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Improve specialisation + add degree computation

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sheaf 2024-04-25 21:53:27 +02:00
parent 6450859e3c
commit c89fba7fd2
17 changed files with 432 additions and 116 deletions
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10
brush-strokes/brush-strokes.cabal
View file

@ -14,6 +14,11 @@ flag use-fma
default: True
manual: False
flag asserts
description: Enable debugging assertions.
default: False
manual: True
common common
build-depends:
@ -89,6 +94,10 @@ common common
base
>= 4.19
if flag(asserts)
cpp-options:
-DASSERTS
common extra
build-depends:
@ -133,6 +142,7 @@ library
, Math.Root.Isolation
, Math.Root.Isolation.Bisection
, Math.Root.Isolation.Core
, Math.Root.Isolation.Degree
, Math.Root.Isolation.GaussSeidel
, Math.Root.Isolation.Narrowing
, Debug.Utils

48
brush-strokes/src/cusps/bench/Bench/Types.hs
View file

@ -12,8 +12,14 @@ module Bench.Types
-- base
import Data.Coerce
( coerce )
import Data.Proxy
( Proxy(..) )
import Data.Type.Equality
( (:~:)(Refl) )
import GHC.Generics
( Generic )
import GHC.TypeNats
( sameNat )
-- containers
import Data.Sequence
@ -111,10 +117,48 @@ getStrokeFunctions ( Brush brushShape brushShapeI mbRot ) sp0 crv =
( fmap nonDecreasing mbRot )
)
{-# INLINEABLE getStrokeFunctions #-}
{-# SPECIALISE getStrokeFunctions
:: Brush ( ℝ 1 )
-> Point 1
-> Curve Open () ( Point 1 )
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE getStrokeFunctions
:: Brush ( ℝ 2 )
-> Point 2
-> Curve Open () ( Point 2 )
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE getStrokeFunctions
:: Brush ( ℝ 3 )
-> Point 3
-> Curve Open () ( Point 3 )
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE getStrokeFunctions
:: Brush ( ℝ 4 )
-> Point 4
-> Curve Open () ( Point 4 )
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
#-}
brushStrokeFunctions
:: BrushStroke
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
brushStrokeFunctions ( BrushStroke { stroke = ( sp0, crv ), brush } ) =
getStrokeFunctions brush sp0 crv
brushStrokeFunctions ( BrushStroke { stroke = ( sp0, crv ), brush = brush :: Brush ( ℝ nbParams ) } )
-- Trick for triggering specialisation... TODO improve this.
| Just Refl <- sameNat @nbParams @1 Proxy Proxy
= getStrokeFunctions @1 brush sp0 crv
| Just Refl <- sameNat @nbParams @2 Proxy Proxy
= getStrokeFunctions @2 brush sp0 crv
| Just Refl <- sameNat @nbParams @3 Proxy Proxy
= getStrokeFunctions @3 brush sp0 crv
| Just Refl <- sameNat @nbParams @4 Proxy Proxy
= getStrokeFunctions @4 brush sp0 crv
| otherwise
= getStrokeFunctions @nbParams brush sp0 crv

5
brush-strokes/src/cusps/bench/Main.hs
View file

@ -92,15 +92,14 @@ benchGroups :: [ ( String, NE.NonEmpty TestCase ) ]
benchGroups =
[ ( "ellipse"
, NE.fromList
[ ellipseTestCase opts ("ε_bis=" ++ show ε_bis ++ if doBox1 then "box(1)" else "")
[ ellipseTestCase opts ("ε_bis=" ++ show ε_bis)
( 0, 1 ) pi
( defaultStartBoxes [ 0 .. 3 ] )
| ε_bis <- [ 1e-6, 5e-6, 1e-5, 5e-5, 1e-4, 5e-4, 1e-4, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2, 0.1, 0.2, 0.3 ]
, doBox1 <- [ False, True ]
, let opts =
RootIsolationOptions
{ rootIsolationAlgorithms =
defaultRootIsolationAlgorithms minWidth ε_bis doBox1
defaultRootIsolationAlgorithms minWidth ε_bis
}
]
)

28
brush-strokes/src/lib/Calligraphy/Brushes.hs
View file

@ -50,9 +50,13 @@ type BrushFn i k brushParams
-- | A brush, described as a base shape + an optional rotation.
data Brush brushParams
= Brush
{ brushShape :: BrushFn () 2 brushParams
, brushShapeI :: BrushFn 𝕀 3 brushParams
, mbRotation :: Maybe ( brushParams -> Double )
{ -- | Base brush shape, before applying any rotation (if any).
brushBaseShape :: BrushFn () 2 brushParams
-- | Base brush shape, before applying any rotation (if any).
, brushBaseShapeI :: BrushFn 𝕀 3 brushParams
-- | Optional rotation angle function
-- (assumed to be a linear function).
, mbRotation :: Maybe ( brushParams -> Double )
}
--------------------------------------------------------------------------------
@ -74,27 +78,27 @@ type ParamsICt k i rec =
circleBrush :: ( 1 <= RepDim params, ParamsCt params ) => Brush params
circleBrush =
Brush
{ brushShape = circleBrushFn @() @2 proxy# id
, brushShapeI = circleBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Nothing
{ brushBaseShape = circleBrushFn @() @2 proxy# id
, brushBaseShapeI = circleBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Nothing
}
{-# INLINEABLE ellipseBrush #-}
ellipseBrush :: ( 3 <= RepDim params, ParamsCt params ) => Brush params
ellipseBrush =
Brush
{ brushShape = ellipseBrushFn @() @2 proxy# id
, brushShapeI = ellipseBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Just ( `index` ( Fin 3 ) )
{ brushBaseShape = ellipseBrushFn @() @2 proxy# id
, brushBaseShapeI = ellipseBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Just ( `index` ( Fin 3 ) )
}
{-# INLINEABLE tearDropBrush #-}
tearDropBrush :: ( 3 <= RepDim params, ParamsCt params ) => Brush params
tearDropBrush =
Brush
{ brushShape = tearDropBrushFn @() @2 proxy# id
, brushShapeI = tearDropBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Just ( `index` ( Fin 3 ) )
{ brushBaseShape = tearDropBrushFn @() @2 proxy# id
, brushBaseShapeI = tearDropBrushFn @𝕀 @3 proxy# singleton
, mbRotation = Just ( `index` ( Fin 3 ) )
}
--------------------------------------------------------------------------------

65
brush-strokes/src/lib/Math/Bezier/Stroke.hs
View file

@ -383,7 +383,7 @@ computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams bru
brushShape :: ptData -> SplinePts Closed
brushShape pt =
let Brush { brushShape = shapeFn, mbRotation = mbRot } = brush
let Brush { brushBaseShape = shapeFn, mbRotation = mbRot } = brush
brushParams = toBrushParams $ ptParams pt
shape = fun @Double shapeFn brushParams
in case mbRot of
@ -546,7 +546,7 @@ outlineFunction
-> Curve Open crvData ptData
-> OutlineInfo
outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams
( Brush { brushShape, brushShapeI, mbRotation } ) = \ sp0 crv ->
( Brush { brushBaseShape, brushBaseShapeI, mbRotation } ) = \ sp0 crv ->
let
usedParams :: C 2 ( ℝ 1 ) usedParams
@ -561,7 +561,7 @@ outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams
coerce coerce
path
( fmap toBrushParams usedParams )
brushShape
brushBaseShape
mbRotation
curvesI :: 𝕀ℝ 1 -- t
@ -571,7 +571,7 @@ outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams
coerce coerce
pathI
( fmap ( nonDecreasing toBrushParams ) usedParamsI )
brushShapeI
brushBaseShapeI
( fmap nonDecreasing mbRotation )
usedParamsI :: C 3 ( 𝕀ℝ 1 ) ( 𝕀 usedParams )
@ -589,9 +589,19 @@ outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams
D21 path_t path'_t _ = runD path t
D21 params_t _ _ = runD usedParams t
brush_t = value @Double @2 @brushParams
$ runD brushShape
$ toBrushParams params_t
brush_t =
let brushParams = toBrushParams params_t
applyRot = case mbRotation of
Nothing -> id
Just getθ ->
let θ = getθ brushParams
cosθ = cos θ
sinθ = sin θ
in fmap ( unT . rotate cosθ sinθ . T )
in
applyRot $
value @Double @2 @brushParams $
runD brushBaseShape brushParams
( potentialCusps, definiteCusps ) =
case mbCuspOptions of
@ -644,6 +654,7 @@ pathAndUsedParams co toI ptParams sp0 crv =
| let bez3 = Cubic.Bezier sp0 sp1 sp2 sp3
-> ( bezier3 @k @i @( ℝ 2 ) co ( fmap ( toI . coords ) bez3 )
, bezier3 @k @i @usedParams co ( fmap ( toI . ptParams ) bez3 ) )
{-# INLINEABLE pathAndUsedParams #-}
-----------------------------------
-- Various utility functions
@ -1030,6 +1041,46 @@ brushStrokeData co1 co2 path params brush mbBrushRotation =
let dbrush_t_s = dbrush_t s
mbRotation = mbBrushRotation <&> \ getTheta -> fmap getTheta dparams_t
in envelopeEquation @k @i Proxy co1 dpath_t dbrush_t_s mbRotation
{-# INLINEABLE brushStrokeData #-}
{-# SPECIALISE brushStrokeData
:: ( I 𝕀 Double -> I 𝕀 ( ℝ 1 ) )
-> ( I 𝕀 ( ℝ 1 ) -> I 𝕀 Double )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 2 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 1 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( Spline Closed () ( I 𝕀 ( ℝ 2 ) ) ) )
-> ( Maybe ( I 𝕀 ( ℝ 1 ) -> I 𝕀 Double ) )
-> ( I 𝕀 ( ℝ 1 ) -> Seq ( I 𝕀 ( ℝ 1 ) -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE brushStrokeData
:: ( I 𝕀 Double -> I 𝕀 ( ℝ 1 ) )
-> ( I 𝕀 ( ℝ 1 ) -> I 𝕀 Double )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 2 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 2 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 2 ) ) ( Spline Closed () ( I 𝕀 ( ℝ 2 ) ) ) )
-> ( Maybe ( I 𝕀 ( ℝ 2 ) -> I 𝕀 Double ) )
-> ( I 𝕀 ( ℝ 1 ) -> Seq ( I 𝕀 ( ℝ 1 ) -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE brushStrokeData
:: ( I 𝕀 Double -> I 𝕀 ( ℝ 1 ) )
-> ( I 𝕀 ( ℝ 1 ) -> I 𝕀 Double )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 2 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 3 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 3 ) ) ( Spline Closed () ( I 𝕀 ( ℝ 2 ) ) ) )
-> ( Maybe ( I 𝕀 ( ℝ 3 ) -> I 𝕀 Double ) )
-> ( I 𝕀 ( ℝ 1 ) -> Seq ( I 𝕀 ( ℝ 1 ) -> StrokeDatum 3 𝕀 ) )
#-}
{-# SPECIALISE brushStrokeData
:: ( I 𝕀 Double -> I 𝕀 ( ℝ 1 ) )
-> ( I 𝕀 ( ℝ 1 ) -> I 𝕀 Double )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 2 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 1 ) ) ( I 𝕀 ( ℝ 4 ) ) )
-> ( C 3 ( I 𝕀 ( ℝ 4 ) ) ( Spline Closed () ( I 𝕀 ( ℝ 2 ) ) ) )
-> ( Maybe ( I 𝕀 ( ℝ 4 ) -> I 𝕀 Double ) )
-> ( I 𝕀 ( ℝ 1 ) -> Seq ( I 𝕀 ( ℝ 1 ) -> StrokeDatum 3 𝕀 ) )
#-}
-- TODO: these specialisations fire in the benchmarking code because
-- we instantiate brushParams with ( ℝ nbBrushParams ), but they won't fire
-- in the main app code because we are using types such as "Record EllipseBrushFields".
--------------------------------------------------------------------------------
-- Solving the envelolpe equation: root-finding.

15
brush-strokes/src/lib/Math/Bezier/Stroke/EnvelopeEquation.hs
View file

@ -151,22 +151,26 @@ instance HasBézier 2 () where
D21 ( lerp @( T b ) t a b )
( a --> b )
origin
{-# INLINEABLE line #-}
bezier2 co ( bez :: Quadratic.Bezier b ) =
D \ ( co -> t ) ->
D21 ( Quadratic.bezier @( T b ) bez t )
( Quadratic.bezier' bez t )
( Quadratic.bezier'' bez )
{-# INLINEABLE bezier2 #-}
bezier3 co ( bez :: Cubic.Bezier b ) =
D \ ( co -> t ) ->
D21 ( Cubic.bezier @( T b ) bez t )
( Cubic.bezier' bez t )
( Cubic.bezier'' bez t )
{-# INLINEABLE bezier3 #-}
instance HasEnvelopeEquation 2 where
uncurryD = uncurryD2
{-# INLINEABLE uncurryD #-}
envelopeEquation ( _ :: Proxy i ) co
dp@( D21 ( T -> p ) p_t p_tt )
@ -247,6 +251,7 @@ instance HasEnvelopeEquation 2 where
, D12 ( unT u ) u_t u_s
, D12 ( unT v ) v_t v_s
)
{-# INLINEABLE envelopeEquation #-}
instance HasBézier 3 () where
@ -256,6 +261,7 @@ instance HasBézier 3 () where
( a --> b )
origin
origin
{-# INLINEABLE line #-}
bezier2 co ( bez :: Quadratic.Bezier b ) =
D \ ( co -> t ) ->
@ -263,6 +269,7 @@ instance HasBézier 3 () where
( Quadratic.bezier' bez t )
( Quadratic.bezier'' bez )
origin
{-# INLINEABLE bezier2 #-}
bezier3 co ( bez :: Cubic.Bezier b ) =
D \ ( co -> t ) ->
@ -270,10 +277,12 @@ instance HasBézier 3 () where
( Cubic.bezier' bez t )
( Cubic.bezier'' bez t )
( Cubic.bezier''' bez )
{-# INLINEABLE bezier3 #-}
instance HasEnvelopeEquation 3 where
uncurryD = uncurryD3
{-# INLINEABLE uncurryD #-}
envelopeEquation ( _ :: Proxy i ) co
dp@( D31 ( T -> p ) p_t p_tt p_ttt )
@ -392,6 +401,7 @@ instance HasEnvelopeEquation 3 where
, D22 ( unT u ) u_t u_s u_tt u_ts u_ss
, D22 ( unT v ) v_t v_s v_tt v_ts v_ss
)
{-# INLINEABLE envelopeEquation #-}
instance HasBézier 3 𝕀 where
@ -401,6 +411,7 @@ instance HasBézier 3 𝕀 where
( a --> b )
origin
origin
{-# INLINEABLE line #-}
bezier2 co ( bez :: Quadratic.Bezier b ) =
D \ ( co -> t ) ->
@ -408,6 +419,7 @@ instance HasBézier 3 𝕀 where
( Quadratic.bezier' bez t )
( Quadratic.bezier'' bez )
origin
{-# INLINEABLE bezier2 #-}
bezier3 co ( bez :: Cubic.Bezier b ) =
D \ ( co -> t ) ->
@ -415,6 +427,7 @@ instance HasBézier 3 𝕀 where
( T $ aabb ( fmap unT $ Cubic.derivative ( fmap T bez ) ) ( `evaluateQuadratic` t ) )
( Cubic.bezier'' bez t )
( Cubic.bezier''' bez )
{-# INLINEABLE bezier3 #-}
{- Note [Computing Béziers over intervals]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@ -455,6 +468,7 @@ evaluateCubic bez t =
maxs = fmap (Cubic.bezier @( T Double ) sup_bez)
$ inf t :| ( sup t : filter ( ∈ t ) ( Cubic.extrema sup_bez ) )
in 𝕀 ( minimum mins ) ( maximum maxs )
{-# INLINEABLE evaluateCubic #-}
-- | Evaluate a quadratic Bézier curve, when both the coefficients and the
-- parameter are intervals.
@ -468,3 +482,4 @@ evaluateQuadratic bez t =
maxs = fmap (Quadratic.bezier @( T Double ) sup_bez)
$ inf t :| ( sup t : filter ( ∈ t ) ( Quadratic.extrema sup_bez ) )
in 𝕀 ( minimum mins ) ( maximum maxs )
{-# INLINEABLE evaluateQuadratic #-}

29
brush-strokes/src/lib/Math/Interval.hs
View file

@ -1,3 +1,5 @@
{-# LANGUAGE CPP #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TemplateHaskell #-}
{-# LANGUAGE UndecidableInstances #-}
@ -19,8 +21,6 @@ module Math.Interval
-- base
import Prelude hiding ( Num(..), Fractional(..) )
import Data.List
( nub )
import qualified Data.List.NonEmpty as NE
-- acts
@ -138,11 +138,23 @@ instance Torsor ( T ( 𝕀 Double ) ) ( 𝕀 Double ) where
-------------------------------------------------------------------------------
-- Extended division
-- | Extended division.
-- | Extended division, returning either 1 or 2 intervals.
--
-- NB: this function can return overlapping intervals if both arguments contain 0.
-- Otherwise, the returned intervals are guaranteed to be disjoint.
(⊘) :: 𝕀 Double -> 𝕀 Double -> [ 𝕀 Double ]
x ⊘ y = nub $ map ( x * ) ( extendedRecip y )
x ⊘ y
#ifdef ASSERTS
| 0 ∈ x && 0 ∈ y
= error $ unlines
[ "x ⊘ y: both arguments contain zero"
, "x: " ++ show x, "y: " ++ show y ]
| otherwise
#endif
= map ( x * ) ( extendedRecip y )
infixl 7 ⊘
-- | Extended reciprocal, returning either 1 or 2 intervals.
extendedRecip :: 𝕀 Double -> [ 𝕀 Double ]
extendedRecip x@( 𝕀 lo hi )
| lo == 0 && hi == 0
@ -150,11 +162,12 @@ extendedRecip x@( 𝕀 lo hi )
| lo >= 0 || hi <= 0
= [ recip x ]
| otherwise
= [ recip $ 𝕀 lo -0, recip $ 𝕀 0 hi ]
= [ 𝕀 negInf ( recip lo ), 𝕀 ( recip hi ) posInf ]
where
negInf, posInf :: Double
negInf = -1 / 0
posInf = 1 / 0
negInf, posInf :: Double
negInf = -1 / 0
posInf = 1 / 0
-------------------------------------------------------------------------------
-- Lattices.

2
brush-strokes/src/lib/Math/Linear.hs
View file

@ -133,7 +133,7 @@ type role Vec nominal representational
deriving newtype instance Show a => Show ( Vec n a )
deriving newtype instance Eq a => Eq ( Vec n a )
deriving newtype instance Ord a => Ord ( Vec n a )
deriving newtype instance Functor ( Vec n )
deriving newtype instance Functor ( Vec n )
deriving newtype instance Foldable ( Vec n )
deriving via ZipList
instance Applicative ( Vec n )

11
brush-strokes/src/lib/Math/Monomial.hs
View file

@ -55,25 +55,24 @@ type family Deg f
type family Vars f
zeroMonomial :: forall k n. KnownNat n => Mon k n
zeroMonomial = Mon $ unsafeCoerce @[ Word ] @( Vec n Word )
$ replicate ( fromIntegral $ word @n ) 0
{-# INLINEABLE zeroMonomial #-}
zeroMonomial = Mon $ Vec $ replicate ( fromIntegral $ word @n ) 0
{-# INLINE zeroMonomial #-}
isZeroMonomial :: Mon k n -> Bool
isZeroMonomial ( Mon ( Vec pows ) ) = all ( == 0 ) pows
{-# INLINE isZeroMonomial #-}
totalDegree :: Mon k n -> Word
totalDegree ( Mon ( Vec pows ) ) = sum pows
linearMonomial :: forall k n. ( KnownNat n, 1 <= k ) => Fin n -> Mon k n
linearMonomial ( Fin i' ) =
Mon $ unsafeCoerce @[ Word ] @( Vec n Word )
$ replicate ( i - 1 ) 0 ++ [ 1 ] ++ replicate ( n - i ) 0
Mon $ Vec $ replicate ( i - 1 ) 0 ++ [ 1 ] ++ replicate ( n - i ) 0
where
n, i :: Int
n = fromIntegral $ word @n
i = fromIntegral i'
{-# INLINEABLE linearMonomial #-}
{-# INLINE linearMonomial #-}
isLinear :: Mon k n -> Maybe ( Fin n )
isLinear ( Mon ( Vec pows ) ) = fmap Fin $ go 1 pows

22
brush-strokes/src/lib/Math/Root/Isolation.hs
View file

@ -102,7 +102,7 @@ newtype RootIsolationOptions n d
defaultRootIsolationOptions :: BoxCt n d => RootIsolationOptions n d
defaultRootIsolationOptions =
RootIsolationOptions
{ rootIsolationAlgorithms = defaultRootIsolationAlgorithms minWidth ε_eq True
{ rootIsolationAlgorithms = defaultRootIsolationAlgorithms minWidth ε_eq
}
where
minWidth = 1e-5
@ -114,11 +114,10 @@ defaultRootIsolationAlgorithms
. BoxCt n d
=> Double -- ^ minimum width of boxes (don't bisect further)
-> Double -- ^ threshold for progress
-> Bool -- ^ do box1
-> BoxHistory n
-> Box n
-> Either String ( NE.NonEmpty ( RootIsolationAlgorithmWithOptions n d ) )
defaultRootIsolationAlgorithms minWidth ε_eq doBox1 history box =
defaultRootIsolationAlgorithms minWidth ε_eq history box =
case history of
lastRoundBoxes : _
-- If, in the last round of strategies, we didn't try bisection...
@ -132,17 +131,19 @@ defaultRootIsolationAlgorithms minWidth ε_eq doBox1 history box =
then Left $ "widths <= " ++ show minWidth
else Right $ NE.singleton $ AlgoWithOptions @Bisection _bisOptions
-- Otherwise, do a normal round.
-- Currently: we try an interval Gauss–Seidel step followed by box(1)-consistency.
-- Currently: we try an interval Gauss–Seidel.
-- (box(1)- and box(2)-consistency don't seem to help when using
-- the complete interval union Gauss–Seidel step)
_ -> Right $ AlgoWithOptions @GaussSeidel _gsOptions
NE.:| [ AlgoWithOptions @Box1 _box1Options
| doBox1 && not verySmall ]
NE.:| []
where
verySmall = and $ ( \ cd -> width cd <= minWidth ) <$> coordinates box
_bisOptions = defaultBisectionOptions @n @d minWidth ε_eq box
_gsOptions = defaultGaussSeidelOptions @n @d history
_box1Options = defaultBox1Options @n @d minWidth ε_eq
_box1Options = defaultBox1Options @n @d ( minWidth * 100 ) ε_eq
_box2Options = ( defaultBox2Options @n @d minWidth ε_eq ) { box2LambdaMin = 0.001 }
-- Did we reduce the box width by at least ε_eq
-- in at least one of the coordinates?
@ -249,8 +250,8 @@ isolateRootsIn ( RootIsolationOptions { rootIsolationAlgorithms } )
-- | Execute a root isolation strategy, replacing the input box with
-- (hopefully smaller) output boxes.
doStrategy
:: BoxCt n d
=> RootIsolationAlgorithmWithOptions n d
:: forall n d
. RootIsolationAlgorithmWithOptions n d
-> [ ( RootIsolationStep, Box n ) ]
-> BoxHistory n
-> ( 𝕀ℝ n -> D 1 ( 𝕀ℝ n ) ( 𝕀ℝ d ) )
@ -260,6 +261,5 @@ doStrategy
doStrategy algo thisRoundHist prevRoundsHist eqs cand =
case algo of
AlgoWithOptions @algo options -> do
( step, res ) <- rootIsolationAlgorithm options thisRoundHist prevRoundsHist eqs cand
( step, res ) <- rootIsolationAlgorithm @algo options thisRoundHist prevRoundsHist eqs cand
return ( SomeRootIsolationStep @algo step, res )
{-# INLINEABLE doStrategy #-}

18
brush-strokes/src/lib/Math/Root/Isolation/Bisection.hs
View file

@ -1,5 +1,6 @@
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
module Math.Root.Isolation.Bisection
( -- * The bisection method for root isolation
@ -35,6 +36,10 @@ import GHC.TypeNats
, type (<=)
)
-- transformers
import Control.Monad.Trans.Writer.CPS
( Writer )
-- MetaBrush
import Math.Algebra.Dual
( D )
@ -52,7 +57,7 @@ import Math.Root.Isolation.Core
-- | The bisection algorithm; see 'bisection'.
data Bisection
instance RootIsolationAlgorithm Bisection where
instance BoxCt n d => RootIsolationAlgorithm Bisection n d where
type instance StepDescription Bisection = ( String, Double )
type instance RootIsolationAlgorithmOptions Bisection n d = BisectionOptions n d
rootIsolationAlgorithm
@ -65,6 +70,15 @@ instance RootIsolationAlgorithm Bisection where
box
return ( whatBis, boxes )
{-# INLINEABLE rootIsolationAlgorithm #-}
{-# SPECIALISE rootIsolationAlgorithm
:: RootIsolationAlgorithmOptions Bisection 2 3
-> [ ( RootIsolationStep, Box 2 ) ]
-> BoxHistory 2
-> ( 𝕀ℝ 2 -> D 1 ( 𝕀ℝ 2 ) ( 𝕀ℝ 3 ) )
-> Box 2
-> Writer ( DoneBoxes 2 ) ( StepDescription Bisection, [ Box 2 ] ) #-}
-- NB: including this to be safe. The specialiser seems to sometimes
-- be able to generate this specialisation on its own, and sometimes not.
-- | Options for the bisection method.
type BisectionOptions :: Nat -> Nat -> Type

39
brush-strokes/src/lib/Math/Root/Isolation/Core.hs
View file

@ -1,8 +1,9 @@
{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE UndecidableSuperClasses #-}
-- | Core definitions and utilities common to root isolation methods.
module Math.Root.Isolation.Core
@ -122,9 +123,11 @@ noDoneBoxes = DoneBoxes [] []
-- | Existential wrapper over any root isolation algorithm,
-- with the options necessary to run it.
type RootIsolationAlgorithmWithOptions :: Nat -> Nat -> Type
data RootIsolationAlgorithmWithOptions n d where
AlgoWithOptions
:: RootIsolationAlgorithm ty
:: forall {k :: Type} {n :: Nat} {d :: Nat} ( ty :: k )
. RootIsolationAlgorithm ty n d
=> RootIsolationAlgorithmOptions ty n d
-> RootIsolationAlgorithmWithOptions n d
@ -133,15 +136,15 @@ data RootIsolationAlgorithmWithOptions n d where
-- This design keeps the set of root isolation algorithms open-ended,
-- while retaining the ability to inspect previous steps (using the
-- 'IsolationStep' pattern).
type RootIsolationAlgorithm :: forall {k}. k -> Constraint
class ( Typeable ty, Show ( StepDescription ty ) )
=> RootIsolationAlgorithm ty where
type RootIsolationAlgorithm :: forall {k :: Type}. k -> Nat -> Nat -> Constraint
class ( Typeable ty, Show ( StepDescription ty ), BoxCt n d )
=> RootIsolationAlgorithm ty n d where
-- | The type of additional information about an algorithm step.
--
-- Only really useful for debugging; gets stored in 'RootIsolationTree's.
type StepDescription ty
-- | Configuration options expected by this root isolation method.
type RootIsolationAlgorithmOptions ty (n :: Nat) (d :: Nat) = r | r -> ty n d
type RootIsolationAlgorithmOptions ty n d = r | r -> ty n d
-- | Run one step of the root isolation method.
--
-- This gets given the equations and a box, and should attempt to
@ -155,9 +158,7 @@ class ( Typeable ty, Show ( StepDescription ty ) )
-- bix does not contain any solutions;
-- - (as a writer side-effect) boxes to definitely stop processing; see 'DoneBoxes'.
rootIsolationAlgorithm
:: forall (n :: Nat) (d :: Nat)
. BoxCt n d
=> RootIsolationAlgorithmOptions ty n d
:: RootIsolationAlgorithmOptions ty n d
-- ^ options for this root isolation algorithm
-> [ ( RootIsolationStep, Box n ) ]
-- ^ history of the current round
@ -171,20 +172,22 @@ class ( Typeable ty, Show ( StepDescription ty ) )
-- | Match on an unknown root isolation algorithm step with a known algorithm.
pattern IsolationStep
:: forall (ty :: Type)
. RootIsolationAlgorithm ty
=> StepDescription ty -> RootIsolationStep
:: forall ( ty :: Type )
. Typeable ty
=> StepDescription ty
-> RootIsolationStep
pattern IsolationStep stepDescr
<- ( rootIsolationAlgorithmStep_maybe @ty -> Just stepDescr )
where
IsolationStep stepDescr = SomeRootIsolationStep @ty stepDescr
-- NB: this pattern could also return @RootIsolationAlgorithm n d ty@ evidence,
-- but it's simpler to not do so for now.
-- | Helper function used to define the 'IsolationStep' pattern.
--
-- Inspects whether an existential 'RootIsolationStep' packs a step for
-- the given algorithm.
rootIsolationAlgorithmStep_maybe
:: forall ty. RootIsolationAlgorithm ty
:: forall ty
. Typeable ty
=> RootIsolationStep -> Maybe ( StepDescription ty )
rootIsolationAlgorithmStep_maybe ( SomeRootIsolationStep @existential descr )
| Just HRefl <- heqT @existential @ty

126
brush-strokes/src/lib/Math/Root/Isolation/Degree.hs Normal file
View file

@ -0,0 +1,126 @@
{-# LANGUAGE ScopedTypeVariables #-}
module Math.Root.Isolation.Degree
( -- * Computing the topological degree
topologicalDegree
)
where
-- base
import Data.Kind
( Type )
import GHC.TypeNats
( Nat )
-- primitive
import Data.Primitive.SmallArray
-- MetaBrush
import Math.Interval
import Math.Linear
--------------------------------------------------------------------------------
-- Topological degree.
-- | Compute the topological degree of the given interval function (2D only).
topologicalDegree
:: Double
-- ^ minimum width when bisecting facets
-> ( 𝕀ℝ 2 -> 𝕀ℝ 2 )
-- ^ function
-> 𝕀ℝ 2
-- ^ box
-> Maybe Int
topologicalDegree ε_bis f ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
topologicalDegreeFromContour $
smallArrayFromList $
concatMap ( tagFacet ε_bis f )
[ ( Tag ( Fin 2 ) P, 𝕀 ( ℝ2 x_hi y_lo ) ( ℝ2 x_hi y_hi ) )
, ( Tag ( Fin 1 ) N, 𝕀 ( ℝ2 x_lo y_hi ) ( ℝ2 x_hi y_hi ) )
, ( Tag ( Fin 2 ) N, 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_lo y_hi ) )
, ( Tag ( Fin 1 ) P, 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_lo ) ) ]
-- | Tag a facet with the sign of one of the equations that is non-zero
-- on that facet.
--
-- If all equations take the value 0 on that facet, bisect and recur.
tagFacet
:: Double
-> ( 𝕀ℝ 2 -> 𝕀ℝ 2 )
-> ( Tag 2, 𝕀ℝ 2 )
-> [ Tag 2 ]
tagFacet ε_bis f ( tag@( Tag i _ ), facet0 ) = go facet0
where
go facet
| f1_b_lo > 0
= [ Tag ( Fin 1 ) P ]
| f1_b_hi < 0
= [ Tag ( Fin 1 ) N ]
| f2_b_lo > 0
= [ Tag ( Fin 2 ) P ]
| f2_b_hi < 0
= [ Tag ( Fin 2 ) N ]
| width ( facet `index` i ) < ε_bis
= [ NoTag ] -- TODO: shortcut the whole computation;
-- if we fail to tag one segment, the final answer could
-- be off by { -2, -1, 0, 1, 2 } (I believe)
| otherwise
= concatMap go $ bisectFacet tag facet
where
𝕀 f1_b_lo f1_b_hi = f facet `index` Fin 1
𝕀 f2_b_lo f2_b_hi = f facet `index` Fin 2
tagFacet _ _ ( NoTag, _ ) = error "impossible: input always tagged"
bisectFacet :: Tag 2 -> 𝕀ℝ 2 -> [ 𝕀ℝ 2 ]
bisectFacet ( Tag i s ) x =
( if s == P then id else reverse ) $ bisectInCoord i x
bisectFacet NoTag _ = error "impossible: input always tagged"
bisectInCoord :: Fin n -> 𝕀ℝ 2 -> [ 𝕀ℝ 2 ]
bisectInCoord ( Fin 1 ) ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
[ 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_mid y_hi ), 𝕀 ( ℝ2 x_mid y_lo ) ( ℝ2 x_hi y_hi ) ]
where x_mid = 0.5 * ( x_lo + x_hi )
bisectInCoord _ ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
[ 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_mid ), 𝕀 ( ℝ2 x_lo y_mid ) ( ℝ2 x_hi y_hi ) ]
where y_mid = 0.5 * ( y_lo + y_hi )
-- | Compute the topological degree of \( f \colon \mathbb{IR}^n \to \mathbb{IR}^n \)
-- on a box \( D \subset \mathbb{IR}^n \) by using the signs of the components
-- of \( f \) on a counter-clockwise polygonal contour describing the boundary of \( D \).
topologicalDegreeFromContour :: SmallArray ( Tag 2 ) -> Maybe Int
topologicalDegreeFromContour facetTags = go 0 0
where
n = sizeofSmallArray facetTags
go :: Int -> Int -> Maybe Int
go !d !i
| i >= n
= Just d
| otherwise
= case indexSmallArray facetTags i of
NoTag -> Nothing
Tag ( Fin 1 ) P -> go ( d + δ ) ( i + 1 )
where
δ = if indexSmallArray facetTags ( if i == n - 1 then 0 else i + 1 ) == Tag ( Fin 2 ) P
then 1 else 0
- if indexSmallArray facetTags ( if i == 0 then n - 1 else i - 1 ) == Tag ( Fin 2 ) P
then 1 else 0
_ -> go d ( i + 1 )
--------------------------------------------------------------------------------
-- Tagging edges with signs of certain components of the function.
data Sign = P | N
deriving stock ( Eq, Ord )
instance Show Sign where
showsPrec _ = \case { P -> showString "+"; N -> showString "-" }
type Tag :: Nat -> Type
newtype Tag d = MkTag Int
deriving newtype ( Eq, Ord )
pattern NoTag :: Tag d
pattern NoTag = MkTag 0
pattern Tag :: Fin d -> Sign -> Tag d
pattern Tag c s <- ( getTag -> (# c, s #) )
where Tag ( Fin c ) s = MkTag $ case s of { P -> fromIntegral c; N -> -( fromIntegral c ) }
{-# COMPLETE Tag, NoTag #-}
getTag :: Tag d -> (# Fin d, Sign #)
getTag ( MkTag t ) = (# Fin ( fromIntegral $ abs t ), if t >= 0 then P else N #)

75
brush-strokes/src/lib/Math/Root/Isolation/GaussSeidel.hs
View file

@ -1,4 +1,5 @@
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
module Math.Root.Isolation.GaussSeidel
( -- * The interval Newton method with Gauss–Seidel step
@ -37,7 +38,7 @@ import GHC.TypeNats
-- eigen
import qualified Eigen.Matrix as Eigen
( Matrix
, determinant, generate, inverse, unsafeCoeff
, generate, inverse, unsafeCoeff
)
-- transformers
@ -47,8 +48,6 @@ import Control.Monad.Trans.Writer.CPS
-- MetaBrush
import Math.Algebra.Dual
( D )
import Math.Epsilon
( nearZero )
import Math.Interval
import Math.Linear
import Math.Module
@ -62,13 +61,22 @@ import Math.Root.Isolation.Core
-- | The interval Newton method with a Gauss–Seidel step; see 'intervalGaussSeidel'.
data GaussSeidel
instance RootIsolationAlgorithm GaussSeidel where
instance BoxCt n d => RootIsolationAlgorithm GaussSeidel n d where
type instance StepDescription GaussSeidel = ()
type instance RootIsolationAlgorithmOptions GaussSeidel n d = GaussSeidelOptions n d
rootIsolationAlgorithm opts _thisRoundHist _prevRoundsHist eqs box = do
res <- intervalGaussSeidel opts eqs box
res <- intervalGaussSeidel @n @d opts eqs box
return ( (), res )
{-# INLINEABLE rootIsolationAlgorithm #-}
{-# SPECIALISE rootIsolationAlgorithm
:: RootIsolationAlgorithmOptions GaussSeidel 2 3
-> [ ( RootIsolationStep, Box 2 ) ]
-> BoxHistory 2
-> ( 𝕀ℝ 2 -> D 1 ( 𝕀ℝ 2 ) ( 𝕀ℝ 3 ) )
-> Box 2
-> Writer ( DoneBoxes 2 ) ( StepDescription GaussSeidel, [ Box 2 ] ) #-}
-- NB: including this to be safe. The specialiser seems to sometimes
-- be able to generate this specialisation on its own, and sometimes not.
-- | Options for the interval Gauss–Seidel method.
type GaussSeidelOptions :: Nat -> Nat -> Type
@ -144,13 +152,15 @@ intervalGaussSeidel
eqs
x
| let x_mid = singleton $ boxMidpoint x
f :: 𝕀ℝ n -> 𝕀ℝ n
f = \ x_0 -> pickEqs $ eqs x_0 `monIndex` zeroMonomial
f'_x :: Vec n ( 𝕀ℝ n )
f'_x = fmap ( \ i -> pickEqs $ eqs x `monIndex` linearMonomial i ) ( universe @n )
f_x_mid = pickEqs $ eqs x_mid `monIndex` zeroMonomial
= let -- Interval Newton method: take one Gauss–Seidel step
-- for the system of equations f'(x) ( x - x_mid ) = - f(x_mid).
minus_f_x_mid = unT $ -1 *^ T ( boxMidpoint f_x_mid )
minus_f_x_mid = unT $ -1 *^ T ( boxMidpoint $ f x_mid )
-- Precondition the above linear system into A ( x - x_mid ) = B.
( a, b ) = precondition precondMeth
@ -160,18 +170,34 @@ intervalGaussSeidel
-- at the origin, in order to take a Gauss–Seidel step.
gsGuesses = map ( first ( \ x' -> unT $ x' ^+^ T x_mid ) )
$ gaussSeidelUpdate gsUpdate a b ( T x ^-^ T x_mid )
in
-- If the Gauss–Seidel step was a contraction, then the box
-- contains a unique solution (by the Banach fixed point theorem).
--
-- These boxes can thus be directly added to the solution set:
-- Newton's method is guaranteed to converge to the unique solution.
let ( done, todo ) = bimap ( map fst ) ( map fst )
$ partition snd gsGuesses
in do tell $ noDoneBoxes { doneSolBoxes = done }
return todo
where
( done, todo ) = bimap ( map fst ) ( map fst )
$ partition snd gsGuesses
in -- If the Gauss–Seidel step was a contraction, then the box
-- contains a unique solution (by the Banach fixed point theorem).
--
-- These boxes can thus be directly added to the solution set:
-- Newton's method is guaranteed to converge to the unique solution.
do tell $ noDoneBoxes { doneSolBoxes = done }
return todo
{-# INLINEABLE intervalGaussSeidel #-}
{-
mbDeg = topologicalDegree 0.005 f x
det = case f'_x of
Vec [ c1, c2 ] ->
let a_11 = c1 `index` Fin 1
a_12 = c2 `index` Fin 1
a_21 = c1 `index` Fin 2
a_22 = c2 `index` Fin 2
in a_11 * a_22 - a_12 * a_21
_ -> error "TODO: just testing n=2 here"
if | not $ 0 ∈ det
, mbDeg == Just 0
-> return []
-- If the Jacobian is invertible over the box, then the topological
-- degree tells us exactly how many solutions there are in the box.
-}
-- | A partial or complete Gauss–Seidel step for the equation \( A X = B \),
-- refining the initial guess box for \( X \) into up to \( 2^n \) (disjoint) new boxes.
@ -278,10 +304,7 @@ fromComponents f = do
-- | The midpoint of a box.
boxMidpoint :: Representable Double ( ℝ n ) => 𝕀ℝ n -> ℝ n
boxMidpoint box =
tabulate $ \ i ->
let 𝕀 z_lo z_hi = index box i
z_mid = 0.5 * ( z_lo + z_hi )
in z_mid
tabulate $ \ i -> midpoint ( box `index` i )
{-# INLINEABLE boxMidpoint #-}
-- | Pre-condition the system \( AX = B \).
@ -298,14 +321,10 @@ precondition meth as b =
-> ( as, b )
InverseMidpoint
| let mat = toEigen $ fmap boxMidpoint as
det = Eigen.determinant mat
, not $ nearZero det
-- (TODO: a bit wasteful to compute determinant then inverse.)
, let precond = Eigen.inverse mat
doPrecond = matMulVec ( fromEigen precond )
-- TODO: avoid this when condition number is small?
-> ( fmap doPrecond as, doPrecond b )
| otherwise
-> ( as, b )
where
toEigen :: Vec n ( ℝ n ) -> Eigen.Matrix n n Double
toEigen cols =

27
brush-strokes/src/lib/Math/Root/Isolation/Narrowing.hs
View file

@ -1,4 +1,5 @@
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE UndecidableInstances #-}
module Math.Root.Isolation.Narrowing
( -- * @box(1)@-consistency
@ -39,6 +40,8 @@ import GHC.TypeNats
-- transformers
import Control.Monad.Trans.State.Strict as State
( State, evalState, get, put )
import Control.Monad.Trans.Writer.CPS
( Writer )
-- brush-strokes
import Math.Algebra.Dual
@ -62,21 +65,39 @@ import Math.Root.Isolation.Core
-- | A @box(1)@-consistency enforcing algorithm; see 'makeBox1Consistent'.
data Box1
instance RootIsolationAlgorithm Box1 where
instance BoxCt n d => RootIsolationAlgorithm Box1 n d where
type instance StepDescription Box1 = ()
type instance RootIsolationAlgorithmOptions Box1 n d = Box1Options n d
rootIsolationAlgorithm opts _thisRoundHist _prevRoundsHist eqs box =
return $ ( (), makeBox1Consistent opts eqs box )
{-# INLINEABLE rootIsolationAlgorithm #-}
{-# SPECIALISE rootIsolationAlgorithm
:: RootIsolationAlgorithmOptions Box1 2 3
-> [ ( RootIsolationStep, Box 2 ) ]
-> BoxHistory 2
-> ( 𝕀ℝ 2 -> D 1 ( 𝕀ℝ 2 ) ( 𝕀ℝ 3 ) )
-> Box 2
-> Writer ( DoneBoxes 2 ) ( StepDescription Box1, [ Box 2 ] ) #-}
-- NB: including this to be safe. The specialiser seems to sometimes
-- be able to generate this specialisation on its own, and sometimes not.
-- | A @box(2)@-consistency enforcing algorithm; see 'makeBox1Consistent'.
data Box2
instance RootIsolationAlgorithm Box2 where
instance BoxCt n d => RootIsolationAlgorithm Box2 n d where
type instance StepDescription Box2 = ()
type instance RootIsolationAlgorithmOptions Box2 n d = Box2Options n d
rootIsolationAlgorithm opts _thisRoundHist _prevRoundsHist eqs box =
return ( () , [ makeBox2Consistent opts eqs box ] )
{-# INLINEABLE rootIsolationAlgorithm #-}
{-# SPECIALISE rootIsolationAlgorithm
:: RootIsolationAlgorithmOptions Box2 2 3
-> [ ( RootIsolationStep, Box 2 ) ]
-> BoxHistory 2
-> ( 𝕀ℝ 2 -> D 1 ( 𝕀ℝ 2 ) ( 𝕀ℝ 3 ) )
-> Box 2
-> Writer ( DoneBoxes 2 ) ( StepDescription Box2, [ Box 2 ] ) #-}
-- NB: including this to be safe. The specialiser seems to sometimes
-- be able to generate this specialisation on its own, and sometimes not.
-- | Options for the @box(1)@-consistency method.
data Box1Options n d =

18
src/app/MetaBrush/Application.hs
View file

@ -74,9 +74,7 @@ import Control.Monad.Trans.Reader
-- MetaBrush
import Math.Root.Isolation
( RootIsolationOptions(..), defaultRootIsolationOptions
, N
)
( RootIsolationOptions(..), defaultRootIsolationOptions )
import Math.Bezier.Cubic.Fit
( FitParameters(..) )
import Math.Bezier.Spline
@ -208,18 +206,18 @@ runApplication application = do
maxHistorySizeTVar <- STM.newTVarIO @Int 1000
fitParametersTVar <- STM.newTVarIO @FitParameters $
FitParameters
{ maxSubdiv = 5 --2 --3 -- 6
, nbSegments = 3 --3 --6 -- 12
, dist_tol = 0.1 -- 5e-3
, t_tol = 0.1 -- 1e-4
, maxIters = 5 -- 100
{ maxSubdiv = 0 --5 --2 --3 -- 6
, nbSegments = 1 --5
, dist_tol = 5e-3
, t_tol = 1e-4
, maxIters = 20
}
rootsAlgoTVar <- STM.newTVarIO @RootSolvingAlgorithm $
--HalleyM2
NewtonRaphson
{ maxIters = 20, precision = 8 }
cuspFindingOptionsTVar <- STM.newTVarIO @( Maybe ( RootIsolationOptions N 3 ) ) $
Just defaultRootIsolationOptions
cuspFindingOptionsTVar <- STM.newTVarIO @( Maybe ( RootIsolationOptions 2 3 ) ) $
Nothing --Just defaultRootIsolationOptions
-- Put all these stateful variables in a record for conciseness.
let

10
src/app/MetaBrush/Render/Document.hs
View file

@ -83,7 +83,7 @@ import Math.Linear
import Math.Module
( Module((*^)), normalise )
import Math.Root.Isolation
( RootIsolationOptions, N )
( RootIsolationOptions )
import MetaBrush.Asset.Colours
( Colours, ColourRecord(..) )
import MetaBrush.Brush
@ -153,7 +153,7 @@ blankRender _ = pure ()
getDocumentRender
:: Colours
-> RootSolvingAlgorithm -> Maybe ( RootIsolationOptions N 3 ) -> FitParameters
-> RootSolvingAlgorithm -> Maybe ( RootIsolationOptions 2 3 ) -> FitParameters
-> Mode -> Bool
-> Set Modifier -> Maybe ( ℝ 2 ) -> Maybe HoldAction -> Maybe PartialPath
-> Document
@ -289,7 +289,7 @@ instance NFData StrokeRenderData where
-- - Otherwise, this consists of the underlying spline path only.
strokeRenderData
:: RootSolvingAlgorithm
-> Maybe ( RootIsolationOptions N 3 )
-> Maybe ( RootIsolationOptions 2 3 )
-> FitParameters
-> Stroke
-> Maybe ( ST RealWorld StrokeRenderData )
@ -304,7 +304,7 @@ strokeRenderData rootAlgo mbCuspOptions fitParams
Just ( NamedBrush { brushFunction = fn } )
| WithParams
{ defaultParams = brush_defaults
, withParams = brush@( Brush { brushShape, mbRotation = mbRot } )
, withParams = brush@( Brush { brushBaseShape, mbRotation = mbRot } )
} <- fn
-> -- This is the key place where we need to perform impedance matching
-- between the collection of parameters supplied along a stroke and
@ -328,7 +328,7 @@ strokeRenderData rootAlgo mbCuspOptions fitParams
, strokeBrushFunction =
\ params ->
let brushParams = embedUsedParams $ toUsedParams params
shape = fun @Double brushShape brushParams
shape = fun @Double brushBaseShape brushParams
-- TODO: remove this logic which is duplicated
-- from elsewhere. The type should make it
-- impossible to forget to apply the rotation.