8> Clone for QuaternionPair<T, K>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Copy, const K: i8> Copy for QuaternionPair<T, K>

impl<T: Debug, const K: i8> Debug for QuaternionPair<T, K>

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

Formats the value using the given formatter.

impl<T: Zero, const K: i8> Default for QuaternionPair<T, K>

fn default() -> Self

Returns the “default value” for a type.

impl<T: Div<Output = T> + Copy, const K: i8> Div<T> for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the / operator.

fn div(self, scalar: T) -> Self

Performs the / operation.

impl<T: Num + Copy, const K: i8> Mul for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: Mul<Output = T> + Copy, const K: i8> Mul<T> for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the * operator.

fn mul(self, scalar: T) -> Self

Performs the * operation.

impl<T: Neg<Output = T>, const K: i8> Neg for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T: Num + Copy, const K: i8> One for QuaternionPair<T, K>

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<T: PartialEq, const K: i8> PartialEq for QuaternionPair<T, K>

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

Equality operator ==.

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

Inequality operator !=.

impl<T: PartialEq, const K: i8> StructuralPartialEq for QuaternionPair<T, K>

impl<T: Sub<Output = T>, const K: i8> Sub for QuaternionPair<T, K>

type Output = QuaternionPair<T, K>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: Zero, const K: i8> Zero for QuaternionPair<T, K>

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.