[−][src]Struct nannou::math::Basis2
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> AsRef<Matrix2<S>> for Basis2<S> where
S: BaseFloat,
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S: BaseFloat,
impl<S> Rotation2<S> for Basis2<S> where
S: BaseFloat,
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S: BaseFloat,
fn from_angle<A>(theta: A) -> Basis2<S> where
A: Into<Rad<S>>,
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A: Into<Rad<S>>,
impl<S> Copy for Basis2<S> where
S: Copy,
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S: Copy,
impl<S> Serialize for Basis2<S> where
S: Serialize,
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S: Serialize,
fn serialize<__S>(
&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
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&self,
__serializer: __S
) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error> where
__S: Serializer,
impl<'de, S> Deserialize<'de> for Basis2<S> where
S: Deserialize<'de>,
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S: Deserialize<'de>,
fn deserialize<__D>(
__deserializer: __D
) -> Result<Basis2<S>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
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__deserializer: __D
) -> Result<Basis2<S>, <__D as Deserializer<'de>>::Error> where
__D: Deserializer<'de>,
impl<S> One for Basis2<S> where
S: BaseFloat,
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S: BaseFloat,
fn one() -> Basis2<S>
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fn set_one(&mut self)
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fn is_one(&self) -> bool where
Self: PartialEq<Self>,
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Self: PartialEq<Self>,
impl<S> Debug for Basis2<S> where
S: Debug,
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S: Debug,
impl<S> PartialEq<Basis2<S>> for Basis2<S> where
S: PartialEq<S>,
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S: PartialEq<S>,
impl<'a, S> Mul<Basis2<S>> for &'a Basis2<S> where
S: BaseFloat,
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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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impl<S> Mul<Basis2<S>> for Basis2<S> where
S: BaseFloat,
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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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impl<'a, S> Mul<&'a Basis2<S>> for Basis2<S> where
S: BaseFloat,
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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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impl<'a, 'b, S> Mul<&'a Basis2<S>> for &'b Basis2<S> where
S: BaseFloat,
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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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impl<S> Rotation<Point2<S>> for Basis2<S> where
S: BaseFloat,
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S: BaseFloat,
fn look_at(dir: Vector2<S>, up: Vector2<S>) -> Basis2<S>
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fn between_vectors(a: Vector2<S>, b: Vector2<S>) -> Basis2<S>
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fn rotate_vector(&self, vec: Vector2<S>) -> Vector2<S>
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fn invert(&self) -> Basis2<S>
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fn rotate_point(&self, point: P) -> P
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impl<S> Product<Basis2<S>> for Basis2<S> where
S: BaseFloat,
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S: BaseFloat,
impl<'a, S> Product<&'a Basis2<S>> for Basis2<S> where
S: 'a + BaseFloat,
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S: 'a + BaseFloat,
impl<S> ApproxEq for Basis2<S> where
S: BaseFloat,
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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_max_relative() -> <S as ApproxEq>::Epsilon
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fn default_max_ulps() -> u32
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fn relative_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_relative: <S as ApproxEq>::Epsilon
) -> bool
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&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_relative: <S as ApproxEq>::Epsilon
) -> bool
fn ulps_eq(
&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_ulps: u32
) -> bool
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&self,
other: &Basis2<S>,
epsilon: <S as ApproxEq>::Epsilon,
max_ulps: u32
) -> bool
fn relative_ne(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
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&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
fn ulps_ne(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool
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impl<S> Clone for Basis2<S> where
S: Clone,
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S: Clone,
impl<S> From<Basis2<S>> for Matrix2<S> where
S: BaseFloat,
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S: BaseFloat,
Auto Trait Implementations
impl<S> Send for Basis2<S> where
S: Send,
S: Send,
impl<S> Unpin for Basis2<S> where
S: Unpin,
S: Unpin,
impl<S> Sync for Basis2<S> where
S: Sync,
S: Sync,
impl<S> UnwindSafe for Basis2<S> where
S: UnwindSafe,
S: UnwindSafe,
impl<S> RefUnwindSafe for Basis2<S> where
S: RefUnwindSafe,
S: RefUnwindSafe,
Blanket Implementations
impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
fn to_owned(&self) -> T
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fn clone_into(&self, target: &mut T)
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> From<T> for T
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impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,
type Error = <U as TryFrom<T>>::Error
The type returned in the event of a conversion error.
fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>
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impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
fn borrow_mut(&mut self) -> &mut T
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impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Style for T where
T: Any + Debug + PartialEq<T>,
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T: Any + Debug + PartialEq<T>,
impl<T> DeserializeOwned for T where
T: Deserialize<'de>,
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T: Deserialize<'de>,
impl<T> Content for T
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fn ref_from_ptr(ptr: *mut c_void, size: usize) -> Option<*mut T>
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fn is_size_suitable(size: usize) -> bool
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fn indiv_size() -> usize
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impl<T> One for T where
T: One,
T: One,
fn one() -> T
impl<T> SafeBorrow<T> for T
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impl<S, D, Swp, Dwp, T> AdaptInto<D, Swp, Dwp, T> for S where
D: AdaptFrom<S, Swp, Dwp, T>,
Dwp: WhitePoint,
Swp: WhitePoint,
T: Component + Float,
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D: AdaptFrom<S, Swp, Dwp, T>,
Dwp: WhitePoint,
Swp: WhitePoint,
T: Component + Float,
fn adapt_into_using<M>(self, method: M) -> D where
M: TransformMatrix<Swp, Dwp, T>,
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M: TransformMatrix<Swp, Dwp, T>,
fn adapt_into(self) -> D
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impl<T> SetParameter for T
fn set<T>(&mut self, value: T) -> <T as Parameter<Self>>::Result where
T: Parameter<Self>,
T: Parameter<Self>,
impl<T> SetParameter for T
fn set<T>(&mut self, value: T) -> <T as Parameter<Self>>::Result where
T: Parameter<Self>,
T: Parameter<Self>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
V: MultiLane<T>,