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.

Methods

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

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

Clones this point into one that owns its data.

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.

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

Creates a new point with the given coordinates.

pub fn len(&self) -> usize

The dimension of this point.

pub fn stride(&self) -> usize

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

Important traits for MatrixIter<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + Storage<N, R, C>> Iterator for MatrixIter<'a, N, R, C, S> type Item = &'a N;

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

Iterates through this point coordinates.

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

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

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

Important traits for MatrixIterMut<'a, N, R, C, S>

impl<'a, N: Scalar, R: Dim, C: Dim, S: 'a + StorageMut<N, R, C>> Iterator for MatrixIterMut<'a, N, R, C, S> type Item = &'a mut N;

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

Mutably iterates through this point coordinates.

Important traits for &'a mut W

impl<'a, W> Write for &'a mut W where
    W: Write + ?Sized, impl<'a, R> Read for &'a mut R where
    R: Read + ?Sized, impl<'a, I> Iterator for &'a mut I where
    I: Iterator + ?Sized,  type Item = <I as Iterator>::Item;

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() -> Self where
    N: Zero, 

Creates a new point with all coordinates equal to zero.

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.

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

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

Initializes this matrix from its components.

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

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

Initializes this matrix from its components.

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 matrix from its components.

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 matrix from its components.

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 matrix from its components.

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 matrix from its components.

Trait Implementations

impl<N: Real, D: DimNameSub<U1>> Transformation<Point<N, DimNameDiff<D, U1>>> 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: Debug + Scalar, D: Debug + DimName> Debug for Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

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, 

Feeds a slice of this type into the given [Hasher].

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

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

type Epsilon = 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: &Self, epsilon: Self::Epsilon) -> bool

The inverse of ApproxEq::abs_diff_eq.

impl<N: Scalar + RelativeEq, D: DimName> RelativeEq 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: &Self,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

impl<N: Scalar + UlpsEq, D: DimName> UlpsEq 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: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of ApproxEq::ulps_eq.

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

impl<N: Scalar, D: DimName> PartialEq 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 !=.

impl<N: Scalar + PartialOrd, D: DimName> PartialOrd 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: 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 + 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: Scalar, D: DimName> Distribution<Point<N, D>> for Standard where
    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.

Important traits for DistIter<'a, D, R, T>

impl<'a, D, R, T> Iterator for DistIter<'a, D, R, T> where
    D: Distribution<T>,
    R: Rng + 'a,  type Item = T;

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

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

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

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

type Output = VectorSum<N, D, D>

The resulting type after applying the - operator.

fn sub(self, right: &'b Point<N, D>) -> 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> + Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

type Output = VectorSum<N, D, D>

The resulting type after applying the - operator.

fn sub(self, right: 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> + Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

type Output = VectorSum<N, D, D>

The resulting type after applying the - operator.

fn sub(self, right: &'b 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> + Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

type Output = VectorSum<N, D, D>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Vector<N, D2, 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<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Vector<N, D2, 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<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<&'b Vector<N, D2, 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<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Sub<Vector<N, D2, 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, 'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Vector<N, D2, 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<'a, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Vector<N, D2, 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<'b, N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<&'b Vector<N, D2, 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<N, D1: DimName, D2: Dim, SB: Storage<N, D2>> Add<Vector<N, D2, 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 Vector<N, D2, 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<Vector<N, D2, 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<'b, N, D1: DimName, D2: Dim, SB> SubAssign<&'b Vector<N, D2, 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<Vector<N, D2, 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<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, 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<'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, 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<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: 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> MulAssign<N> for Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn mul_assign(&mut self, right: N)

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<'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> DivAssign<N> for Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn div_assign(&mut self, right: N)

Performs the /= operation.

impl<D: DimName> Mul<Point<u8, D>> for u8 where
    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<'b, D: DimName> Mul<&'b Point<u8, D>> for u8 where
    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<D: DimName> Mul<Point<u16, D>> for u16 where
    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<'b, D: DimName> Mul<&'b Point<u16, D>> for u16 where
    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<D: DimName> Mul<Point<u32, D>> for u32 where
    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<'b, D: DimName> Mul<&'b Point<u32, D>> for u32 where
    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<D: DimName> Mul<Point<u64, D>> for u64 where
    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<'b, D: DimName> Mul<&'b Point<u64, D>> for u64 where
    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<D: DimName> Mul<Point<usize, D>> for usize where
    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<'b, D: DimName> Mul<&'b Point<usize, D>> for usize where
    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<D: DimName> Mul<Point<i8, D>> for i8 where
    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<'b, D: DimName> Mul<&'b Point<i8, D>> for i8 where
    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<D: DimName> Mul<Point<i16, D>> for i16 where
    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<'b, D: DimName> Mul<&'b Point<i16, D>> for i16 where
    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<D: DimName> Mul<Point<i32, D>> for i32 where
    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<'b, D: DimName> Mul<&'b Point<i32, D>> for i32 where
    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<D: DimName> Mul<Point<i64, D>> for i64 where
    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<'b, D: DimName> Mul<&'b Point<i64, D>> for i64 where
    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<D: DimName> Mul<Point<isize, D>> for isize where
    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<'b, D: DimName> Mul<&'b Point<isize, D>> for isize where
    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<D: DimName> Mul<Point<f32, D>> for f32 where
    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<'b, D: DimName> Mul<&'b Point<f32, D>> for f32 where
    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<D: DimName> Mul<Point<f64, D>> for f64 where
    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<'b, D: DimName> Mul<&'b Point<f64, D>> for f64 where
    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<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D> where
    N: Scalar + Field,
    DefaultAllocator: Allocator<N, D>, 

type Translation = VectorN<N, D>

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

type Coordinates = VectorN<N, D>

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

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

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

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

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

Sorts two values in increasing order using a partial ordering.

fn partial_clamp(&'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<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<N1, N2, D> SubsetOf<VectorN<N2, DimNameSum<D, U1>>> 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<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> 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> 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> 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> 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> 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> 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> 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> 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> 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> 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, U6> where
    DefaultAllocator: Allocator<N, U6>, 

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

Mutably dereferences the value.

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> + 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, 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> + 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<'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> + 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, 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> + 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<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> 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> AffineTransformation<Point<N, D>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>, 

type Rotation = Self

Type of the first rotation to be applied.

type NonUniformScaling = Id

Type of the non-uniform scaling to be applied.

type Translation = Id

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

type Scaling = Id

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> Isometry<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 Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>, 

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, 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<'a, 'b, N, D: DimName> Mul<&'b Point<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + 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, N, D: DimName> Mul<Point<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + 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<'b, N, D: DimName> Mul<&'b Point<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + 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<N, D: DimName> Mul<Point<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + 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> 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, 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, D: DimName> AffineTransformation<Point<N, D>> for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

type Rotation = Id

Type of the first rotation to be applied.

type NonUniformScaling = Id

Type of the non-uniform scaling to be applied.

type Translation = Self

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

type Scaling = Id

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

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

impl<N: Real, D: DimName> AlgaTranslation<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: 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<'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<'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<'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<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, 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, 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

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

type Scaling = Id

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, R> AlgaIsometry<Point<N, D>> for Isometry<N, D, R> where
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D>, 

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, 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<'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<'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<'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<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: 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: 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, R> AlgaSimilarity<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, 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<'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<'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<'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<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, 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.