Copyright	(c) Justus Sagemüller 2016
License	GPL v3
Maintainer	(@) sagemueller $ geo.uni-koeln.de
Stability	experimental
Portability	portable
Safe Haskell	None
Language	Haskell2010

Math.Manifold.Core.Types

Description

Several low-dimensional manifolds, represented in some simple way as Haskell data types. All these are in the PseudoAffine class.

Synopsis

Documentation

data S⁰ Source

The zero-dimensional sphere is actually just two points. Implementation might therefore change to ℝ⁰ + ℝ⁰: the disjoint sum of two single-point spaces.

Constructors

PositiveHalfSphere
NegativeHalfSphere

Instances

Eq S⁰ Source
Show S⁰ Source
PseudoAffine S⁰ Source
Semimanifold S⁰ Source
type Needle S⁰ = ZeroDim ℝ Source
type Interior S⁰ = S⁰

otherHalfSphere :: S⁰ -> S⁰ Source

newtype S¹ Source

The unit circle.

Constructors

S¹
Fields φParamS¹ :: Double Must be in range `[-π, π[`.

Instances

Show S¹ Source
PseudoAffine S¹ Source
Semimanifold S¹ Source
type Needle S¹ = ℝ Source
type Interior S¹ = S¹

type ℝP¹ = S¹ Source

newtype D¹ Source

The “one-dimensional disk” – really just the line segment between the two points -1 and 1 of 'S⁰', i.e. this is simply a closed interval.

Constructors

D¹
Fields xParamD¹ :: Double Range `[-1, 1]`.

Instances

Show D¹ Source
PseudoAffine D¹ Source
Semimanifold D¹ Source
type Needle D¹ = ℝ Source
type Interior D¹ = ℝ Source

fromIntv0to1 :: ℝ -> D¹ Source

type ℝ = Double Source

type ℝ⁰ = ZeroDim ℝ Source