# Struct euclid::rotation::Rotation3D[−][src]

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

## Implementations

### `impl<T, Src, Dst> Rotation3D<T, Src, Dst>`[src]

#### `pub fn quaternion(a: T, b: T, c: T, r: T) -> Self`[src]

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, `[src]

Creates the identity rotation.

### `impl<T, Src, Dst> Rotation3D<T, Src, Dst> where    T: Copy, `[src]

#### `pub fn vector_part(&self) -> Vector3D<T, UnknownUnit>`[src]

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

#### `pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2>`[src]

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>`[src]

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`[src]

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: Float, `[src]

#### `pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Self`[src]

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`[src]

Creates a rotation around a given axis.

#### `pub fn around_x(angle: Angle<T>) -> Self`[src]

Creates a rotation around the x axis.

#### `pub fn around_y(angle: Angle<T>) -> Self`[src]

Creates a rotation around the y axis.

#### `pub fn around_z(angle: Angle<T>) -> Self`[src]

Creates a rotation around the z axis.

#### `pub fn euler(roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>) -> Self`[src]

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>`[src]

Returns the inverse of this rotation.

#### `pub fn norm(&self) -> T`[src]

Computes the norm of this quaternion.

#### `pub fn square_norm(&self) -> T`[src]

Computes the squared norm of this quaternion.

#### `pub fn normalize(&self) -> Self`[src]

Returns a unit quaternion from this one.

#### `pub fn is_normalized(&self) -> bool where    T: ApproxEq<T>, `[src]

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

#### `pub fn slerp(&self, other: &Self, t: T) -> Self where    T: ApproxEq<T>, `[src]

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`[src]

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>, `[src]

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>, `[src]

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>, `[src]

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>, `[src]

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>, `[src]

Returns the matrix representation of this rotation.

#### `pub fn pre_rotate<NewSrc>(    &self,     other: &Rotation3D<T, NewSrc, Src>) -> Rotation3D<T, NewSrc, Dst> where    T: ApproxEq<T>, `[src]

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

#### `pub fn post_rotate<NewDst>(    &self,     other: &Rotation3D<T, Dst, NewDst>) -> Rotation3D<T, Src, NewDst> where    T: ApproxEq<T>, `[src]

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

## Blanket Implementations

### `impl<T> ToOwned for T where    T: Clone, `[src]

#### `type Owned = T`

The resulting type after obtaining ownership.

### `impl<T, U> TryFrom<U> for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto<U> for T where    U: TryFrom<T>, `[src]

#### `type Error = <U as TryFrom<T>>::Error`

The type returned in the event of a conversion error.