Struct TypedRotation3D

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

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.

Implementations

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

pub fn quaternion(a: T, b: T, c: T, r: T) -> TypedRotation3D<T, Src, Dst>

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) -> TypedVector3D<T, UnknownUnit>

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

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

where T: Float,

pub fn identity() -> TypedRotation3D<T, Src, Dst>

Creates the identity rotation.

pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> TypedRotation3D<T, Src, Dst>

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>, ) -> TypedRotation3D<T, Src, Dst>

Creates a rotation around a given axis.

pub fn around_x(angle: Angle<T>) -> TypedRotation3D<T, Src, Dst>

Creates a rotation around the x axis.

pub fn around_y(angle: Angle<T>) -> TypedRotation3D<T, Src, Dst>

Creates a rotation around the y axis.

pub fn around_z(angle: Angle<T>) -> TypedRotation3D<T, Src, Dst>

Creates a rotation around the z axis.

pub fn euler( roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>, ) -> TypedRotation3D<T, Src, Dst>

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) -> TypedRotation3D<T, Src, Dst>

Returns a unit quaternion from this one.

pub fn is_normalized(&self) -> bool

where T: ApproxEq<T>,

pub fn slerp( &self, other: &TypedRotation3D<T, Src, Dst>, t: T, ) -> TypedRotation3D<T, Src, Dst>

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: &TypedRotation3D<T, Src, Dst>, t: T, ) -> TypedRotation3D<T, Src, Dst>

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: &TypedRotation3D<T, Src, Dst>) -> bool

fn approx_eq_eps(&self, other: &TypedRotation3D<T, Src, Dst>, eps: &T) -> bool

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

where T: Clone,

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

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

where T: Debug,

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

Formats the value using the given formatter.

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

where T: Display,

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

Formats the value using the given formatter.

impl<'l> From<&'l TypedRotation3D<f32, UnknownUnit, UnknownUnit>> for Variant

fn from(val: &'l TypedRotation3D<f32, UnknownUnit, UnknownUnit>) -> Variant

Converts to this type from the input type.

impl<T, Src, Dst> From<TypedRotation3D<T, Src, Dst>> for TypedRigidTransform3D<T, Src, Dst>

where T: Float + ApproxEq<T>,

fn from(rot: TypedRotation3D<T, Src, Dst>) -> TypedRigidTransform3D<T, Src, Dst>

Converts to this type from the input type.

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

where T: Hash,

fn hash<H>(&self, h: &mut H)

where H: Hasher,

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

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

where T: PartialEq,

fn eq(&self, other: &TypedRotation3D<T, Src, Dst>) -> 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, Src, Dst> Copy for TypedRotation3D<T, Src, Dst>

where T: Copy,

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

where T: Eq,