Struct Basis2

pub struct Basis2<S> { /* private fields */ }

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::UlpsEq;
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 approx's assert_ulps_eq!() feature to show that it is close enough.
// assert_ulps_eq!(&unit_y, &Vector2::unit_y()); // TODO: Figure out how to use this

// 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_ulps_eq!(&unit_y3, &unit_y2); // TODO: Figure out how to use this

Implementations

impl<S> Basis2<S>

where S: BaseFloat,

pub fn look_at_stable(dir: Vector2<S>, flip: bool) -> Basis2<S>

Trait Implementations

impl<S> AbsDiffEq for Basis2<S>

where S: BaseFloat,

type Epsilon = <S as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> <S as AbsDiffEq>::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq( &self, other: &Basis2<S>, epsilon: <S as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<S> AsRef<Matrix2<S>> for Basis2<S>

where S: BaseFloat,

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

Converts this type into a shared reference of the (usually inferred) input type.

impl<S> Clone for Basis2<S>

where S: Clone,

fn clone(&self) -> Basis2<S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<S> Debug for Basis2<S>

where S: Debug,

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

Formats the value using the given formatter.

impl<S> From<Basis2<S>> for Matrix2<S>

where S: BaseFloat,

fn from(b: Basis2<S>) -> Matrix2<S>

Converts to this type from the input type.

impl<'a, 'b, S> Mul<&'a Basis2<S>> for &'b Basis2<S>

where S: BaseFloat,

type Output = Basis2<S>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, S> Mul<&'a Basis2<S>> for Basis2<S>

where S: BaseFloat,

type Output = Basis2<S>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, S> Mul<Basis2<S>> for &'a Basis2<S>

where S: BaseFloat,

type Output = Basis2<S>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<S> Mul for Basis2<S>

where S: BaseFloat,

type Output = Basis2<S>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<S> One for Basis2<S>

where S: BaseFloat,

fn one() -> Basis2<S>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<S> PartialEq for Basis2<S>

where S: PartialEq,

fn eq(&self, other: &Basis2<S>) -> 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<'a, S> Product<&'a Basis2<S>> for Basis2<S>

where S: 'a + BaseFloat,

fn product<I>(iter: I) -> Basis2<S>

where I: Iterator<Item = &'a Basis2<S>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<S> Product for Basis2<S>

where S: BaseFloat,

fn product<I>(iter: I) -> Basis2<S>

where I: Iterator<Item = Basis2<S>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<S> RelativeEq for Basis2<S>

where S: BaseFloat,

fn default_max_relative() -> <S as AbsDiffEq>::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Basis2<S>, epsilon: <S as AbsDiffEq>::Epsilon, max_relative: <S as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<S> Rotation for Basis2<S>

where S: BaseFloat,

type Space = Point2<S>

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.

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.

fn rotate_point(&self, point: Self::Space) -> Self::Space

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

impl<S> Rotation2 for Basis2<S>

where S: BaseFloat,

type Scalar = S

fn from_angle<A>(theta: A) -> Basis2<S>

where A: Into<Rad<S>>,

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

impl<S> UlpsEq for Basis2<S>

where S: BaseFloat,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq( &self, other: &Basis2<S>, epsilon: <S as AbsDiffEq>::Epsilon, max_ulps: u32, ) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<S> Copy for Basis2<S>

where S: Copy,

impl<S> StructuralPartialEq for Basis2<S>