Trait alga::linear::AffineTransformation

pub trait AffineTransformation<E: EuclideanSpace>: ProjectiveTransformation<E> {
    type Rotation: Rotation<E>;
    type NonUniformScaling: AffineTransformation<E>;
    type Translation: Translation<E>;
    fn decompose(
        &self
    ) -> (Self::Translation, Self::Rotation, Self::NonUniformScaling, Self::Rotation);
    fn append_translation(&self, t: &Self::Translation) -> Self;
    fn prepend_translation(&self, t: &Self::Translation) -> Self;
    fn append_rotation(&self, r: &Self::Rotation) -> Self;
    fn prepend_rotation(&self, r: &Self::Rotation) -> Self;
    fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self;
    fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self;

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

The group of affine transformations. They are decomposable into a rotation, a non-uniform scaling, a second rotation, and a translation (applied in that order).

Associated Types

type Rotation: Rotation<E>

Type of the first rotation to be applied.

type NonUniformScaling: AffineTransformation<E>

Type of the non-uniform scaling to be applied.

type Translation: Translation<E>

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

Required Methods

fn decompose(
    &self
) -> (Self::Translation, Self::Rotation, Self::NonUniformScaling, Self::Rotation)

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.

Provided Methods

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.

May return None if Self does not have enough translational degree of liberty to perform this computation.

Implementors

• impl<R, E> AffineTransformation<E> for R where
    R: Real,
    E: EuclideanSpace<Real = R>,
    E::Coordinates: ClosedMul<R> + ClosedDiv<R> + ClosedNeg, 
• impl<E: EuclideanSpace> AffineTransformation<E> for Id