Copyright	(c) Justus Sagemüller 2015
License	GPL v3
Maintainer	(@) jsag $ hvl.no
Stability	experimental
Portability	portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Manifold.Atlas

Description

Synopsis

class SemimanifoldWithBoundary m => Atlas m where
- type ChartIndex m :: *
- chartReferencePoint :: ChartIndex m -> m
- lookupAtlas :: m -> ChartIndex m
type NumPrime s = (Num' s, Eq s, OpenManifold s, ProjectableBoundary s)
type Atlas' m = (Atlas m, HasTrie (ChartIndex m))
type AffineManifold m = (Atlas' m, Manifold m, AffineSpace m, Needle m ~ Diff m)
type EuclidSpace x = (AffineManifold x, InnerSpace (Diff x), DualVector (Diff x) ~ Diff x, Floating (Scalar (Diff x)))
euclideanMetric :: EuclidSpace x => proxy x -> Metric x

Documentation

class SemimanifoldWithBoundary m => Atlas m where Source #

Associated Types

type ChartIndex m :: * Source #

Methods

chartReferencePoint :: ChartIndex m -> m Source #

lookupAtlas :: m -> ChartIndex m Source #

Instances

Instances details

Atlas S² Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex S² Source # Methods chartReferencePoint :: ChartIndex S² -> S² Source # lookupAtlas :: S² -> ChartIndex S² Source #
Atlas S¹ Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex S¹ Source # Methods chartReferencePoint :: ChartIndex S¹ -> S¹ Source # lookupAtlas :: S¹ -> ChartIndex S¹ Source #
Atlas S⁰ Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex S⁰ Source # Methods chartReferencePoint :: ChartIndex S⁰ -> S⁰ Source # lookupAtlas :: S⁰ -> ChartIndex S⁰ Source #
Atlas ℝ Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex ℝ Source # Methods chartReferencePoint :: ChartIndex ℝ -> ℝ Source # lookupAtlas :: ℝ -> ChartIndex ℝ Source #
NumPrime s => Atlas (V0 s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (V0 s) Source # Methods chartReferencePoint :: ChartIndex (V0 s) -> V0 s Source # lookupAtlas :: V0 s -> ChartIndex (V0 s) Source #
NumPrime s => Atlas (V1 s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (V1 s) Source # Methods chartReferencePoint :: ChartIndex (V1 s) -> V1 s Source # lookupAtlas :: V1 s -> ChartIndex (V1 s) Source #
NumPrime s => Atlas (V2 s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (V2 s) Source # Methods chartReferencePoint :: ChartIndex (V2 s) -> V2 s Source # lookupAtlas :: V2 s -> ChartIndex (V2 s) Source #
NumPrime s => Atlas (V3 s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (V3 s) Source # Methods chartReferencePoint :: ChartIndex (V3 s) -> V3 s Source # lookupAtlas :: V3 s -> ChartIndex (V3 s) Source #
NumPrime s => Atlas (V4 s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (V4 s) Source # Methods chartReferencePoint :: ChartIndex (V4 s) -> V4 s Source # lookupAtlas :: V4 s -> ChartIndex (V4 s) Source #
NumPrime s => Atlas (ZeroDim s) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (ZeroDim s) Source # Methods chartReferencePoint :: ChartIndex (ZeroDim s) -> ZeroDim s Source # lookupAtlas :: ZeroDim s -> ChartIndex (ZeroDim s) Source #
(Num'' n, LinearManifold (a n), Scalar (a n) ~ n, Needle (a n) ~ a n) => Atlas (Point a n) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (Point a n) Source # Methods chartReferencePoint :: ChartIndex (Point a n) -> Point a n Source # lookupAtlas :: Point a n -> ChartIndex (Point a n) Source #
(Atlas x, Atlas y, SemimanifoldWithBoundary (x, y)) => Atlas (x, y) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (x, y) Source # Methods chartReferencePoint :: ChartIndex (x, y) -> (x, y) Source # lookupAtlas :: (x, y) -> ChartIndex (x, y) Source #
(NumPrime s, LinearSpace v, Scalar v ~ s, LinearSpace w, Scalar w ~ s) => Atlas (LinearMap s v w) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (LinearMap s v w) Source # Methods chartReferencePoint :: ChartIndex (LinearMap s v w) -> LinearMap s v w Source # lookupAtlas :: LinearMap s v w -> ChartIndex (LinearMap s v w) Source #
(NumPrime s, LinearSpace v, Scalar v ~ s, LinearSpace w, Scalar w ~ s) => Atlas (Tensor s v w) Source #
Instance details Defined in Data.Manifold.Atlas Associated Types type ChartIndex (Tensor s v w) Source # Methods chartReferencePoint :: ChartIndex (Tensor s v w) -> Tensor s v w Source # lookupAtlas :: Tensor s v w -> ChartIndex (Tensor s v w) Source #

type NumPrime s = (Num' s, Eq s, OpenManifold s, ProjectableBoundary s) Source #

type Atlas' m = (Atlas m, HasTrie (ChartIndex m)) Source #

type AffineManifold m = (Atlas' m, Manifold m, AffineSpace m, Needle m ~ Diff m) Source #

The AffineSpace class plus manifold constraints.

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

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

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