Enum rlifesrc_lib::config::d8::Symmetry

pub enum Symmetry {
    C1,
    C2,
    C4,
    D2Row,
    D2Col,
    D2Diag,
    D2Antidiag,
    D4Ortho,
    D4Diag,
    D8,
}

Symmetries of the pattern.

For each symmetry, its symmetry group is a subgroup of the dihedral group D₈. 10 different symmetries correspond to 10 subgroups of D₈.

The notations are stolen from Oscar Cunningham’s Logic Life Search. Please see the Life Wiki for details.

Some of the symmetries are only valid when the world is square, and some are only valid when the world has no diagonal width.

Variants

C1

C1.

No symmetry at all.

C2

C2.

Symmetry under 180° rotation.

C4

C4.

Symmetry under 90° rotation.

Requires the world to be square and have no diagonal width.

D2Row

D2-.

Symmetry under reflection across the middle row.

Requires the world to have no diagonal width.

D2Col

D2|.

Symmetry under reflection across the middle column.

Requires the world to have no diagonal width.

D2Diag

D2\.

Symmetry under reflection across the diagonal.

Requires the world to be square.

D2Antidiag

D2/.

Symmetry under reflection across the antidiagonal.

Requires the world to be square.

D4Ortho

D4+.

Symmetry under reflections across the middle row and the middle column.

Requires the world to have no diagonal width.

D4Diag

D4X.

Symmetry under reflections across the diagonal and the antidiagonal.

Requires the world to be square.

D8

D8.

Symmetry under all 8 transformations.

Requires the world to be square and have no diagonal width.

Implementations

impl Symmetry

pub const ALL: [Self; 10] = _

pub const fn is_subgroup_of(self, other: Self) -> bool

Whether the symmetry group of self is a subgroup of that of other, i.e., all patterns with symmetry other also have symmetry self.

For example, the symmetry group of Symmetry::C1 is a subgroup of that of all other symmetries.

pub const fn require_square_world(self) -> bool

Whether this symmetry requires the world to be square.

Returns true for C4, D2\, D2/, D4X and D8.

pub const fn require_no_diagonal_width(self) -> bool

Whether this transformation requires the world to have no diagonal width.

Returns true for C4, D2-, D2|, D4+ and D8.

pub fn members(self) -> Vec<Transform>

Transformations contained in the symmetry group.

pub fn cosets(self) -> Vec<Transform>

A list of coset representatives, seeing the symmetry group as a subgroup of D₈.

The first element in the result is always Transform::Id.

pub const fn generated_with(self, transform: Transform) -> Self

The symmetry group “generated by” the given symmetry and the transformation. i.e., the smallest symmetry group which is larger than the given symmetry group and contains that transformation.

pub fn generated_by(transforms: impl IntoIterator<Item = Transform>) -> Self

The symmetry group generated by the given transformations, i.e., the smallest symmetry group containing all these transformations.

Trait Implementations

impl Clone for Symmetry

fn clone(&self) -> Symmetry

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Symmetry

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

Formats the value using the given formatter.

impl Default for Symmetry

fn default() -> Symmetry

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Symmetry

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Symmetry

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

Formats the value using the given formatter.

impl FromStr for Symmetry

type Err = String

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl Hash for Symmetry

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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for Symmetry

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

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Symmetry

fn partial_cmp(&self, other: &Self) -> Option<Ordering>

We say that symmetry a is smaller than symmetry b, when the symmetry group of a is a subgroup of that of b, i.e., all patterns with symmetry b also have symmetry a.

For example, Symmetry::C1 is smaller than all other symmetries.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl Serialize for Symmetry

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Copy for Symmetry

impl Eq for Symmetry

impl StructuralEq for Symmetry

impl StructuralPartialEq for Symmetry