Data.Manifold.Atlas

Documentation

class Semimanifold m => Atlas m where

Minimal complete definition

interiorChartReferencePoint, lookupAtlas

Associated Types

type ChartIndex m :: *

Methods

chartReferencePoint :: ChartIndex m -> m

interiorChartReferencePoint :: Functor p => p m -> ChartIndex m -> Interior m

lookupAtlas :: m -> ChartIndex m

Instances

Atlas ℝ

Atlas S⁰

Atlas S¹

Atlas S²

Num s => Atlas (V4 s)

Num s => Atlas (V3 s)

Num s => Atlas (V2 s)

Num s => Atlas (V1 s)

Num s => Atlas (V0 s)

Atlas (ZeroDim s)

(Atlas x, Atlas y) => Atlas (x, y)

(LinearSpace (a n), (~) * (Needle (a n)) (a n), (~) * (Interior (a n)) (a n)) => Atlas (Point a n)

(TensorSpace v, (~) * (Scalar v) s, TensorSpace w, (~) * (Scalar w) s) => Atlas (Tensor s v w)

(LinearSpace v, (~) * (Scalar v) s, TensorSpace w, (~) * (Scalar w) s) => Atlas (LinearMap s v w)

type AffineManifold m = (Atlas m, Manifold m, AffineSpace m, Needle m ~ Diff m, HasTrie (ChartIndex m))

The AffineSpace class plus manifold constraints.

type EuclidSpace x = (AffineManifold x, InnerSpace (Diff x), DualVector (Diff x) ~ Diff x, Floating (Scalar (Diff x)))

An euclidean space is a real affine space whose tangent space is a Hilbert space.

euclideanMetric :: EuclidSpace x => proxy x -> Metric x