Enum lowdim::Sym2d

pub enum Sym2d {
    R(u8),
    S(u8),
}

The symmetries of discrete 2d vectors.

These preserve length and the origin, and correspond to multiplication with orthogonal integer matrices. This can be viewed as a concise representation of the orthogonal matrices, conversion is possible via Matrix2d::from.

This is the dihedral group D4, the symmetry group of a square. It consists of four rotations and four reflections.

Variants

R(u8)

Tuple Fields

0: u8

Rotates by the given number of right angles to the left.

S(u8)

Tuple Fields

0: u8

Reflects by an axis through the origin so that the point (1, 0) is rotated by the given number of right angles to the left.

The axis of reflection then forms an angle of 45 degrees times the given number with the x axis.

Implementations

impl Sym2d

pub fn elements() -> Vec<Sym2d>

Returns a vector containing the elements of the symmetry group.

pub fn rotations() -> Vec<Sym2d>

Returns a vector containing the rotations of the symmetry group.

The rotations are closed under multiplication. That is, they form a subgroup.

pub fn inv(&self) -> Sym2d

Returns the inverse of an element.

pub fn is_rotation(&self) -> bool

Returns true if this a rotation.

pub fn is_reflection(&self) -> bool

Returns true if this a reflection.

Trait Implementations

impl Clone for Sym2d

fn clone(&self) -> Sym2d

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Sym2d

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for Sym2d

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<S: Integer> From<Sym2d> for Matrix2d<S>

fn from(s: Sym2d) -> Self

Performs the conversion.

impl Hash for Sym2d

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<'a> Mul<&'a Sym2d> for Sym2d

type Output = Sym2d

The resulting type after applying the * operator.

fn mul(self, other: &Sym2d) -> Sym2d

Performs the * operation.

impl<'a> Mul<&'a Sym2d> for &'a Sym2d

type Output = Sym2d

The resulting type after applying the * operator.

fn mul(self, other: &Sym2d) -> Sym2d

Performs the * operation.

impl Mul<Sym2d> for Sym2d

type Output = Sym2d

The resulting type after applying the * operator.

fn mul(self, other: Sym2d) -> Sym2d

Performs the * operation.

impl<'a> Mul<Sym2d> for &'a Sym2d

type Output = Sym2d

The resulting type after applying the * operator.

fn mul(self, other: Sym2d) -> Sym2d

Performs the * operation.

impl PartialEq<Sym2d> for Sym2d

fn eq(&self, other: &Sym2d) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Sym2d) -> bool

This method tests for !=.

impl Copy for Sym2d

impl Eq for Sym2d

impl StructuralEq for Sym2d

impl StructuralPartialEq for Sym2d