Struct nalgebra::geometry::Point

#[repr(C)]
pub struct Point<N: Scalar, D: DimName>where
    DefaultAllocator: Allocator<N, D>,{
    pub coords: VectorN<N, D>,
}

A point in a n-dimensional euclidean space.

Fields

coords: VectorN<N, D>

The coordinates of this point, i.e., the shift from the origin.

Implementations

impl<N: Scalar, D: DimName> Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

pub fn to_homogeneous(&self) -> VectorN<N, DimNameSum<D, U1>>where
    N: One,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>>,

Converts this point into a vector in homogeneous coordinates, i.e., appends a 1 at the end of it.

This is the same as .into().

Example

let p = Point2::new(10.0, 20.0);
assert_eq!(p.to_homogeneous(), Vector3::new(10.0, 20.0, 1.0));

// This works in any dimension.
let p = Point3::new(10.0, 20.0, 30.0);
assert_eq!(p.to_homogeneous(), Vector4::new(10.0, 20.0, 30.0, 1.0));

pub fn from_coordinates(coords: VectorN<N, D>) -> Point<N, D>

👎Deprecated: Use Point::from(vector) instead.

Creates a new point with the given coordinates.

pub fn len(&self) -> usize

The dimension of this point.

Example

let p = Point2::new(1.0, 2.0);
assert_eq!(p.len(), 2);

// This works in any dimension.
let p = Point3::new(10.0, 20.0, 30.0);
assert_eq!(p.len(), 3);

pub fn stride(&self) -> usize

👎Deprecated: This methods is no longer significant and will always return 1.

The stride of this point. This is the number of buffer element separating each component of this point.

pub fn iter(
    &self
) -> MatrixIter<'_, N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer>

Iterates through this point coordinates.

Example

let p = Point3::new(1.0, 2.0, 3.0);
let mut it = p.iter().cloned();

assert_eq!(it.next(), Some(1.0));
assert_eq!(it.next(), Some(2.0));
assert_eq!(it.next(), Some(3.0));
assert_eq!(it.next(), None);

pub unsafe fn get_unchecked(&self, i: usize) -> &N

Gets a reference to i-th element of this point without bound-checking.

pub fn iter_mut(
    &mut self
) -> MatrixIterMut<'_, N, D, U1, <DefaultAllocator as Allocator<N, D>>::Buffer>

Mutably iterates through this point coordinates.

Example

let mut p = Point3::new(1.0, 2.0, 3.0);

for e in p.iter_mut() {
    *e *= 10.0;
}

assert_eq!(p, Point3::new(10.0, 20.0, 30.0));

pub unsafe fn get_unchecked_mut(&mut self, i: usize) -> &mut N

Gets a mutable reference to i-th element of this point without bound-checking.

pub unsafe fn swap_unchecked(&mut self, i1: usize, i2: usize)

Swaps two entries without bound-checking.

impl<N: Scalar, D: DimName> Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

pub unsafe fn new_uninitialized() -> Self

Creates a new point with uninitialized coordinates.

pub fn origin() -> Selfwhere
    N: Zero,

Creates a new point with all coordinates equal to zero.

Example

// This works in any dimension.
// The explicit ::<f32> type annotation may not always be needed,
// depending on the context of type inference.
let pt = Point2::<f32>::origin();
assert!(pt.x == 0.0 && pt.y == 0.0);

let pt = Point3::<f32>::origin();
assert!(pt.x == 0.0 && pt.y == 0.0 && pt.z == 0.0);

pub fn from_slice(components: &[N]) -> Self

Creates a new point from a slice.

Example

let data = [ 1.0, 2.0, 3.0 ];

let pt = Point2::from_slice(&data[..2]);
assert_eq!(pt, Point2::new(1.0, 2.0));

let pt = Point3::from_slice(&data);
assert_eq!(pt, Point3::new(1.0, 2.0, 3.0));

pub fn from_homogeneous(v: VectorN<N, DimNameSum<D, U1>>) -> Option<Self>where
    N: Scalar + Zero + One + ClosedDiv,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>>,

Creates a new point from its homogeneous vector representation.

In practice, this builds a D-dimensional points with the same first D component as v divided by the last component of v. Returns None if this divisor is zero.

Example

let coords = Vector4::new(1.0, 2.0, 3.0, 1.0);
let pt = Point3::from_homogeneous(coords);
assert_eq!(pt, Some(Point3::new(1.0, 2.0, 3.0)));

// All component of the result will be divided by the
// last component of the vector, here 2.0.
let coords = Vector4::new(1.0, 2.0, 3.0, 2.0);
let pt = Point3::from_homogeneous(coords);
assert_eq!(pt, Some(Point3::new(0.5, 1.0, 1.5)));

// Fails because the last component is zero.
let coords = Vector4::new(1.0, 2.0, 3.0, 0.0);
let pt = Point3::from_homogeneous(coords);
assert!(pt.is_none());

// Works also in other dimensions.
let coords = Vector3::new(1.0, 2.0, 1.0);
let pt = Point2::from_homogeneous(coords);
assert_eq!(pt, Some(Point2::new(1.0, 2.0)));

impl<N: Scalar> Point<N, U1>where
    DefaultAllocator: Allocator<N, U1>,

pub fn new(x: N) -> Point<N, U1>

Initializes this point from its components.

Example

let p = Point1::new(1.0);
assert!(p.x == 1.0);

impl<N: Scalar> Point<N, U2>where
    DefaultAllocator: Allocator<N, U2>,

pub fn new(x: N, y: N) -> Point<N, U2>

Initializes this point from its components.

Example

let p = Point2::new(1.0, 2.0);
assert!(p.x == 1.0 && p.y == 2.0);

impl<N: Scalar> Point<N, U3>where
    DefaultAllocator: Allocator<N, U3>,

pub fn new(x: N, y: N, z: N) -> Point<N, U3>

Initializes this point from its components.

Example

let p = Point3::new(1.0, 2.0, 3.0);
assert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0);

impl<N: Scalar> Point<N, U4>where
    DefaultAllocator: Allocator<N, U4>,

pub fn new(x: N, y: N, z: N, w: N) -> Point<N, U4>

Initializes this point from its components.

Example

let p = Point4::new(1.0, 2.0, 3.0, 4.0);
assert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0);

impl<N: Scalar> Point<N, U5>where
    DefaultAllocator: Allocator<N, U5>,

pub fn new(x: N, y: N, z: N, w: N, a: N) -> Point<N, U5>

Initializes this point from its components.

Example

let p = Point5::new(1.0, 2.0, 3.0, 4.0, 5.0);
assert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0);

impl<N: Scalar> Point<N, U6>where
    DefaultAllocator: Allocator<N, U6>,

pub fn new(x: N, y: N, z: N, w: N, a: N, b: N) -> Point<N, U6>

Initializes this point from its components.

Example

let p = Point6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
assert!(p.x == 1.0 && p.y == 2.0 && p.z == 3.0 && p.w == 4.0 && p.a == 5.0 && p.b == 6.0);

impl<N: Scalar, D: DimName> Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    D::Value: Cmp<U0, Output = Greater>,

pub fn xx(&self) -> Point2<N>

Builds a new point from components of self.

pub fn xxx(&self) -> Point3<N>

Builds a new point from components of self.

impl<N: Scalar, D: DimName> Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    D::Value: Cmp<U1, Output = Greater>,

pub fn xy(&self) -> Point2<N>

Builds a new point from components of self.

pub fn yx(&self) -> Point2<N>

Builds a new point from components of self.

pub fn yy(&self) -> Point2<N>

Builds a new point from components of self.

pub fn xxy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xyx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xyy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yxx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yxy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yyx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yyy(&self) -> Point3<N>

Builds a new point from components of self.

impl<N: Scalar, D: DimName> Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    D::Value: Cmp<U2, Output = Greater>,

pub fn xz(&self) -> Point2<N>

Builds a new point from components of self.

pub fn yz(&self) -> Point2<N>

Builds a new point from components of self.

pub fn zx(&self) -> Point2<N>

Builds a new point from components of self.

pub fn zy(&self) -> Point2<N>

Builds a new point from components of self.

pub fn zz(&self) -> Point2<N>

Builds a new point from components of self.

pub fn xxz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xyz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xzx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xzy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn xzz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yxz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yyz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yzx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yzy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn yzz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zxx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zxy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zxz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zyx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zyy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zyz(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zzx(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zzy(&self) -> Point3<N>

Builds a new point from components of self.

pub fn zzz(&self) -> Point3<N>

Builds a new point from components of self.

Trait Implementations

impl<N: Scalar + AbsDiffEq, D: DimName> AbsDiffEq<Point<N, D>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    N::Epsilon: Copy,

type Epsilon = <N as AbsDiffEq<N>>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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.

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

The inverse of ApproxEq::abs_diff_eq.

impl<'a, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Matrix<N, D2, U1, SB>> for &'a Point<N, D1>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Matrix<N, D2, U1, SB>> for &'a Point<N, D1>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the + operator.

fn add(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the + operation.

impl<'b, N, D1: DimName, D2: Dim, SB> AddAssign<&'b Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedAdd,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>,

fn add_assign(&mut self, right: &'b Vector<N, D2, SB>)

Performs the += operation.

impl<N, D1: DimName, D2: Dim, SB> AddAssign<Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedAdd,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>,

fn add_assign(&mut self, right: Vector<N, D2, SB>)

Performs the += operation.

impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>where
    N: Scalar + Field,
    DefaultAllocator: Allocator<N, D>,

type Translation = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The associated vector space.

fn translate_by(&self, t: &Self::Translation) -> Self

Same as *self + *t. Applies the additive group action of this affine space’s associated vector space on self.

fn subtract(&self, right: &Self) -> Self::Translation

Same as *self - *other. Returns the unique element v of the associated vector space such that self = right + v.

impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Rotation = R

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Translation<N, D>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Translation<N, D>, R, Id, R)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, t: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, t: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(
    &self,
    r: &Self::Rotation,
    p: &Point<N, D>
) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

type Rotation = Rotation<N, D>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Id, Self, Id, Self)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, _: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, _: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type NonUniformScaling = N

Type of the non-uniform scaling to be applied.

type Rotation = R

Type of the first rotation to be applied.

type Translation = Translation<N, D>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Translation<N, D>, R, N, R)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, t: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, t: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(
    &self,
    r: &Self::Rotation,
    p: &Point<N, D>
) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Rotation = Id<Multiplicative>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Translation<N, D>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Self, Id, Id, Id)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, t: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, t: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, _: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, _: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real> AffineTransformation<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

type Rotation = Unit<Complex<N>>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Id, Self, Id, Self)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, _: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, _: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real> AffineTransformation<Point<N, U3>> for UnitQuaternion<N>

type Rotation = Unit<Quaternion<N>>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Id, Self, Id, Self)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, _: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, _: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Scalar + Bounded, D: DimName> Bounded for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn max_value() -> Self

Returns the largest finite number this type can represent

fn min_value() -> Self

Returns the smallest finite number this type can represent

impl<N: Clone + Scalar, D: Clone + DimName> Clone for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn clone(&self) -> Point<N, D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug + Scalar, D: Debug + DimName> Debug for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

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

Formats the value using the given formatter.

impl<N: Scalar> Deref for Point<N, U1>where
    DefaultAllocator: Allocator<N, U1>,

type Target = X<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Point<N, U2>where
    DefaultAllocator: Allocator<N, U2>,

type Target = XY<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Point<N, U3>where
    DefaultAllocator: Allocator<N, U3>,

type Target = XYZ<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Point<N, U4>where
    DefaultAllocator: Allocator<N, U4>,

type Target = XYZW<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Point<N, U5>where
    DefaultAllocator: Allocator<N, U5>,

type Target = XYZWA<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Point<N, U6>where
    DefaultAllocator: Allocator<N, U6>,

type Target = XYZWAB<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U1>where
    DefaultAllocator: Allocator<N, U1>,

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

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U2>where
    DefaultAllocator: Allocator<N, U2>,

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

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U3>where
    DefaultAllocator: Allocator<N, U3>,

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

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U4>where
    DefaultAllocator: Allocator<N, U4>,

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

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U5>where
    DefaultAllocator: Allocator<N, U5>,

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

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Point<N, U6>where
    DefaultAllocator: Allocator<N, U6>,

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

Mutably dereferences the value.

impl<N: Scalar + Display, D: DimName> Display for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

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

Formats the value using the given formatter.

impl<N: Scalar, D: DimName> Distribution<Point<N, D>> for Standardwhere
    DefaultAllocator: Allocator<N, D>,
    Standard: Distribution<N>,

fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Point<N, D>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R, 'a>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T>where
    Self: Sized,
    R: Rng,

Create an iterator that generates random values of T, using rng as the source of randomness.

impl<'a, N: Scalar + ClosedDiv, D: DimName> Div<N> for &'a Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the / operator.

fn div(self, right: N) -> Self::Output

Performs the / operation.

impl<N: Scalar + ClosedDiv, D: DimName> Div<N> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the / operator.

fn div(self, right: N) -> Self::Output

Performs the / operation.

impl<N: Scalar + ClosedDiv, D: DimName> DivAssign<N> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, right: N)

Performs the /= operation.

impl<N: Real, D: DimName> EuclideanSpace for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Coordinates = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The underlying finite vector space.

type Real = N

The underlying reals.

fn origin() -> Self

The preferred origin of this euclidean space.

fn coordinates(&self) -> Self::Coordinates

The coordinates of this point, i.e., the translation from the origin.

fn from_coordinates(coords: Self::Coordinates) -> Self

Builds a point from its coordinates relative to the origin.

fn scale_by(&self, n: N) -> Self

Multiplies the distance of this point to Self::origin() by s.

fn distance_squared(&self, b: &Self) -> Self::Real

The distance between two points.

fn distance(&self, b: &Self) -> Self::Real

The distance between two points.

impl<N: Scalar> From<[N; 1]> for Point<N, U1>

fn from(coords: [N; 1]) -> Self

Converts to this type from the input type.

impl<N: Scalar> From<[N; 2]> for Point<N, U2>

fn from(coords: [N; 2]) -> Self

Converts to this type from the input type.

impl<N: Scalar> From<[N; 3]> for Point<N, U3>

fn from(coords: [N; 3]) -> Self

Converts to this type from the input type.

impl<N: Scalar> From<[N; 4]> for Point<N, U4>

fn from(coords: [N; 4]) -> Self

Converts to this type from the input type.

impl<N: Scalar> From<[N; 5]> for Point<N, U5>

fn from(coords: [N; 5]) -> Self

Converts to this type from the input type.

impl<N: Scalar> From<[N; 6]> for Point<N, U6>

fn from(coords: [N; 6]) -> Self

Converts to this type from the input type.

impl<N: Scalar, D: DimName> From<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn from(coords: VectorN<N, D>) -> Self

Converts to this type from the input type.

impl<N: Scalar + Zero + One, D: DimName> From<Point<N, D>> for VectorN<N, DimNameSum<D, U1>>where
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>>,

fn from(t: Point<N, D>) -> Self

Converts to this type from the input type.

impl<N: Scalar + Hash, D: DimName + Hash> Hash for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    <DefaultAllocator as Allocator<N, D>>::Buffer: Hash,

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

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)where
    H: Hasher,
    Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<N: Scalar, D: DimName> Index<usize> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = N

The returned type after indexing.

fn index(&self, i: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

impl<N: Scalar, D: DimName> IndexMut<usize> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn index_mut(&mut self, i: usize) -> &mut Self::Output

Performs the mutable indexing (container[index]) operation.

impl<N, D: DimName> JoinSemilattice for Point<N, D>where
    N: Scalar + JoinSemilattice,
    DefaultAllocator: Allocator<N, D>,

fn join(&self, other: &Self) -> Self

Returns the join (aka. supremum) of two values.

impl<N, D: DimName> Lattice for Point<N, D>where
    N: Scalar + Lattice,
    DefaultAllocator: Allocator<N, D>,

fn meet_join(&self, other: &Self) -> (Self, Self)

Returns the infimum and the supremum simultaneously.

fn partial_min<'a>(&'a self, other: &'a Self) -> Option<&'a Self>

Return the minimum of self and other if they are comparable.

fn partial_max<'a>(&'a self, other: &'a Self) -> Option<&'a Self>

Return the maximum of self and other if they are comparable.

fn partial_sort2<'a>(&'a self, other: &'a Self) -> Option<(&'a Self, &'a Self)>

Sorts two values in increasing order using a partial ordering.

fn partial_clamp<'a>(&'a self, min: &'a Self, max: &'a Self) -> Option<&'a Self>

Clamp value between min and max. Returns None if value is not comparable to min or max.

impl<N, D: DimName> MeetSemilattice for Point<N, D>where
    N: Scalar + MeetSemilattice,
    DefaultAllocator: Allocator<N, D>,

fn meet(&self, other: &Self) -> Self

Returns the meet (aka. infimum) of two values.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for &'a Isometry<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Point<N, D>> for &'a Rotation<N, D>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for &'a Similarity<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategory> Mul<&'b Point<N, D>> for &'a Transform<N, D, C>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,
    DefaultAllocator: Allocator<N, D, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Point<N, D>> for &'a Translation<N, D>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for Isometry<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimName> Mul<&'b Point<N, D>> for Rotation<N, D>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for Similarity<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategory> Mul<&'b Point<N, D>> for Transform<N, D, C>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,
    DefaultAllocator: Allocator<N, D, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimName> Mul<&'b Point<N, D>> for Translation<N, D>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Point<N, D2>> for &'a Matrix<N, R1, C1, SA>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>,

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Point<N, D2>> for Matrix<N, R1, C1, SA>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>,

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real> Mul<&'b Point<N, U2>> for &'a UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2, U1>,

type Output = Point<N, U2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point2<N>) -> Self::Output

Performs the * operation.

impl<'b, N: Real> Mul<&'b Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2, U1>,

type Output = Point<N, U2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point2<N>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real> Mul<&'b Point<N, U3>> for &'a UnitQuaternion<N>where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Point<N, U3>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point3<N>) -> Self::Output

Performs the * operation.

impl<'b, N: Real> Mul<&'b Point<N, U3>> for UnitQuaternion<N>where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Point<N, U3>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Point3<N>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<f32, D>> for f32where
    DefaultAllocator: Allocator<f32, D>,

type Output = Point<f32, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<f32, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<f64, D>> for f64where
    DefaultAllocator: Allocator<f64, D>,

type Output = Point<f64, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<f64, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<i16, D>> for i16where
    DefaultAllocator: Allocator<i16, D>,

type Output = Point<i16, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<i16, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<i32, D>> for i32where
    DefaultAllocator: Allocator<i32, D>,

type Output = Point<i32, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<i32, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<i64, D>> for i64where
    DefaultAllocator: Allocator<i64, D>,

type Output = Point<i64, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<i64, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<i8, D>> for i8where
    DefaultAllocator: Allocator<i8, D>,

type Output = Point<i8, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<i8, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<isize, D>> for isizewhere
    DefaultAllocator: Allocator<isize, D>,

type Output = Point<isize, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<isize, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<u16, D>> for u16where
    DefaultAllocator: Allocator<u16, D>,

type Output = Point<u16, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<u16, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<u32, D>> for u32where
    DefaultAllocator: Allocator<u32, D>,

type Output = Point<u32, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<u32, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<u64, D>> for u64where
    DefaultAllocator: Allocator<u64, D>,

type Output = Point<u64, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<u64, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<u8, D>> for u8where
    DefaultAllocator: Allocator<u8, D>,

type Output = Point<u8, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<u8, D>) -> Self::Output

Performs the * operation.

impl<'b, D: DimName> Mul<&'b Point<usize, D>> for usizewhere
    DefaultAllocator: Allocator<usize, D>,

type Output = Point<usize, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<usize, D>) -> Self::Output

Performs the * operation.

impl<'a, N: Scalar + ClosedMul, D: DimName> Mul<N> for &'a Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: N) -> Self::Output

Performs the * operation.

impl<N: Scalar + ClosedMul, D: DimName> Mul<N> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: N) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Point<N, D>> for &'a Isometry<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimName> Mul<Point<N, D>> for &'a Rotation<N, D>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Point<N, D>> for &'a Similarity<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategory> Mul<Point<N, D>> for &'a Transform<N, D, C>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,
    DefaultAllocator: Allocator<N, D, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimName> Mul<Point<N, D>> for &'a Translation<N, D>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Mul<Point<N, D>> for Isometry<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N, D: DimName> Mul<Point<N, D>> for Rotation<N, D>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Mul<Point<N, D>> for Similarity<N, D, R>where
    R: AlgaRotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategory> Mul<Point<N, D>> for Transform<N, D, C>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,
    DefaultAllocator: Allocator<N, D, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, rhs: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N, D: DimName> Mul<Point<N, D>> for Translation<N, D>where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Point<N, D2>> for &'a Matrix<N, R1, C1, SA>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>,

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D2>) -> Self::Output

Performs the * operation.

impl<N, R1: DimName, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Point<N, D2>> for Matrix<N, R1, C1, SA>where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, U1> + Allocator<N, R1, U1>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, U1>,

type Output = Point<N, R1>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, N: Real> Mul<Point<N, U2>> for &'a UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2, U1>,

type Output = Point<N, U2>

The resulting type after applying the * operator.

fn mul(self, rhs: Point2<N>) -> Self::Output

Performs the * operation.

impl<N: Real> Mul<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2, U1>,

type Output = Point<N, U2>

The resulting type after applying the * operator.

fn mul(self, rhs: Point2<N>) -> Self::Output

Performs the * operation.

impl<'a, N: Real> Mul<Point<N, U3>> for &'a UnitQuaternion<N>where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Point<N, U3>

The resulting type after applying the * operator.

fn mul(self, rhs: Point3<N>) -> Self::Output

Performs the * operation.

impl<N: Real> Mul<Point<N, U3>> for UnitQuaternion<N>where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Point<N, U3>

The resulting type after applying the * operator.

fn mul(self, rhs: Point3<N>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<f32, D>> for f32where
    DefaultAllocator: Allocator<f32, D>,

type Output = Point<f32, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<f32, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<f64, D>> for f64where
    DefaultAllocator: Allocator<f64, D>,

type Output = Point<f64, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<f64, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<i16, D>> for i16where
    DefaultAllocator: Allocator<i16, D>,

type Output = Point<i16, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<i16, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<i32, D>> for i32where
    DefaultAllocator: Allocator<i32, D>,

type Output = Point<i32, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<i32, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<i64, D>> for i64where
    DefaultAllocator: Allocator<i64, D>,

type Output = Point<i64, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<i64, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<i8, D>> for i8where
    DefaultAllocator: Allocator<i8, D>,

type Output = Point<i8, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<i8, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<isize, D>> for isizewhere
    DefaultAllocator: Allocator<isize, D>,

type Output = Point<isize, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<isize, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<u16, D>> for u16where
    DefaultAllocator: Allocator<u16, D>,

type Output = Point<u16, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<u16, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<u32, D>> for u32where
    DefaultAllocator: Allocator<u32, D>,

type Output = Point<u32, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<u32, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<u64, D>> for u64where
    DefaultAllocator: Allocator<u64, D>,

type Output = Point<u64, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<u64, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<u8, D>> for u8where
    DefaultAllocator: Allocator<u8, D>,

type Output = Point<u8, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<u8, D>) -> Self::Output

Performs the * operation.

impl<D: DimName> Mul<Point<usize, D>> for usizewhere
    DefaultAllocator: Allocator<usize, D>,

type Output = Point<usize, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<usize, D>) -> Self::Output

Performs the * operation.

impl<N: Scalar + ClosedMul, D: DimName> MulAssign<N> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, right: N)

Performs the *= operation.

impl<'a, N: Scalar + ClosedNeg, D: DimName> Neg for &'a Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<N: Scalar + ClosedNeg, D: DimName> Neg for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<N: Scalar, D: DimName> PartialEq<Point<N, D>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn eq(&self, right: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

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.

impl<N: Scalar + PartialOrd, D: DimName> PartialOrd<Point<N, D>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, right: &Self) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, right: &Self) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, right: &Self) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, right: &Self) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>where
    N: Real,
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Real, D: DimName> ProjectiveTransformation<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Real> ProjectiveTransformation<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Real> ProjectiveTransformation<Point<N, U3>> for UnitQuaternion<N>

fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N>

Applies this group’s inverse action on a point from the euclidean space.

fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N>

Applies this group’s inverse action on a vector from the euclidean space.

impl<N: Scalar + RelativeEq, D: DimName> RelativeEq<Point<N, D>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    N::Epsilon: Copy,

fn default_max_relative() -> Self::Epsilon

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

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.

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

The inverse of ApproxEq::relative_eq.

impl<N: Real, D: DimName> Rotation<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

Subgroups of the n-dimensional rotation group SO(n).

fn powf(&self, _: N) -> Option<Self>

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n.

fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self>

Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self.

fn scaled_rotation_between(
    _: &VectorN<N, D>,
    _: &VectorN<N, D>,
    _: N
) -> Option<Self>

Computes the rotation between a and b and raises it to the power n.

impl<N: Real> Rotation<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

fn powf(&self, n: N) -> Option<Self>

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n.

fn rotation_between(a: &Vector2<N>, b: &Vector2<N>) -> Option<Self>

Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self.

fn scaled_rotation_between(a: &Vector2<N>, b: &Vector2<N>, s: N) -> Option<Self>

Computes the rotation between a and b and raises it to the power n.

impl<N: Real> Rotation<Point<N, U3>> for UnitQuaternion<N>

fn powf(&self, n: N) -> Option<Self>

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n.

fn rotation_between(a: &Vector3<N>, b: &Vector3<N>) -> Option<Self>

Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self.

fn scaled_rotation_between(a: &Vector3<N>, b: &Vector3<N>, s: N) -> Option<Self>

Computes the rotation between a and b and raises it to the power n.

impl<N: Real, D: DimName, R> Similarity<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Translation<N, D>

The pure translational component of this similarity transformation.

fn rotation(&self) -> R

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<N: Real, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Id

The pure translational component of this similarity transformation.

fn rotation(&self) -> Self

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<N: Real, D: DimName, R> Similarity<Point<N, D>> for Similarity<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

type Scaling = N

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Translation<N, D>

The pure translational component of this similarity transformation.

fn rotation(&self) -> R

The pure rotational component of this similarity transformation.

fn scaling(&self) -> N

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<N: Real, D: DimName> Similarity<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Self

The pure translational component of this similarity transformation.

fn rotation(&self) -> Id

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<N: Real> Similarity<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Id

The pure translational component of this similarity transformation.

fn rotation(&self) -> Self

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<N: Real> Similarity<Point<N, U3>> for UnitQuaternion<N>

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Id

The pure translational component of this similarity transformation.

fn rotation(&self) -> Self

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

impl<'a, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Matrix<N, D2, U1, SB>> for &'a Point<N, D1>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: &'b Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<'a, 'b, N, D: DimName> Sub<&'b Point<N, D>> for &'a Point<N, D>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>,

type Output = Matrix<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, U1, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, <ShapeConstraint as SameNumberOfColumns<U1, U1>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub(self, right: &'b Point<N, D>) -> Self::Output

Performs the - operation.

impl<'b, N, D: DimName> Sub<&'b Point<N, D>> for Point<N, D>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>,

type Output = Matrix<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, U1, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, <ShapeConstraint as SameNumberOfColumns<U1, U1>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub(self, right: &'b Point<N, D>) -> Self::Output

Performs the - operation.

impl<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Matrix<N, D2, U1, SB>> for &'a Point<N, D1>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D1, U1> + Allocator<N, D2, U1> + SameShapeAllocator<N, D1, U1, D2, U1>,
    ShapeConstraint: SameNumberOfRows<D1, D2, Representative = D1> + SameNumberOfColumns<U1, U1>,

type Output = Point<N, D1>

The resulting type after applying the - operator.

fn sub(self, right: Vector<N, D2, SB>) -> Self::Output

Performs the - operation.

impl<'a, N, D: DimName> Sub<Point<N, D>> for &'a Point<N, D>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>,

type Output = Matrix<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, U1, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, <ShapeConstraint as SameNumberOfColumns<U1, U1>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub(self, right: Point<N, D>) -> Self::Output

Performs the - operation.

impl<N, D: DimName> Sub<Point<N, D>> for Point<N, D>where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>,

type Output = Matrix<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, U1, <DefaultAllocator as Allocator<N, <ShapeConstraint as SameNumberOfRows<D, D>>::Representative, <ShapeConstraint as SameNumberOfColumns<U1, U1>>::Representative>>::Buffer>

The resulting type after applying the - operator.

fn sub(self, right: Point<N, D>) -> Self::Output

Performs the - operation.

impl<'b, N, D1: DimName, D2: Dim, SB> SubAssign<&'b Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedSub,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>,

fn sub_assign(&mut self, right: &'b Vector<N, D2, SB>)

Performs the -= operation.

impl<N, D1: DimName, D2: Dim, SB> SubAssign<Matrix<N, D2, U1, SB>> for Point<N, D1>where
    N: Scalar + ClosedSub,
    SB: Storage<N, D2>,
    DefaultAllocator: Allocator<N, D1>,
    ShapeConstraint: SameNumberOfRows<D1, D2>,

fn sub_assign(&mut self, right: Vector<N, D2, SB>)

Performs the -= operation.

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, U1, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, U1>>::Buffer>> for Point<N1, D>where
    D: DimNameAdd<U1>,
    N1: Scalar,
    N2: Scalar + Zero + One + ClosedDiv + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>> + Allocator<N2, D>,

fn to_superset(&self) -> VectorN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(v: &VectorN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(v: &VectorN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D> SubsetOf<Point<N2, D>> for Point<N1, D>where
    D: DimName,
    N1: Scalar,
    N2: Scalar + SupersetOf<N1>,
    DefaultAllocator: Allocator<N2, D> + Allocator<N1, D>,

fn to_superset(&self) -> Point<N2, D>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &Point<N2, D>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

unsafe fn from_superset_unchecked(m: &Point<N2, D>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, <D as DimNameSub<U1>>::Output>> for MatrixN<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameDiff<D, U1>> + Allocator<N, DimNameDiff<D, U1>, DimNameDiff<D, U1>>,

fn transform_vector(
    &self,
    v: &VectorN<N, DimNameDiff<D, U1>>
) -> VectorN<N, DimNameDiff<D, U1>>

Applies this group’s action on a vector from the euclidean space.

fn transform_point(
    &self,
    pt: &Point<N, DimNameDiff<D, U1>>
) -> Point<N, DimNameDiff<D, U1>>

Applies this group’s action on a point from the euclidean space.

impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real, D: DimName> Transformation<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s action on a vector from the euclidean space.

impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>where
    N: Real,
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real, D: DimName> Transformation<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real> Transformation<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

fn transform_point(&self, pt: &Point2<N>) -> Point2<N>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real> Transformation<Point<N, U3>> for UnitQuaternion<N>

fn transform_point(&self, pt: &Point3<N>) -> Point3<N>

Applies this group’s action on a point from the euclidean space.

fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N>

Applies this group’s action on a vector from the euclidean space.

impl<N: Real, D: DimName> Translation<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

Subgroups of the n-dimensional translation group T(n).

fn to_vector(&self) -> VectorN<N, D>

Converts this translation to a vector.

fn from_vector(v: VectorN<N, D>) -> Option<Self>

Attempts to convert a vector to this translation. Returns None if the translation represented by v is not part of the translation subgroup represented by Self.

fn powf(&self, n: N) -> Option<Self>

Raises the translation to a power. The result must be equivalent to self.to_superset() * n. Returns None if the result is not representable by Self.

fn translation_between(a: &Point<N, D>, b: &Point<N, D>) -> Option<Self>

The translation needed to make a coincide with b, i.e., b = a * translation_to(a, b).

impl<N: Scalar + UlpsEq, D: DimName> UlpsEq<Point<N, D>> for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    N::Epsilon: Copy,

fn default_max_ulps() -> u32

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

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.

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

The inverse of ApproxEq::ulps_eq.

impl<N: Scalar, D: DimName> Copy for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,
    <DefaultAllocator as Allocator<N, D>>::Buffer: Copy,

impl<N: Real, D: DimName, R> DirectIsometry<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName> DirectIsometry<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

impl<N: Real, D: DimName> DirectIsometry<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

impl<N: Real> DirectIsometry<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

impl<N: Real> DirectIsometry<Point<N, U3>> for UnitQuaternion<N>

impl<N: Scalar + Eq, D: DimName> Eq for Point<N, D>where
    DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName, R> Isometry<Point<N, D>> for Isometry<N, D, R>where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName> Isometry<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

impl<N: Real, D: DimName> Isometry<Point<N, D>> for Translation<N, D>where
    DefaultAllocator: Allocator<N, D>,

impl<N: Real> Isometry<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

impl<N: Real> Isometry<Point<N, U3>> for UnitQuaternion<N>

impl<N: Real, D: DimName> OrthogonalTransformation<Point<N, D>> for Rotation<N, D>where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,

impl<N: Real> OrthogonalTransformation<Point<N, U2>> for UnitComplex<N>where
    DefaultAllocator: Allocator<N, U2>,

impl<N: Real> OrthogonalTransformation<Point<N, U3>> for UnitQuaternion<N>