Struct LensSpace 

pub struct LensSpace { /* private fields */ }

Lens space with z₁ = x + iy, z₂ = z + iw and deck action (z₁, z₂) ↦ (e^(2πi/p) z₁, e^(2πiq/p) z₂).

Implementations

impl LensSpace

pub fn new(p: u32, q: u32) -> Self

Panics unless p ≥ 2 and gcd(p, q) = 1; q is reduced mod p.

pub fn p(&self) -> u32

pub fn q(&self) -> u32

Twist of the gluing, reduced mod p.

pub fn injectivity_radius(&self) -> f32

pub fn deck(&self, power: i32) -> Iso4

g^power, with the power reduced mod p in integers so deck(0) is exact.

pub fn wgsl_prelude(&self) -> String

Emits an ambient vec4<f32> prelude, outside the WgslSpace ABI.

Trait Implementations

impl Clone for LensSpace

fn clone(&self) -> LensSpace

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl CoveringSpace for LensSpace

type CoverIso = Iso4

fn cover_identity(&self) -> Iso4

fn cover_compose(&self, a: Iso4, b: Iso4) -> Iso4

fn cover_inverse(&self, a: Iso4) -> Iso4

fn cover_apply(&self, iso: Iso4, p: Vec4) -> Vec4

fn cover_transport(&self, iso: Iso4, at: Vec4, v: Vec4) -> Vec4

impl Debug for LensSpace

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

Formats the value using the given formatter.

impl PartialEq for LensSpace

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl QuotientSpace for LensSpace

fn face_pairings(&self) -> impl Iterator<Item = Iso4>

Iteration order is part of the contract.

fn in_fundamental_domain(&self, p: Vec4) -> bool

fn wrap_to_domain(&self, p: Vec4) -> (Vec4, Iso4)

impl Space for LensSpace

type Point = Vec4

type Vector = Vec4

type Frame = Iso4

fn frame_at(&self, at: Vec4) -> Iso4

fn distance(&self, a: Vec4, b: Vec4) -> f32

fn exp(&self, at: Vec4, v: Vec4) -> Vec4

Advances for unit time along the geodesic with initial velocity v.

fn log(&self, from: Vec4, to: Vec4) -> Vec4

fn parallel_transport(&self, from: Vec4, to: Vec4, v: Vec4) -> Vec4

fn chart_envelope(&self) -> f32

Geodesic distance from the chart origin beyond which Self::valid_point refuses a point.

fn valid_point(&self, p: Vec4) -> bool

Finite, inside the chart, and within Self::chart_envelope of the origin.

fn parallel_transport_along( &self, path: &[Self::Point], v: Self::Vector, ) -> Self::Vector

Composes transport along consecutive points; fewer than two points leave v unchanged.

fn is_chart_flat(&self) -> bool

True when chart arithmetic respects the global geometry, including identifications.

impl Copy for LensSpace

impl Eq for LensSpace

impl StructuralPartialEq for LensSpace