math_utils

Struct LinearAuto

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pub struct LinearAuto<S, V>(pub LinearIso<S, V, V, V::LinearEndo>)
where
    V: Module<S>,
    V::LinearEndo: MaybeSerDes,
    S: Ring;
Expand description

Invertible linear endomorphism

Tuple Fields§

§0: LinearIso<S, V, V, V::LinearEndo>

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impl<S, V> LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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pub fn is_orthonormal(&self) -> bool

Returns false if called with a matrix that is not orthogonal with determinant +/-1.

This method checks whether mat * mat^T == I and mat.determinant() == +/-1.

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pub fn is_orthonormal_approx(&self) -> bool
where S: RelativeEq<Epsilon = S>, V::LinearEndo: RelativeEq<Epsilon = S>,

Returns None if called with a matrix that is not orthogonal with determinant +/-1.

This method checks whether mat * mat^T == I and mat.determinant() == +/-1 (approximately using relative equality).

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pub fn is_rotation(&self) -> bool

Checks whether the transformation is a special orthogonal matrix.

This method checks whether mat * mat^T == I and mat.determinant() == 1.

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pub fn is_rotation_approx(&self) -> bool
where S: RelativeEq<Epsilon = S>, V::LinearEndo: RelativeEq<Epsilon = S>,

Checks whether the transformation is a special orthogonal matrix.

This method checks whether mat * mat^T == I and mat.determinant() == 1 (approximately using relative equality).

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impl<S, V> Clone for LinearAuto<S, V>
where V: Module<S> + Clone, V::LinearEndo: MaybeSerDes + Clone, S: Ring + Clone,

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fn clone(&self) -> LinearAuto<S, V>

Returns a duplicate of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<S, V> Debug for LinearAuto<S, V>
where V: Module<S> + Debug, V::LinearEndo: MaybeSerDes + Debug, S: Ring + Debug,

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

Formats the value using the given formatter. Read more
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impl<S, V> Default for LinearAuto<S, V>
where V: Module<S> + Default, V::LinearEndo: MaybeSerDes + Default, S: Ring + Default,

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fn default() -> LinearAuto<S, V>

Returns the “default value” for a type. Read more
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impl<S, V> Deref for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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type Target = LinearIso<S, V, V, <V as Module<S>>::LinearEndo>

The resulting type after dereferencing.
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fn deref(&self) -> &Self::Target

Dereferences the value.
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impl<S, V> Display for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring, LinearIso<S, V, V, V::LinearEndo>: Display,

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

Formats the value using the given formatter. Read more
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impl<S> Div for LinearAuto<S, Vector2<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec2<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S> Div for LinearAuto<S, Vector3<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec3<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S> Div for LinearAuto<S, Vector4<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec4<S>>

The resulting type after applying the / operator.
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fn div(self, rhs: Self) -> Self::Output

Performs the / operation. Read more
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impl<S> DivAssign for LinearAuto<S, Vector2<S>>
where S: Ring + Float + MaybeSerDes,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S> DivAssign for LinearAuto<S, Vector3<S>>
where S: Ring + Float + MaybeSerDes,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S> DivAssign for LinearAuto<S, Vector4<S>>
where S: Ring + Float + MaybeSerDes,

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fn div_assign(&mut self, rhs: Self)

Performs the /= operation. Read more
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impl<S, V> From<LinearIso<S, V, V, <V as Module<S>>::LinearEndo>> for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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fn from(value: LinearIso<S, V, V, V::LinearEndo>) -> Self

Converts to this type from the input type.
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impl<S> Inv for LinearAuto<S, Vector2<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec2<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S> Inv for LinearAuto<S, Vector3<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec3<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S> Inv for LinearAuto<S, Vector4<S>>
where S: Ring + Float + MaybeSerDes,

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type Output = LinearAuto<S, Vec4<S>>

The result after applying the operator.
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fn inv(self) -> Self::Output

Returns the multiplicative inverse of self. Read more
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impl<S> Mul<LinearAuto<S, Vec2<S>>> for Vector2<S>
where S: Ring + MaybeSerDes,

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type Output = Vec2<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearAuto<S, Self>) -> Self::Output

Performs the * operation. Read more
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impl<S> Mul<LinearAuto<S, Vec3<S>>> for Vector3<S>
where S: Ring + MaybeSerDes,

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type Output = Vec3<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearAuto<S, Self>) -> Self::Output

Performs the * operation. Read more
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impl<S> Mul<LinearAuto<S, Vec4<S>>> for Vector4<S>
where S: Ring + MaybeSerDes,

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type Output = Vec4<S>

The resulting type after applying the * operator.
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fn mul(self, rhs: LinearAuto<S, Self>) -> Self::Output

Performs the * operation. Read more
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impl<S, V> Mul<V> for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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type Output = V

The resulting type after applying the * operator.
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fn mul(self, rhs: V) -> Self::Output

Performs the * operation. Read more
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impl<S, V> Mul for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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type Output = LinearAuto<S, V>

The resulting type after applying the * operator.
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fn mul(self, rhs: Self) -> Self::Output

Performs the * operation. Read more
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impl<S, V> MulAssign for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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fn mul_assign(&mut self, rhs: Self)

Performs the *= operation. Read more
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impl<S, V> One for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

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fn one() -> Self

Returns the multiplicative identity element of Self, 1. Read more
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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl<S, V> PartialEq for LinearAuto<S, V>
where V: Module<S> + PartialEq, V::LinearEndo: MaybeSerDes + PartialEq, S: Ring + PartialEq,

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fn eq(&self, other: &LinearAuto<S, V>) -> bool

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl<S, V> Copy for LinearAuto<S, V>
where V: Module<S> + Copy, V::LinearEndo: MaybeSerDes + Copy, S: Ring + Copy,

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impl<S> MultiplicativeGroup for LinearAuto<S, Vector2<S>>
where S: Ring + Float + MaybeSerDes,

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impl<S> MultiplicativeGroup for LinearAuto<S, Vector3<S>>
where S: Ring + Float + MaybeSerDes,

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impl<S> MultiplicativeGroup for LinearAuto<S, Vector4<S>>
where S: Ring + Float + MaybeSerDes,

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impl<S, V> MultiplicativeMonoid for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes + PartialEq, S: Ring,

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impl<S, V> StructuralPartialEq for LinearAuto<S, V>
where V: Module<S>, V::LinearEndo: MaybeSerDes, S: Ring,

Auto Trait Implementations§

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impl<S, V> Freeze for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: Freeze,

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impl<S, V> RefUnwindSafe for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: RefUnwindSafe, S: RefUnwindSafe, V: RefUnwindSafe,

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impl<S, V> Send for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: Send, S: Send, V: Send,

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impl<S, V> Sync for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: Sync, S: Sync, V: Sync,

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impl<S, V> Unpin for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: Unpin, S: Unpin, V: Unpin,

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impl<S, V> UnwindSafe for LinearAuto<S, V>
where <V as Module<S>>::LinearEndo: UnwindSafe, S: UnwindSafe, V: UnwindSafe,

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Az for T

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fn az<Dst>(self) -> Dst
where T: Cast<Dst>,

Casts the value.
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<Src, Dst> CastFrom<Src> for Dst
where Src: Cast<Dst>,

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fn cast_from(src: Src) -> Dst

Casts the value.
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impl<T> CheckedAs for T

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fn checked_as<Dst>(self) -> Option<Dst>
where T: CheckedCast<Dst>,

Casts the value.
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impl<Src, Dst> CheckedCastFrom<Src> for Dst
where Src: CheckedCast<Dst>,

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fn checked_cast_from(src: Src) -> Option<Dst>

Casts the value.
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> IntoEither for T

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fn into_either(self, into_left: bool) -> Either<Self, Self>

Converts self into a Left variant of Either<Self, Self> if into_left is true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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fn into_either_with<F>(self, into_left: F) -> Either<Self, Self>
where F: FnOnce(&Self) -> bool,

Converts self into a Left variant of Either<Self, Self> if into_left(&self) returns true. Converts self into a Right variant of Either<Self, Self> otherwise. Read more
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impl<Src, Dst> LosslessTryInto<Dst> for Src
where Dst: LosslessTryFrom<Src>,

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fn lossless_try_into(self) -> Option<Dst>

Performs the conversion.
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impl<Src, Dst> LossyInto<Dst> for Src
where Dst: LossyFrom<Src>,

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fn lossy_into(self) -> Dst

Performs the conversion.
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impl<T> OverflowingAs for T

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fn overflowing_as<Dst>(self) -> (Dst, bool)
where T: OverflowingCast<Dst>,

Casts the value.
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impl<Src, Dst> OverflowingCastFrom<Src> for Dst
where Src: OverflowingCast<Dst>,

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fn overflowing_cast_from(src: Src) -> (Dst, bool)

Casts the value.
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impl<P, T> Receiver for P
where P: Deref<Target = T> + ?Sized, T: ?Sized,

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type Target = T

🔬This is a nightly-only experimental API. (arbitrary_self_types)
The target type on which the method may be called.
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impl<T> Same for T

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type Output = T

Should always be Self
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impl<T> SaturatingAs for T

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fn saturating_as<Dst>(self) -> Dst
where T: SaturatingCast<Dst>,

Casts the value.
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impl<Src, Dst> SaturatingCastFrom<Src> for Dst
where Src: SaturatingCast<Dst>,

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fn saturating_cast_from(src: Src) -> Dst

Casts the value.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T> UnwrappedAs for T

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fn unwrapped_as<Dst>(self) -> Dst
where T: UnwrappedCast<Dst>,

Casts the value.
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impl<Src, Dst> UnwrappedCastFrom<Src> for Dst
where Src: UnwrappedCast<Dst>,

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fn unwrapped_cast_from(src: Src) -> Dst

Casts the value.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> WrappingAs for T

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fn wrapping_as<Dst>(self) -> Dst
where T: WrappingCast<Dst>,

Casts the value.
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impl<Src, Dst> WrappingCastFrom<Src> for Dst
where Src: WrappingCast<Dst>,

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fn wrapping_cast_from(src: Src) -> Dst

Casts the value.
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impl<T> MaybeSerDes for T