Struct Rotation3D

#[repr(C)]
pub struct Rotation3D<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> Rotation3D<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.

pub fn identity() -> Self

where T: Zero + One,

Creates the identity rotation.

impl<T, Src, Dst> Rotation3D<T, Src, Dst>

where T: Copy,

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

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

pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2>

Cast the unit, preserving the numeric value.

Example

enum Local {}
enum World {}

enum Local2 {}
enum World2 {}

let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(to_world.i, to_world.cast_unit::<Local2, World2>().i);
assert_eq!(to_world.j, to_world.cast_unit::<Local2, World2>().j);
assert_eq!(to_world.k, to_world.cast_unit::<Local2, World2>().k);
assert_eq!(to_world.r, to_world.cast_unit::<Local2, World2>().r);

pub fn to_untyped(&self) -> Rotation3D<T, UnknownUnit, UnknownUnit>

Drop the units, preserving only the numeric value.

Example

enum Local {}
enum World {}

let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(to_world.i, to_world.to_untyped().i);
assert_eq!(to_world.j, to_world.to_untyped().j);
assert_eq!(to_world.k, to_world.to_untyped().k);
assert_eq!(to_world.r, to_world.to_untyped().r);

pub fn from_untyped(r: &Rotation3D<T, UnknownUnit, UnknownUnit>) -> Self

Tag a unitless value with units.

Example

use euclid::UnknownUnit;
enum Local {}
enum World {}

let rot: Rotation3D<_, UnknownUnit, UnknownUnit> = Rotation3D::quaternion(1, 2, 3, 4);

assert_eq!(rot.i, Rotation3D::<_, Local, World>::from_untyped(&rot).i);
assert_eq!(rot.j, Rotation3D::<_, Local, World>::from_untyped(&rot).j);
assert_eq!(rot.k, Rotation3D::<_, Local, World>::from_untyped(&rot).k);
assert_eq!(rot.r, Rotation3D::<_, Local, World>::from_untyped(&rot).r);

impl<T, Src, Dst> Rotation3D<T, Src, Dst>

where T: Real,

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: Vector3D<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) -> Rotation3D<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

Computes the squared norm of this quaternion.

pub fn normalize(&self) -> Self

Returns a unit quaternion from this one.

pub fn is_normalized(&self) -> bool

where T: ApproxEq<T>,

Returns true if norm of this quaternion is (approximately) one.

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.

pub fn transform_point3d(&self, point: Point3D<T, Src>) -> Point3D<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 transform_point2d(&self, point: Point2D<T, Src>) -> Point2D<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 transform_vector3d(&self, vector: Vector3D<T, Src>) -> Vector3D<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 transform_vector2d(&self, vector: Vector2D<T, Src>) -> Vector2D<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) -> Transform3D<T, Src, Dst>

where T: ApproxEq<T>,

Returns the matrix representation of this rotation.

pub fn then<NewDst>( &self, other: &Rotation3D<T, Dst, NewDst>, ) -> Rotation3D<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 Rotation3D<T, Src, Dst>

where T: Copy + Neg<Output = T> + ApproxEq<T>,

fn approx_epsilon() -> T

Default epsilon value

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

Returns true if this object is approximately equal to the other one, using a provided epsilon value.

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

Returns true if this object is approximately equal to the other one, using the approx_epsilon epsilon value.

impl<T: Clone, Src, Dst> Clone for Rotation3D<T, Src, Dst>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug, Src, Dst> Debug for Rotation3D<T, Src, Dst>

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

Formats the value using the given formatter.

impl<T: Real + ApproxEq<T>, Src, Dst> From<Rotation3D<T, Src, Dst>> for RigidTransform3D<T, Src, Dst>

fn from(rot: Rotation3D<T, Src, Dst>) -> Self

Converts to this type from the input type.

impl<T, Src, Dst> Hash for Rotation3D<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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T, Src, Dst> PartialEq for Rotation3D<T, Src, Dst>

where T: PartialEq,

fn eq(&self, other: &Self) -> 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: Copy, Src, Dst> Copy for Rotation3D<T, Src, Dst>

impl<T, Src, Dst> Eq for Rotation3D<T, Src, Dst>

where T: Eq,