Struct nannou::math::Basis2 [−][src]
pub struct Basis2<S> { /* 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 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
Trait Implementations
impl<S> Clone for Basis2<S> where
S: Clone,
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impl<S> Clone for Basis2<S> where
S: Clone,
fn clone(&self) -> Basis2<S>
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fn clone(&self) -> Basis2<S>
Returns a copy of the value. Read more
fn clone_from(&mut self, source: &Self)
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fn clone_from(&mut self, source: &Self)
Performs copy-assignment from source
. Read more
impl<S> Debug for Basis2<S> where
S: Debug,
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impl<S> Debug for Basis2<S> where
S: Debug,
fn fmt(&self, f: &mut Formatter) -> Result<(), Error>
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fn fmt(&self, f: &mut Formatter) -> Result<(), Error>
Formats the value using the given formatter. Read more
impl<'a, 'b, S> Mul<&'a Basis2<S>> for &'b Basis2<S> where
S: BaseFloat,
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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>
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fn mul(self, other: &'a Basis2<S>) -> Basis2<S>
Performs the *
operation.
impl<S> Mul<Basis2<S>> for Basis2<S> where
S: BaseFloat,
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impl<S> Mul<Basis2<S>> 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>
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fn mul(self, other: Basis2<S>) -> Basis2<S>
Performs the *
operation.
impl<'a, S> Mul<Basis2<S>> for &'a Basis2<S> where
S: BaseFloat,
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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>
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fn mul(self, other: Basis2<S>) -> Basis2<S>
Performs the *
operation.
impl<'a, S> Mul<&'a Basis2<S>> for Basis2<S> where
S: BaseFloat,
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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>
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fn mul(self, other: &'a Basis2<S>) -> Basis2<S>
Performs the *
operation.
impl<S> One for Basis2<S> where
S: BaseFloat,
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impl<S> One for Basis2<S> where
S: BaseFloat,
fn one() -> Basis2<S>
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fn one() -> Basis2<S>
Returns the multiplicative identity element of Self
, 1
. Read more
fn is_one(&self) -> bool where
Self: PartialEq<Self>,
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fn is_one(&self) -> bool where
Self: PartialEq<Self>,
Returns true
if self
is equal to the multiplicative identity. Read more
impl<S> Serialize for Basis2<S> where
S: Serialize,
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impl<S> Serialize for Basis2<S> where
S: Serialize,
fn serialize<__S>(
&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
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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
impl<S> AsRef<Matrix2<S>> for Basis2<S> where
S: BaseFloat,
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impl<S> AsRef<Matrix2<S>> for Basis2<S> where
S: BaseFloat,
impl<'de, S> Deserialize<'de> for Basis2<S> where
S: Deserialize<'de>,
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impl<'de, S> Deserialize<'de> for Basis2<S> where
S: Deserialize<'de>,
fn deserialize<__D>(
__deserializer: __D
) -> Result<Basis2<S>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
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fn deserialize<__D>(
__deserializer: __D
) -> Result<Basis2<S>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
Deserialize this value from the given Serde deserializer. Read more
impl<S> From<Basis2<S>> for Matrix2<S> where
S: BaseFloat,
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impl<S> From<Basis2<S>> for Matrix2<S> where
S: BaseFloat,
impl<S> ApproxEq for Basis2<S> where
S: BaseFloat,
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impl<S> ApproxEq for Basis2<S> where
S: BaseFloat,
type Epsilon = <S as ApproxEq>::Epsilon
Used for specifying relative comparisons.
fn default_epsilon() -> <S as ApproxEq>::Epsilon
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fn default_epsilon() -> <S as ApproxEq>::Epsilon
The default tolerance to use when testing values that are close together. Read more
fn default_max_relative() -> <S as ApproxEq>::Epsilon
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fn default_max_relative() -> <S as ApproxEq>::Epsilon
The default relative tolerance for testing values that are far-apart. Read more
fn default_max_ulps() -> u32
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fn default_max_ulps() -> u32
The default ULPs to tolerate when testing values that are far-apart. Read more
fn relative_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_relative: <S as ApproxEq>::Epsilon
) -> bool
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fn relative_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_relative: <S as ApproxEq>::Epsilon
) -> bool
A test for equality that uses a relative comparison if the values are far apart.
fn ulps_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_ulps: u32
) -> bool
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fn ulps_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_ulps: u32
) -> bool
A test for equality that uses units in the last place (ULP) if the values are far apart.
fn relative_ne(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
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fn relative_ne(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
The inverse of ApproxEq::relative_eq
.
fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool
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fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool
The inverse of ApproxEq::ulps_eq
.
impl<S> Product<Basis2<S>> for Basis2<S> where
S: BaseFloat,
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impl<S> Product<Basis2<S>> for Basis2<S> where
S: BaseFloat,
fn product<I>(iter: I) -> Basis2<S> where
I: Iterator<Item = Basis2<S>>,
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fn product<I>(iter: I) -> Basis2<S> where
I: Iterator<Item = Basis2<S>>,
Method which takes an iterator and generates Self
from the elements by multiplying the items. Read more
impl<'a, S> Product<&'a Basis2<S>> for Basis2<S> where
S: 'a + BaseFloat,
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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>>,
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fn product<I>(iter: I) -> Basis2<S> where
I: Iterator<Item = &'a Basis2<S>>,
Method which takes an iterator and generates Self
from the elements by multiplying the items. Read more
impl<S> Copy for Basis2<S> where
S: Copy,
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impl<S> Copy for Basis2<S> where
S: Copy,
impl<S> PartialEq<Basis2<S>> for Basis2<S> where
S: PartialEq<S>,
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impl<S> PartialEq<Basis2<S>> for Basis2<S> where
S: PartialEq<S>,
fn eq(&self, other: &Basis2<S>) -> bool
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fn eq(&self, other: &Basis2<S>) -> bool
This method tests for self
and other
values to be equal, and is used by ==
. Read more
fn ne(&self, other: &Basis2<S>) -> bool
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fn ne(&self, other: &Basis2<S>) -> bool
This method tests for !=
.
impl<S> Rotation2<S> for Basis2<S> where
S: BaseFloat,
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impl<S> Rotation2<S> for Basis2<S> where
S: BaseFloat,
fn from_angle<A>(theta: A) -> Basis2<S> where
A: Into<Rad<S>>,
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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. Read more
impl<S> Rotation<Point2<S>> for Basis2<S> where
S: BaseFloat,
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impl<S> Rotation<Point2<S>> for Basis2<S> where
S: BaseFloat,
fn look_at(dir: Vector2<S>, up: Vector2<S>) -> Basis2<S>
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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>
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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>
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fn rotate_vector(&self, vec: Vector2<S>) -> Vector2<S>
Rotate a vector using this rotation.
fn invert(&self) -> Basis2<S>
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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
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fn rotate_point(&self, point: P) -> P
Rotate a point using this rotation, by converting it to its representation as a vector. Read more