Scale in nalgebra::geometry - Rust
Description: A scale which supports non-uniform scaling.
Keywords: rust, rustlang, rust-lang, Scale

# Struct nalgebra::geometry::Scale

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    #[repr(C)]pub struct Scale<T, const D: usize> {
        pub vector: SVector<T, D>,
    }

Expand description

A scale which supports non-uniform scaling.

## Fields§

§`vector: SVector<T, D>`

The scale coordinates, i.e., how much is multiplied to a point’s coordinates when it is scaled.

## Implementations§

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### impl<T: Scalar, const D: usize> Scale<T, D>

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#### pub fn try_inverse(&self) -> Option<Scale<T, D>>where
T: ClosedDiv + One + Zero,

Inverts `self`.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    assert_eq!(t * t.try_inverse().unwrap(), Scale3::identity());
    assert_eq!(t.try_inverse().unwrap() * t, Scale3::identity());

    // Work in all dimensions.
    let t = Scale2::new(1.0, 2.0);
    assert_eq!(t * t.try_inverse().unwrap(), Scale2::identity());
    assert_eq!(t.try_inverse().unwrap() * t, Scale2::identity());

    // Returns None if any coordinate is 0.
    let t = Scale2::new(0.0, 2.0);
    assert_eq!(t.try_inverse(), None);

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#### pub unsafe fn inverse_unchecked(&self) -> Scale<T, D>where
T: ClosedDiv + One,

Inverts `self`.

##### Example

    unsafe {
        let t = Scale3::new(1.0, 2.0, 3.0);
        assert_eq!(t * t.inverse_unchecked(), Scale3::identity());
        assert_eq!(t.inverse_unchecked() * t, Scale3::identity());

        // Work in all dimensions.
        let t = Scale2::new(1.0, 2.0);
        assert_eq!(t * t.inverse_unchecked(), Scale2::identity());
        assert_eq!(t.inverse_unchecked() * t, Scale2::identity());
    }

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#### pub fn pseudo_inverse(&self) -> Scale<T, D>where
T: ClosedDiv + One + Zero,

Inverts `self`.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    assert_eq!(t * t.pseudo_inverse(), Scale3::identity());
    assert_eq!(t.pseudo_inverse() * t, Scale3::identity());

    // Work in all dimensions.
    let t = Scale2::new(1.0, 2.0);
    assert_eq!(t * t.pseudo_inverse(), Scale2::identity());
    assert_eq!(t.pseudo_inverse() * t, Scale2::identity());

    // Inverts only non-zero coordinates.
    let t = Scale2::new(0.0, 2.0);
    assert_eq!(t * t.pseudo_inverse(), Scale2::new(0.0, 1.0));
    assert_eq!(t.pseudo_inverse() * t, Scale2::new(0.0, 1.0));

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#### pub fn to_homogeneous(
&self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
T: Zero + One + Clone,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, DimNameSum<Const<D>, U1>, U1>,

Converts this Scale into its equivalent homogeneous transformation matrix.

##### Example

    let t = Scale3::new(10.0, 20.0, 30.0);
    let expected = Matrix4::new(10.0, 0.0, 0.0, 0.0,
                                0.0, 20.0, 0.0, 0.0,
                                0.0, 0.0, 30.0, 0.0,
                                0.0, 0.0, 0.0, 1.0);
    assert_eq!(t.to_homogeneous(), expected);

    let t = Scale2::new(10.0, 20.0);
    let expected = Matrix3::new(10.0, 0.0, 0.0,
                                0.0, 20.0, 0.0,
                                0.0, 0.0, 1.0);
    assert_eq!(t.to_homogeneous(), expected);

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#### pub fn try_inverse_mut(&mut self) -> bool where
T: ClosedDiv + One + Zero,

Inverts `self` in-place.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    let mut inv_t = Scale3::new(1.0, 2.0, 3.0);
    assert!(inv_t.try_inverse_mut());
    assert_eq!(t * inv_t, Scale3::identity());
    assert_eq!(inv_t * t, Scale3::identity());

    // Work in all dimensions.
    let t = Scale2::new(1.0, 2.0);
    let mut inv_t = Scale2::new(1.0, 2.0);
    assert!(inv_t.try_inverse_mut());
    assert_eq!(t * inv_t, Scale2::identity());
    assert_eq!(inv_t * t, Scale2::identity());

    // Does not perform any operation if a coordinate is 0.
    let mut t = Scale2::new(0.0, 2.0);
    assert!(!t.try_inverse_mut());

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### impl<T: Scalar + ClosedMul, const D: usize> Scale<T, D>

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#### pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, D>

Translate the given point.

This is the same as the multiplication `self * pt`.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    let transformed_point = t.transform_point(&Point3::new(4.0, 5.0, 6.0));
    assert_eq!(transformed_point, Point3::new(4.0, 10.0, 18.0));

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### impl<T: Scalar + ClosedDiv + ClosedMul + One + Zero, const D: usize> Scale<T, D>

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#### pub fn try_inverse_transform_point(
&self,
pt: &Point<T, D>
) -> Option<Point<T, D>>

Translate the given point by the inverse of this Scale.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0)).unwrap();
    assert_eq!(transformed_point, Point3::new(4.0, 3.0, 2.0));

    // Returns None if the inverse doesn't exist.
    let t = Scale3::new(1.0, 0.0, 3.0);
    let transformed_point = t.try_inverse_transform_point(&Point3::new(4.0, 6.0, 6.0));
    assert_eq!(transformed_point, None);

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### impl<T: Scalar, const D: usize> Scale<T, D>

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#### pub fn identity() -> Scale<T, D>where
T: One,

Creates a new identity scale.

##### Example

    let t = Scale2::identity();
    let p = Point2::new(1.0, 2.0);
    assert_eq!(t * p, p);

    // Works in all dimensions.
    let t = Scale3::identity();
    let p = Point3::new(1.0, 2.0, 3.0);
    assert_eq!(t * p, p);

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#### pub fn cast<To: Scalar>(self) -> Scale<To, D>where
Scale<To, D>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let tra = Scale2::new(1.0f64, 2.0);
    let tra2 = tra.cast::<f32>();
    assert_eq!(tra2, Scale2::new(1.0f32, 2.0));

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### impl<T> Scale<T, 1>

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#### pub const fn new(x: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale1::new(1.0);
    assert!(t.vector.x == 1.0);

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### impl<T> Scale<T, 2>

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#### pub const fn new(x: T, y: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale2::new(1.0, 2.0);
    assert!(t.vector.x == 1.0 && t.vector.y == 2.0);

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### impl<T> Scale<T, 3>

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#### pub const fn new(x: T, y: T, z: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale3::new(1.0, 2.0, 3.0);
    assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0);

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### impl<T> Scale<T, 4>

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#### pub const fn new(x: T, y: T, z: T, w: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale4::new(1.0, 2.0, 3.0, 4.0);
    assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0);

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### impl<T> Scale<T, 5>

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#### pub const fn new(x: T, y: T, z: T, w: T, a: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale5::new(1.0, 2.0, 3.0, 4.0, 5.0);
    assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0);

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### impl<T> Scale<T, 6>

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#### pub const fn new(x: T, y: T, z: T, w: T, a: T, b: T) -> Self

Initializes this Scale from its components.

##### Example

    let t = Scale6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
    assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0 && t.vector.b == 6.0);

## Trait Implementations§

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### impl<T: Scalar + AbsDiffEq, const D: usize> AbsDiffEq<Scale<T, D>> for Scale<T, D>where
T::Epsilon: Clone,

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#### type Epsilon = <T as AbsDiffEq<T>>::Epsilon

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T: Clone, const D: usize> Clone for Scale<T, D>

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#### fn clone(&self) -> Scale<T, D>

Returns a copy 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<T: Debug, const D: usize> Debug for Scale<T, D>

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

Formats the value using the given formatter. Read more
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### impl<T: Scalar> Deref for Scale<T, 1>

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#### type Target = X<T>

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

Dereferences the value.
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### impl<T: Scalar> Deref for Scale<T, 2>

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#### type Target = XY<T>

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

Dereferences the value.
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### impl<T: Scalar> Deref for Scale<T, 3>

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#### type Target = XYZ<T>

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

Dereferences the value.
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### impl<T: Scalar> Deref for Scale<T, 4>

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#### type Target = XYZW<T>

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

Dereferences the value.
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### impl<T: Scalar> Deref for Scale<T, 5>

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#### type Target = XYZWA<T>

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

Dereferences the value.
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### impl<T: Scalar> Deref for Scale<T, 6>

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#### type Target = XYZWAB<T>

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

Dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 1>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 2>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 3>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 4>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 5>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar> DerefMut for Scale<T, 6>

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#### fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.
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### impl<T: Scalar + Display, const D: usize> Display for Scale<T, D>

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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<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 16]> for Scale<T, D>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,

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#### fn from(arr: [Scale<T::Element, D>; 16]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 2]> for Scale<T, D>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,

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#### fn from(arr: [Scale<T::Element, D>; 2]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 4]> for Scale<T, D>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,

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#### fn from(arr: [Scale<T::Element, D>; 4]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Scale<<T as SimdValue>::Element, D>; 8]> for Scale<T, D>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,

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#### fn from(arr: [Scale<T::Element, D>; 8]) -> Self

Converts to this type from the input type.
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### impl<T: Scalar, const D: usize> From<[T; D]> for Scale<T, D>

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#### fn from(coords: [T; D]) -> Self

Converts to this type from the input type.
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### impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>, Const<1>>>::Buffer>> for Scale<T, D>

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#### fn from(vector: OVector<T, Const<D>>) -> Self

Converts to this type from the input type.
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### impl<T: Scalar, const D: usize> From<OPoint<T, Const<D>>> for Scale<T, D>

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#### fn from(pt: Point<T, D>) -> Self

Converts to this type from the input type.
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### impl<T: Scalar, const D: usize> From<Scale<T, D>> for [T; D]

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#### fn from(t: Scale<T, D>) -> Self

Converts to this type from the input type.
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### impl<T: Scalar + Zero + One, const D: usize> From<Scale<T, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, DimNameSum<Const<D>, U1>, U1> + Allocator<T, Const<D>>,

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#### fn from(t: Scale<T, D>) -> Self

Converts to this type from the input type.
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### impl<T: Scalar + Hash, const D: usize> Hash for Scale<T, D>where
Owned<T, Const<D>>: Hash,

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#### fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given `Hasher`. Read more
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#### fn hash_slice<H>(data: &[Self], state: &mut H)where
H: Hasher,
Self: Sized,

Feeds a slice of this type into the given `Hasher`. Read more
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### impl<'a, 'b, T, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, const D: usize> Mul<&'b Scale<T, D>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Scale<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> Mul<&'b Scale<T, D>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Scale<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<OPoint<T, Const<D>>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<Scale<T, D>> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Scale<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<Scale<T, D>> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Scale<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<T> for &'a Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

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

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<T> for Scale<T, D>where
T: Scalar + ClosedMul,
ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>,

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#### type Output = Scale<T, D>

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

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> MulAssign<&'b Scale<T, D>> for Scale<T, D>where
T: Scalar + ClosedMul,

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#### fn mul_assign(&mut self, right: &'b Scale<T, D>)

Performs the `*=` operation. Read more
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### impl<T, const D: usize> MulAssign<Scale<T, D>> for Scale<T, D>where
T: Scalar + ClosedMul,

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#### fn mul_assign(&mut self, right: Scale<T, D>)

Performs the `*=` operation. Read more
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### impl<T, const D: usize> MulAssign<T> for Scale<T, D>where
T: Scalar + ClosedMul,

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#### fn mul_assign(&mut self, right: T)

Performs the `*=` operation. Read more
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### impl<T: Scalar + One + ClosedMul, const D: usize> One for Scale<T, D>

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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<Self>,

Returns `true` if `self` is equal to the multiplicative identity. Read more
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### impl<T: Scalar + PartialEq, const D: usize> PartialEq<Scale<T, D>> for Scale<T, D>

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#### fn eq(&self, right: &Scale<T, D>) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
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#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: Scalar + RelativeEq, const D: usize> RelativeEq<Scale<T, D>> for Scale<T, D>where
T::Epsilon: Clone,

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T: Scalar + SimdValue, const D: usize> SimdValue for Scale<T, D>where
T::Element: Scalar,

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#### type Element = Scale<<T as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.
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#### type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like `self`.
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#### fn lanes() -> usize

The number of lanes of this SIMD value.
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#### fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to `val`.
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#### fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self`. Read more
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#### unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self` without bound-checking.
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#### fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val`. Read more
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#### unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val` without bound-checking.
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#### fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges `self` and `other` depending on the lanes of `cond`. Read more
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#### fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self`. Read more
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#### fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self` paired with the corresponding lane of `b`. Read more
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### impl<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Scale<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T1, DimNameSum<Const<D>, U1>, U1> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn to_superset(
&self
) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2, const D: usize> SubsetOf<Scale<T2, D>> for Scale<T1, D>where
T1: Scalar,
T2: Scalar + SupersetOf<T1>,

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#### fn to_superset(&self) -> Scale<T2, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(rot: &Scale<T2, D>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(rot: &Scale<T2, D>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Scale<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T1, DimNameSum<Const<D>, U1>, U1> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn to_superset(&self) -> Transform<T2, C, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(t: &Transform<T2, C, D>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(t: &Transform<T2, C, D>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T: Scalar + UlpsEq, const D: usize> UlpsEq<Scale<T, D>> for Scale<T, D>where
T::Epsilon: Clone,

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: Copy, const D: usize> Copy for Scale<T, D>

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### impl<T: Scalar + Eq, const D: usize> Eq for Scale<T, D>

## Auto Trait Implementations§

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### impl<T, const D: usize> RefUnwindSafe for Scale<T, D>where
T: RefUnwindSafe,

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### impl<T, const D: usize> Send for Scale<T, D>where
T: Send,

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### impl<T, const D: usize> Sync for Scale<T, D>where
T: Sync,

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### impl<T, const D: usize> Unpin for Scale<T, D>where
T: Unpin,

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### impl<T, const D: usize> UnwindSafe for Scale<T, D>where
T: UnwindSafe,

## Blanket Implementations§

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### impl<T> Any for Twhere
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> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

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

const: unstable · source§

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

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### 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> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T> ToOwned for Twhere
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 Twhere
T: Display + ?Sized,

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#### default fn to_string(&self) -> String

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

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#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### 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 Twhere
U: TryFrom<T>,

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

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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### impl<T, Right> ClosedMul<Right> for Twhere
T: Mul<Right, Output = T> + MulAssign<Right>,