# Struct cgmath::Basis2 [−] [src]

```pub struct Basis2<S> {
// some fields omitted
}```

A two-dimensional rotation matrix.

The matrix is guaranteed to be orthogonal, so some operations can be implemented more efficiently than the implementations for `math::Matrix2`. To enforce orthogonality at the type level the operations have been restricted to a subset of those implemented on `Matrix2`.

## Example

Suppose we want to rotate a vector that lies in the x-y plane by some angle. We can accomplish this quite easily with a two-dimensional rotation matrix:

```use cgmath::Rad;
use cgmath::Vector2;
use cgmath::{Matrix, Matrix2};
use cgmath::{Rotation, Rotation2, Basis2};
use cgmath::ApproxEq;
use std::f64;

// For simplicity, we will rotate the unit x vector to the unit y vector --
// so the angle is 90 degrees, or π/2.
let unit_x: Vector2<f64> = Vector2::unit_x();
let rot: Basis2<f64> = Rotation2::from_angle(Rad(0.5f64 * f64::consts::PI));

// Rotate the vector using the two-dimensional rotation matrix:
let unit_y = rot.rotate_vector(unit_x);

// Since sin(π/2) may not be exactly zero due to rounding errors, we can
// use cgmath's approx_eq() feature to show that it is close enough.
assert!(unit_y.approx_eq(&Vector2::unit_y()));

// This is exactly equivalent to using the raw matrix itself:
let unit_y2: Matrix2<_> = rot.into();
let unit_y2 = unit_y2 * unit_x;
assert_eq!(unit_y2, unit_y);

// Note that we can also concatenate rotations:
let rot_half: Basis2<f64> = Rotation2::from_angle(Rad(0.25f64 * f64::consts::PI));
let unit_y3 = (rot_half * rot_half).rotate_vector(unit_x);
assert!(unit_y3.approx_eq(&unit_y2));```

## Trait Implementations

### `impl<S: Clone> Clone for Basis2<S>`[src]

#### `fn clone(&self) -> Basis2<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 Basis2<S>`[src]

#### `fn eq(&self, __arg_0: &Basis2<S>) -> bool`

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

#### `fn ne(&self, __arg_0: &Basis2<S>) -> bool`

This method tests for `!=`.

### `impl<S: BaseFloat> AsRef<Matrix2<S>> for Basis2<S>`[src]

#### `fn as_ref(&self) -> &Matrix2<S>`

Performs the conversion.

### `impl<S: BaseFloat> Rotation<Point2<S>> for Basis2<S>`[src]

#### `fn look_at(dir: Vector2<S>, up: Vector2<S>) -> Basis2<S>`

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

#### `fn between_vectors(a: Vector2<S>, b: Vector2<S>) -> Basis2<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: Vector2<S>) -> Vector2<S>`

Rotate a vector using this rotation.

#### `fn invert(&self) -> Basis2<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 Basis2<S>`[src]

#### `fn one() -> Basis2<S>`

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

### `impl<S: BaseFloat> Mul<Basis2<S>> for Basis2<S>`[src]

#### `type Output = Basis2<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Basis2<S>) -> Basis2<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<&'a Basis2<S>> for Basis2<S>`[src]

#### `type Output = Basis2<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Basis2<S>) -> Basis2<S>`

The method for the `*` operator

### `impl<'a, S: BaseFloat> Mul<Basis2<S>> for &'a Basis2<S>`[src]

#### `type Output = Basis2<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: Basis2<S>) -> Basis2<S>`

The method for the `*` operator

### `impl<'a, 'b, S: BaseFloat> Mul<&'a Basis2<S>> for &'b Basis2<S>`[src]

#### `type Output = Basis2<S>`

The resulting type after applying the `*` operator

#### `fn mul(self, other: &'a Basis2<S>) -> Basis2<S>`

The method for the `*` operator

### `impl<S: BaseFloat> Rotation2<S> for Basis2<S>`[src]

#### `fn from_angle<A: Into<Rad<S>>>(theta: A) -> Basis2<S>`

Create a rotation by a given angle. Thus is a redundant case of both from_axis_angle() and from_euler() for 2D space. Read more

### `impl<S: Debug> Debug for Basis2<S>`[src]

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

Formats the value using the given formatter.