Struct acgmath::Quaternion

#[repr(C)]
pub struct Quaternion<S> {
    pub s: S,
    pub v: Vector3<S>,
}

A quaternion in scalar/vector form.

This type is marked as #[repr(C)].

Fields

s: S

The scalar part of the quaternion.

v: Vector3<S>

The vector part of the quaternion.

Methods

impl<S: BaseFloat> Quaternion<S>

fn new(w: S, xi: S, yj: S, zk: S) -> Quaternion<S>

Construct a new quaternion from one scalar component and three imaginary components

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

Construct a new quaternion from a scalar and a vector

fn from_arc(
    src: Vector3<S>,
    dst: Vector3<S>,
    fallback: Option<Vector3<S>>
) -> Quaternion<S>

Construct a new quaternion as a closest arc between two vectors

Return the closest rotation that turns src vector into dst.

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fn conjugate(self) -> Quaternion<S>

The conjugate of the quaternion.

fn nlerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>

Do a normalized linear interpolation with other, by amount.

fn slerp(self, other: Quaternion<S>, amount: S) -> Quaternion<S>

Spherical Linear Intoperlation

Return the spherical linear interpolation between the quaternion and other. Both quaternions should be normalized first.

Performance notes

The acos operation used in slerp is an expensive operation, so unless your quarternions are far away from each other it's generally more advisable to use nlerp when you know your rotations are going to be small.

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Trait Implementations

impl<S: BaseFloat> From<Matrix3<S>> for Quaternion<S>

fn from(mat: Matrix3<S>) -> Quaternion<S>

Convert the matrix to a quaternion

impl<S: Copy> Copy for Quaternion<S>

impl<S: Clone> Clone for Quaternion<S>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<S: Debug> Debug for Quaternion<S>

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl<S: PartialEq> PartialEq for Quaternion<S>

fn eq(&self, __arg_0: &Quaternion<S>) -> bool

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

fn ne(&self, __arg_0: &Quaternion<S>) -> bool

This method tests for !=.

impl<S: BaseFloat> Zero for Quaternion<S>

fn zero() -> Quaternion<S>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

impl<S: BaseFloat> One for Quaternion<S>

fn one() -> Quaternion<S>

Returns the multiplicative identity element of Self, 1.

impl<S: BaseFloat> VectorSpace for Quaternion<S>

type Scalar = S

The associated scalar.

impl<S: BaseFloat> MetricSpace for Quaternion<S>

type Metric = S

The metric to be returned by the distance function.

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

Returns the squared distance.

fn distance(self, other: Self) -> Self::Metric

The distance between two values.

impl<S: BaseFloat> InnerSpace for Quaternion<S>

fn dot(self, other: Quaternion<S>) -> S

Vector dot (or inner) product.

fn is_perpendicular(self, other: Self) -> bool

Returns true if the vector is perpendicular (at right angles) to the other vector.

fn magnitude2(self) -> Self::Scalar

Returns the squared magnitude.

fn magnitude(self) -> Self::Scalar

The distance from the tail to the tip of the vector.

fn angle(self, other: Self) -> Rad<Self::Scalar>

Returns the angle between two vectors in radians.

fn normalize(self) -> Self

Returns a vector with the same direction, but with a magnitude of 1.

fn normalize_to(self, magnitude: Self::Scalar) -> Self

Returns a vector with the same direction and a given magnitude.

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

Returns the result of linearly interpolating the magnitude of the vector towards the magnitude of other by the specified amount.

impl<A> From<Euler<A>> for Quaternion<<A as Angle>::Unitless> where
    A: Angle + Into<Rad<<A as Angle>::Unitless>>, 

fn from(src: Euler<A>) -> Quaternion<A::Unitless>

Performs the conversion.

impl<S: BaseFloat> Neg for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn neg(self) -> Quaternion<S>

The method for the unary - operator

impl<'a, S: BaseFloat> Neg for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn neg(self) -> Quaternion<S>

The method for the unary - operator

impl<S: BaseFloat> Mul<S> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: S) -> Quaternion<S>

The method for the * operator

impl<'a, S: BaseFloat> Mul<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: S) -> Quaternion<S>

The method for the * operator

impl<S: BaseFloat + MulAssign<S>> MulAssign<S> for Quaternion<S>

fn mul_assign(&mut self, scalar: S)

The method for the *= operator

impl<S: BaseFloat> Div<S> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the / operator

fn div(self, other: S) -> Quaternion<S>

The method for the / operator

impl<'a, S: BaseFloat> Div<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the / operator

fn div(self, other: S) -> Quaternion<S>

The method for the / operator

impl<S: BaseFloat + DivAssign<S>> DivAssign<S> for Quaternion<S>

fn div_assign(&mut self, scalar: S)

The method for the /= operator

impl<S: BaseFloat> Rem<S> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the % operator

fn rem(self, other: S) -> Quaternion<S>

The method for the % operator

impl<'a, S: BaseFloat> Rem<S> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the % operator

fn rem(self, other: S) -> Quaternion<S>

The method for the % operator

impl<S: BaseFloat + RemAssign<S>> RemAssign<S> for Quaternion<S>

fn rem_assign(&mut self, scalar: S)

The method for the %= operator

impl<S: BaseFloat> Mul<Vector3<S>> for Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator

fn mul(self, other: Vector3<S>) -> Vector3<S>

The method for the * operator

impl<'a, S: BaseFloat> Mul<&'a Vector3<S>> for Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator

fn mul(self, other: &'a Vector3<S>) -> Vector3<S>

The method for the * operator

impl<'a, S: BaseFloat> Mul<Vector3<S>> for &'a Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator

fn mul(self, other: Vector3<S>) -> Vector3<S>

The method for the * operator

impl<'a, 'b, S: BaseFloat> Mul<&'a Vector3<S>> for &'b Quaternion<S>

type Output = Vector3<S>

The resulting type after applying the * operator

fn mul(self, other: &'a Vector3<S>) -> Vector3<S>

The method for the * operator

impl<S: BaseFloat> Add<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator

fn add(self, other: Quaternion<S>) -> Quaternion<S>

The method for the + operator

impl<'a, S: BaseFloat> Add<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator

fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the + operator

impl<'a, S: BaseFloat> Add<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator

fn add(self, other: Quaternion<S>) -> Quaternion<S>

The method for the + operator

impl<'a, 'b, S: BaseFloat> Add<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the + operator

fn add(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the + operator

impl<S: BaseFloat + AddAssign<S>> AddAssign<Quaternion<S>> for Quaternion<S>

fn add_assign(&mut self, other: Quaternion<S>)

The method for the += operator

impl<S: BaseFloat> Sub<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn sub(self, other: Quaternion<S>) -> Quaternion<S>

The method for the - operator

impl<'a, S: BaseFloat> Sub<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the - operator

impl<'a, S: BaseFloat> Sub<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn sub(self, other: Quaternion<S>) -> Quaternion<S>

The method for the - operator

impl<'a, 'b, S: BaseFloat> Sub<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the - operator

fn sub(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the - operator

impl<S: BaseFloat + SubAssign<S>> SubAssign<Quaternion<S>> for Quaternion<S>

fn sub_assign(&mut self, other: Quaternion<S>)

The method for the -= operator

impl<S: BaseFloat> Mul<Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: Quaternion<S>) -> Quaternion<S>

The method for the * operator

impl<'a, S: BaseFloat> Mul<&'a Quaternion<S>> for Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the * operator

impl<'a, S: BaseFloat> Mul<Quaternion<S>> for &'a Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: Quaternion<S>) -> Quaternion<S>

The method for the * operator

impl<'a, 'b, S: BaseFloat> Mul<&'a Quaternion<S>> for &'b Quaternion<S>

type Output = Quaternion<S>

The resulting type after applying the * operator

fn mul(self, other: &'a Quaternion<S>) -> Quaternion<S>

The method for the * operator

impl<S: BaseFloat> ApproxEq for Quaternion<S>

type Epsilon = S::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> S::Epsilon

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

fn default_max_relative() -> S::Epsilon

The default relative tolerance for testing values that are far-apart.

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn relative_eq(
    &self,
    other: &Self,
    epsilon: S::Epsilon,
    max_relative: S::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn ulps_eq(&self, other: &Self, epsilon: S::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

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

The inverse of ApproxEq::relative_eq.

fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of ApproxEq::ulps_eq.

impl<S: BaseFloat> Rotation<Point3<S>> for Quaternion<S>

fn look_at(dir: Vector3<S>, up: Vector3<S>) -> Quaternion<S>

Create a rotation to a given direction with an 'up' vector

fn between_vectors(a: Vector3<S>, b: Vector3<S>) -> Quaternion<S>

Create a shortest rotation to transform vector 'a' into 'b'. Both given vectors are assumed to have unit length.

fn rotate_vector(&self, vec: Vector3<S>) -> Vector3<S>

Rotate a vector using this rotation.

fn invert(&self) -> Quaternion<S>

Create a new rotation which "un-does" this rotation. That is, r * r.invert() is the identity.

fn rotate_point(&self, point: P) -> P

Rotate a point using this rotation, by converting it to its representation as a vector.

impl<S: BaseFloat> Rotation3<S> for Quaternion<S>

fn from_axis_angle<A: Into<Rad<S>>>(axis: Vector3<S>, angle: A) -> Quaternion<S>

Create a rotation using an angle around a given axis.

fn from_angle_x<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the x axis (pitch).

fn from_angle_y<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the y axis (yaw).

fn from_angle_z<A: Into<Rad<S>>>(theta: A) -> Self

Create a rotation from an angle around the z axis (roll).

impl<S: BaseFloat> Into<[S; 4]> for Quaternion<S>

fn into(self) -> [S; 4]

Performs the conversion.

impl<S: BaseFloat> AsRef<[S; 4]> for Quaternion<S>

fn as_ref(&self) -> &[S; 4]

Performs the conversion.

impl<S: BaseFloat> AsMut<[S; 4]> for Quaternion<S>

fn as_mut(&mut self) -> &mut [S; 4]

Performs the conversion.

impl<S: BaseFloat> From<[S; 4]> for Quaternion<S>

fn from(v: [S; 4]) -> Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a [S; 4]> for &'a Quaternion<S>

fn from(v: &'a [S; 4]) -> &'a Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a mut [S; 4]> for &'a mut Quaternion<S>

fn from(v: &'a mut [S; 4]) -> &'a mut Quaternion<S>

Performs the conversion.

impl<S: BaseFloat> Into<(S, S, S, S)> for Quaternion<S>

fn into(self) -> (S, S, S, S)

Performs the conversion.

impl<S: BaseFloat> AsRef<(S, S, S, S)> for Quaternion<S>

fn as_ref(&self) -> &(S, S, S, S)

Performs the conversion.

impl<S: BaseFloat> AsMut<(S, S, S, S)> for Quaternion<S>

fn as_mut(&mut self) -> &mut (S, S, S, S)

Performs the conversion.

impl<S: BaseFloat> From<(S, S, S, S)> for Quaternion<S>

fn from(v: (S, S, S, S)) -> Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a (S, S, S, S)> for &'a Quaternion<S>

fn from(v: &'a (S, S, S, S)) -> &'a Quaternion<S>

Performs the conversion.

impl<'a, S: BaseFloat> From<&'a mut (S, S, S, S)> for &'a mut Quaternion<S>

fn from(v: &'a mut (S, S, S, S)) -> &'a mut Quaternion<S>

Performs the conversion.

impl<S: BaseFloat> Index<usize> for Quaternion<S>

type Output = S

The returned type after indexing

fn index<'a>(&'a self, i: usize) -> &'a S

The method for the indexing (container[index]) operation

impl<S: BaseFloat> IndexMut<usize> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: usize) -> &'a mut S

The method for the mutable indexing (container[index]) operation

impl<S: BaseFloat> Index<Range<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing

fn index<'a>(&'a self, i: Range<usize>) -> &'a [S]

The method for the indexing (container[index]) operation

impl<S: BaseFloat> IndexMut<Range<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: Range<usize>) -> &'a mut [S]

The method for the mutable indexing (container[index]) operation

impl<S: BaseFloat> Index<RangeTo<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing

fn index<'a>(&'a self, i: RangeTo<usize>) -> &'a [S]

The method for the indexing (container[index]) operation

impl<S: BaseFloat> IndexMut<RangeTo<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeTo<usize>) -> &'a mut [S]

The method for the mutable indexing (container[index]) operation

impl<S: BaseFloat> Index<RangeFrom<usize>> for Quaternion<S>

type Output = [S]

The returned type after indexing

fn index<'a>(&'a self, i: RangeFrom<usize>) -> &'a [S]

The method for the indexing (container[index]) operation

impl<S: BaseFloat> IndexMut<RangeFrom<usize>> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeFrom<usize>) -> &'a mut [S]

The method for the mutable indexing (container[index]) operation

impl<S: BaseFloat> Index<RangeFull> for Quaternion<S>

type Output = [S]

The returned type after indexing

fn index<'a>(&'a self, i: RangeFull) -> &'a [S]

The method for the indexing (container[index]) operation

impl<S: BaseFloat> IndexMut<RangeFull> for Quaternion<S>

fn index_mut<'a>(&'a mut self, i: RangeFull) -> &'a mut [S]

The method for the mutable indexing (container[index]) operation

impl<S: BaseFloat + Rand> Rand for Quaternion<S>

fn rand<R: Rng>(rng: &mut R) -> Quaternion<S>

Generates a random instance of this type using the specified source of randomness.

impl<S: BaseFloat> From<Basis3<S>> for Quaternion<S>

fn from(b: Basis3<S>) -> Quaternion<S>

Performs the conversion.