Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Colour.Manifold

Contents

Full colour space
2D/1D projected colour space
Mapping data to colours
Predefined colour maps
Orphan instances

Synopsis

data Colour a
class QuantisedColour c where
- quantiseColour :: Colour ℝ -> c
data ColourMap x
planarColourMap :: ColourPlane -> ColourMap x
colourCurve :: ColourPlane -> ℝ -> ColourMap ℝ
colourMapPlane :: Traversal' (ColourMap x) ColourPlane
spectralSwing :: Needle x ~ ℝ => Traversal' (ColourMap x) ℝ
data ColourPlane
cpCold :: Lens' ColourPlane (Colour ℝ)
cpNeutral :: Lens' ColourPlane (Interior (Colour ℝ))
cpHot :: Lens' ColourPlane (Colour ℝ)
spanColourPlane :: Interior (Colour ℝ) -> (Colour ℝ, Colour ℝ) -> ColourPlane
class Geodesic x => ColourMappable x where
- type ColourMapped x :: *
- type MappingVertex x :: *
- mapToColourWith :: HasCallStack => ColourMap (MappingVertex x) -> Interior (MappingVertex x) -> (MappingVertex x, MappingVertex x) -> x -> ColourMapped x
type SimpleColourMap = forall x. HasSimpleColourMaps x => ColourMap x
blackBlueYellowRed :: SimpleColourMap
brightVsRed :: SimpleColourMap
redVsBlue :: SimpleColourMap

Full colour space

data Colour a #

This type represents the human preception of colour. The a parameter is a numeric type used internally for the representation.

The Monoid instance allows one to add colours, but beware that adding colours can take you out of gamut. Consider using blend whenever possible.

Instances

Instances details

AffineSpace Colour
Instance details Defined in Data.Colour.Internal Methods affineCombo :: Num a => [(a, Colour a)] -> Colour a -> Colour a #
ColourOps Colour
Instance details Defined in Data.Colour.Internal Methods over :: Num a => AlphaColour a -> Colour a -> Colour a # darken :: Num a => a -> Colour a -> Colour a #
Num a => Monoid (Colour a)
Instance details Defined in Data.Colour.Internal Methods mempty :: Colour a # mappend :: Colour a -> Colour a -> Colour a # mconcat :: [Colour a] -> Colour a #
Num a => Semigroup (Colour a)
Instance details Defined in Data.Colour.Internal Methods (<>) :: Colour a -> Colour a -> Colour a # sconcat :: NonEmpty (Colour a) -> Colour a # stimes :: Integral b => b -> Colour a -> Colour a #
Eq a => Eq (Colour a)
Instance details Defined in Data.Colour.Internal Methods (==) :: Colour a -> Colour a -> Bool # (/=) :: Colour a -> Colour a -> Bool #
Atlas (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold Associated Types type ChartIndex (Colour ℝ) # Methods chartReferencePoint :: ChartIndex (Colour ℝ) -> Colour ℝ # lookupAtlas :: Colour ℝ -> ChartIndex (Colour ℝ) #
Geodesic (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold Methods geodesicBetween :: Colour ℝ -> Colour ℝ -> Maybe (D¹ -> Colour ℝ) # middleBetween :: Colour ℝ -> Colour ℝ -> Maybe (Colour ℝ) #
PseudoAffineWithBoundary (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold Methods (.--!) :: Colour ℝ -> Colour ℝ -> Needle (Interior (Colour ℝ)) # (.-\|) :: Colour ℝ -> Boundary (Colour ℝ) -> Maybe (HalfNeedle (Colour ℝ)) # (!-\|) :: Colour ℝ -> Boundary (Colour ℝ) -> HalfNeedle (Colour ℝ) # (.--.) :: Colour ℝ -> Colour ℝ -> Maybe (Needle (Interior (Colour ℝ))) #
SemimanifoldWithBoundary (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold Associated Types type Interior (Colour ℝ) # type Boundary (Colour ℝ) # type HalfNeedle (Colour ℝ) # Methods (.+^\|) :: Colour ℝ -> Needle (Interior (Colour ℝ)) -> Either (Boundary (Colour ℝ), Scalar (Needle (Interior (Colour ℝ)))) (Interior (Colour ℝ)) # fromInterior :: Interior (Colour ℝ) -> Colour ℝ # fromBoundary :: Boundary (Colour ℝ) -> Colour ℝ # (\|+^) :: Boundary (Colour ℝ) -> HalfNeedle (Colour ℝ) -> Colour ℝ # separateInterior :: Colour ℝ -> Either (Boundary (Colour ℝ)) (Interior (Colour ℝ)) # toInterior :: Colour ℝ -> Maybe (Interior (Colour ℝ)) # extendToBoundary :: Interior (Colour ℝ) -> Needle (Interior (Colour ℝ)) -> Maybe (Boundary (Colour ℝ)) # smfdWBoundWitness :: SmfdWBoundWitness (Colour ℝ) # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Colour ℝ))) => r) -> r # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Colour ℝ)))) => r) -> r # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Colour ℝ))), Scalar (Needle (Boundary (Colour ℝ))) ~ Scalar (Needle (Interior (Colour ℝ)))) => r) -> r #
type ChartIndex (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold type ChartIndex (Colour ℝ) = ()
type Boundary (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold type Boundary (Colour ℝ) = ColourBoundary
type HalfNeedle (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold type HalfNeedle (Colour ℝ) = ColourHalfNeedle
type Interior (Colour ℝ) Source #
Instance details Defined in Data.Colour.Manifold type Interior (Colour ℝ) = ColourNeedle

class QuantisedColour c where Source #

Methods

quantiseColour :: Colour ℝ -> c Source #

Instances

Instances details

QuantisedColour PixelRGB8 Source #
Instance details Defined in Data.Colour.Manifold Methods quantiseColour :: Colour ℝ -> PixelRGB8 Source #
QuantisedColour PixelRGBF Source #
Instance details Defined in Data.Colour.Manifold Methods quantiseColour :: Colour ℝ -> PixelRGBF Source #

2D/1D projected colour space

data ColourMap x Source #

A two-dimensional, smoothly varying colour palette.

planarColourMap :: ColourPlane -> ColourMap x Source #

colourCurve :: ColourPlane -> ℝ -> ColourMap ℝ Source #

colourMapPlane :: Traversal' (ColourMap x) ColourPlane Source #

spectralSwing :: Needle x ~ ℝ => Traversal' (ColourMap x) ℝ Source #

data ColourPlane Source #

cpCold :: Lens' ColourPlane (Colour ℝ) Source #

cpNeutral :: Lens' ColourPlane (Interior (Colour ℝ)) Source #

cpHot :: Lens' ColourPlane (Colour ℝ) Source #

spanColourPlane Source #

Arguments

:: Interior (Colour ℝ)	Neutral colour
-> (Colour ℝ, Colour ℝ)	Extreme “cold” / “hot” colours
-> ColourPlane

Mapping data to colours

class Geodesic x => ColourMappable x where Source #

Associated Types

type ColourMapped x :: * Source #

type MappingVertex x :: * Source #

Methods

mapToColourWith :: HasCallStack => ColourMap (MappingVertex x) -> Interior (MappingVertex x) -> (MappingVertex x, MappingVertex x) -> x -> ColourMapped x Source #

Instances

Instances details

ColourMappable ℝ² Source #
Instance details Defined in Data.Colour.Manifold Associated Types type ColourMapped ℝ² Source # type MappingVertex ℝ² Source # Methods mapToColourWith :: ColourMap (MappingVertex ℝ²) -> Interior (MappingVertex ℝ²) -> (MappingVertex ℝ², MappingVertex ℝ²) -> ℝ² -> ColourMapped ℝ² Source #
ColourMappable ℝ Source #
Instance details Defined in Data.Colour.Manifold Associated Types type ColourMapped ℝ Source # type MappingVertex ℝ Source # Methods mapToColourWith :: ColourMap (MappingVertex ℝ) -> Interior (MappingVertex ℝ) -> (MappingVertex ℝ, MappingVertex ℝ) -> ℝ -> ColourMapped ℝ Source #
ColourMappable (ℝ, ℝ) Source #
Instance details Defined in Data.Colour.Manifold Associated Types type ColourMapped (ℝ, ℝ) Source # type MappingVertex (ℝ, ℝ) Source # Methods mapToColourWith :: ColourMap (MappingVertex (ℝ, ℝ)) -> Interior (MappingVertex (ℝ, ℝ)) -> (MappingVertex (ℝ, ℝ), MappingVertex (ℝ, ℝ)) -> (ℝ, ℝ) -> ColourMapped (ℝ, ℝ) Source #

Predefined colour maps

type SimpleColourMap = forall x. HasSimpleColourMaps x => ColourMap x Source #

blackBlueYellowRed :: SimpleColourMap Source #

brightVsRed :: SimpleColourMap Source #

redVsBlue :: SimpleColourMap Source #

Orphan instances

Arbitrary ColourBoundary Source #
Instance details Methods arbitrary :: Gen ColourBoundary # shrink :: ColourBoundary -> [ColourBoundary] #
Arbitrary ColourNeedle Source #
Instance details Methods arbitrary :: Gen ColourNeedle # shrink :: ColourNeedle -> [ColourNeedle] #
Foldable RGB Source #
Instance details Methods fold :: Monoid m => RGB m -> m # foldMap :: Monoid m => (a -> m) -> RGB a -> m # foldMap' :: Monoid m => (a -> m) -> RGB a -> m # foldr :: (a -> b -> b) -> b -> RGB a -> b # foldr' :: (a -> b -> b) -> b -> RGB a -> b # foldl :: (b -> a -> b) -> b -> RGB a -> b # foldl' :: (b -> a -> b) -> b -> RGB a -> b # foldr1 :: (a -> a -> a) -> RGB a -> a # foldl1 :: (a -> a -> a) -> RGB a -> a # toList :: RGB a -> [a] # null :: RGB a -> Bool # length :: RGB a -> Int # elem :: Eq a => a -> RGB a -> Bool # maximum :: Ord a => RGB a -> a # minimum :: Ord a => RGB a -> a # sum :: Num a => RGB a -> a # product :: Num a => RGB a -> a #
AdditiveMonoid ColourHalfNeedle Source #
Instance details Methods zeroHV :: ColourHalfNeedle # addHVs :: ColourHalfNeedle -> ColourHalfNeedle -> ColourHalfNeedle #
HalfSpace ColourHalfNeedle Source #
Instance details Associated Types type FullSubspace ColourHalfNeedle # type Ray ColourHalfNeedle # type MirrorJoin ColourHalfNeedle # Methods scaleNonNeg :: Ray ColourHalfNeedle -> ColourHalfNeedle -> ColourHalfNeedle # fromFullSubspace :: FullSubspace ColourHalfNeedle -> ColourHalfNeedle # projectToFullSubspace :: ColourHalfNeedle -> FullSubspace ColourHalfNeedle # fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace ColourHalfNeedle), ScalarSpace (Scalar (FullSubspace ColourHalfNeedle)), Scalar (FullSubspace ColourHalfNeedle) ~ MirrorJoin (Ray ColourHalfNeedle)) => r) -> r # rayIsHalfSpace :: (HalfSpace (Ray ColourHalfNeedle) => r) -> r # mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin ColourHalfNeedle), Scalar (MirrorJoin ColourHalfNeedle) ~ MirrorJoin (Ray ColourHalfNeedle)) => r) -> r # fromPositiveHalf :: ColourHalfNeedle -> MirrorJoin ColourHalfNeedle # fromNegativeHalf :: ColourHalfNeedle -> MirrorJoin ColourHalfNeedle #
LinearSpace ColourNeedle Source #
Instance details Associated Types type DualVector ColourNeedle # Methods dualSpaceWitness :: DualSpaceWitness ColourNeedle # linearId :: ColourNeedle +> ColourNeedle # idTensor :: ColourNeedle ⊗ DualVector ColourNeedle # sampleLinearFunction :: (TensorSpace w, Scalar ColourNeedle ~ Scalar w) => (ColourNeedle -+> w) -+> (ColourNeedle +> w) # toLinearForm :: DualVector ColourNeedle -+> (ColourNeedle +> Scalar ColourNeedle) # fromLinearForm :: (ColourNeedle +> Scalar ColourNeedle) -+> DualVector ColourNeedle # coerceDoubleDual :: VSCCoercion ColourNeedle (DualVector (DualVector ColourNeedle)) # trace :: (ColourNeedle +> ColourNeedle) -+> Scalar ColourNeedle # contractTensorMap :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle +> (ColourNeedle ⊗ w)) -+> w # contractMapTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ (ColourNeedle +> w)) -+> w # contractTensorFn :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle -+> (ColourNeedle ⊗ w)) -+> w # contractLinearMapAgainst :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (ColourNeedle +> w) (w -+> ColourNeedle) (Scalar ColourNeedle) # applyDualVector :: Bilinear (DualVector ColourNeedle) ColourNeedle (Scalar ColourNeedle) # applyLinear :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (ColourNeedle +> w) ColourNeedle w # composeLinear :: (LinearSpace w, TensorSpace x, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear (w +> x) (ColourNeedle +> w) (ColourNeedle +> x) # tensorId :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) +> (ColourNeedle ⊗ w) # applyTensorFunctional :: (LinearSpace u, Scalar u ~ Scalar ColourNeedle) => Bilinear (DualVector (ColourNeedle ⊗ u)) (ColourNeedle ⊗ u) (Scalar ColourNeedle) # applyTensorLinMap :: (LinearSpace u, TensorSpace w, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle) => Bilinear ((ColourNeedle ⊗ u) +> w) (ColourNeedle ⊗ u) w # useTupleLinearSpaceComponents :: ColourNeedle ~ (x, y) => ((LinearSpace x, LinearSpace y, Scalar x ~ Scalar y) => φ) -> φ #
TensorSpace ColourNeedle Source #
Instance details Associated Types type TensorProduct ColourNeedle w # Methods scalarSpaceWitness :: ScalarSpaceWitness ColourNeedle # linearManifoldWitness :: LinearManifoldWitness ColourNeedle # zeroTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => ColourNeedle ⊗ w # toFlatTensor :: ColourNeedle -+> (ColourNeedle ⊗ Scalar ColourNeedle) # fromFlatTensor :: (ColourNeedle ⊗ Scalar ColourNeedle) -+> ColourNeedle # addTensors :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> ColourNeedle ⊗ w # subtractTensors :: (TensorSpace ColourNeedle, TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> ColourNeedle ⊗ w # scaleTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (Scalar ColourNeedle) (ColourNeedle ⊗ w) (ColourNeedle ⊗ w) # negateTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -+> (ColourNeedle ⊗ w) # tensorProduct :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear ColourNeedle w (ColourNeedle ⊗ w) # tensorProducts :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => [(ColourNeedle, w)] -> ColourNeedle ⊗ w # transposeTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -+> (w ⊗ ColourNeedle) # fmapTensor :: (TensorSpace w, TensorSpace x, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear (w -+> x) (ColourNeedle ⊗ w) (ColourNeedle ⊗ x) # fzipTensorWith :: (TensorSpace u, TensorSpace w, TensorSpace x, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear ((w, x) -+> u) (ColourNeedle ⊗ w, ColourNeedle ⊗ x) (ColourNeedle ⊗ u) # coerceFmapTensorProduct :: Functor p => p ColourNeedle -> VSCCoercion a b -> VSCCoercion (TensorProduct ColourNeedle a) (TensorProduct ColourNeedle b) # wellDefinedVector :: ColourNeedle -> Maybe ColourNeedle # wellDefinedTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> Maybe (ColourNeedle ⊗ w) #
FiniteDimensional ColourNeedle Source #
Instance details Associated Types data SubBasis ColourNeedle # Methods entireBasis :: SubBasis ColourNeedle # enumerateSubBasis :: SubBasis ColourNeedle -> [ColourNeedle] # subbasisDimension :: SubBasis ColourNeedle -> Int # decomposeLinMap :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle +> w) -> (SubBasis ColourNeedle, DList w) # decomposeLinMapWithin :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> (ColourNeedle +> w) -> Either (SubBasis ColourNeedle, DList w) (DList w) # recomposeSB :: SubBasis ColourNeedle -> [Scalar ColourNeedle] -> (ColourNeedle, [Scalar ColourNeedle]) # recomposeSBTensor :: (FiniteDimensional w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> SubBasis w -> [Scalar ColourNeedle] -> (ColourNeedle ⊗ w, [Scalar ColourNeedle]) # recomposeLinMap :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> [w] -> (ColourNeedle +> w, [w]) # recomposeContraLinMap :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle, Functor f) => (f (Scalar w) -> w) -> f (DualVector ColourNeedle) -> ColourNeedle +> w # recomposeContraLinMapTensor :: (FiniteDimensional u, LinearSpace w, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle, Functor f) => (f (Scalar w) -> w) -> f (ColourNeedle +> DualVector u) -> (ColourNeedle ⊗ u) +> w # uncanonicallyFromDual :: DualVector ColourNeedle -+> ColourNeedle # uncanonicallyToDual :: ColourNeedle -+> DualVector ColourNeedle # tensorEquality :: (TensorSpace w, Eq w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> Bool # dualFinitenessWitness :: DualFinitenessWitness ColourNeedle #
SemiInner ColourNeedle Source #
Instance details Methods dualBasisCandidates :: [(Int, ColourNeedle)] -> Forest (Int, DualVector ColourNeedle) # tensorDualBasisCandidates :: (SemiInner w, Scalar w ~ Scalar ColourNeedle) => [(Int, ColourNeedle ⊗ w)] -> Forest (Int, DualVector (ColourNeedle ⊗ w)) # symTensorDualBasisCandidates :: [(Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle)] -> Forest (Int, SymmetricTensor (Scalar ColourNeedle) (DualVector ColourNeedle)) # symTensorTensorDualBasisCandidates :: (SemiInner w, Scalar w ~ Scalar ColourNeedle) => [(Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle ⊗ w)] -> Forest (Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle +> DualVector w) #
Atlas ColourNeedle Source #
Instance details Associated Types type ChartIndex ColourNeedle # Methods chartReferencePoint :: ChartIndex ColourNeedle -> ColourNeedle # lookupAtlas :: ColourNeedle -> ChartIndex ColourNeedle #
Geodesic ColourNeedle Source #
Instance details Methods geodesicBetween :: ColourNeedle -> ColourNeedle -> Maybe (D¹ -> ColourNeedle) # middleBetween :: ColourNeedle -> ColourNeedle -> Maybe ColourNeedle #
ProjectableBoundary ColourNeedle Source #
Instance details Methods projectToBoundary :: ColourNeedle -> Boundary ColourNeedle -> Maybe (Needle (Boundary ColourNeedle), Scalar (Needle (Interior ColourNeedle))) # marginFromBoundary :: Boundary ColourNeedle -> Scalar (Needle (Interior ColourNeedle)) -> ColourNeedle # needleBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Needle (Interior ColourNeedle)) => r) -> r # scalarBoundaryIsTriviallyProjectible :: (ProjectableBoundary (Scalar (Needle (Interior ColourNeedle))) => r) -> r #
PseudoAffineWithBoundary ColourNeedle Source #
Instance details Methods (.--!) :: ColourNeedle -> ColourNeedle -> Needle (Interior ColourNeedle) # (.-\|) :: ColourNeedle -> Boundary ColourNeedle -> Maybe (HalfNeedle ColourNeedle) # (!-\|) :: ColourNeedle -> Boundary ColourNeedle -> HalfNeedle ColourNeedle # (.--.) :: ColourNeedle -> ColourNeedle -> Maybe (Needle (Interior ColourNeedle)) #
SemimanifoldWithBoundary ColourBoundary Source #
Instance details Associated Types type Interior ColourBoundary # type Boundary ColourBoundary # type HalfNeedle ColourBoundary # Methods (.+^\|) :: ColourBoundary -> Needle (Interior ColourBoundary) -> Either (Boundary ColourBoundary, Scalar (Needle (Interior ColourBoundary))) (Interior ColourBoundary) # fromInterior :: Interior ColourBoundary -> ColourBoundary # fromBoundary :: Boundary ColourBoundary -> ColourBoundary # (\|+^) :: Boundary ColourBoundary -> HalfNeedle ColourBoundary -> ColourBoundary # separateInterior :: ColourBoundary -> Either (Boundary ColourBoundary) (Interior ColourBoundary) # toInterior :: ColourBoundary -> Maybe (Interior ColourBoundary) # extendToBoundary :: Interior ColourBoundary -> Needle (Interior ColourBoundary) -> Maybe (Boundary ColourBoundary) # smfdWBoundWitness :: SmfdWBoundWitness ColourBoundary # needleIsOpenMfd :: (OpenManifold (Needle (Interior ColourBoundary)) => r) -> r # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior ColourBoundary))) => r) -> r # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary ColourBoundary)), Scalar (Needle (Boundary ColourBoundary)) ~ Scalar (Needle (Interior ColourBoundary))) => r) -> r #
SemimanifoldWithBoundary ColourNeedle Source #
Instance details Associated Types type Interior ColourNeedle # type Boundary ColourNeedle # type HalfNeedle ColourNeedle # Methods (.+^\|) :: ColourNeedle -> Needle (Interior ColourNeedle) -> Either (Boundary ColourNeedle, Scalar (Needle (Interior ColourNeedle))) (Interior ColourNeedle) # fromInterior :: Interior ColourNeedle -> ColourNeedle # fromBoundary :: Boundary ColourNeedle -> ColourNeedle # (\|+^) :: Boundary ColourNeedle -> HalfNeedle ColourNeedle -> ColourNeedle # separateInterior :: ColourNeedle -> Either (Boundary ColourNeedle) (Interior ColourNeedle) # toInterior :: ColourNeedle -> Maybe (Interior ColourNeedle) # extendToBoundary :: Interior ColourNeedle -> Needle (Interior ColourNeedle) -> Maybe (Boundary ColourNeedle) # smfdWBoundWitness :: SmfdWBoundWitness ColourNeedle # needleIsOpenMfd :: (OpenManifold (Needle (Interior ColourNeedle)) => r) -> r # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior ColourNeedle))) => r) -> r # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary ColourNeedle)), Scalar (Needle (Boundary ColourNeedle)) ~ Scalar (Needle (Interior ColourNeedle))) => r) -> r #
PseudoAffine ColourNeedle Source #
Instance details Methods (.-~.) :: ColourNeedle -> ColourNeedle -> Maybe (Needle ColourNeedle) # (.-~!) :: ColourNeedle -> ColourNeedle -> Needle ColourNeedle # pseudoAffineWitness :: PseudoAffineWitness ColourNeedle #
Semimanifold ColourNeedle Source #
Instance details Associated Types type Needle ColourNeedle # Methods (.+~^) :: ColourNeedle -> Needle ColourNeedle -> ColourNeedle # (.-~^) :: ColourNeedle -> Needle ColourNeedle -> ColourNeedle # semimanifoldWitness :: SemimanifoldWitness ColourNeedle #
AdditiveGroup ColourNeedle Source #
Instance details Methods zeroV :: ColourNeedle # (^+^) :: ColourNeedle -> ColourNeedle -> ColourNeedle # negateV :: ColourNeedle -> ColourNeedle # (^-^) :: ColourNeedle -> ColourNeedle -> ColourNeedle #
AffineSpace ColourNeedle Source #
Instance details Associated Types type Diff ColourNeedle # Methods (.-.) :: ColourNeedle -> ColourNeedle -> Diff ColourNeedle # (.+^) :: ColourNeedle -> Diff ColourNeedle -> ColourNeedle #
VectorSpace ColourNeedle Source #
Instance details Associated Types type Scalar ColourNeedle # Methods (*^) :: Scalar ColourNeedle -> ColourNeedle -> ColourNeedle #
Atlas (Colour ℝ) Source #
Instance details Associated Types type ChartIndex (Colour ℝ) # Methods chartReferencePoint :: ChartIndex (Colour ℝ) -> Colour ℝ # lookupAtlas :: Colour ℝ -> ChartIndex (Colour ℝ) #
Geodesic (Colour ℝ) Source #
Instance details Methods geodesicBetween :: Colour ℝ -> Colour ℝ -> Maybe (D¹ -> Colour ℝ) # middleBetween :: Colour ℝ -> Colour ℝ -> Maybe (Colour ℝ) #
PseudoAffineWithBoundary (Colour ℝ) Source #
Instance details Methods (.--!) :: Colour ℝ -> Colour ℝ -> Needle (Interior (Colour ℝ)) # (.-\|) :: Colour ℝ -> Boundary (Colour ℝ) -> Maybe (HalfNeedle (Colour ℝ)) # (!-\|) :: Colour ℝ -> Boundary (Colour ℝ) -> HalfNeedle (Colour ℝ) # (.--.) :: Colour ℝ -> Colour ℝ -> Maybe (Needle (Interior (Colour ℝ))) #
SemimanifoldWithBoundary (Colour ℝ) Source #
Instance details Associated Types type Interior (Colour ℝ) # type Boundary (Colour ℝ) # type HalfNeedle (Colour ℝ) # Methods (.+^\|) :: Colour ℝ -> Needle (Interior (Colour ℝ)) -> Either (Boundary (Colour ℝ), Scalar (Needle (Interior (Colour ℝ)))) (Interior (Colour ℝ)) # fromInterior :: Interior (Colour ℝ) -> Colour ℝ # fromBoundary :: Boundary (Colour ℝ) -> Colour ℝ # (\|+^) :: Boundary (Colour ℝ) -> HalfNeedle (Colour ℝ) -> Colour ℝ # separateInterior :: Colour ℝ -> Either (Boundary (Colour ℝ)) (Interior (Colour ℝ)) # toInterior :: Colour ℝ -> Maybe (Interior (Colour ℝ)) # extendToBoundary :: Interior (Colour ℝ) -> Needle (Interior (Colour ℝ)) -> Maybe (Boundary (Colour ℝ)) # smfdWBoundWitness :: SmfdWBoundWitness (Colour ℝ) # needleIsOpenMfd :: (OpenManifold (Needle (Interior (Colour ℝ))) => r) -> r # scalarIsOpenMfd :: (OpenManifold (Scalar (Needle (Interior (Colour ℝ)))) => r) -> r # boundaryHasSameScalar :: ((LinearSpace (Needle (Boundary (Colour ℝ))), Scalar (Needle (Boundary (Colour ℝ))) ~ Scalar (Needle (Interior (Colour ℝ)))) => r) -> r #