mirror of
https://gitlab.com/sheaf/metabrush.git
synced 2024-11-05 14:53:37 +00:00
continue interval arithmetic integration
This commit is contained in:
sheaf
parent
a4e9c1cf32
commit
09c1bdd948
|
|
@ -76,6 +76,7 @@ common common
|
|||
PatternSynonyms
|
||||
RankNTypes
|
||||
RecordWildCards
|
||||
RoleAnnotations
|
||||
StandaloneDeriving
|
||||
StandaloneKindSignatures
|
||||
TupleSections
|
||||
|
|
|
|||
|
|
@ -18,7 +18,7 @@ import Data.Functor.Const
|
|||
import Data.Functor.Identity
|
||||
( Identity(..) )
|
||||
import Data.Kind
|
||||
( Constraint )
|
||||
( Type, Constraint )
|
||||
import Data.Monoid
|
||||
( Ap(..) )
|
||||
import Data.Semigroup
|
||||
|
|
@ -87,7 +87,8 @@ instance SplineTypeI Open where
|
|||
instance SplineTypeI Closed where
|
||||
ssplineType = SClosed
|
||||
|
||||
data family NextPoint ( clo :: SplineType ) ptData
|
||||
type NextPoint :: SplineType -> Type -> Type
|
||||
data family NextPoint clo
|
||||
newtype instance NextPoint Open ptData = NextPoint { nextPoint :: ptData }
|
||||
deriving stock ( Show, Generic, Generic1, Functor, Foldable, Traversable )
|
||||
deriving anyclass ( NFData, NFData1 )
|
||||
|
|
@ -111,7 +112,8 @@ toNextPoint pt = case ssplineType @clo of
|
|||
SOpen -> NextPoint pt
|
||||
SClosed -> BackToStart
|
||||
|
||||
data Curve ( clo :: SplineType ) crvData ptData
|
||||
type Curve :: SplineType -> Type -> Type -> Type
|
||||
data Curve clo crvData ptData
|
||||
= LineTo
|
||||
{ curveEnd :: !( NextPoint clo ptData )
|
||||
, curveData :: !crvData
|
||||
|
|
@ -157,7 +159,8 @@ openCurveStart ( LineTo ( NextPoint p ) _ ) = p
|
|||
openCurveStart ( Bezier2To p _ _ ) = p
|
||||
openCurveStart ( Bezier3To p _ _ _ ) = p
|
||||
|
||||
data family Curves ( clo :: SplineType ) crvData ptData
|
||||
type Curves :: SplineType -> Type -> Type -> Type
|
||||
data family Curves clo
|
||||
|
||||
newtype instance Curves Open crvData ptData
|
||||
= OpenCurves { openCurves :: Seq ( Curve Open crvData ptData ) }
|
||||
|
|
|
|||
|
|
@ -1,8 +1,7 @@
|
|||
{-# LANGUAGE AllowAmbiguousTypes #-}
|
||||
{-# LANGUAGE QuantifiedConstraints #-}
|
||||
{-# LANGUAGE ScopedTypeVariables #-}
|
||||
|
||||
{-# LANGUAGE DuplicateRecordFields #-}
|
||||
{-# LANGUAGE UndecidableInstances #-}
|
||||
|
||||
module Math.Bezier.Stroke
|
||||
( Offset(..)
|
||||
|
|
@ -32,11 +31,13 @@ import Control.Monad.ST
|
|||
import Data.Bifunctor
|
||||
( Bifunctor(bimap) )
|
||||
import Data.Coerce
|
||||
( coerce )
|
||||
( Coercible, coerce )
|
||||
import Data.Foldable
|
||||
( for_ )
|
||||
import Data.Functor.Identity
|
||||
( Identity(..) )
|
||||
import Data.Kind
|
||||
( Type )
|
||||
import Data.List.NonEmpty
|
||||
( unzip )
|
||||
import Data.Maybe
|
||||
|
|
@ -434,13 +435,16 @@ outlineFunction ptParams toBrushParams brushFromParams sp0 crv =
|
|||
case crv of
|
||||
LineTo { curveEnd = NextPoint sp1 }
|
||||
| let seg = Segment sp0 sp1
|
||||
-> ( line ( fmap coords seg ), line ( fmap ptParams seg ) )
|
||||
-> ( line @Point ( fmap coords seg )
|
||||
, line @Point ( fmap ptParams seg ) )
|
||||
Bezier2To { controlPoint = sp1, curveEnd = NextPoint sp2 }
|
||||
| let bez2 = Quadratic.Bezier sp0 sp1 sp2
|
||||
-> ( bezier2 ( fmap coords bez2 ), bezier2 ( fmap ptParams bez2 ) )
|
||||
-> ( bezier2 @Point ( fmap coords bez2 )
|
||||
, bezier2 @Point ( fmap ptParams bez2 ) )
|
||||
Bezier3To { controlPoint1 = sp1, controlPoint2 = sp2, curveEnd = NextPoint sp3 }
|
||||
| let bez3 = Cubic.Bezier sp0 sp1 sp2 sp3
|
||||
-> ( bezier3 ( fmap coords bez3 ), bezier3 ( fmap ptParams bez3 ) )
|
||||
-> ( bezier3 @Point ( fmap coords bez3 )
|
||||
, bezier3 @Point ( fmap ptParams bez3 ) )
|
||||
|
||||
fwdBwd :: OutlineFn
|
||||
fwdBwd t
|
||||
|
|
@ -449,8 +453,12 @@ outlineFunction ptParams toBrushParams brushFromParams sp0 crv =
|
|||
-- , ( offset bwdOffset • path_t, -1 *^ path'_t ) )
|
||||
where
|
||||
|
||||
curves :: Seq ( ℝ 1 -> StrokeDatum )
|
||||
curves = brushStrokeData path ( usedParams `chainRule` toBrushParams ) brushFromParams t
|
||||
curves :: Seq ( ℝ 1 -> StrokeDatum Point )
|
||||
curves = brushStrokeData @Point @brushParams
|
||||
path
|
||||
( usedParams `chainRule` toBrushParams )
|
||||
brushFromParams
|
||||
t
|
||||
|
||||
fwdOffset = withTangent path'_t brush_t
|
||||
bwdOffset = withTangent ( -1 *^ path'_t ) brush_t
|
||||
|
|
@ -771,7 +779,7 @@ brushStroke ( D1 p dpdt d2pdt2 ) ( D2 b dbdt dbds d2bdt2 d2bdtds d2bds2 ) =
|
|||
|
||||
-- | The envelope equation
|
||||
--
|
||||
-- \[ E = \frac{\partial c}{\partial t} \times \frac{\partial c}{\partial s} = 0, ]
|
||||
-- \[ E = \frac{\partial c}{\partial t} \times \frac{\partial c}{\partial s} = 0, \]
|
||||
--
|
||||
-- together with the total derivative
|
||||
--
|
||||
|
|
@ -782,12 +790,13 @@ brushStroke ( D1 p dpdt d2pdt2 ) ( D2 b dbdt dbds d2bdt2 d2bdtds d2bds2 ) =
|
|||
-- \[ \frac{\partial E}{\partial s}, \qquad \frac{\partial E}{\partial s}. \]
|
||||
--
|
||||
-- NB: if \( \frac{\partial E}{\partial s} \) is zero, the total derivative is ill-defined.
|
||||
envelopeEquation :: ( D ( i ( ℝ 2 ) ) ~ D ( ℝ 2 )
|
||||
, Cross ( i Double ) ( T ( i ( ℝ 2 ) ) )
|
||||
, Fractional ( i Double )
|
||||
envelopeEquation :: forall i
|
||||
. ( D ( I i ( ℝ 2 ) ) ~ D ( ℝ 2 )
|
||||
, Cross ( I i Double ) ( T ( I i ( ℝ 2 ) ) )
|
||||
, Fractional ( I i Double )
|
||||
)
|
||||
=> D ( i ( ℝ 2 ) ) ( i ( ℝ 2 ) )
|
||||
-> ( i Double, T ( i ( ℝ 2 ) ), i Double, i Double )
|
||||
=> D ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) )
|
||||
-> ( I i Double, T ( I i ( ℝ 2 ) ), I i Double, I i Double )
|
||||
envelopeEquation ( D2 _ dcdt dcds d2cdt2 d2cdtds d2cds2 ) =
|
||||
let ee = dcdt `cross` dcds
|
||||
dEdt = d2cdt2 `cross` dcds + dcdt `cross` d2cdtds
|
||||
|
|
@ -802,30 +811,47 @@ envelopeEquation ( D2 _ dcdt dcds d2cdt2 d2cdtds d2cds2 ) =
|
|||
-- ∂E/∂s dc/dt = ∂E/∂s ∂c/∂t - ∂E/∂t ∂c/∂s.
|
||||
|
||||
-- | Linear interpolation, as a differentiable function.
|
||||
line :: forall b. ( Module Double ( T b ), Torsor ( T b ) b )
|
||||
=> Segment b -> ℝ 1 ~> b
|
||||
line ( Segment a b ) = D \ ( ℝ1 t ) ->
|
||||
line :: forall i b
|
||||
. ( Module ( I i Double ) ( T b ), Torsor ( T b ) b
|
||||
, D ( I i ( ℝ 1 ) ) ~ D ( ℝ 1 )
|
||||
, Coercible ( I i ( ℝ 1 ) ) ( I i Double )
|
||||
)
|
||||
=> Segment b -> I i ( ℝ 1 ) ~> b
|
||||
line ( Segment a b ) = D \ ( coerce -> t ) ->
|
||||
D1 ( lerp @( T b ) t a b )
|
||||
( a --> b )
|
||||
origin
|
||||
|
||||
-- | A quadratic Bézier curve, as a differentiable function.
|
||||
bezier2 :: forall b. ( Module Double ( T b ), Torsor ( T b ) b )
|
||||
=> Quadratic.Bezier b -> ℝ 1 ~> b
|
||||
bezier2 bez = D \ ( ℝ1 t ) ->
|
||||
bezier2 :: forall i b
|
||||
. ( Module ( I i Double ) ( T b ), Torsor ( T b ) b
|
||||
, D ( I i ( ℝ 1 ) ) ~ D ( ℝ 1 )
|
||||
, Coercible ( I i ( ℝ 1 ) ) ( I i Double )
|
||||
)
|
||||
=> Quadratic.Bezier b -> I i ( ℝ 1 ) ~> b
|
||||
bezier2 bez = D \ ( coerce -> t ) ->
|
||||
D1 ( Quadratic.bezier @( T b ) bez t )
|
||||
( Quadratic.bezier' bez t )
|
||||
( Quadratic.bezier'' bez )
|
||||
|
||||
-- | A cubic Bézier curve, as a differentiable function.
|
||||
bezier3 :: forall b. ( Module Double ( T b ), Torsor ( T b ) b )
|
||||
=> Cubic.Bezier b -> ℝ 1 ~> b
|
||||
bezier3 bez = D \ ( ℝ1 t ) ->
|
||||
bezier3 :: forall i b
|
||||
. ( Module ( I i Double ) ( T b ), Torsor ( T b ) b
|
||||
, D ( I i ( ℝ 1 ) ) ~ D ( ℝ 1 )
|
||||
, Coercible ( I i ( ℝ 1 ) ) ( I i Double )
|
||||
)
|
||||
=> Cubic.Bezier b -> I i ( ℝ 1 ) ~> b
|
||||
bezier3 bez = D \ ( coerce -> t ) ->
|
||||
D1 ( Cubic.bezier @( T b ) bez t )
|
||||
( Cubic.bezier' bez t )
|
||||
( Cubic.bezier'' bez t )
|
||||
|
||||
splineCurveFns :: SplinePts Closed -> Seq ( ℝ 1 ~> ℝ 2 )
|
||||
splineCurveFns :: forall i
|
||||
. ( D ( I i ( ℝ 1 ) ) ~ D ( ℝ 1 )
|
||||
, Module ( I i Double ) ( T ( I i ( ℝ 2 ) ) )
|
||||
, Torsor ( T ( I i ( ℝ 2 ) ) ) ( I i ( ℝ 2 ) )
|
||||
, Coercible ( I i ( ℝ 1 ) ) ( I i Double ) )
|
||||
=> Spline Closed () ( I i ( ℝ 2 ) ) -> Seq ( I i ( ℝ 1 ) ~> I i ( ℝ 2 ) )
|
||||
splineCurveFns spls
|
||||
= runIdentity
|
||||
. bifoldSpline
|
||||
|
|
@ -834,21 +860,23 @@ splineCurveFns spls
|
|||
. adjustSplineType @Open
|
||||
$ spls
|
||||
where
|
||||
curveFn :: ℝ 2 -> Curve Open () ( ℝ 2 ) -> ( ℝ 1 ~> ℝ 2 )
|
||||
curveFn :: I i ( ℝ 2 )
|
||||
-> Curve Open () ( I i ( ℝ 2 ) )
|
||||
-> ( I i ( ℝ 1 ) ~> I i ( ℝ 2 ) )
|
||||
curveFn p0 = \case
|
||||
LineTo { curveEnd = NextPoint p1 }
|
||||
-> line $ Segment p0 p1
|
||||
-> line @i $ Segment p0 p1
|
||||
Bezier2To { controlPoint = p1, curveEnd = NextPoint p2 }
|
||||
-> bezier2 $ Quadratic.Bezier p0 p1 p2
|
||||
-> bezier2 @i $ Quadratic.Bezier p0 p1 p2
|
||||
Bezier3To { controlPoint1 = p1, controlPoint2 = p2, curveEnd = NextPoint p3 }
|
||||
-> bezier3 $ Cubic.Bezier p0 p1 p2 p3
|
||||
-> bezier3 @i $ Cubic.Bezier p0 p1 p2 p3
|
||||
|
||||
-- | Solve the envelope equations at a given point \( t = t_0 \), to find
|
||||
-- \( s_0 \) such that \( c(t_0, s_0) \) is on the envelope of the brush stroke.
|
||||
solveEnvelopeEquations :: ℝ 2
|
||||
-> T ( ℝ 2 )
|
||||
-> ( Offset, Offset )
|
||||
-> Seq ( ℝ 1 -> StrokeDatum )
|
||||
-> Seq ( ℝ 1 -> StrokeDatum Point )
|
||||
-> ( ( ℝ 2, T ( ℝ 2 ) ), ( ℝ 2, T ( ℝ 2 ) ) )
|
||||
solveEnvelopeEquations path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
||||
= ( fwdSol, ( bwdPt, -1 *^ bwdTgt ) )
|
||||
|
|
@ -909,7 +937,7 @@ solveEnvelopeEquations path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
|||
| otherwise
|
||||
= i + 1
|
||||
|
||||
sol :: Double -> ( ℝ 1 -> StrokeDatum ) -> ( Bool, ℝ 1, ℝ 2, T ( ℝ 2 ) )
|
||||
sol :: Double -> ( ℝ 1 -> StrokeDatum Point ) -> ( Bool, ℝ 1, ℝ 2, T ( ℝ 2 ) )
|
||||
sol initialGuess f =
|
||||
let (good, s) = case newtonRaphson maxIters precision domain ( eqn f ) initialGuess of
|
||||
Nothing -> ( False, initialGuess )
|
||||
|
|
@ -937,7 +965,7 @@ solveEnvelopeEquations path_t path'_t ( fwdOffset, bwdOffset ) strokeData
|
|||
-- ] )
|
||||
( good, ℝ1 s, value @Double @( ℝ 2 ) dstroke, totDeriv )
|
||||
|
||||
eqn :: ( ℝ 1 -> StrokeDatum ) -> ( Double -> ( Double, Double ) )
|
||||
eqn :: ( ℝ 1 -> StrokeDatum Point ) -> ( Double -> ( Double, Double ) )
|
||||
eqn f s =
|
||||
case f ( ℝ1 s ) of
|
||||
StrokeDatum { ee, 𝛿E𝛿s } ->
|
||||
|
|
@ -956,36 +984,47 @@ instance Applicative ZipSeq where
|
|||
pure _ = error "only use Applicative ZipSeq with non-empty Traversable functors"
|
||||
liftA2 f ( ZipSeq xs ) ( ZipSeq ys ) = ZipSeq ( Seq.zipWith f xs ys )
|
||||
|
||||
brushStrokeData :: forall brushParams
|
||||
. ( Diffy Double brushParams, Show brushParams )
|
||||
=> ( ℝ 1 ~> ℝ 2 ) -- ^ path
|
||||
-> ( ℝ 1 ~> brushParams ) -- ^ brush parameters
|
||||
-> ( brushParams ~> SplinePts Closed ) -- ^ brush from parameters
|
||||
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum ) )
|
||||
brushStrokeData :: forall i brushParams
|
||||
. ( Diffy ( I i Double ) ( I i brushParams )
|
||||
, Fractional ( I i Double )
|
||||
, D ( I i ( ℝ 1 ) ) ~ D ( ℝ 1 )
|
||||
, D ( I i ( ℝ 2 ) ) ~ D ( ℝ 2 )
|
||||
, Cross ( I i Double ) ( T ( I i ( ℝ 2 ) ) )
|
||||
, Torsor ( T ( I i ( ℝ 2 ) ) ) ( I i ( ℝ 2 ) )
|
||||
, Coercible ( I i ( ℝ 1 ) ) ( I i Double )
|
||||
, Show brushParams
|
||||
)
|
||||
=> ( I i ( ℝ 1 ) ~> I i ( ℝ 2 ) )
|
||||
-- ^ path
|
||||
-> ( I i ( ℝ 1 ) ~> I i brushParams )
|
||||
-- ^ brush parameters
|
||||
-> ( I i brushParams ~> Spline Closed () ( I i ( ℝ 2 ) ) )
|
||||
-- ^ brush from parameters
|
||||
-> ( I i ( ℝ 1 ) -> Seq ( I i ( ℝ 1 ) -> StrokeDatum i ) )
|
||||
brushStrokeData path params brush =
|
||||
\ t ->
|
||||
let
|
||||
dpath_t :: D ( ℝ 1 ) ( ℝ 2 )
|
||||
dpath_t :: D ( I i ( ℝ 1 ) ) ( I i ( ℝ 2 ) )
|
||||
!dpath_t = runD path t
|
||||
dparams_t :: D ( ℝ 1 ) brushParams
|
||||
dparams_t :: D ( I i ( ℝ 1 ) ) ( I i brushParams )
|
||||
!dparams_t@( D1 { v = params_t } ) = runD params t
|
||||
dbrush_params :: D brushParams ( SplinePts Closed )
|
||||
dbrush_params :: D ( I i brushParams ) ( Spline Closed () ( I i ( ℝ 2 ) ) )
|
||||
!dbrush_params = runD brush params_t
|
||||
splines :: Seq ( D brushParams ( ℝ 1 ~> ℝ 2 ) )
|
||||
!splines = getZipSeq $ traverse ( ZipSeq . splineCurveFns ) dbrush_params
|
||||
dbrushes_t :: Seq ( ℝ 1 -> D ( ℝ 2 ) ( ℝ 2 ) )
|
||||
splines :: Seq ( D ( I i brushParams ) ( I i ( ℝ 1 ) ~> I i ( ℝ 2 ) ) )
|
||||
!splines = getZipSeq $ traverse ( ZipSeq . splineCurveFns @i ) dbrush_params
|
||||
dbrushes_t :: Seq ( I i ( ℝ 1 ) -> D ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) ) )
|
||||
!dbrushes_t = force $ fmap ( uncurryD . ( dparams_t `chain` ) ) splines
|
||||
|
||||
in fmap ( mkStrokeDatum dpath_t ) dbrushes_t
|
||||
where
|
||||
|
||||
mkStrokeDatum :: D ( ℝ 1 ) ( ℝ 2 )
|
||||
-> ( ℝ 1 -> D ( ℝ 2 ) ( ℝ 2 ) )
|
||||
-> ( ℝ 1 -> StrokeDatum )
|
||||
mkStrokeDatum :: D ( I i ( ℝ 1 ) ) ( I i ( ℝ 2 ) )
|
||||
-> ( I i ( ℝ 1 ) -> D ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) ) )
|
||||
-> ( I i ( ℝ 1 ) -> StrokeDatum i )
|
||||
mkStrokeDatum dpath_t dbrush_t s =
|
||||
let dbrush_t_s = dbrush_t s
|
||||
dstroke@( D2 _c _𝛿c𝛿t _𝛿c𝛿s _ _ _ ) = brushStroke dpath_t dbrush_t_s
|
||||
( ee, dcdt, 𝛿E𝛿t, 𝛿E𝛿s ) = coerce $ envelopeEquation @Identity $ coerce dstroke
|
||||
( ee, dcdt, 𝛿E𝛿t, 𝛿E𝛿s ) = envelopeEquation @i dstroke
|
||||
in -- trace
|
||||
-- ( unlines
|
||||
-- [ "envelopeEquation:"
|
||||
|
|
@ -1004,34 +1043,46 @@ brushStrokeData path params brush =
|
|||
, dstroke
|
||||
, ee, dcdt, 𝛿E𝛿t, 𝛿E𝛿s }
|
||||
|
||||
|
||||
-- | The value and derivative of a brush stroke at a given coordinate
|
||||
-- \( (t_0, s_0) \), together with the value of the envelope equation at that
|
||||
-- point.
|
||||
data StrokeDatum
|
||||
data StrokeDatum i
|
||||
= StrokeDatum
|
||||
{ -- | Path \( p(t_0) \) (with its 1st and 2nd derivatives).
|
||||
dpath :: D ( ℝ 1 ) ( ℝ 2 )
|
||||
dpath :: D ( I i ( ℝ 1 ) ) ( I i ( ℝ 2 ) )
|
||||
-- | Brush shape \( b(t_0, s_0) \) (with its 1st and 2nd derivatives).
|
||||
, dbrush :: D ( ℝ 2 ) ( ℝ 2 )
|
||||
, dbrush :: D ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) )
|
||||
|
||||
-- Everything below can be computed in terms of the first two fields.
|
||||
|
||||
-- | Stroke \( c(t_0,s_0) = p(t_0) + b(t_0,s_0) \) (with its 1st and 2nd derivatives).
|
||||
, dstroke :: D ( ℝ 2 ) ( ℝ 2 )
|
||||
, dstroke :: D ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) )
|
||||
-- | Envelope
|
||||
--
|
||||
-- \[ E(t_0,s_0) = \left ( \frac{\partial c}{\partial t} \times \frac{\partial c}{\partial s} \right )_{(t_0,s_0)}. \]
|
||||
, ee :: Double
|
||||
, ee :: I i Double
|
||||
-- | \( \left ( \frac{\partial E}{\partial s} \right )_{(t_0,s_0)}. \)
|
||||
, 𝛿E𝛿s :: Double
|
||||
, 𝛿E𝛿s :: I i Double
|
||||
-- | \( \left ( \frac{\partial E}{\partial t} \right )_{(t_0,s_0)}. \)
|
||||
, 𝛿E𝛿t :: Double
|
||||
, 𝛿E𝛿t :: I i Double
|
||||
-- | Total derivative
|
||||
--
|
||||
-- \[ \left ( \frac{\mathrm{d} c}{\mathrm{d} t} \right )_{(t_0,s_0)}. \]
|
||||
--
|
||||
-- This is ill-defined when \( \frac{\partial E}{\partial s} = 0 \).
|
||||
, dcdt :: T ( ℝ 2 )
|
||||
, dcdt :: T ( I i ( ℝ 2 ) )
|
||||
|
||||
}
|
||||
deriving stock Show
|
||||
|
||||
deriving stock instance Show ( StrokeDatum Point )
|
||||
deriving stock instance Show ( StrokeDatum Interval )
|
||||
|
||||
|
||||
-- Handling points and intervals uniformly.
|
||||
data Extent = Point | Interval
|
||||
|
||||
type I :: Extent -> Type -> Type
|
||||
type family I i a where
|
||||
I Point a = a
|
||||
I Interval a = 𝕀 a
|
||||
|
|
|
|||
|
|
@ -11,8 +11,6 @@ import Control.Applicative
|
|||
( liftA2 )
|
||||
import Data.Coerce
|
||||
( coerce )
|
||||
import Data.Functor.Identity
|
||||
( Identity(..) )
|
||||
import Data.Kind
|
||||
( Type, Constraint )
|
||||
import GHC.Generics
|
||||
|
|
@ -45,7 +43,6 @@ type instance D ( ℝ 1 ) = Dℝ1
|
|||
type instance D ( ℝ 2 ) = Dℝ2
|
||||
type instance D ( ℝ 3 ) = Dℝ3
|
||||
|
||||
type instance D ( Identity a ) = D a
|
||||
type instance D ( 𝕀 u ) = D u
|
||||
|
||||
newtype Dℝ0 v = D0 { v :: v }
|
||||
|
|
|
|||
|
|
@ -18,10 +18,6 @@ import Control.Applicative
|
|||
( liftA2 )
|
||||
import Control.Monad
|
||||
( guard )
|
||||
import Data.Coerce
|
||||
( coerce )
|
||||
import Data.Functor.Identity
|
||||
( Identity(..) )
|
||||
import Data.Kind
|
||||
( Type, Constraint )
|
||||
import Data.Monoid
|
||||
|
|
@ -176,16 +172,6 @@ instance Inner Double ( T ( ℝ 2 ) ) where
|
|||
instance Cross Double ( T ( ℝ 2 ) ) where
|
||||
cross ( V2 x1 y1 ) ( V2 x2 y2 ) = x1 * y2 - x2 * y1
|
||||
|
||||
instance Module r ( T m ) => Module ( Identity r ) ( T ( Identity m ) ) where
|
||||
origin = coerce $ origin @r @( T m )
|
||||
(^+^) = coerce $ (^+^) @r @( T m )
|
||||
(^-^) = coerce $ (^-^) @r @( T m )
|
||||
(*^) = coerce $ (*^) @r @( T m )
|
||||
instance Inner r ( T m ) => Inner ( Identity r ) ( T ( Identity m ) ) where
|
||||
(^.^) = coerce $ (^.^) @r @( T m )
|
||||
instance Cross r ( T m ) => Cross ( Identity r ) ( T ( Identity m ) ) where
|
||||
cross = coerce $ cross @r @( T m )
|
||||
|
||||
-- | Compute whether two vectors point in the same direction,
|
||||
-- that is, whether each vector is a (strictly) positive multiple of the other.
|
||||
--
|
||||
|
|
|
|||
Loading…
Reference in a new issue