Struct euclid::TypedRotation3D

#[repr(C)]
pub struct TypedRotation3D<T, Src, Dst> {
    pub i: T,
    pub j: T,
    pub k: T,
    pub r: T,
    // some fields omitted
}

A transform that can represent rotations in 3d, represented as a quaternion.

Most methods expect the quaternion to be normalized. When in doubt, use unit_quaternion instead of quaternion to create a rotation as the former will ensure that its result is normalized.

Some people use the x, y, z, w (or w, x, y, z) notations. The equivalence is as follows: x -> i, y -> j, z -> k, w -> r. The memory layout of this type corresponds to the x, y, z, w notation

Fields

i: T

Component multiplied by the imaginary number i.

j: T

Component multiplied by the imaginary number j.

k: T

Component multiplied by the imaginary number k.

r: T

The real part.

Methods

impl<T, Src, Dst> TypedRotation3D<T, Src, Dst>

pub fn quaternion(a: T, b: T, c: T, r: T) -> Self

Creates a rotation around from a quaternion representation.

The parameters are a, b, c and r compose the quaternion a*i + b*j + c*k + r where a, b and c describe the vector part and the last parameter r is the real part.

The resulting quaternion is not necessarily normalized. See unit_quaternion.

impl<T, Src, Dst> TypedRotation3D<T, Src, Dst> where
    T: Copy, 

pub fn vector_part(&self) -> Vector3D<T>

Returns the vector part (i, j, k) of this quaternion.

impl<T, Src, Dst> TypedRotation3D<T, Src, Dst> where
    T: Float, 

pub fn identity() -> Self

Creates the identity rotation.

pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Self

Creates a rotation around from a quaternion representation and normalizes it.

The parameters are a, b, c and r compose the quaternion a*i + b*j + c*k + r before normalization, where a, b and c describe the vector part and the last parameter r is the real part.

pub fn around_axis(axis: TypedVector3D<T, Src>, angle: Angle<T>) -> Self

Creates a rotation around a given axis.

pub fn around_x(angle: Angle<T>) -> Self

Creates a rotation around the x axis.

pub fn around_y(angle: Angle<T>) -> Self

Creates a rotation around the y axis.

pub fn around_z(angle: Angle<T>) -> Self

Creates a rotation around the z axis.

pub fn euler(roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>) -> Self

Creates a rotation from Euler angles.

The rotations are applied in roll then pitch then yaw order.

• Roll (also called bank) is a rotation around the x axis.
• Pitch (also called bearing) is a rotation around the y axis.
• Yaw (also called heading) is a rotation around the z axis.

pub fn inverse(&self) -> TypedRotation3D<T, Dst, Src>

Returns the inverse of this rotation.

pub fn norm(&self) -> T

Computes the norm of this quaternion

pub fn square_norm(&self) -> T

pub fn normalize(&self) -> Self

Returns a unit quaternion from this one.

pub fn is_normalized(&self) -> bool where
    T: ApproxEq<T>, 

pub fn slerp(&self, other: &Self, t: T) -> Self where
    T: ApproxEq<T>, 

Spherical linear interpolation between this rotation and another rotation.

t is expected to be between zero and one.

pub fn lerp(&self, other: &Self, t: T) -> Self

Basic Linear interpolation between this rotation and another rotation.

t is expected to be between zero and one.

pub fn rotate_point3d(
    &self,
    point: &TypedPoint3D<T, Src>
) -> TypedPoint3D<T, Dst> where
    T: ApproxEq<T>, 

Returns the given 3d point transformed by this rotation.

The input point must be use the unit Src, and the returned point has the unit Dst.

pub fn rotate_point2d(
    &self,
    point: &TypedPoint2D<T, Src>
) -> TypedPoint2D<T, Dst> where
    T: ApproxEq<T>, 

Returns the given 2d point transformed by this rotation then projected on the xy plane.

The input point must be use the unit Src, and the returned point has the unit Dst.

pub fn rotate_vector3d(
    &self,
    vector: &TypedVector3D<T, Src>
) -> TypedVector3D<T, Dst> where
    T: ApproxEq<T>, 

Returns the given 3d vector transformed by this rotation.

The input vector must be use the unit Src, and the returned point has the unit Dst.

pub fn rotate_vector2d(
    &self,
    vector: &TypedVector2D<T, Src>
) -> TypedVector2D<T, Dst> where
    T: ApproxEq<T>, 

Returns the given 2d vector transformed by this rotation then projected on the xy plane.

The input vector must be use the unit Src, and the returned point has the unit Dst.

pub fn to_transform(&self) -> TypedTransform3D<T, Src, Dst> where
    T: ApproxEq<T>, 

Returns the matrix representation of this rotation.

pub fn pre_rotate<NewSrc>(
    &self,
    other: &TypedRotation3D<T, NewSrc, Src>
) -> TypedRotation3D<T, NewSrc, Dst> where
    T: ApproxEq<T>, 

Returns a rotation representing the other rotation followed by this rotation.

pub fn post_rotate<NewDst>(
    &self,
    other: &TypedRotation3D<T, Dst, NewDst>
) -> TypedRotation3D<T, Src, NewDst> where
    T: ApproxEq<T>, 

Returns a rotation representing this rotation followed by the other rotation.

Trait Implementations

impl<T, Src, Dst> ApproxEq<T> for TypedRotation3D<T, Src, Dst> where
    T: Copy + Neg<Output = T> + ApproxEq<T>, 

fn approx_epsilon() -> T

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

fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool

impl<T, Src, Dst> PartialEq<TypedRotation3D<T, Src, Dst>> for TypedRotation3D<T, Src, Dst> where
    T: PartialEq, 

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

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

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<T, Src, Dst> Eq for TypedRotation3D<T, Src, Dst> where
    T: Eq, 

impl<T, Src, Dst> Hash for TypedRotation3D<T, Src, Dst> where
    T: Hash, 

fn hash<H: Hasher>(&self, h: &mut H)

Feeds this value into the given [Hasher].

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

Feeds a slice of this type into the given [Hasher].

impl<T: Display, Src, Dst> Display for TypedRotation3D<T, Src, Dst>

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

Formats the value using the given formatter.

impl<T: Debug, Src, Dst> Debug for TypedRotation3D<T, Src, Dst>

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

Formats the value using the given formatter.

impl<T, Src, Dst> Copy for TypedRotation3D<T, Src, Dst> where
    T: Copy, 

impl<T: Float + ApproxEq<T>, Src, Dst> From<TypedRotation3D<T, Src, Dst>> for TypedRigidTransform3D<T, Src, Dst>

fn from(rot: TypedRotation3D<T, Src, Dst>) -> Self

Performs the conversion.

impl<T, Src, Dst> Clone for TypedRotation3D<T, Src, Dst> where
    T: Clone, 

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.