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 S⁰

Associated Types

type ChartIndex S⁰ :: *

Methods

chartReferencePoint :: ChartIndex S⁰ -> S⁰

interiorChartReferencePoint :: Functor p => p S⁰ -> ChartIndex S⁰ -> Interior S⁰

lookupAtlas :: S⁰ -> ChartIndex S⁰

Atlas S¹

Associated Types

type ChartIndex S¹ :: *

Methods

chartReferencePoint :: ChartIndex S¹ -> S¹

interiorChartReferencePoint :: Functor p => p S¹ -> ChartIndex S¹ -> Interior S¹

lookupAtlas :: S¹ -> ChartIndex S¹

Atlas ℝ

Associated Types

type ChartIndex ℝ :: *

Methods

chartReferencePoint :: ChartIndex ℝ -> ℝ

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

lookupAtlas :: ℝ -> ChartIndex ℝ

Atlas S²

Associated Types

type ChartIndex S² :: *

Methods

chartReferencePoint :: ChartIndex S² -> S²

interiorChartReferencePoint :: Functor p => p S² -> ChartIndex S² -> Interior S²

lookupAtlas :: S² -> ChartIndex S²

Num s => Atlas (V0 s)

Associated Types

type ChartIndex (V0 s) :: *

Methods

chartReferencePoint :: ChartIndex (V0 s) -> V0 s

interiorChartReferencePoint :: Functor p => p (V0 s) -> ChartIndex (V0 s) -> Interior (V0 s)

lookupAtlas :: V0 s -> ChartIndex (V0 s)

Num s => Atlas (V1 s)

Associated Types

type ChartIndex (V1 s) :: *

Methods

chartReferencePoint :: ChartIndex (V1 s) -> V1 s

interiorChartReferencePoint :: Functor p => p (V1 s) -> ChartIndex (V1 s) -> Interior (V1 s)

lookupAtlas :: V1 s -> ChartIndex (V1 s)

Num s => Atlas (V2 s)

Associated Types

type ChartIndex (V2 s) :: *

Methods

chartReferencePoint :: ChartIndex (V2 s) -> V2 s

interiorChartReferencePoint :: Functor p => p (V2 s) -> ChartIndex (V2 s) -> Interior (V2 s)

lookupAtlas :: V2 s -> ChartIndex (V2 s)

Num s => Atlas (V3 s)

Associated Types

type ChartIndex (V3 s) :: *

Methods

chartReferencePoint :: ChartIndex (V3 s) -> V3 s

interiorChartReferencePoint :: Functor p => p (V3 s) -> ChartIndex (V3 s) -> Interior (V3 s)

lookupAtlas :: V3 s -> ChartIndex (V3 s)

Num s => Atlas (V4 s)

Associated Types

type ChartIndex (V4 s) :: *

Methods

chartReferencePoint :: ChartIndex (V4 s) -> V4 s

interiorChartReferencePoint :: Functor p => p (V4 s) -> ChartIndex (V4 s) -> Interior (V4 s)

lookupAtlas :: V4 s -> ChartIndex (V4 s)

Atlas (ZeroDim s)

Associated Types

type ChartIndex (ZeroDim s) :: *

Methods

chartReferencePoint :: ChartIndex (ZeroDim s) -> ZeroDim s

interiorChartReferencePoint :: Functor p => p (ZeroDim s) -> ChartIndex (ZeroDim s) -> Interior (ZeroDim s)

lookupAtlas :: ZeroDim s -> ChartIndex (ZeroDim s)

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

Associated Types

type ChartIndex (x, y) :: *

Methods

chartReferencePoint :: ChartIndex (x, y) -> (x, y)

interiorChartReferencePoint :: Functor p => p (x, y) -> ChartIndex (x, y) -> Interior (x, y)

lookupAtlas :: (x, y) -> ChartIndex (x, y)

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

Associated Types

type ChartIndex (Point a n) :: *

Methods

chartReferencePoint :: ChartIndex (Point a n) -> Point a n

interiorChartReferencePoint :: Functor p => p (Point a n) -> ChartIndex (Point a n) -> Interior (Point a n)

lookupAtlas :: Point a n -> ChartIndex (Point a n)

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

Associated Types

type ChartIndex (LinearMap s v w) :: *

Methods

chartReferencePoint :: ChartIndex (LinearMap s v w) -> LinearMap s v w

interiorChartReferencePoint :: Functor p => p (LinearMap s v w) -> ChartIndex (LinearMap s v w) -> Interior (LinearMap s v w)

lookupAtlas :: LinearMap s v w -> ChartIndex (LinearMap s v w)

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

Associated Types

type ChartIndex (Tensor s v w) :: *

Methods

chartReferencePoint :: ChartIndex (Tensor s v w) -> Tensor s v w

interiorChartReferencePoint :: Functor p => p (Tensor s v w) -> ChartIndex (Tensor s v w) -> Interior (Tensor s v w)

lookupAtlas :: Tensor s v w -> ChartIndex (Tensor 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