Struct vecmat::Quaternion

#[repr(transparent)]
pub struct Quaternion<T> { /* private fields */ }

Quaternion.

Implementations

impl<T> Quaternion<T>

pub fn new(w: T, x: T, y: T, z: T) -> Self

pub fn from_vector(vec: Vector4<T>) -> Self

pub fn from_array(arr: [T; 4]) -> Self

pub fn from_tuple(tup: (T, T, T, T)) -> Self

pub fn from_scalar_and_vector3(w: T, vec: Vector3<T>) -> Self

pub fn into_vector(self) -> Vector4<T>

pub fn into_array(self) -> [T; 4]

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

pub fn into_scalar_and_vector3(self) -> (T, Vector3<T>)

impl<T> Quaternion<T> where
    T: Copy, 

pub fn w(&self) -> T

pub fn x(&self) -> T

pub fn y(&self) -> T

pub fn z(&self) -> T

pub fn xyz(&self) -> Vector3<T>

impl<T> Quaternion<T>

pub fn w_ref(&self) -> &T

pub fn x_ref(&self) -> &T

pub fn y_ref(&self) -> &T

pub fn z_ref(&self) -> &T

pub fn w_mut(&mut self) -> &mut T

pub fn x_mut(&mut self) -> &mut T

pub fn y_mut(&mut self) -> &mut T

pub fn z_mut(&mut self) -> &mut T

impl<T> Quaternion<T> where
    T: Neg<Output = T> + Copy, 

pub fn into_matrix(self) -> Matrix4x4<T>

impl<T> Quaternion<T> where
    T: Neg<Output = T>, 

pub fn conj(self) -> Self

impl<T> Quaternion<T> where
    T: Zero + One, 

pub fn i() -> Self

pub fn j() -> Self

pub fn k() -> Self

impl<T> Quaternion<T> where
    T: Add<Output = T> + Mul<Output = T> + Copy, 

pub fn norm_sqr(self) -> T

impl<T: Float> Quaternion<T>

pub fn norm(self) -> T

impl<T> Quaternion<T> where
    T: Float, 

pub fn normalize(self) -> Self

impl<T> Quaternion<T> where
    T: Neg<Output = T> + Num + Copy, 

pub fn inv(self) -> Self

Trait Implementations

impl<T> AbsDiffEq<Quaternion<T>> for Quaternion<T> where
    T: AbsDiffEq<Epsilon = T> + Copy, 

type Epsilon = T

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<T> Add<Complex<T>> for Quaternion<T> where
    T: Add<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the + operator.

fn add(self, other: Complex<T>) -> Self

Performs the + operation.

impl<T> Add<Quaternion<T>> for Quaternion<T> where
    T: Add<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<Quaternion<f32>> for f32

Workaround for reverse addition.

type Output = Quaternion<f32>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f32>) -> Self::Output

Performs the + operation.

impl Add<Quaternion<f32>> for Complex<f32>

Workaround for reverse addition.

type Output = Quaternion<f32>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f32>) -> Self::Output

Performs the + operation.

impl Add<Quaternion<f64>> for f64

Workaround for reverse addition.

type Output = Quaternion<f64>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f64>) -> Self::Output

Performs the + operation.

impl Add<Quaternion<f64>> for Complex<f64>

Workaround for reverse addition.

type Output = Quaternion<f64>

The resulting type after applying the + operator.

fn add(self, other: Quaternion<f64>) -> Self::Output

Performs the + operation.

impl<T> Add<T> for Quaternion<T> where
    T: Add<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T> AddAssign<Complex<T>> for Quaternion<T> where
    T: AddAssign, 

fn add_assign(&mut self, other: Complex<T>)

Performs the += operation.

impl<T> AddAssign<Quaternion<T>> for Quaternion<T> where
    T: AddAssign, 

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<T> AddAssign<T> for Quaternion<T> where
    T: AddAssign, 

fn add_assign(&mut self, other: T)

Performs the += operation.

impl<T: Clone> Clone for Quaternion<T>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T> Conj for Quaternion<T> where
    T: Neg<Output = T>, 

fn conj(self) -> Self

Perform complex conjugation.

impl<T: Debug> Debug for Quaternion<T>

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

Formats the value using the given formatter.

impl<T: Default> Default for Quaternion<T>

fn default() -> Quaternion<T>

Returns the “default value” for a type.

impl<T> Directional<Quaternion<T>> for Moebius<Complex<T>> where
    Self: Transform<Quaternion<T>>,
    Quaternion<T>: Normalize, 

fn apply_dir(&self, pos: Quaternion<T>, dir: Quaternion<T>) -> Quaternion<T>

Returns the result of the direction transformation at the specified position.

fn apply_normal(
    &self,
    pos: Quaternion<T>,
    normal: Quaternion<T>
) -> Quaternion<T>

Returns the result of the normal transformation at the specified position.

impl<T: Display> Display for Quaternion<T>

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

Formats the value using the given formatter.

impl<T> Distribution<Quaternion<T>> for Normal where
    Normal: Distribution<Vector<T, 4>>, 

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Quaternion<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T: Float> Distribution<Quaternion<T>> for NonZero where
    NonZero: Distribution<Vector<T, 4>>, 

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Quaternion<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T: Float> Distribution<Quaternion<T>> for Unit where
    Unit: Distribution<Vector<T, 4>>, 

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Quaternion<T>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<T> Div<Complex<T>> for Quaternion<T> where
    T: Neg<Output = T> + Num + Copy, 

type Output = Quaternion<T>

The resulting type after applying the / operator.

fn div(self, other: Complex<T>) -> Self

Performs the / operation.

impl<T> Div<Quaternion<T>> for Quaternion<T> where
    T: Neg<Output = T> + Num + Copy, 

type Output = Quaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> Div<Quaternion<T>> for Complex<T> where
    T: Neg<Output = T> + Num + Copy, 

type Output = Quaternion<T>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<T>) -> Self::Output

Performs the / operation.

impl Div<Quaternion<f32>> for f32

Workaround for reverse division.

type Output = Quaternion<f32>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<f32>) -> Self::Output

Performs the / operation.

impl Div<Quaternion<f64>> for f64

Workaround for reverse division.

type Output = Quaternion<f64>

The resulting type after applying the / operator.

fn div(self, other: Quaternion<f64>) -> Self::Output

Performs the / operation.

impl<T> Div<T> for Quaternion<T> where
    T: Div<Output = T> + Copy, 

type Output = Quaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> DivAssign<Complex<T>> for Quaternion<T> where
    Self: Div<Complex<T>, Output = Self> + Copy, 

fn div_assign(&mut self, other: Complex<T>)

Performs the /= operation.

impl<T> DivAssign<Quaternion<T>> for Quaternion<T> where
    Self: Div<Output = Self> + Copy, 

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<T> DivAssign<T> for Quaternion<T> where
    Self: Div<T, Output = Self> + Copy, 

fn div_assign(&mut self, other: T)

Performs the /= operation.

impl<T> Dot<Quaternion<T>> for Quaternion<T> where
    T: Add<Output = T> + Mul<Output = T>, 

type Output = T

Dot product output type.

fn dot(self, other: Self) -> T

Perform dot product.

impl<T> From<[T; 4]> for Quaternion<T>

fn from(arr: [T; 4]) -> Self

Converts to this type from the input type.

impl<T> From<(T, T, T, T)> for Quaternion<T>

fn from(tup: (T, T, T, T)) -> Self

Converts to this type from the input type.

impl<T> From<(T, Vector<T, 3_usize>)> for Quaternion<T>

fn from((w, vec): (T, Vector3<T>)) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for Vector4<T>

fn from(quat: Quaternion<T>) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for (T, Vector3<T>)

fn from(quat: Quaternion<T>) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for [T; 4]

fn from(quat: Quaternion<T>) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for (T, T, T, T)

fn from(quat: Quaternion<T>) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for Rotation3<T>

fn from(quat: Quaternion<T>) -> Self

Converts to this type from the input type.

impl<T> From<Rotation3<T>> for Quaternion<T>

fn from(rot: Rotation3<T>) -> Self

Converts to this type from the input type.

impl<T> From<Vector<T, 4_usize>> for Quaternion<T>

fn from(vec: Vector4<T>) -> Self

Converts to this type from the input type.

impl<T> Inv for Quaternion<T> where
    T: Float, 

type Output = Quaternion<T>

The result after applying the operator.

fn inv(self) -> Self

Returns the multiplicative inverse of self.

impl<T> Mul<Complex<T>> for Quaternion<T> where
    T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy, 

type Output = Quaternion<T>

The resulting type after applying the * operator.

fn mul(self, other: Complex<T>) -> Self

Performs the * operation.

impl<T> Mul<Quaternion<T>> for Quaternion<T> where
    T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy, 

type Output = Quaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<Quaternion<T>> for Complex<T> where
    T: Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Copy, 

type Output = Quaternion<T>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<T>) -> Self::Output

Performs the * operation.

impl Mul<Quaternion<f32>> for f32

Workaround for reverse multiplication.

type Output = Quaternion<f32>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<f32>) -> Self::Output

Performs the * operation.

impl Mul<Quaternion<f64>> for f64

Workaround for reverse multiplication.

type Output = Quaternion<f64>

The resulting type after applying the * operator.

fn mul(self, other: Quaternion<f64>) -> Self::Output

Performs the * operation.

impl<T> Mul<T> for Quaternion<T> where
    T: Mul<Output = T> + Copy, 

type Output = Quaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> MulAssign<Complex<T>> for Quaternion<T> where
    Self: Mul<Complex<T>, Output = Self> + Copy, 

fn mul_assign(&mut self, other: Complex<T>)

Performs the *= operation.

impl<T> MulAssign<Quaternion<T>> for Quaternion<T> where
    Self: Mul<Output = Self> + Copy, 

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<T> MulAssign<T> for Quaternion<T> where
    Self: Mul<T, Output = Self> + Copy, 

fn mul_assign(&mut self, other: T)

Performs the *= operation.

impl<T> Neg for Quaternion<T> where
    T: Neg<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<T> NormL1 for Quaternion<T> where
    Vector4<T>: NormL1<Output = T>, 

type Output = T

Type of the norm.

fn norm_l1(self) -> T

Norm of the element.

impl<T: Float> NormL2 for Quaternion<T>

type Output = T

Type of the norm.

fn norm_l2(self) -> T

Norm of the element.

fn norm_l2_sqr(self) -> T

Square norm of the element.

impl<T> Normalize for Quaternion<T> where
    T: Float, 

fn normalize(self) -> Self

Normalize object.

impl<T: Neg<Output = T> + Num + Copy> Num for Quaternion<T>

type FromStrRadixErr = <T as Num>::FromStrRadixErr

fn from_str_radix(_s: &str, _radix: u32) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl<T> One for Quaternion<T> where
    T: Zero + One + Sub<Output = T> + Copy, 

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<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<T: PartialEq> PartialEq<Quaternion<T>> for Quaternion<T>

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

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Quaternion<T>) -> bool

This method tests for !=.

impl<T> Product<Quaternion<T>> for Quaternion<T> where
    Self: One + Mul, 

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<T: Neg<Output = T> + Num + Copy> Rem<Quaternion<T>> for Quaternion<T>

type Output = Quaternion<T>

The resulting type after applying the % operator.

fn rem(self, _other: Self) -> Self

Performs the % operation.

impl<T> Sub<Complex<T>> for Quaternion<T> where
    T: Sub<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the - operator.

fn sub(self, other: Complex<T>) -> Self

Performs the - operation.

impl<T> Sub<Quaternion<T>> for Quaternion<T> where
    T: Sub<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<Quaternion<f32>> for f32

Workaround for reverse subtraction.

type Output = Quaternion<f32>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f32>) -> Self::Output

Performs the - operation.

impl Sub<Quaternion<f32>> for Complex<f32>

Workaround for reverse subtraction.

type Output = Quaternion<f32>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f32>) -> Self::Output

Performs the - operation.

impl Sub<Quaternion<f64>> for f64

Workaround for reverse subtraction.

type Output = Quaternion<f64>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f64>) -> Self::Output

Performs the - operation.

impl Sub<Quaternion<f64>> for Complex<f64>

Workaround for reverse subtraction.

type Output = Quaternion<f64>

The resulting type after applying the - operator.

fn sub(self, other: Quaternion<f64>) -> Self::Output

Performs the - operation.

impl<T> Sub<T> for Quaternion<T> where
    T: Sub<Output = T>, 

type Output = Quaternion<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T> SubAssign<Complex<T>> for Quaternion<T> where
    T: SubAssign, 

fn sub_assign(&mut self, other: Complex<T>)

Performs the -= operation.

impl<T> SubAssign<Quaternion<T>> for Quaternion<T> where
    T: SubAssign, 

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<T> SubAssign<T> for Quaternion<T> where
    T: SubAssign, 

fn sub_assign(&mut self, other: T)

Performs the -= operation.

impl<T> Sum<Quaternion<T>> for Quaternion<T> where
    Self: Zero + Add, 

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl<T> Transform<Quaternion<T>> for Moebius<Complex<T>> where
    T: Neg<Output = T> + Num + NumCast + Copy, 

fn identity() -> Self

Identity transformation.

fn inv(self) -> Self

Inverse transformation.

fn apply(&self, pos: Quaternion<T>) -> Quaternion<T>

Perform the transformation itself.

fn deriv(&self, pos: Quaternion<T>, dir: Quaternion<T>) -> Quaternion<T>

Find transformation directional derivative at specified point.

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

Chain two transformations into a new one.

impl<T> Zero for Quaternion<T> where
    T: Zero, 

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.

impl<T: Copy> Copy for Quaternion<T>

impl<T> StructuralPartialEq for Quaternion<T>