Trait EuclideanSpace

Source

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;

    // Required method
    fn origin() -> Self;

    // Provided methods
    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 { ... }
}

Expand description

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

Required Associated Types§

Source

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.

Source

type RealField: RealField

The underlying reals.

Required Methods§

Source

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.