# Struct bevy::math::Rotation2d

``````pub struct Rotation2d {
pub cos: f32,
pub sin: f32,
}``````
Expand description

A counterclockwise 2D rotation in radians.

The rotation angle is wrapped to be within the `(-pi, pi]` range.

## §Example

``````use std::f32::consts::PI;

// Create rotations from radians or degrees
let rotation1 = Rotation2d::radians(PI / 2.0);
let rotation2 = Rotation2d::degrees(45.0);

// Get the angle back as radians or degrees
assert_eq!(rotation1.as_degrees(), 90.0);

// "Add" rotations together using `*`
assert_relative_eq!(rotation1 * rotation2, Rotation2d::degrees(135.0));

// Rotate vectors
assert_relative_eq!(rotation1 * Vec2::X, Vec2::Y);``````

## Fields§

§`cos: f32`

The cosine of the rotation angle in radians.

This is the real part of the unit complex number representing the rotation.

§`sin: f32`

The sine of the rotation angle in radians.

This is the imaginary part of the unit complex number representing the rotation.

## Implementations§

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### impl Rotation2d

No rotation.

#### pub const FRAC_PI_2: Rotation2d = _

A counterclockwise rotation of π/2 radians.

#### pub const FRAC_PI_3: Rotation2d = _

A counterclockwise rotation of π/3 radians.

#### pub const FRAC_PI_4: Rotation2d = _

A counterclockwise rotation of π/4 radians.

#### pub const FRAC_PI_6: Rotation2d = _

A counterclockwise rotation of π/6 radians.

#### pub const FRAC_PI_8: Rotation2d = _

A counterclockwise rotation of π/8 radians.

Creates a `Rotation2d` from a counterclockwise angle in radians.

#### pub fn degrees(degrees: f32) -> Rotation2d

Creates a `Rotation2d` from a counterclockwise angle in degrees.

#### pub fn from_sin_cos(sin: f32, cos: f32) -> Rotation2d

Creates a `Rotation2d` from the sine and cosine of an angle in radians.

The rotation is only valid if `sin * sin + cos * cos == 1.0`.

##### §Panics

Panics if `sin * sin + cos * cos != 1.0` when the `glam_assert` feature is enabled.

#### pub fn as_radians(self) -> f32

Returns the rotation in radians in the `(-pi, pi]` range.

#### pub fn as_degrees(self) -> f32

Returns the rotation in degrees in the `(-180, 180]` range.

#### pub const fn sin_cos(self) -> (f32, f32)

Returns the sine and cosine of the rotation angle in radians.

#### pub fn length(self) -> f32

Computes the length or norm of the complex number used to represent the rotation.

The length is typically expected to be `1.0`. Unexpectedly denormalized rotations can be a result of incorrect construction or floating point error caused by successive operations.

#### pub fn length_squared(self) -> f32

Computes the squared length or norm of the complex number used to represent the rotation.

This is generally faster than `Rotation2d::length()`, as it avoids a square root operation.

The length is typically expected to be `1.0`. Unexpectedly denormalized rotations can be a result of incorrect construction or floating point error caused by successive operations.

#### pub fn length_recip(self) -> f32

Computes `1.0 / self.length()`.

For valid results, `self` must not have a length of zero.

#### pub fn try_normalize(self) -> Option<Rotation2d>

Returns `self` with a length of `1.0` if possible, and `None` otherwise.

`None` will be returned if the sine and cosine of `self` are both zero (or very close to zero), or if either of them is NaN or infinite.

Note that `Rotation2d` should typically already be normalized by design. Manual normalization is only needed when successive operations result in accumulated floating point error, or if the rotation was constructed with invalid values.

#### pub fn normalize(self) -> Rotation2d

Returns `self` with a length of `1.0`.

Note that `Rotation2d` should typically already be normalized by design. Manual normalization is only needed when successive operations result in accumulated floating point error, or if the rotation was constructed with invalid values.

##### §Panics

Panics if `self` has a length of zero, NaN, or infinity when debug assertions are enabled.

#### pub fn is_finite(self) -> bool

Returns `true` if the rotation is neither infinite nor NaN.

#### pub fn is_nan(self) -> bool

Returns `true` if the rotation is NaN.

#### pub fn is_normalized(self) -> bool

Returns whether `self` has a length of `1.0` or not.

Uses a precision threshold of approximately `1e-4`.

#### pub fn is_near_identity(self) -> bool

Returns `true` if the rotation is near `Rotation2d::IDENTITY`.

#### pub fn angle_between(self, other: Rotation2d) -> f32

Returns the angle in radians needed to make `self` and `other` coincide.

#### pub fn inverse(self) -> Rotation2d

Returns the inverse of the rotation. This is also the conjugate of the unit complex number representing the rotation.

#### pub fn nlerp(self, end: Rotation2d, s: f32) -> Rotation2d

Performs a linear interpolation between `self` and `rhs` based on the value `s`, and normalizes the rotation afterwards.

When `s == 0.0`, the result will be equal to `self`. When `s == 1.0`, the result will be equal to `rhs`.

This is slightly more efficient than `slerp`, and produces a similar result when the difference between the two rotations is small. At larger differences, the result resembles a kind of ease-in-out effect.

If you would like the angular velocity to remain constant, consider using `slerp` instead.

##### §Details

`nlerp` corresponds to computing an angle for a point at position `s` on a line drawn between the endpoints of the arc formed by `self` and `rhs` on a unit circle, and normalizing the result afterwards.

Note that if the angles are opposite like 0 and π, the line will pass through the origin, and the resulting angle will always be either `self` or `rhs` depending on `s`. If `s` happens to be `0.5` in this case, a valid rotation cannot be computed, and `self` will be returned as a fallback.

##### §Example
``````let rot1 = Rotation2d::IDENTITY;
let rot2 = Rotation2d::degrees(135.0);

let result1 = rot1.nlerp(rot2, 1.0 / 3.0);
assert_eq!(result1.as_degrees(), 28.675055);

let result2 = rot1.nlerp(rot2, 0.5);
assert_eq!(result2.as_degrees(), 67.5);``````

#### pub fn slerp(self, end: Rotation2d, s: f32) -> Rotation2d

Performs a spherical linear interpolation between `self` and `end` based on the value `s`.

This corresponds to interpolating between the two angles at a constant angular velocity.

When `s == 0.0`, the result will be equal to `self`. When `s == 1.0`, the result will be equal to `rhs`.

If you would like the rotation to have a kind of ease-in-out effect, consider using the slightly more efficient `nlerp` instead.

##### §Example
``````let rot1 = Rotation2d::IDENTITY;
let rot2 = Rotation2d::degrees(135.0);

let result1 = rot1.slerp(rot2, 1.0 / 3.0);
assert_eq!(result1.as_degrees(), 45.0);

let result2 = rot1.slerp(rot2, 0.5);
assert_eq!(result2.as_degrees(), 67.5);``````

## Trait Implementations§

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### impl Clone for Rotation2d

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#### fn clone(&self) -> Rotation2d

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl Debug for Rotation2d

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

Formats the value using the given formatter. Read more
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### impl Default for Rotation2d

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#### fn default() -> Rotation2d

Returns the “default value” for a type. Read more
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### impl<'de> Deserialize<'de> for Rotation2d

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#### fn deserialize<__D>( __deserializer: __D ) -> Result<Rotation2d, <__D as Deserializer<'de>>::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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### impl From<Rotation2d> for Mat2

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#### fn from(rot: Rotation2d) -> Mat2

Creates a `Mat2` rotation matrix from a `Rotation2d`.

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### impl From<f32> for Rotation2d

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#### fn from(rotation: f32) -> Rotation2d

Creates a `Rotation2d` from a counterclockwise angle in radians.

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### impl FromReflect for Rotation2dwhere Rotation2d: Any + Send + Sync, f32: FromReflect + TypePath + RegisterForReflection,

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#### fn from_reflect(reflect: &(dyn Reflect + 'static)) -> Option<Rotation2d>

Constructs a concrete instance of `Self` from a reflected value.
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#### fn take_from_reflect( reflect: Box<dyn Reflect> ) -> Result<Self, Box<dyn Reflect>>

Attempts to downcast the given value to `Self` using, constructing the value using `from_reflect` if that fails. Read more
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### impl GetTypeRegistration for Rotation2dwhere Rotation2d: Any + Send + Sync, f32: FromReflect + TypePath + RegisterForReflection,

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#### fn get_type_registration() -> TypeRegistration

Returns the default `TypeRegistration` for this type.
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#### fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this type. Read more
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### impl Mul<Dir2> for Rotation2d

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#### type Output = Dir2

The resulting type after applying the `*` operator.
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### impl Mul<Vec2> for Rotation2d

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#### type Output = Vec2

The resulting type after applying the `*` operator.
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### impl Mul for Rotation2d

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#### type Output = Rotation2d

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation2d) -> <Rotation2d as Mul>::Output

Performs the `*` operation. Read more
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### impl MulAssign for Rotation2d

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#### fn mul_assign(&mut self, rhs: Rotation2d)

Performs the `*=` operation. Read more
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### impl PartialEq for Rotation2d

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#### fn eq(&self, other: &Rotation2d) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`.
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#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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### impl Reflect for Rotation2dwhere Rotation2d: Any + Send + Sync, f32: FromReflect + TypePath + RegisterForReflection,

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#### fn get_represented_type_info(&self) -> Option<&'static TypeInfo>

Returns the `TypeInfo` of the type represented by this value. Read more
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#### fn into_any(self: Box<Rotation2d>) -> Box<dyn Any>

Returns the value as a `Box<dyn Any>`.
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#### fn as_any(&self) -> &(dyn Any + 'static)

Returns the value as a `&dyn Any`.
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#### fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)

Returns the value as a `&mut dyn Any`.
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#### fn into_reflect(self: Box<Rotation2d>) -> Box<dyn Reflect>

Casts this type to a boxed reflected value.
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#### fn as_reflect(&self) -> &(dyn Reflect + 'static)

Casts this type to a reflected value.
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#### fn as_reflect_mut(&mut self) -> &mut (dyn Reflect + 'static)

Casts this type to a mutable reflected value.
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#### fn clone_value(&self) -> Box<dyn Reflect>

Clones the value as a `Reflect` trait object. Read more
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Performs a type-checked assignment of a reflected value to this value. Read more
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Tries to `apply` a reflected value to this value. Read more
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Returns a zero-sized enumeration of “kinds” of type. Read more
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Returns an immutable enumeration of “kinds” of type. Read more
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#### fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type. Read more
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#### fn reflect_owned(self: Box<Rotation2d>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type. Read more
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#### fn reflect_partial_eq(&self, value: &(dyn Reflect + 'static)) -> Option<bool>

Returns a “partial equality” comparison result. Read more
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#### fn debug(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Debug formatter for the value. Read more
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#### fn apply(&mut self, value: &(dyn Reflect + 'static))

Applies a reflected value to this value. Read more
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#### fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type). Read more
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Returns a serializable version of the value. Read more
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#### fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type. Read more
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### impl Serialize for Rotation2d

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

Serialize this value into the given Serde serializer. Read more
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### impl Struct for Rotation2dwhere Rotation2d: Any + Send + Sync, f32: FromReflect + TypePath + RegisterForReflection,

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#### fn field(&self, name: &str) -> Option<&(dyn Reflect + 'static)>

Returns a reference to the value of the field named `name` as a `&dyn Reflect`.
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Returns a mutable reference to the value of the field named `name` as a `&mut dyn Reflect`.
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Returns a reference to the value of the field with index `index` as a `&dyn Reflect`.
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Returns a mutable reference to the value of the field with index `index` as a `&mut dyn Reflect`.
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#### fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index `index`.
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#### fn field_len(&self) -> usize

Returns the number of fields in the struct.
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#### fn iter_fields(&self) -> FieldIter<'_> ⓘ

Returns an iterator over the values of the reflectable fields for this struct.
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#### fn clone_dynamic(&self) -> DynamicStruct

Clones the struct into a `DynamicStruct`.
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### impl TypePath for Rotation2dwhere Rotation2d: Any + Send + Sync,

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#### fn type_path() -> &'static str

Returns the fully qualified path of the underlying type. Read more
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#### fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type. Read more
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Returns the name of the type, or `None` if it is anonymous. Read more
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#### fn crate_name() -> Option<&'static str>

Returns the name of the crate the type is in, or `None` if it is anonymous. Read more
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#### fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or `None` if it is anonymous. Read more
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### impl Typed for Rotation2dwhere Rotation2d: Any + Send + Sync, f32: FromReflect + TypePath + RegisterForReflection,

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#### fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.
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Gets the `TypeId` of `self`. Read more
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Return the `T` `ShaderType` for `self`. When used in `AsBindGroup` derives, it is safe to assume that all images in `self` exist.
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Mutably borrows from an owned value. Read more
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Convert `Box<dyn Trait>` (where `Trait: Downcast`) to `Box<dyn Any>`. `Box<dyn Any>` can then be further `downcast` into `Box<ConcreteType>` where `ConcreteType` implements `Trait`.
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Convert `&Trait` (where `Trait: Downcast`) to `&Any`. This is needed since Rust cannot generate `&Any`’s vtable from `&Trait`’s.
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Returns a reference to the value of the field named `name`, downcast to `T`.
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Returns a mutable reference to the value of the field named `name`, downcast to `T`.
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Converts `self` into a `Left` variant of `Either<Self, Self>` if `into_left` is `true`. Converts `self` into a `Right` variant of `Either<Self, Self>` otherwise. Read more
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The none-equivalent value.
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The alignment of pointer.
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The type for initializers.
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Dereferences the given pointer. Read more
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