Trait alga::linear::Similarity

pub trait Similarity<E: EuclideanSpace>: AffineTransformation<E, NonUniformScaling = Self::Scaling> {
    type Scaling: Scaling<E>;
    fn translation(&self) -> Self::Translation;
    fn rotation(&self) -> Self::Rotation;
    fn scaling(&self) -> Self::Scaling;

    fn translate_point(&self, pt: &E) -> E { ... }
    fn rotate_point(&self, pt: &E) -> E { ... }
    fn scale_point(&self, pt: &E) -> E { ... }
    fn rotate_vector(&self, pt: &E::Coordinates) -> E::Coordinates { ... }
    fn scale_vector(&self, pt: &E::Coordinates) -> E::Coordinates { ... }
    fn inverse_translate_point(&self, pt: &E) -> E { ... }
    fn inverse_rotate_point(&self, pt: &E) -> E { ... }
    fn inverse_scale_point(&self, pt: &E) -> E { ... }
    fn inverse_rotate_vector(&self, pt: &E::Coordinates) -> E::Coordinates { ... }
    fn inverse_scale_vector(&self, pt: &E::Coordinates) -> E::Coordinates { ... }
}

Subgroups of the similarity group S(n), i.e., rotations, translations, and (signed) uniform scaling.

Similarities map lines to lines and preserve angles.

Associated Types

type Scaling: Scaling<E>

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

Required Methods

fn translation(&self) -> Self::Translation

The pure translational component of this similarity transformation.

fn rotation(&self) -> Self::Rotation

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Self::Scaling

The pure scaling component of this similarity transformation.

Provided Methods

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::Coordinates) -> E::Coordinates

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

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

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

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

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

Implementors

• impl<R, E> Similarity<E> for R where
    R: Real + SubsetOf<R>,
    E: EuclideanSpace<Real = R>,
    E::Coordinates: ClosedMul<R> + ClosedDiv<R> + ClosedNeg,  type Scaling = R;
• impl<E: EuclideanSpace> Similarity<E> for Id type Scaling = Id;