Trait alga::linear::EuclideanSpace

pub trait EuclideanSpace: AffineSpace<Translation = Self::Coordinates> + ClosedMul<Self::RealField> + ClosedDiv<Self::RealField> + Neg<Output = Self> {
    type Coordinates: FiniteDimInnerSpace<RealField = Self::RealField, ComplexField = Self::RealField> + Add<Self::Coordinates, Output = Self::Coordinates> + AddAssign<Self::Coordinates> + Sub<Self::Coordinates, Output = Self::Coordinates> + SubAssign<Self::Coordinates> + Mul<Self::RealField, Output = Self::Coordinates> + MulAssign<Self::RealField> + Div<Self::RealField, Output = Self::Coordinates> + DivAssign<Self::RealField> + Neg<Output = Self::Coordinates>;
    type RealField: RealField;
    fn origin() -> Self;

    fn scale_by(&self, s: Self::RealField) -> Self { ... }
    fn coordinates(&self) -> Self::Coordinates { ... }
    fn from_coordinates(coords: Self::Coordinates) -> Self { ... }
    fn distance_squared(&self, b: &Self) -> Self::RealField { ... }
    fn distance(&self, b: &Self) -> Self::RealField { ... }
}

The finite-dimensional affine space based on the field of reals.

Associated Types

type Coordinates: FiniteDimInnerSpace<RealField = Self::RealField, ComplexField = Self::RealField> + Add<Self::Coordinates, Output = Self::Coordinates> + AddAssign<Self::Coordinates> + Sub<Self::Coordinates, Output = Self::Coordinates> + SubAssign<Self::Coordinates> + Mul<Self::RealField, Output = Self::Coordinates> + MulAssign<Self::RealField> + Div<Self::RealField, Output = Self::Coordinates> + DivAssign<Self::RealField> + Neg<Output = Self::Coordinates>

The underlying finite vector space.

type RealField: RealField

The underlying reals.

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Required methods

fn origin() -> Self

The preferred origin of this euclidean space.

Theoretically, an euclidean space has no clearly defined origin. Though it is almost always useful to have some reference point to express all the others as translations of it.

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Provided methods

fn scale_by(&self, s: Self::RealField) -> Self

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

Same as self * s.

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 distance_squared(&self, b: &Self) -> Self::RealField

The distance between two points.

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

The distance between two points.

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Implementors

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