# Struct cgmath::Basis3 [−] [src]

```pub struct Basis3<S> {
// some fields omitted
}```

A three-dimensional rotation matrix.

The matrix is guaranteed to be orthogonal, so some operations, specifically inversion, can be implemented more efficiently than the implementations for `math::Matrix3`. To ensure orthogonality is maintained, the operations have been restricted to a subeset of those implemented on `Matrix3`.

## Methods

### `impl<S: BaseFloat> Basis3<S>`[src]

#### `fn from_quaternion(quaternion: &Quaternion<S>) -> Basis3<S>`

Create a new rotation matrix from a quaternion.

## Trait Implementations

### `impl<S: BaseFloat> From<Quaternion<S>> for Basis3<S>`[src]

#### `fn from(quat: Quaternion<S>) -> Basis3<S>`

Performs the conversion.

### `impl<S: Clone> Clone for Basis3<S>`[src]

#### `fn clone(&self) -> Basis3<S>`

Returns a copy of the value. Read more

#### `fn clone_from(&mut self, source: &Self)`1.0.0

Performs copy-assignment from `source`. Read more

### `impl<S: PartialEq> PartialEq for Basis3<S>`[src]

#### `fn eq(&self, __arg_0: &Basis3<S>) -> bool`

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

#### `fn ne(&self, __arg_0: &Basis3<S>) -> bool`

This method tests for `!=`.

### `impl<S> AsRef<Matrix3<S>> for Basis3<S>`[src]

#### `fn as_ref(&self) -> &Matrix3<S>`

Performs the conversion.

### `impl<S: BaseFloat> Rotation<Point3<S>> for Basis3<S>`[src]

#### `fn look_at(dir: Vector3<S>, up: Vector3<S>) -> Basis3<S>`

Create a rotation to a given direction with an 'up' vector

#### `fn between_vectors(a: Vector3<S>, b: Vector3<S>) -> Basis3<S>`

Create a shortest rotation to transform vector 'a' into 'b'. Both given vectors are assumed to have unit length. Read more

#### `fn rotate_vector(&self, vec: Vector3<S>) -> Vector3<S>`

Rotate a vector using this rotation.

#### `fn invert(&self) -> Basis3<S>`

Create a new rotation which "un-does" this rotation. That is, `r * r.invert()` is the identity. Read more

#### `fn rotate_point(&self, point: P) -> P`

Rotate a point using this rotation, by converting it to its representation as a vector. Read more

### `impl<S: BaseFloat> One for Basis3<S>`[src]

#### `fn one() -> Basis3<S>`

Returns the multiplicative identity element of `Self`, `1`. Read more

### `impl<S: BaseFloat> Mul<Basis3<S>> for Basis3<S>`[src]

#### `type Output = Basis3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Basis3<S>) -> Basis3<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<&'a Basis3<S>> for Basis3<S>`[src]

#### `type Output = Basis3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Basis3<S>) -> Basis3<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<Basis3<S>> for &'a Basis3<S>`[src]

#### `type Output = Basis3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Basis3<S>) -> Basis3<S>`

The method for the `*` operator

### `impl<'a, 'b, S: BaseFloat> Mul<&'a Basis3<S>> for &'b Basis3<S>`[src]

#### `type Output = Basis3<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Basis3<S>) -> Basis3<S>`

The method for the `*` operator

### `impl<S: BaseFloat> Rotation3<S> for Basis3<S>`[src]

#### `fn from_axis_angle<A: Into<Rad<S>>>(axis: Vector3<S>, angle: A) -> Basis3<S>`

Create a rotation using an angle around a given axis. Read more

#### `fn from_angle_x<A: Into<Rad<S>>>(theta: A) -> Basis3<S>`

Create a rotation from an angle around the `x` axis (pitch).

#### `fn from_angle_y<A: Into<Rad<S>>>(theta: A) -> Basis3<S>`

Create a rotation from an angle around the `y` axis (yaw).

#### `fn from_angle_z<A: Into<Rad<S>>>(theta: A) -> Basis3<S>`

Create a rotation from an angle around the `z` axis (roll).

### `impl<A: Angle> From<Euler<A>> for Basis3<A::Unitless> where A: Into<Rad<A::Unitless>>`[src]

#### `fn from(src: Euler<A>) -> Basis3<A::Unitless>`

Create a three-dimensional rotation matrix from a set of euler angles.

### `impl<S: Debug> Debug for Basis3<S>`[src]

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

Formats the value using the given formatter.