Struct Quaternion

pub struct Quaternion<T> {
    pub s: T,
    pub v: Vector3<T>,
}

A quaternion, composed of a scalar and a Vector3.

Fields

s: T

v: Vector3<T>

Implementations

impl<T> Quaternion<T>

pub const fn new(w: T, xi: T, yj: T, zk: T) -> Quaternion<T>

Constructs a Quaternion from one scalar and three imaginary components.

pub fn from_sv(s: T, v: Vector3<T>) -> Quaternion<T>

Constructs a Quaternion from a scalar and a vector.

impl<T> Quaternion<T>

where T: Real + Clone + Debug,

pub fn from_axis_angle(axis: Vector3<T>, angle: T) -> Self

Constructs the rotation as a rotation along an axis.

impl<T> Quaternion<T>

where T: Zero + One,

pub fn identity() -> Self

Return the identity quaternion.

impl<T> Quaternion<T>

where T: Clone,

pub fn s(&self) -> &T

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

impl<T> Quaternion<T>

where T: Neg<Output = T>,

pub fn conjugate(self) -> Self

Returns the conjugate of the quaternion.

Trait Implementations

impl<T> Add for Quaternion<T>

where T: Add<T, Output = T>,

type Output = Quaternion<T>

The resulting type after applying the + operator.

fn add(self, rhs: Quaternion<T>) -> Self

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> Debug for Quaternion<T>

where T: Debug,

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

Formats the value using the given formatter.

impl<'de, T> Deserialize<'de> for Quaternion<T>

where T: Deserialize<'de>,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<T> Div<T> for Quaternion<T>

where T: Real + Clone,

type Output = Quaternion<T>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T> DivAssign<T> for Quaternion<T>

where T: Real + Clone,

fn div_assign(&mut self, scalar: T)

Performs the /= operation.

impl<T> From<Euler<T>> for Quaternion<T>

where T: Real + Clone,

fn from(euler: Euler<T>) -> Quaternion<T>

Converts to this type from the input type.

impl<T> From<Orthonormal<T, 3>> for Quaternion<T>

where T: Copy + Clone + PartialOrd + Product + Real + One + Zero + Neg<Output = T> + Add<T, Output = T> + Sub<T, Output = T> + Mul<T, Output = T> + Div<T, Output = T>,

fn from(orthonormal: Orthonormal<T, 3>) -> Self

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for Matrix3<T>

where T: Real + One + Copy + Clone,

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

Converts to this type from the input type.

impl<T> From<Quaternion<T>> for Matrix4<T>

where T: Add + Mul + Sub + Real + Zero + One + Copy + Clone,

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

Converts to this type from the input type.

impl From<Quaternion<f32>> for Euler<f32>

fn from(q: Quaternion<f32>) -> Euler<f32>

Converts to this type from the input type.

impl From<Quaternion<f64>> for Euler<f64>

fn from(q: Quaternion<f64>) -> Euler<f64>

Converts to this type from the input type.

impl<T> InnerSpace for Quaternion<T>

where T: Real + Zero + Clone,

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

Return the inner (also known as “dot”) product.

fn magnitude2(self) -> Self::Scalar

Returns the squared length of the value.

fn reflect(self, surface_normal: Unit<Self>) -> Self

Returns the reflection of the current vector with respect to the given surface normal. The surface normal must be of length 1 for the return value to be correct. The current vector is interpreted as pointing toward the surface, and does not need to be normalized.

impl<T> MetricSpace for Quaternion<T>

where T: Real + Zero + Clone,

type Metric = T

fn distance2(self, other: Self) -> T

Returns the distance squared between the two values.

impl Mul<Quaternion<f32>> for f32

type Output = Quaternion<f32>

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<Quaternion<f64>> for f64

type Output = Quaternion<f64>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<T> for Quaternion<T>

where T: Real + Clone,

type Output = Quaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> Mul<Vector3<T>> for Quaternion<T>

where T: Real + Clone,

type Output = Vector3<T>

The resulting type after applying the * operator.

fn mul(self, rhs: Vector3<T>) -> Vector3<T>

Performs the * operation.

impl<T> Mul for Quaternion<T>

where T: Real + Clone,

type Output = Quaternion<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T> MulAssign<T> for Quaternion<T>

where T: Real + Clone,

fn mul_assign(&mut self, scalar: 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> One for Quaternion<T>

where T: One,

fn one() -> Self

Returns the multiplicative identity for Self.

fn is_one(&self) -> bool

Returns true if the value is the multiplicative identity.

impl<A, B> PartialEq<Quaternion<B>> for Quaternion<A>

where A: PartialEq<B>, Vector3<A>: PartialEq<Vector3<B>>,

fn eq(&self, other: &Quaternion<B>) -> 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<T> Rotation3 for Quaternion<T>

where T: Real + Clone + Zero + AddAssign,

type Scalar = T

fn invert(&self) -> Self

Returns the multiplicative inverse of the rotation. Effectively does the opposite of the given rotation.

fn rotate_vector(&self, v: Vector3<T>) -> Vector3<T>

Rotates a vector.

fn rotate_point(&self, p: Point3<Self::Scalar>) -> Point3<Self::Scalar>

Rotates a point around the origin.

impl<T> Serialize for Quaternion<T>

where T: Serialize,

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<T> Sub for Quaternion<T>

where T: Sub<T, Output = T>,

type Output = Quaternion<T>

The resulting type after applying the - operator.

fn sub(self, rhs: Quaternion<T>) -> Self

Performs the - operation.

impl<T> VectorSpace for Quaternion<T>

where T: Clone + Real + Zero,

type Scalar = T

fn lerp(self, other: Self, t: Self::Scalar) -> Self

Linear interpolate between the two vectors with a weight of t.

impl<T> Zero for Quaternion<T>

where T: Zero,

fn zero() -> Self

Returns the additive identity of Self.

fn is_zero(&self) -> bool

Returns true if the value is the additive identity.

impl<T: Copy> Copy for Quaternion<T>

impl<T> Eq for Quaternion<T>

where T: Eq,