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Fixes and restructuring
This commit is contained in:
sheaf
parent
26cfdada8f
commit
2289468a84
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@ -187,49 +187,6 @@ library metabrushes
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, bytestring
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, bytestring
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>= 0.10.10.0 && < 0.12
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>= 0.10.10.0 && < 0.12
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executable cusps
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import:
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common
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hs-source-dirs:
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src/cusps
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default-language:
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Haskell2010
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main-is:
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Main.hs
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other-modules:
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Math.Interval.Abstract
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executable convert-metafont
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import:
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common, extras
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hs-source-dirs:
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src/convert
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default-language:
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Haskell2010
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main-is:
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Main.hs
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other-modules:
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MetaBrush.MetaFont.Convert
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build-depends:
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metabrushes,
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diagrams-contrib,
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diagrams-lib,
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linear,
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parsec
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executable MetaBrush
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executable MetaBrush
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import:
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import:
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@ -1,370 +0,0 @@
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{-# LANGUAGE PolyKinds #-}
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{-# LANGUAGE ScopedTypeVariables #-}
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{-# LANGUAGE UndecidableInstances #-}
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module Main
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( main
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-- Testing
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, TestCase(..)
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, testCases
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, testCaseStrokeFunctions
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, eval
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, mkVal, mkBox
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, potentialCusp
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, dEdsdcdt
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)
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where
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-- base
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import Control.Concurrent.MVar
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( newMVar )
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import Data.Coerce
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( coerce )
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import Data.Foldable
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( for_ )
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import Data.List
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( intercalate )
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import GHC.Exts
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( Proxy#, proxy# )
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import GHC.Generics
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( Generic )
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import GHC.TypeNats
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( type (-) )
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import Numeric
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( showFFloat )
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-- containers
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import Data.Sequence
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( Seq )
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import qualified Data.Sequence as Seq
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( index )
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import Data.Tree
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( foldTree )
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-- brush-strokes
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import Calligraphy.Brushes
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import Debug.Utils
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( logToFile )
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import Math.Algebra.Dual
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import Math.Bezier.Spline
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import Math.Bezier.Stroke
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import Math.Bezier.Stroke.EnvelopeEquation
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import Math.Differentiable
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import Math.Interval
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import Math.Linear
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import Math.Module
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import Math.Ring
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( Transcendental )
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--------------------------------------------------------------------------------
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main :: IO ()
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main = for_ testCases $ \ testCase@( TestCase { testName, testAlgorithmParams } ) -> do
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let ( _, testStrokeFnI ) = testCaseStrokeFunctions testCase
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( newtTrees, ( dunno, sols ) ) = computeCusps testAlgorithmParams testStrokeFnI
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showedTrees = map ( uncurry showIntervalNewtonTree ) newtTrees
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putStrLn $ unlines $
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[ ""
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, "Test case '" ++ testName ++ "':" ] ++
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map ( " " ++ )
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[ " #sols: " ++ show (length sols)
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, "#dunno: " ++ show (length dunno)
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, "#trees: " ++ show @Int (sum @_ @Int $ map (foldTree ( \ _ bs -> 1 + sum bs )) showedTrees)
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, " dunno: " ++ show dunno
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, " sols: " ++ show sols
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]
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--logFileMVar <- newMVar "logs/trickyCusp.log"
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--logToFile logFileMVar (unlines logLines)
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-- `seq` return ()
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testCases :: [ TestCase ]
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testCases = [ ellipse , trickyCusp2 ]
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--------------------------------------------------------------------------------
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data TestCase =
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forall nbParams. ParamsCt nbParams =>
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TestCase
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{ testName :: !String
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, testBrush :: !( Brush nbParams )
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, testStroke :: !( Point nbParams, Curve Open () ( Point nbParams ))
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, testAlgorithmParams :: !CuspAlgorithmParams
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}
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testCaseStrokeFunctions
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:: TestCase
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-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
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, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
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testCaseStrokeFunctions ( TestCase { testStroke = ( sp0, crv ), testBrush } ) =
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getStrokeFunctions testBrush sp0 crv
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-- Utilities to use in GHCi to help debugging.
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eval
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:: ( I i ( ℝ 1 ) -> Seq ( I i ( ℝ 1 ) -> StrokeDatum k i ) )
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-> ( I i ( ℝ 1 ), Int, I i ( ℝ 1 ) )
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-> StrokeDatum k i
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eval f ( t, i, s ) = ( f t `Seq.index` i ) s
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mkVal :: Double -> Int -> Double -> ( ℝ 1, Int, ℝ 1 )
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mkVal t i s = ( ℝ1 t, i, ℝ1 s )
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mkBox :: ( Double, Double ) -> Int -> ( Double, Double ) -> Box
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mkBox ( t_min, t_max ) i ( s_min, s_max ) =
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( 𝕀 ( ℝ1 t_min ) ( ℝ1 t_max ) , i, 𝕀 ( ℝ1 s_min ) ( ℝ1 s_max ) )
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potentialCusp :: StrokeDatum 3 𝕀 -> Bool
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potentialCusp
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( StrokeDatum
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{ ee = D22 { _D22_v = 𝕀 ( ℝ1 ee_min ) ( ℝ1 ee_max ) }
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, 𝛿E𝛿sdcdt = D12 { _D12_v = T ( 𝕀 ( ℝ2 vx_min vy_min ) ( ℝ2 vx_max vy_max ) )}
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}
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) = ee_min <= 0 && ee_max >= 0
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&& vx_min <= 0 && vx_max >= 0
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&& vy_min <= 0 && vy_max >= 0
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dEdsdcdt :: StrokeDatum k i -> D ( k - 2 ) ( I i ( ℝ 2 ) ) ( T ( I i ( ℝ 2 ) ) )
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dEdsdcdt ( StrokeDatum { 𝛿E𝛿sdcdt = v } ) = v
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{-
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let (f, fI) = testCaseStrokeFunctions trickyCusp2
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take 10 $ Data.List.sortOn ( \ ( _, ℝ1 e, v) -> abs e + norm v ) [ let { v = mkVal x 3 y; d = eval f v } in ( v, _D12_v $ ee d, _D0_v $ dEdsdcdt d ) | x <- [0.57,0.5701 .. 0.58], y <- [0.29,0.291..0.3] ]
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> ((ℝ1 0.5798800000000057,3,ℝ1 0.267980000000008),ℝ1 -2.8596965543670194e-4,V2 7.79559474412963e-2 2.0389671921293484e-2)
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potentialCusp $ eval fI $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
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> True
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let nbPotentialSols b = let ( _newtTrees, ( dunno, sols ) ) = intervalNewtonGSFrom NoPreconditioning 1e-7 fI b in length dunno + length sols
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nbPotentialSols $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
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1
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nbPotentialSols $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
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0
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let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI b
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putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
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([ℝ1 0.5798, ℝ1 0.675],3,[ℝ1 0.26798, ℝ1 0.26799]) (area 0.000001) N []
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└─ ([ℝ1 0.5973000285624527, ℝ1 0.6750000000000002],3,[ℝ1 0.26798, ℝ1 0.26799000000000006]) (area 0.000001) NoSolution "ee" ([ℝ1 0.5973000285624527, ℝ1 0.6750000000000002],3,[ℝ1 0.26798, ℝ1 0.26799000000000006])
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eval fI $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
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> D12 {_D12_v = T[ℝ2 -10088.6674944889 -3281.3820867312834, ℝ2 4124.668381545453 4524.807156085763], _D12_dx = TT[ℝ2 -173746.97965005718 -33281.18494907289, ℝ2 298.2609121556852 23639.772884799597], _D12_dy = TT[ℝ2 -18454.27716258352 -28337.509817580823, ℝ2 1163.6949532017436 -13936.383137525536]}}
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i.e.
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> f = [ℝ2 -10088.6674944889 -3281.3820867312834, ℝ2 4124.668381545453 4524.807156085763]
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> f_t = [ℝ2 -173746.97965005718 -33281.18494907289, ℝ2 298.2609121556852 23639.772884799597]
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> f_s = [ℝ2 -18454.27716258352 -28337.509817580823, ℝ2 1163.6949532017436 -13936.383137525536]
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(f, fI) = testCaseStrokeFunctions trickyCusp2
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t = 𝕀 (ℝ1 0.5798) (ℝ1 0.675)
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s = 𝕀 (ℝ1 0.26798) (ℝ1 0.26799)
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t_mid = 0.5 * ( 0.5798 + 0.675 )
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s_mid = 0.5 * ( 0.26798 + 0.26799 )
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D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) = dEdsdcdt $ eval fI (t, 3, s)
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t' = coerce ( (-) @( 𝕀 Double ) ) t ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
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s' = coerce ( (-) @( 𝕀 Double ) ) s ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
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a = ( f_t, f_s )
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b = negV2 $ singleton $ midV2 f
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[((t2', s2'), isContr)] = gaussSeidel a b (t', s')
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t2 = coerce ( (+) @( 𝕀 Double ) ) t2' ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
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s2 = coerce ( (+) @( 𝕀 Double ) ) s2' ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
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t2
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> [ℝ1 0.6102365832093095, ℝ1 0.6750000000000002]
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s2
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> [ℝ1 0.26798, ℝ1 0.26799000000000006]
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let ( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi ), 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) ) = a
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let ( 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi ) ) = b
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let ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) ) = ( t', s' )
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a11 = 𝕀 a11_lo a11_hi
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a12 = 𝕀 a12_lo a12_hi
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a21 = 𝕀 a21_lo a21_hi
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a22 = 𝕀 a22_lo a22_hi
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b1 = 𝕀 b1_lo b1_hi
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b2 = 𝕀 b2_lo b2_hi
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x1 = 𝕀 x1_lo x1_hi
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x2 = 𝕀 x2_lo x2_hi
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( b1 - a12 * x2 )
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> [2981.90728508591, 2982.0918278575364]
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extendedRecip a11
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-}
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negV2 :: 𝕀ℝ 2 -> 𝕀ℝ 2
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negV2 ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
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let !( 𝕀 x'_lo x'_hi ) = negate $ 𝕀 x_lo x_hi
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!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
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in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
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midV2 :: 𝕀ℝ 2 -> ℝ 2
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midV2 ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
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ℝ2 ( 0.5 * ( x_lo + x_hi ) ) ( 0.5 * ( y_lo + y_hi ) )
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logLines :: [ String ]
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logLines =
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[ "f = dE/ds * dc/dt: f, df/dt, df/ds"
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, "{" ++
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(intercalate ","
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[ "{" ++ showD (midPoint t) ++ "," ++ showD (midPoint s) ++ ",{" ++ intercalate "," vals ++ "}}"
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| t <- map ( around 0.5798 ) [-0.05, -0.049.. 0.05]
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, let i = 3
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, s <- map ( around 0.26798 ) [-0.05, -0.049.. 0.05]
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, let StrokeDatum
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{ 𝛿E𝛿sdcdt = D12 (T f) (T (T f_t)) (T (T f_s))
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} = (curvesI t `Seq.index` i) s
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ℝ2 vx vy = midPoint2 f
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ℝ2 vx_t vy_t = midPoint2 f_t
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ℝ2 vx_s vy_s = midPoint2 f_s
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vals = [ "{" ++ showD vx ++ "," ++ showD vy ++ "}"
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, "{" ++ showD vx_t ++ "," ++ showD vy_t ++ "}"
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, "{" ++ showD vx_s ++ "," ++ showD vy_s ++ "}"
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]
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]
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) ++ "}"
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]
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where
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around :: Double -> Double -> 𝕀ℝ 1
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around z0 z = 𝕀 ( ℝ1 ( z + z0 - 1e-6 ) ) ( ℝ1 ( z + z0 + 1e-6 ) )
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( _, curvesI ) = testCaseStrokeFunctions trickyCusp2
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midPoint (𝕀 (ℝ1 lo) (ℝ1 hi)) = 0.5 * ( lo + hi )
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midPoint2 (𝕀 (ℝ2 lo_x lo_y) (ℝ2 hi_x hi_y))
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= ℝ2 ( 0.5 * ( lo_x + hi_x ) ) ( 0.5 * ( lo_y + hi_y ) )
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showD :: Double -> String
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showD float = showFFloat (Just 6) float ""
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--------------------------------------------------------------------------------
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ellipse :: TestCase
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ellipse =
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TestCase
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{ testName = "ellipse"
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, testBrush = ellipseBrush
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, testStroke = ( p0, LineTo ( NextPoint p1 ) () )
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, testAlgorithmParams =
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CuspAlgorithmParams
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{ preconditioning = NoPreconditioning
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, maxWidth = 1e-7
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}
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}
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where
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mkPt x y w h phi =
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Point
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{ pointCoords = ℝ2 x y
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, pointParams = Params $ ℝ3 w h phi
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}
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p0 = mkPt 0 0 10 25 0
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p1 = mkPt 100 0 15 40 pi
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trickyCusp2 :: TestCase
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trickyCusp2 =
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TestCase
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{ testName = "trickyCusp2"
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, testBrush = circleBrush
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, testStroke = ( p0, Bezier3To p1 p2 ( NextPoint p3 ) () )
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, testAlgorithmParams =
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CuspAlgorithmParams
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{ preconditioning = NoPreconditioning
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, maxWidth = 1e-7
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}
|
|
||||||
}
|
|
||||||
where
|
|
||||||
mkPt x y =
|
|
||||||
Point
|
|
||||||
{ pointCoords = ℝ2 x y
|
|
||||||
, pointParams = Params $ ℝ1 5.0
|
|
||||||
}
|
|
||||||
p0 = mkPt 5e+1 -5e+1
|
|
||||||
p1 = mkPt -7.72994362904069e+1 -3.124468786098509e+1
|
|
||||||
p2 = mkPt -5.1505430313958364e+1 -3.9826386521527986e+1
|
|
||||||
p3 = mkPt -5e+1 -5e+1
|
|
||||||
|
|
||||||
--------------------------------------------------------------------------------
|
|
||||||
|
|
||||||
type ParamsCt nbParams
|
|
||||||
= ( Show ( ℝ nbParams )
|
|
||||||
, HasChainRule Double 2 ( ℝ nbParams )
|
|
||||||
, HasChainRule ( 𝕀 Double ) 3 ( 𝕀 ( ℝ nbParams ) )
|
|
||||||
, Applicative ( D 2 ( ℝ nbParams ) )
|
|
||||||
, Applicative ( D 3 ( ℝ nbParams ) )
|
|
||||||
, Traversable ( D 2 ( ℝ nbParams ) )
|
|
||||||
, Traversable ( D 3 ( ℝ nbParams ) )
|
|
||||||
, Representable Double ( ℝ nbParams )
|
|
||||||
, Module Double ( T ( ℝ nbParams ) )
|
|
||||||
, Module ( 𝕀 Double ) ( T ( 𝕀 ( ℝ nbParams ) ) )
|
|
||||||
, Module ( D 2 ( ℝ nbParams ) Double ) ( D 2 ( ℝ nbParams ) ( ℝ 2 ) )
|
|
||||||
, Module ( D 3 ( ℝ nbParams ) ( 𝕀 Double ) ) ( D 3 ( ℝ nbParams ) ( 𝕀 ( ℝ 2 ) ) )
|
|
||||||
, Transcendental ( D 2 ( ℝ nbParams ) Double )
|
|
||||||
, Transcendental ( D 3 ( ℝ nbParams ) ( 𝕀 Double ) )
|
|
||||||
)
|
|
||||||
|
|
||||||
newtype Params nbParams = Params { getParams :: ( ℝ nbParams ) }
|
|
||||||
deriving newtype instance Show ( ℝ nbParams ) => Show ( Params nbParams )
|
|
||||||
|
|
||||||
data Point nbParams =
|
|
||||||
Point
|
|
||||||
{ pointCoords :: !( ℝ 2 )
|
|
||||||
, pointParams :: !( Params nbParams ) }
|
|
||||||
deriving stock Generic
|
|
||||||
deriving stock instance Show ( ℝ nbParams ) => Show ( Point nbParams )
|
|
||||||
|
|
||||||
data CuspAlgorithmParams =
|
|
||||||
CuspAlgorithmParams
|
|
||||||
{ preconditioning :: !Preconditioner
|
|
||||||
, maxWidth :: !Double
|
|
||||||
}
|
|
||||||
deriving stock Show
|
|
||||||
|
|
||||||
type Brush nbParams
|
|
||||||
= forall {t} k (i :: t)
|
|
||||||
. DiffInterp k i ( ℝ nbParams )
|
|
||||||
=> Proxy# i
|
|
||||||
-> ( forall a. a -> I i a )
|
|
||||||
-> C k ( I i ( ℝ nbParams ) )
|
|
||||||
( Spline Closed () ( I i ( ℝ 2 ) ) )
|
|
||||||
|
|
||||||
getStrokeFunctions
|
|
||||||
:: forall nbParams
|
|
||||||
. ParamsCt nbParams
|
|
||||||
=> Brush nbParams
|
|
||||||
-- ^ brush shape
|
|
||||||
-> Point nbParams
|
|
||||||
-- ^ start point
|
|
||||||
-> Curve Open () ( Point nbParams )
|
|
||||||
-- ^ curve points
|
|
||||||
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
|
|
||||||
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
|
||||||
getStrokeFunctions brush sp0 crv =
|
|
||||||
let
|
|
||||||
usedParams :: C 2 ( ℝ 1 ) ( ℝ nbParams )
|
|
||||||
path :: C 2 ( ℝ 1 ) ( ℝ 2 )
|
|
||||||
( path, usedParams ) =
|
|
||||||
pathAndUsedParams @2 @() coerce id ( getParams . pointParams )
|
|
||||||
sp0 crv
|
|
||||||
usedParamsI :: C 3 ( 𝕀ℝ 1 ) ( 𝕀ℝ nbParams )
|
|
||||||
pathI :: C 3 ( 𝕀ℝ 1 ) ( 𝕀ℝ 2 )
|
|
||||||
( pathI, usedParamsI ) =
|
|
||||||
pathAndUsedParams @3 @𝕀 coerce singleton ( getParams . pointParams )
|
|
||||||
sp0 crv
|
|
||||||
in ( brushStrokeData @2 @( ℝ nbParams ) coerce coerce
|
|
||||||
path usedParams $
|
|
||||||
brush @2 @() proxy# id
|
|
||||||
, brushStrokeData @3 @( ℝ nbParams ) coerce coerce
|
|
||||||
pathI usedParamsI $
|
|
||||||
brush @3 @𝕀 proxy# singleton )
|
|
||||||
{-# INLINEABLE getStrokeFunctions #-}
|
|
||||||
|
|
||||||
computeCusps
|
|
||||||
:: CuspAlgorithmParams
|
|
||||||
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
|
||||||
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
|
||||||
computeCusps params =
|
|
||||||
intervalNewtonGS ( preconditioning params ) ( maxWidth params )
|
|
||||||
|
|
@ -83,13 +83,23 @@ common common
|
||||||
base
|
base
|
||||||
>= 4.19
|
>= 4.19
|
||||||
|
|
||||||
|
common extra
|
||||||
|
|
||||||
|
build-depends:
|
||||||
|
acts
|
||||||
|
^>= 0.3.1.0
|
||||||
|
, generic-lens
|
||||||
|
>= 2.2 && < 2.3
|
||||||
|
, groups
|
||||||
|
^>= 0.5.3
|
||||||
|
|
||||||
library
|
library
|
||||||
|
|
||||||
import:
|
import:
|
||||||
common
|
common, extra
|
||||||
|
|
||||||
hs-source-dirs:
|
hs-source-dirs:
|
||||||
src
|
src/lib
|
||||||
|
|
||||||
default-language:
|
default-language:
|
||||||
Haskell2010
|
Haskell2010
|
||||||
|
|
@ -129,9 +139,6 @@ library
|
||||||
build-depends:
|
build-depends:
|
||||||
template-haskell
|
template-haskell
|
||||||
>= 2.18 && < 2.22
|
>= 2.18 && < 2.22
|
||||||
|
|
||||||
, acts
|
|
||||||
^>= 0.3.1.0
|
|
||||||
, bifunctors
|
, bifunctors
|
||||||
>= 5.5.4 && < 5.7
|
>= 5.5.4 && < 5.7
|
||||||
, code-page
|
, code-page
|
||||||
|
|
@ -144,10 +151,6 @@ library
|
||||||
^>= 3.3.7.0
|
^>= 3.3.7.0
|
||||||
, filepath
|
, filepath
|
||||||
>= 1.4 && < 1.6
|
>= 1.4 && < 1.6
|
||||||
, generic-lens
|
|
||||||
>= 2.2 && < 2.3
|
|
||||||
, groups
|
|
||||||
^>= 0.5.3
|
|
||||||
, groups-generic
|
, groups-generic
|
||||||
^>= 0.3.1.0
|
^>= 0.3.1.0
|
||||||
, parallel
|
, parallel
|
||||||
|
|
@ -161,13 +164,58 @@ library
|
||||||
, transformers
|
, transformers
|
||||||
>= 0.5.6.2 && < 0.7
|
>= 0.5.6.2 && < 0.7
|
||||||
|
|
||||||
|
--executable convert-metafont
|
||||||
|
--
|
||||||
|
-- import:
|
||||||
|
-- common
|
||||||
|
--
|
||||||
|
-- hs-source-dirs:
|
||||||
|
-- src/metafont
|
||||||
|
--
|
||||||
|
-- default-language:
|
||||||
|
-- Haskell2010
|
||||||
|
--
|
||||||
|
-- main-is:
|
||||||
|
-- Main.hs
|
||||||
|
--
|
||||||
|
-- other-modules:
|
||||||
|
-- Calligraphy.MetaFont.Convert
|
||||||
|
--
|
||||||
|
-- build-depends:
|
||||||
|
-- diagrams-contrib,
|
||||||
|
-- diagrams-lib,
|
||||||
|
-- linear,
|
||||||
|
-- parsec
|
||||||
|
|
||||||
|
executable inspect
|
||||||
|
|
||||||
|
import:
|
||||||
|
common, extra
|
||||||
|
|
||||||
|
hs-source-dirs:
|
||||||
|
src/cusps/inspect
|
||||||
|
|
||||||
|
default-language:
|
||||||
|
Haskell2010
|
||||||
|
|
||||||
|
main-is:
|
||||||
|
Main.hs
|
||||||
|
|
||||||
|
other-modules:
|
||||||
|
Math.Interval.Abstract
|
||||||
|
|
||||||
|
build-depends:
|
||||||
|
brush-strokes,
|
||||||
|
data-reify
|
||||||
|
^>= 0.6.3
|
||||||
|
|
||||||
benchmark cusps
|
benchmark cusps
|
||||||
|
|
||||||
import:
|
import:
|
||||||
common
|
common
|
||||||
|
|
||||||
hs-source-dirs:
|
hs-source-dirs:
|
||||||
bench
|
src/cusps/bench
|
||||||
|
|
||||||
main-is:
|
main-is:
|
||||||
Main.hs
|
Main.hs
|
||||||
|
|
|
||||||
616
brush-strokes/src/cusps/bench/Main.hs
Normal file
616
brush-strokes/src/cusps/bench/Main.hs
Normal file
|
|
@ -0,0 +1,616 @@
|
||||||
|
{-# LANGUAGE PolyKinds #-}
|
||||||
|
{-# LANGUAGE ScopedTypeVariables #-}
|
||||||
|
{-# LANGUAGE UndecidableInstances #-}
|
||||||
|
|
||||||
|
module Main
|
||||||
|
( main
|
||||||
|
|
||||||
|
-- Testing
|
||||||
|
, TestCase(..)
|
||||||
|
, testCases
|
||||||
|
, BrushStroke(..)
|
||||||
|
, brushStrokeFunctions
|
||||||
|
, eval
|
||||||
|
, mkVal, mkBox
|
||||||
|
, potentialCusp
|
||||||
|
, dEdsdcdt
|
||||||
|
)
|
||||||
|
where
|
||||||
|
|
||||||
|
-- base
|
||||||
|
import Control.Concurrent.MVar
|
||||||
|
( newMVar )
|
||||||
|
import Data.Coerce
|
||||||
|
( coerce )
|
||||||
|
import Data.Foldable
|
||||||
|
( for_ )
|
||||||
|
import Data.List
|
||||||
|
( intercalate )
|
||||||
|
import GHC.Exts
|
||||||
|
( Proxy#, proxy# )
|
||||||
|
import GHC.Generics
|
||||||
|
( Generic )
|
||||||
|
import GHC.TypeNats
|
||||||
|
( type (-) )
|
||||||
|
import Numeric
|
||||||
|
( showFFloat )
|
||||||
|
|
||||||
|
-- containers
|
||||||
|
import Data.Sequence
|
||||||
|
( Seq )
|
||||||
|
import qualified Data.Sequence as Seq
|
||||||
|
( index )
|
||||||
|
import Data.Tree
|
||||||
|
( foldTree )
|
||||||
|
|
||||||
|
-- tree-view
|
||||||
|
import Data.Tree.View
|
||||||
|
( showTree )
|
||||||
|
|
||||||
|
-- brush-strokes
|
||||||
|
import Calligraphy.Brushes
|
||||||
|
import Debug.Utils
|
||||||
|
( logToFile )
|
||||||
|
import Math.Algebra.Dual
|
||||||
|
import Math.Bezier.Spline
|
||||||
|
import Math.Bezier.Stroke
|
||||||
|
import Math.Bezier.Stroke.EnvelopeEquation
|
||||||
|
import Math.Differentiable
|
||||||
|
import Math.Interval
|
||||||
|
import Math.Linear
|
||||||
|
import Math.Module
|
||||||
|
import Math.Ring
|
||||||
|
( Transcendental )
|
||||||
|
|
||||||
|
--------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
main :: IO ()
|
||||||
|
main = do
|
||||||
|
for_ testCases $ \ testCase@( TestCase { testName, testBrushStroke, testAlgorithmParams, testStartBoxes } ) -> do
|
||||||
|
let ( _, testStrokeFnI ) = brushStrokeFunctions testBrushStroke
|
||||||
|
( newtTrees, ( dunno, sols ) ) = computeCusps testAlgorithmParams testStrokeFnI testStartBoxes
|
||||||
|
showedTrees = map ( uncurry showIntervalNewtonTree ) newtTrees
|
||||||
|
testHeader =
|
||||||
|
[ "", "Test case '" ++ testName ++ "':" ]
|
||||||
|
putStrLn $ unlines $
|
||||||
|
testHeader ++
|
||||||
|
map ( " " ++ )
|
||||||
|
[ " #sols: " ++ show (length sols)
|
||||||
|
, "#dunno: " ++ show (length dunno)
|
||||||
|
, "#trees: " ++ show @Int (sum @_ @Int $ map (foldTree ( \ _ bs -> 1 + sum bs )) showedTrees)
|
||||||
|
, " dunno: " ++ show dunno
|
||||||
|
, " sols: " ++ show sols
|
||||||
|
]
|
||||||
|
-- logFileMVar <- newMVar "logs/fnData.log"
|
||||||
|
-- logToFile logFileMVar (unlines logLines)
|
||||||
|
-- `seq` return ()
|
||||||
|
|
||||||
|
testCases :: [ TestCase ]
|
||||||
|
testCases = benchCases
|
||||||
|
-- [ --trickyCusp2
|
||||||
|
-- ellipse "full" (0,1) pi $ defaultStartBoxes [ 2 ]
|
||||||
|
-- ]
|
||||||
|
-- ++
|
||||||
|
{-
|
||||||
|
[ ellipse ( "(k1, k2) = " ++ show (k1, k2) ) (k1, k2) pi $ defaultStartBoxes [ 2 ]
|
||||||
|
| (k1, k2) <-
|
||||||
|
[(0.5,0.6), (0.55, 0.56)]
|
||||||
|
] ++
|
||||||
|
[ ellipse ( "'(k1, k2) = " ++ show (k1, k2) ) (0,1) pi [ mkBox (k1 + zero, k2 + zero) 2 (zero, one) ]
|
||||||
|
| (k1, k2) <-
|
||||||
|
[(0.5,0.6), (0.55, 0.56)]
|
||||||
|
]
|
||||||
|
-}
|
||||||
|
|
||||||
|
benchCases :: [ TestCase ]
|
||||||
|
benchCases = [ ellipseTestCase "full" ( 0, 1 ) pi $ defaultStartBoxes [ 0 .. 3 ] ]
|
||||||
|
|
||||||
|
--------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
data BrushStroke =
|
||||||
|
forall nbParams. ParamsCt nbParams =>
|
||||||
|
BrushStroke
|
||||||
|
{ brush :: !( Brush nbParams )
|
||||||
|
, stroke :: !( Point nbParams, Curve Open () ( Point nbParams ) )
|
||||||
|
}
|
||||||
|
|
||||||
|
|
||||||
|
data TestCase =
|
||||||
|
TestCase
|
||||||
|
{ testName :: String
|
||||||
|
, testBrushStroke :: BrushStroke
|
||||||
|
, testAlgorithmParams :: CuspAlgorithmParams
|
||||||
|
, testStartBoxes :: [ Box ]
|
||||||
|
}
|
||||||
|
|
||||||
|
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
|
||||||
|
|
||||||
|
-- Utilities to use in GHCi to help debugging.
|
||||||
|
|
||||||
|
eval
|
||||||
|
:: ( I i ( ℝ 1 ) -> Seq ( I i ( ℝ 1 ) -> StrokeDatum k i ) )
|
||||||
|
-> ( I i ( ℝ 1 ), Int, I i ( ℝ 1 ) )
|
||||||
|
-> StrokeDatum k i
|
||||||
|
eval f ( t, i, s ) = ( f t `Seq.index` i ) s
|
||||||
|
|
||||||
|
mkVal :: Double -> Int -> Double -> ( ℝ 1, Int, ℝ 1 )
|
||||||
|
mkVal t i s = ( ℝ1 t, i, ℝ1 s )
|
||||||
|
|
||||||
|
mkBox :: ( Double, Double ) -> Int -> ( Double, Double ) -> Box
|
||||||
|
mkBox ( t_min, t_max ) i ( s_min, s_max ) =
|
||||||
|
( 𝕀 ( ℝ1 t_min ) ( ℝ1 t_max ) , i, 𝕀 ( ℝ1 s_min ) ( ℝ1 s_max ) )
|
||||||
|
|
||||||
|
zero, one :: Double
|
||||||
|
zero = 1e-6
|
||||||
|
one = 1 - zero
|
||||||
|
{-# INLINE zero #-}
|
||||||
|
{-# INLINE one #-}
|
||||||
|
|
||||||
|
potentialCusp :: StrokeDatum 3 𝕀 -> Bool
|
||||||
|
potentialCusp
|
||||||
|
( StrokeDatum
|
||||||
|
{ ee = D22 { _D22_v = 𝕀 ( ℝ1 ee_min ) ( ℝ1 ee_max ) }
|
||||||
|
, 𝛿E𝛿sdcdt = D12 { _D12_v = T ( 𝕀 ( ℝ2 vx_min vy_min ) ( ℝ2 vx_max vy_max ) )}
|
||||||
|
}
|
||||||
|
) = ee_min <= 0 && ee_max >= 0
|
||||||
|
&& vx_min <= 0 && vx_max >= 0
|
||||||
|
&& vy_min <= 0 && vy_max >= 0
|
||||||
|
|
||||||
|
dEdsdcdt :: StrokeDatum k i -> D ( k - 2 ) ( I i ( ℝ 2 ) ) ( T ( I i ( ℝ 2 ) ) )
|
||||||
|
dEdsdcdt ( StrokeDatum { 𝛿E𝛿sdcdt = v } ) = v
|
||||||
|
|
||||||
|
{-
|
||||||
|
let (f, fI) = testCaseStrokeFunctions trickyCusp2
|
||||||
|
|
||||||
|
take 10 $ Data.List.sortOn ( \ ( _, ℝ1 e, v) -> abs e + norm v ) [ let { v = mkVal x 3 y; d = eval f v } in ( v, _D12_v $ ee d, _D0_v $ dEdsdcdt d ) | x <- [0.57,0.5701 .. 0.58], y <- [0.29,0.291..0.3] ]
|
||||||
|
> ((ℝ1 0.5798800000000057,3,ℝ1 0.267980000000008),ℝ1 -2.8596965543670194e-4,V2 7.79559474412963e-2 2.0389671921293484e-2)
|
||||||
|
|
||||||
|
potentialCusp $ eval fI $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
|
||||||
|
> True
|
||||||
|
|
||||||
|
let nbPotentialSols b = let ( _newtTrees, ( dunno, sols ) ) = intervalNewtonGSFrom NoPreconditioning 1e-7 fI b in length dunno + length sols
|
||||||
|
|
||||||
|
nbPotentialSols $ mkBox (0.5798, 0.5799) 3 (0.26798, 0.26799)
|
||||||
|
1
|
||||||
|
|
||||||
|
nbPotentialSols $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
|
||||||
|
0
|
||||||
|
|
||||||
|
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI b
|
||||||
|
|
||||||
|
putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
|
||||||
|
|
||||||
|
([ℝ1 0.5798, ℝ1 0.675],3,[ℝ1 0.26798, ℝ1 0.26799]) (area 0.000001) N []
|
||||||
|
└─ ([ℝ1 0.5973000285624527, ℝ1 0.6750000000000002],3,[ℝ1 0.26798, ℝ1 0.26799000000000006]) (area 0.000001) NoSolution "ee" ([ℝ1 0.5973000285624527, ℝ1 0.6750000000000002],3,[ℝ1 0.26798, ℝ1 0.26799000000000006])
|
||||||
|
|
||||||
|
eval fI $ mkBox (0.5798, 0.675) 3 (0.26798, 0.26799)
|
||||||
|
> D12 {_D12_v = T[ℝ2 -10088.6674944889 -3281.3820867312834, ℝ2 4124.668381545453 4524.807156085763], _D12_dx = TT[ℝ2 -173746.97965005718 -33281.18494907289, ℝ2 298.2609121556852 23639.772884799597], _D12_dy = TT[ℝ2 -18454.27716258352 -28337.509817580823, ℝ2 1163.6949532017436 -13936.383137525536]}}
|
||||||
|
i.e.
|
||||||
|
> f = [ℝ2 -10088.6674944889 -3281.3820867312834, ℝ2 4124.668381545453 4524.807156085763]
|
||||||
|
> f_t = [ℝ2 -173746.97965005718 -33281.18494907289, ℝ2 298.2609121556852 23639.772884799597]
|
||||||
|
> f_s = [ℝ2 -18454.27716258352 -28337.509817580823, ℝ2 1163.6949532017436 -13936.383137525536]
|
||||||
|
|
||||||
|
(f, fI) = testCaseStrokeFunctions trickyCusp2
|
||||||
|
t = 𝕀 (ℝ1 0.5798) (ℝ1 0.675)
|
||||||
|
s = 𝕀 (ℝ1 0.26798) (ℝ1 0.26799)
|
||||||
|
t_mid = 0.5 * ( 0.5798 + 0.675 )
|
||||||
|
s_mid = 0.5 * ( 0.26798 + 0.26799 )
|
||||||
|
D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) = dEdsdcdt $ eval fI (t, 3, s)
|
||||||
|
t' = coerce ( (-) @( 𝕀 Double ) ) t ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s' = coerce ( (-) @( 𝕀 Double ) ) s ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
a = ( f_t, f_s )
|
||||||
|
b = negV2 $ singleton $ midV2 f
|
||||||
|
[((t2', s2'), isContr)] = gaussSeidel a b (t', s')
|
||||||
|
t2 = coerce ( (+) @( 𝕀 Double ) ) t2' ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s2 = coerce ( (+) @( 𝕀 Double ) ) s2' ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
|
||||||
|
t2
|
||||||
|
> [ℝ1 0.6102365832093095, ℝ1 0.6750000000000002]
|
||||||
|
s2
|
||||||
|
> [ℝ1 0.26798, ℝ1 0.26799000000000006]
|
||||||
|
|
||||||
|
|
||||||
|
let ( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi ), 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) ) = a
|
||||||
|
let ( 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi ) ) = b
|
||||||
|
let ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) ) = ( t', s' )
|
||||||
|
|
||||||
|
a11 = 𝕀 a11_lo a11_hi
|
||||||
|
a12 = 𝕀 a12_lo a12_hi
|
||||||
|
a21 = 𝕀 a21_lo a21_hi
|
||||||
|
a22 = 𝕀 a22_lo a22_hi
|
||||||
|
b1 = 𝕀 b1_lo b1_hi
|
||||||
|
b2 = 𝕀 b2_lo b2_hi
|
||||||
|
x1 = 𝕀 x1_lo x1_hi
|
||||||
|
x2 = 𝕀 x2_lo x2_hi
|
||||||
|
|
||||||
|
( b1 - a12 * x2 )
|
||||||
|
> [2981.90728508591, 2982.0918278575364]
|
||||||
|
|
||||||
|
extendedRecip a11
|
||||||
|
|
||||||
|
-----------------------
|
||||||
|
|
||||||
|
fI k rot = snd $ testCaseStrokeFunctions $ ellipse k rot
|
||||||
|
d k rot = width $ _D22_v $ ee $ eval (fI k rot) $ mkBox (1e-6, 1-1e-6) 3 (1e-6, 1-1e-6)
|
||||||
|
|
||||||
|
-----------------------
|
||||||
|
|
||||||
|
(f, fI) = testCaseStrokeFunctions $ ellipse 1 pi
|
||||||
|
t = 𝕀 (ℝ1 0.001) (ℝ1 0.099)
|
||||||
|
s = 𝕀 (ℝ1 0.001) (ℝ1 0.999)
|
||||||
|
t_mid = 0.5 * ( 0.001 + 0.099 )
|
||||||
|
s_mid = 0.5 * ( 0.001 + 0.999 )
|
||||||
|
D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) = dEdsdcdt $ eval fI (t, 3, s)
|
||||||
|
t' = coerce ( (-) @( 𝕀 Double ) ) t ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s' = coerce ( (-) @( 𝕀 Double ) ) s ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
a = ( f_t, f_s )
|
||||||
|
b = negV2 $ singleton $ midV2 f
|
||||||
|
[((t2', s2'), isContr)] = gaussSeidel a b (t', s')
|
||||||
|
t2 = coerce ( (+) @( 𝕀 Double ) ) t2' ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s2 = coerce ( (+) @( 𝕀 Double ) ) s2' ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
|
||||||
|
> t = [0.001, 0.099]
|
||||||
|
> t' = [-0.049, 0.049]
|
||||||
|
|
||||||
|
(f, fI) = testCaseStrokeFunctions $ ellipse 0.1 pi
|
||||||
|
t = 𝕀 (ℝ1 0.001) (ℝ1 0.999)
|
||||||
|
s = 𝕀 (ℝ1 0.001) (ℝ1 0.999)
|
||||||
|
t_mid = 0.5 * ( 0.001 + 0.999 )
|
||||||
|
s_mid = 0.5 * ( 0.001 + 0.999 )
|
||||||
|
D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) = dEdsdcdt $ eval fI (t, 3, s)
|
||||||
|
t' = coerce ( (-) @( 𝕀 Double ) ) t ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s' = coerce ( (-) @( 𝕀 Double ) ) s ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
a = ( f_t, f_s )
|
||||||
|
b = negV2 $ singleton $ midV2 f
|
||||||
|
[((t2', s2'), isContr)] = gaussSeidel a b (t', s')
|
||||||
|
t2 = coerce ( (+) @( 𝕀 Double ) ) t2' ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s2 = coerce ( (+) @( 𝕀 Double ) ) s2' ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
|
||||||
|
> t = [0.001, 0.999]
|
||||||
|
> t' = [-0.499, 0.499]
|
||||||
|
|
||||||
|
-}
|
||||||
|
|
||||||
|
width :: 𝕀ℝ 1 -> Double
|
||||||
|
width (𝕀 (ℝ1 lo) (ℝ1 hi)) = hi - lo
|
||||||
|
|
||||||
|
negV2 :: 𝕀ℝ 2 -> 𝕀ℝ 2
|
||||||
|
negV2 ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
|
||||||
|
let !( 𝕀 x'_lo x'_hi ) = negate $ 𝕀 x_lo x_hi
|
||||||
|
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
||||||
|
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
||||||
|
|
||||||
|
midV2 :: 𝕀ℝ 2 -> ℝ 2
|
||||||
|
midV2 ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
|
||||||
|
ℝ2 ( 0.5 * ( x_lo + x_hi ) ) ( 0.5 * ( y_lo + y_hi ) )
|
||||||
|
|
||||||
|
|
||||||
|
logLines :: [ String ]
|
||||||
|
logLines =
|
||||||
|
[ "E, dE/ds * dc/dt"
|
||||||
|
, "{" ++
|
||||||
|
(intercalate ","
|
||||||
|
[ "{" ++ showD t ++ "," ++ showD s ++ ",{" ++ intercalate "," vals ++ "}}"
|
||||||
|
| t <- [ 0.5484, 0.5484 + 0.00001 .. 0.5488 ]
|
||||||
|
, s <- [ 0.5479, 0.5479 + 0.00001 .. 0.5483 ]
|
||||||
|
, let StrokeDatum
|
||||||
|
{ ee = D22 ee _ _ _ _ _
|
||||||
|
, 𝛿E𝛿sdcdt = D12 (T f) (T (T f_t)) (T (T f_s))
|
||||||
|
} = (curvesI (singleton (ℝ1 t)) `Seq.index` i) (singleton (ℝ1 s))
|
||||||
|
ℝ2 vx vy = midPoint2 f
|
||||||
|
--ℝ2 vx_t vy_t = midPoint2 f_t
|
||||||
|
--ℝ2 vx_s vy_s = midPoint2 f_s
|
||||||
|
vals = [ showD ( midPoint ee )
|
||||||
|
, "{" ++ showD vx ++ "," ++ showD vy ++ "}"
|
||||||
|
-- , "{" ++ showD vx_t ++ "," ++ showD vy_t ++ "}"
|
||||||
|
-- , "{" ++ showD vx_s ++ "," ++ showD vy_s ++ "}"
|
||||||
|
]
|
||||||
|
]
|
||||||
|
) ++ "}"
|
||||||
|
]
|
||||||
|
where
|
||||||
|
i = 2
|
||||||
|
( curves, curvesI ) = brushStrokeFunctions $ ellipseBrushStroke ( 0, 1 ) pi
|
||||||
|
midPoint (𝕀 (ℝ1 lo) (ℝ1 hi)) = 0.5 * ( lo + hi )
|
||||||
|
midPoint2 (𝕀 (ℝ2 lo_x lo_y) (ℝ2 hi_x hi_y))
|
||||||
|
= ℝ2 ( 0.5 * ( lo_x + hi_x ) ) ( 0.5 * ( lo_y + hi_y ) )
|
||||||
|
|
||||||
|
|
||||||
|
-- t = 0.5486102, s = 0.5480951
|
||||||
|
|
||||||
|
|
||||||
|
bloo =
|
||||||
|
[ ( e * e + vx * vx + vy * vy, ( t, s ) )
|
||||||
|
| t <- [ 0.548609, 0.548609 + 0.0000001 .. 0.54862 ]
|
||||||
|
, s <- [ 0.548094, 0.548094 + 0.0000001 .. 0.548096 ]
|
||||||
|
, let StrokeDatum
|
||||||
|
{ ee = D22 ee _ _ _ _ _
|
||||||
|
, 𝛿E𝛿sdcdt = D12 (T f) _ _
|
||||||
|
} = (curvesI (singleton (ℝ1 t)) `Seq.index` i) (singleton (ℝ1 s))
|
||||||
|
e = midPoint ee
|
||||||
|
ℝ2 vx vy = midPoint2 f
|
||||||
|
vals = [ showD ( midPoint ee )
|
||||||
|
, "{" ++ showD vx ++ "," ++ showD vy ++ "}"
|
||||||
|
]
|
||||||
|
]
|
||||||
|
where
|
||||||
|
i = 2
|
||||||
|
( curves, curvesI ) = brushStrokeFunctions $ ellipseBrushStroke ( 0, 1 ) pi
|
||||||
|
midPoint (𝕀 (ℝ1 lo) (ℝ1 hi)) = 0.5 * ( lo + hi )
|
||||||
|
midPoint2 (𝕀 (ℝ2 lo_x lo_y) (ℝ2 hi_x hi_y))
|
||||||
|
= ℝ2 ( 0.5 * ( lo_x + hi_x ) ) ( 0.5 * ( lo_y + hi_y ) )
|
||||||
|
|
||||||
|
{-
|
||||||
|
|
||||||
|
(f, fI) = brushStrokeFunctions $ ellipseBrushStroke ( 0, 1 ) pi
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
_D22_v $ ee $ eval fI $ mkBox (0.5, 0.6) 2 (0,1)
|
||||||
|
> [ℝ1 -9531.427315889887, ℝ1 10135.074304695485]
|
||||||
|
|
||||||
|
minimum $ map inf $ [ _D22_v $ ee $ eval fI $ mkBox (t, t + 0.01) 2 (0,1) | t <- [ 0.5, 0.51 .. 0.59 ] ]
|
||||||
|
> ℝ1 -5718.905635365308
|
||||||
|
|
||||||
|
maximum $ map sup $ [ _D22_v $ ee $ eval fI $ mkBox (t, t + 0.01) 2 (0,1) | t <- [ 0.5, 0.51 .. 0.59 ] ]
|
||||||
|
> ℝ1 5099.008191092755
|
||||||
|
|
||||||
|
minimum $ map inf $ [ _D22_v $ ee $ eval fI $ mkBox (t, t) 2 (s, s) | t <- [ 0.5, 0.501 .. 0.6 ], s <- [ zero, zero + 0.001 .. one ] ]
|
||||||
|
> ℝ1 -675.9595496147458
|
||||||
|
|
||||||
|
maximum $ map sup $ [ _D22_v $ ee $ eval fI $ mkBox (t, t) 2 (s, s) | t <- [ 0.5, 0.501 .. 0.6 ], s <- [ zero, zero + 0.001 .. one ] ]
|
||||||
|
> ℝ1 2401.9644509525997
|
||||||
|
|
||||||
|
_D12_v $ dEdsdcdt $ eval fI $ mkBox (0.5, 0.6) 2 (0,1)
|
||||||
|
> T[ℝ2 -1.7300637136531524e7 -1.262824151868635e7, ℝ2 1.632868898735965e7 1.1869759856947478e7]
|
||||||
|
|
||||||
|
minimum [ _x $ inf $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t + 0.01) 2 (0,1) | t <- [ 0.5, 0.51 .. 0.59 ] ]
|
||||||
|
-5606615.948203902
|
||||||
|
|
||||||
|
maximum [ _x $ sup $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t + 0.01) 2 (0,1) | t <- [ 0.5, 0.51 .. 0.59 ] ]
|
||||||
|
4340858.832347277
|
||||||
|
|
||||||
|
minimum [ _x $ inf $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t) 2 (s, s) | t <- [ 0.5, 0.501 .. 0.6 ], s <- [ zero, zero + 0.001 .. one ] ]
|
||||||
|
-1785730.2396688666
|
||||||
|
|
||||||
|
maximum [ _x $ sup $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t) 2 (s, s) | t <- [ 0.5, 0.501 .. 0.6 ], s <- [ zero, zero + 0.001 .. one ] ]
|
||||||
|
974842.6547409865
|
||||||
|
|
||||||
|
maximum [ _y $ sup $ unT $ _D12_v $ dEdsdcdt $ eval fI $ mkBox (t, t) 2 (s, s) | t <- [ 0.5, 0.501 .. 0.6 ], s <- [ zero, zero + 0.001 .. one ] ]
|
||||||
|
845211.4833711373
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
let showTrees b = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI b
|
||||||
|
|
||||||
|
putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees $ mkBox (0.5486101933245248, 0.5486102071493622) 2 (0.548095036738487, 0.5480952)
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
([ℝ1 0.5486101960904595, ℝ1 0.5486102071493623],2,[ℝ1 0.5480950771755867, ℝ1 0.5480952000000001])
|
||||||
|
|
||||||
|
-}
|
||||||
|
|
||||||
|
_x ( ℝ2 x _ ) = x
|
||||||
|
_y ( ℝ2 _ y ) = y
|
||||||
|
|
||||||
|
showD :: Double -> String
|
||||||
|
showD float = showFFloat (Just 6) float ""
|
||||||
|
|
||||||
|
--------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
ellipseTestCase :: String -> ( Double, Double ) -> Double -> [ Box ] -> TestCase
|
||||||
|
ellipseTestCase str k0k1 rot startBoxes =
|
||||||
|
TestCase
|
||||||
|
{ testName = "ellipse (" ++ str ++ ")"
|
||||||
|
, testBrushStroke = ellipseBrushStroke k0k1 rot
|
||||||
|
, testAlgorithmParams =
|
||||||
|
CuspAlgorithmParams
|
||||||
|
{ preconditioning = InverseMidJacobian
|
||||||
|
, maxWidth = 1e-7
|
||||||
|
}
|
||||||
|
, testStartBoxes = startBoxes
|
||||||
|
}
|
||||||
|
|
||||||
|
ellipseBrushStroke :: ( Double, Double ) -> Double -> BrushStroke
|
||||||
|
ellipseBrushStroke ( k0, k1 ) rot =
|
||||||
|
BrushStroke
|
||||||
|
{ brush = ellipseBrush
|
||||||
|
, stroke = ( p0, LineTo ( NextPoint p1 ) () ) }
|
||||||
|
where
|
||||||
|
mkPt x y w h phi =
|
||||||
|
Point
|
||||||
|
{ pointCoords = ℝ2 x y
|
||||||
|
, pointParams = Params $ ℝ3 w h phi
|
||||||
|
}
|
||||||
|
l k = lerp @( T Double ) k
|
||||||
|
p k = mkPt ( l k 0 100 ) 0 ( l k 10 15 ) ( l k 25 40 ) ( l k 0 rot )
|
||||||
|
p0 = p k0
|
||||||
|
p1 = p k1
|
||||||
|
|
||||||
|
trickyCusp2TestCase :: TestCase
|
||||||
|
trickyCusp2TestCase =
|
||||||
|
TestCase
|
||||||
|
{ testName = "trickyCusp2"
|
||||||
|
, testBrushStroke = trickyCusp2BrushStroke
|
||||||
|
, testAlgorithmParams =
|
||||||
|
CuspAlgorithmParams
|
||||||
|
{ preconditioning = InverseMidJacobian
|
||||||
|
, maxWidth = 1e-7
|
||||||
|
}
|
||||||
|
, testStartBoxes = defaultStartBoxes [ 0 .. 3 ]
|
||||||
|
}
|
||||||
|
|
||||||
|
trickyCusp2BrushStroke :: BrushStroke
|
||||||
|
trickyCusp2BrushStroke =
|
||||||
|
BrushStroke
|
||||||
|
{ brush = circleBrush
|
||||||
|
, stroke = ( p0, Bezier3To p1 p2 ( NextPoint p3 ) () )
|
||||||
|
}
|
||||||
|
where
|
||||||
|
mkPt x y =
|
||||||
|
Point
|
||||||
|
{ pointCoords = ℝ2 x y
|
||||||
|
, pointParams = Params $ ℝ1 5.0
|
||||||
|
}
|
||||||
|
p0 = mkPt 5e+1 -5e+1
|
||||||
|
p1 = mkPt -7.72994362904069e+1 -3.124468786098509e+1
|
||||||
|
p2 = mkPt -5.1505430313958364e+1 -3.9826386521527986e+1
|
||||||
|
p3 = mkPt -5e+1 -5e+1
|
||||||
|
|
||||||
|
--------------------------------------------------------------------------------
|
||||||
|
|
||||||
|
type ParamsCt nbParams
|
||||||
|
= ( Show ( ℝ nbParams )
|
||||||
|
, HasChainRule Double 2 ( ℝ nbParams )
|
||||||
|
, HasChainRule ( 𝕀 Double ) 3 ( 𝕀 ( ℝ nbParams ) )
|
||||||
|
, Applicative ( D 2 ( ℝ nbParams ) )
|
||||||
|
, Applicative ( D 3 ( ℝ nbParams ) )
|
||||||
|
, Traversable ( D 2 ( ℝ nbParams ) )
|
||||||
|
, Traversable ( D 3 ( ℝ nbParams ) )
|
||||||
|
, Representable Double ( ℝ nbParams )
|
||||||
|
, Module Double ( T ( ℝ nbParams ) )
|
||||||
|
, Module ( 𝕀 Double ) ( T ( 𝕀 ( ℝ nbParams ) ) )
|
||||||
|
, Module ( D 2 ( ℝ nbParams ) Double ) ( D 2 ( ℝ nbParams ) ( ℝ 2 ) )
|
||||||
|
, Module ( D 3 ( ℝ nbParams ) ( 𝕀 Double ) ) ( D 3 ( ℝ nbParams ) ( 𝕀 ( ℝ 2 ) ) )
|
||||||
|
, Transcendental ( D 2 ( ℝ nbParams ) Double )
|
||||||
|
, Transcendental ( D 3 ( ℝ nbParams ) ( 𝕀 Double ) )
|
||||||
|
)
|
||||||
|
|
||||||
|
newtype Params nbParams = Params { getParams :: ( ℝ nbParams ) }
|
||||||
|
deriving newtype instance Show ( ℝ nbParams ) => Show ( Params nbParams )
|
||||||
|
|
||||||
|
data Point nbParams =
|
||||||
|
Point
|
||||||
|
{ pointCoords :: !( ℝ 2 )
|
||||||
|
, pointParams :: !( Params nbParams ) }
|
||||||
|
deriving stock Generic
|
||||||
|
deriving stock instance Show ( ℝ nbParams ) => Show ( Point nbParams )
|
||||||
|
|
||||||
|
data CuspAlgorithmParams =
|
||||||
|
CuspAlgorithmParams
|
||||||
|
{ preconditioning :: !Preconditioner
|
||||||
|
, maxWidth :: !Double
|
||||||
|
}
|
||||||
|
deriving stock Show
|
||||||
|
|
||||||
|
type Brush nbParams
|
||||||
|
= forall {t} k (i :: t)
|
||||||
|
. DiffInterp k i ( ℝ nbParams )
|
||||||
|
=> Proxy# i
|
||||||
|
-> ( forall a. a -> I i a )
|
||||||
|
-> C k ( I i ( ℝ nbParams ) )
|
||||||
|
( Spline Closed () ( I i ( ℝ 2 ) ) )
|
||||||
|
|
||||||
|
getStrokeFunctions
|
||||||
|
:: forall nbParams
|
||||||
|
. ParamsCt nbParams
|
||||||
|
=> Brush nbParams
|
||||||
|
-- ^ brush shape
|
||||||
|
-> Point nbParams
|
||||||
|
-- ^ start point
|
||||||
|
-> Curve Open () ( Point nbParams )
|
||||||
|
-- ^ curve points
|
||||||
|
-> ( ℝ 1 -> Seq ( ℝ 1 -> StrokeDatum 2 () )
|
||||||
|
, 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||||
|
getStrokeFunctions brush sp0 crv =
|
||||||
|
let
|
||||||
|
usedParams :: C 2 ( ℝ 1 ) ( ℝ nbParams )
|
||||||
|
path :: C 2 ( ℝ 1 ) ( ℝ 2 )
|
||||||
|
( path, usedParams ) =
|
||||||
|
pathAndUsedParams @2 @() coerce id ( getParams . pointParams )
|
||||||
|
sp0 crv
|
||||||
|
usedParamsI :: C 3 ( 𝕀ℝ 1 ) ( 𝕀ℝ nbParams )
|
||||||
|
pathI :: C 3 ( 𝕀ℝ 1 ) ( 𝕀ℝ 2 )
|
||||||
|
( pathI, usedParamsI ) =
|
||||||
|
pathAndUsedParams @3 @𝕀 coerce singleton ( getParams . pointParams )
|
||||||
|
sp0 crv
|
||||||
|
in ( brushStrokeData @2 @( ℝ nbParams ) coerce coerce
|
||||||
|
path usedParams $
|
||||||
|
brush @2 @() proxy# id
|
||||||
|
, brushStrokeData @3 @( ℝ nbParams ) coerce coerce
|
||||||
|
pathI usedParamsI $
|
||||||
|
brush @3 @𝕀 proxy# singleton )
|
||||||
|
{-# INLINEABLE getStrokeFunctions #-}
|
||||||
|
|
||||||
|
computeCusps
|
||||||
|
:: CuspAlgorithmParams
|
||||||
|
-> ( 𝕀ℝ 1 -> Seq ( 𝕀ℝ 1 -> StrokeDatum 3 𝕀 ) )
|
||||||
|
-> [ Box ]
|
||||||
|
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||||
|
computeCusps params eqs startBoxes =
|
||||||
|
foldMap
|
||||||
|
( intervalNewtonGSFrom ( preconditioning params ) ( maxWidth params ) eqs )
|
||||||
|
startBoxes
|
||||||
|
|
||||||
|
defaultStartBoxes :: [ Int ] -> [ Box ]
|
||||||
|
defaultStartBoxes is =
|
||||||
|
[ mkBox (zero, one) i (zero, one) | i <- is ]
|
||||||
|
|
||||||
|
getR1 (ℝ1 u) = u
|
||||||
|
|
||||||
|
{-
|
||||||
|
|
||||||
|
(f, fI) = brushStrokeFunctions $ ellipseBrushStroke (0,1) pi
|
||||||
|
nbPotentialSols box = let ( _newtTrees, ( dunno, sols ) ) = intervalNewtonGSFrom NoPreconditioning 1e-7 fI box in length dunno + length sols
|
||||||
|
showTrees box = map ( uncurry showIntervalNewtonTree ) $ fst $ intervalNewtonGSFrom NoPreconditioning 1e-7 fI box
|
||||||
|
|
||||||
|
(t, i, s) = mkBox (0.548610200176363, 0.5486102071493623) 2 (0.5480950215354709, 0.5480952)
|
||||||
|
putStrLn $ unlines $ map Data.Tree.View.showTree $ showTrees (t,i,s)
|
||||||
|
|
||||||
|
|
||||||
|
t_mid = 0.5 * ( getR1 ( inf t ) + getR1 ( sup t ) )
|
||||||
|
s_mid = 0.5 * ( getR1 ( inf s ) + getR1 ( sup s ) )
|
||||||
|
D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) = dEdsdcdt $ eval fI (t, i, s)
|
||||||
|
t' = coerce ( (-) @( 𝕀 Double ) ) t ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s' = coerce ( (-) @( 𝕀 Double ) ) s ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
a = ( f_t, f_s )
|
||||||
|
b = negV2 $ singleton $ midV2 f
|
||||||
|
[((t2', s2'), isContr)] = gaussSeidel a b (t', s')
|
||||||
|
t2 = coerce ( (+) @( 𝕀 Double ) ) t2' ( singleton ( ℝ1 t_mid ) ) :: 𝕀ℝ 1
|
||||||
|
s2 = coerce ( (+) @( 𝕀 Double ) ) s2' ( singleton ( ℝ1 s_mid ) ) :: 𝕀ℝ 1
|
||||||
|
|
||||||
|
t2
|
||||||
|
> [ℝ1 0.548610200176363, ℝ1 0.5486102071493624]
|
||||||
|
s2
|
||||||
|
> [ℝ1 0.5480950911334656, ℝ1 0.5480952000000001]
|
||||||
|
|
||||||
|
mkBox (0.548610200176363, 0.5486102071493624) i (0.5480950911334656, 0.5480952000000001)
|
||||||
|
|
||||||
|
t inf (no change)
|
||||||
|
|
||||||
|
t sup (no change)
|
||||||
|
|
||||||
|
s_inf:
|
||||||
|
0.5480950215354709
|
||||||
|
0.5480950911334656
|
||||||
|
|
||||||
|
s_sup (no change)
|
||||||
|
|
||||||
|
ghci> potentialCusp $ eval fI $ mkBox (0.548610200176363, 0.5486102071493623) 2 (0.54809502, 0.5480952)
|
||||||
|
True
|
||||||
|
ghci> potentialCusp $ eval fI $ mkBox (0.548610200176363, 0.5486102071493623) 2 (0.54809503, 0.5480952)
|
||||||
|
False
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
let ( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi ), 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) ) = a
|
||||||
|
let ( 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi ) ) = b
|
||||||
|
let ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) ) = ( t', s' )
|
||||||
|
|
||||||
|
a11 = 𝕀 a11_lo a11_hi
|
||||||
|
a12 = 𝕀 a12_lo a12_hi
|
||||||
|
a21 = 𝕀 a21_lo a21_hi
|
||||||
|
a22 = 𝕀 a22_lo a22_hi
|
||||||
|
b1 = 𝕀 b1_lo b1_hi
|
||||||
|
b2 = 𝕀 b2_lo b2_hi
|
||||||
|
x1 = 𝕀 x1_lo x1_hi
|
||||||
|
x2 = 𝕀 x2_lo x2_hi
|
||||||
|
|
||||||
|
-}
|
||||||
|
|
@ -32,7 +32,7 @@ import qualified Data.Sequence as Seq
|
||||||
import Data.Generics.Product.Typed
|
import Data.Generics.Product.Typed
|
||||||
( HasType )
|
( HasType )
|
||||||
|
|
||||||
-- MetaBrush
|
-- brush-strokes
|
||||||
import Math.Algebra.Dual
|
import Math.Algebra.Dual
|
||||||
import qualified Math.Bezier.Quadratic as Quadratic
|
import qualified Math.Bezier.Quadratic as Quadratic
|
||||||
import qualified Math.Bezier.Cubic as Cubic
|
import qualified Math.Bezier.Cubic as Cubic
|
||||||
|
|
@ -58,6 +58,7 @@ import Math.Ring
|
||||||
, ifThenElse
|
, ifThenElse
|
||||||
)
|
)
|
||||||
|
|
||||||
|
-- brush-strokes:inspect-cusps
|
||||||
import Math.Interval.Abstract
|
import Math.Interval.Abstract
|
||||||
|
|
||||||
--------------------------------------------------------------------------------
|
--------------------------------------------------------------------------------
|
||||||
|
|
@ -43,7 +43,7 @@ import qualified Data.Map.Strict as Map
|
||||||
import Data.Group
|
import Data.Group
|
||||||
( Group(..) )
|
( Group(..) )
|
||||||
|
|
||||||
-- MetaBrush
|
-- brush-strokes
|
||||||
import Math.Algebra.Dual
|
import Math.Algebra.Dual
|
||||||
import qualified Math.Bezier.Quadratic as Quadratic
|
import qualified Math.Bezier.Quadratic as Quadratic
|
||||||
import qualified Math.Bezier.Cubic as Cubic
|
import qualified Math.Bezier.Cubic as Cubic
|
||||||
|
|
@ -66,3 +66,5 @@ logToFile logFileMVar logContents =
|
||||||
FilePath.takeDirectory logFile
|
FilePath.takeDirectory logFile
|
||||||
appendFile logFile logContentsWithHeader
|
appendFile logFile logContentsWithHeader
|
||||||
return logFile
|
return logFile
|
||||||
|
{-# NOINLINE logToFile #-}
|
||||||
|
|
||||||
|
|
@ -60,8 +60,8 @@ newtype D𝔸0 v = D0 { _D0_v :: v }
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x]/(x)^2 \).
|
-- | \( \mathbb{Z}[x]/(x)^2 \).
|
||||||
data D1𝔸1 v =
|
data D1𝔸1 v =
|
||||||
D11 { _D11_v :: !v
|
D11 { _D11_v :: v
|
||||||
, _D11_dx :: !( T v )
|
, _D11_dx :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -70,9 +70,9 @@ data D1𝔸1 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x]/(x)^3 \).
|
-- | \( \mathbb{Z}[x]/(x)^3 \).
|
||||||
data D2𝔸1 v =
|
data D2𝔸1 v =
|
||||||
D21 { _D21_v :: !v
|
D21 { _D21_v :: v
|
||||||
, _D21_dx :: !( T v )
|
, _D21_dx :: ( T v )
|
||||||
, _D21_dxdx :: !( T v )
|
, _D21_dxdx :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -81,10 +81,10 @@ data D2𝔸1 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x]/(x)^4 \).
|
-- | \( \mathbb{Z}[x]/(x)^4 \).
|
||||||
data D3𝔸1 v =
|
data D3𝔸1 v =
|
||||||
D31 { _D31_v :: !v
|
D31 { _D31_v :: v
|
||||||
, _D31_dx :: !( T v )
|
, _D31_dx :: ( T v )
|
||||||
, _D31_dxdx :: !( T v )
|
, _D31_dxdx :: ( T v )
|
||||||
, _D31_dxdxdx :: !( T v )
|
, _D31_dxdxdx :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -93,8 +93,8 @@ data D3𝔸1 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y]/(x, y)^2 \).
|
-- | \( \mathbb{Z}[x, y]/(x, y)^2 \).
|
||||||
data D1𝔸2 v =
|
data D1𝔸2 v =
|
||||||
D12 { _D12_v :: !v
|
D12 { _D12_v :: v
|
||||||
, _D12_dx, _D12_dy :: !( T v )
|
, _D12_dx, _D12_dy :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -103,9 +103,9 @@ data D1𝔸2 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y]/(x, y)^3 \).
|
-- | \( \mathbb{Z}[x, y]/(x, y)^3 \).
|
||||||
data D2𝔸2 v =
|
data D2𝔸2 v =
|
||||||
D22 { _D22_v :: !v
|
D22 { _D22_v :: v
|
||||||
, _D22_dx, _D22_dy :: !( T v )
|
, _D22_dx, _D22_dy :: ( T v )
|
||||||
, _D22_dxdx, _D22_dxdy, _D22_dydy :: !( T v )
|
, _D22_dxdx, _D22_dxdy, _D22_dydy :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -114,10 +114,10 @@ data D2𝔸2 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y]/(x, y)^4 \).
|
-- | \( \mathbb{Z}[x, y]/(x, y)^4 \).
|
||||||
data D3𝔸2 v =
|
data D3𝔸2 v =
|
||||||
D32 { _D32_v :: !v
|
D32 { _D32_v :: v
|
||||||
, _D32_dx, _D32_dy :: !( T v )
|
, _D32_dx, _D32_dy :: ( T v )
|
||||||
, _D32_dxdx, _D32_dxdy, _D32_dydy :: !( T v )
|
, _D32_dxdx, _D32_dxdy, _D32_dydy :: ( T v )
|
||||||
, _D32_dxdxdx, _D32_dxdxdy, _D32_dxdydy, _D32_dydydy :: !( T v )
|
, _D32_dxdxdx, _D32_dxdxdy, _D32_dxdydy, _D32_dydydy :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -126,8 +126,8 @@ data D3𝔸2 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^2 \).
|
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^2 \).
|
||||||
data D1𝔸3 v =
|
data D1𝔸3 v =
|
||||||
D13 { _D13_v :: !v
|
D13 { _D13_v :: v
|
||||||
, _D13_dx, _D13_dy, _D13_dz :: !( T v )
|
, _D13_dx, _D13_dy, _D13_dz :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -136,8 +136,8 @@ data D1𝔸3 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^3 \).
|
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^3 \).
|
||||||
data D2𝔸3 v =
|
data D2𝔸3 v =
|
||||||
D23 { _D23_v :: !v
|
D23 { _D23_v :: v
|
||||||
, _D23_dx, _D23_dy, _D23_dz :: !( T v )
|
, _D23_dx, _D23_dy, _D23_dz :: ( T v )
|
||||||
, _D23_dxdx, _D23_dxdy, _D23_dydy, _D23_dxdz, _D23_dydz, _D23_dzdz :: !( T v )
|
, _D23_dxdx, _D23_dxdy, _D23_dydy, _D23_dxdz, _D23_dydz, _D23_dzdz :: !( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
|
|
@ -147,8 +147,8 @@ data D2𝔸3 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^4 \).
|
-- | \( \mathbb{Z}[x, y, z]/(x, y, z)^4 \).
|
||||||
data D3𝔸3 v =
|
data D3𝔸3 v =
|
||||||
D33 { _D33_v :: !v
|
D33 { _D33_v :: v
|
||||||
, _D33_dx, _D33_dy, _D33_dz :: !( T v )
|
, _D33_dx, _D33_dy, _D33_dz :: ( T v )
|
||||||
, _D33_dxdx, _D33_dxdy, _D33_dydy, _D33_dxdz, _D33_dydz, _D33_dzdz :: !( T v )
|
, _D33_dxdx, _D33_dxdy, _D33_dydy, _D33_dxdz, _D33_dydz, _D33_dzdz :: !( T v )
|
||||||
, _D33_dxdxdx, _D33_dxdxdy, _D33_dxdydy, _D33_dydydy
|
, _D33_dxdxdx, _D33_dxdxdy, _D33_dxdydy, _D33_dydydy
|
||||||
, _D33_dxdxdz, _D33_dxdydz, _D33_dxdzdz, _D33_dydydz, _D33_dydzdz, _D33_dzdzdz :: !( T v )
|
, _D33_dxdxdz, _D33_dxdydz, _D33_dxdzdz, _D33_dydydz, _D33_dydzdz, _D33_dzdzdz :: !( T v )
|
||||||
|
|
@ -160,8 +160,8 @@ data D3𝔸3 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^2 \).
|
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^2 \).
|
||||||
data D1𝔸4 v =
|
data D1𝔸4 v =
|
||||||
D14 { _D14_v :: !v
|
D14 { _D14_v :: v
|
||||||
, _D14_dx, _D14_dy, _D14_dz, _D14_dw :: !( T v )
|
, _D14_dx, _D14_dy, _D14_dz, _D14_dw :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -170,10 +170,10 @@ data D1𝔸4 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^3 \).
|
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^3 \).
|
||||||
data D2𝔸4 v =
|
data D2𝔸4 v =
|
||||||
D24 { _D24_v :: !v
|
D24 { _D24_v :: v
|
||||||
, _D24_dx, _D24_dy, _D24_dz, _D24_dw :: !( T v )
|
, _D24_dx, _D24_dy, _D24_dz, _D24_dw :: ( T v )
|
||||||
, _D24_dxdx, _D24_dxdy, _D24_dydy, _D24_dxdz
|
, _D24_dxdx, _D24_dxdy, _D24_dydy, _D24_dxdz
|
||||||
, _D24_dydz, _D24_dzdz, _D24_dxdw, _D24_dydw, _D24_dzdw, _D24_dwdw :: !( T v )
|
, _D24_dydz, _D24_dzdz, _D24_dxdw, _D24_dydw, _D24_dzdw, _D24_dwdw :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -182,14 +182,14 @@ data D2𝔸4 v =
|
||||||
|
|
||||||
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^4 \).
|
-- | \( \mathbb{Z}[x, y, z, w]/(x, y, z, w)^4 \).
|
||||||
data D3𝔸4 v =
|
data D3𝔸4 v =
|
||||||
D34 { _D34_v :: !v
|
D34 { _D34_v :: v
|
||||||
, _D34_dx, _D34_dy, _D34_dz, _D34_dw :: !( T v )
|
, _D34_dx, _D34_dy, _D34_dz, _D34_dw :: ( T v )
|
||||||
, _D34_dxdx, _D34_dxdy, _D34_dydy, _D34_dxdz, _D34_dydz, _D34_dzdz
|
, _D34_dxdx, _D34_dxdy, _D34_dydy, _D34_dxdz, _D34_dydz, _D34_dzdz
|
||||||
, _D34_dxdw, _D34_dydw, _D34_dzdw, _D34_dwdw :: !( T v )
|
, _D34_dxdw, _D34_dydw, _D34_dzdw, _D34_dwdw :: ( T v )
|
||||||
, _D34_dxdxdx, _D34_dxdxdy, _D34_dxdydy, _D34_dydydy,
|
, _D34_dxdxdx, _D34_dxdxdy, _D34_dxdydy, _D34_dydydy,
|
||||||
_D34_dxdxdz, _D34_dxdydz, _D34_dxdzdz, _D34_dydzdz, _D34_dydydz, _D34_dzdzdz,
|
_D34_dxdxdz, _D34_dxdydz, _D34_dxdzdz, _D34_dydzdz, _D34_dydydz, _D34_dzdzdz,
|
||||||
_D34_dxdxdw, _D34_dxdydw, _D34_dydydw, _D34_dxdzdw, _D34_dydzdw, _D34_dzdzdw,
|
_D34_dxdxdw, _D34_dxdydw, _D34_dydydw, _D34_dxdzdw, _D34_dydzdw, _D34_dzdzdw,
|
||||||
_D34_dxdwdw, _D34_dydwdw, _D34_dzdwdw, _D34_dwdwdw :: !( T v )
|
_D34_dxdwdw, _D34_dydwdw, _D34_dzdwdw, _D34_dwdwdw :: ( T v )
|
||||||
}
|
}
|
||||||
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
deriving stock ( Show, Eq, Functor, Foldable, Traversable, Generic, Generic1 )
|
||||||
deriving anyclass NFData
|
deriving anyclass NFData
|
||||||
|
|
@ -8,7 +8,7 @@ module Math.Bezier.Cubic
|
||||||
, bezier, bezier', bezier'', bezier'''
|
, bezier, bezier', bezier'', bezier'''
|
||||||
, derivative
|
, derivative
|
||||||
, curvature, squaredCurvature, signedCurvature
|
, curvature, squaredCurvature, signedCurvature
|
||||||
, subdivide
|
, subdivide, restrict
|
||||||
, ddist, closestPoint
|
, ddist, closestPoint
|
||||||
, drag, selfIntersectionParameters
|
, drag, selfIntersectionParameters
|
||||||
, extrema
|
, extrema
|
||||||
|
|
@ -180,6 +180,17 @@ subdivide ( Bezier {..} ) t = ( Bezier p0 q1 q2 pt, Bezier pt r1 r2 p3 )
|
||||||
pt = lerp @v t q2 r1
|
pt = lerp @v t q2 r1
|
||||||
{-# INLINEABLE subdivide #-}
|
{-# INLINEABLE subdivide #-}
|
||||||
|
|
||||||
|
-- | Restrict a cubic Bézier curve to a sub-interval, re-parametrising
|
||||||
|
-- to \( [0,1] \).
|
||||||
|
restrict :: forall v r p. ( Torsor v p, Ring.Field r, Module r v ) => Bezier p -> ( r , r ) -> Bezier p
|
||||||
|
restrict bez ( a, b ) = fst $ ( flip ( subdivide @v ) b' ) $ snd $ subdivide @v bez a
|
||||||
|
where
|
||||||
|
b' = ( b Ring.- a ) Ring./ ( Ring.fromInteger 1 Ring.- a )
|
||||||
|
-- TODO: this could be made more efficient.
|
||||||
|
-- See e.g. "https://math.stackexchange.com/questions/4172835/cubic-b%C3%A9zier-spline-multiple-split"
|
||||||
|
-- or the paper "On the numerical condition of Bernstein-Bézier subdivision process".
|
||||||
|
{-# INLINEABLE restrict #-}
|
||||||
|
|
||||||
-- | Polynomial coefficients of the derivative of the distance to a cubic Bézier curve.
|
-- | Polynomial coefficients of the derivative of the distance to a cubic Bézier curve.
|
||||||
ddist :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> [ r ]
|
ddist :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> [ r ]
|
||||||
ddist ( Bezier {..} ) c = [ a5, a4, a3, a2, a1, a0 ]
|
ddist ( Bezier {..} ) c = [ a5, a4, a3, a2, a1, a0 ]
|
||||||
|
|
@ -6,7 +6,7 @@ module Math.Bezier.Quadratic
|
||||||
( Bezier(..)
|
( Bezier(..)
|
||||||
, bezier, bezier', bezier''
|
, bezier, bezier', bezier''
|
||||||
, curvature, squaredCurvature, signedCurvature
|
, curvature, squaredCurvature, signedCurvature
|
||||||
, subdivide
|
, subdivide, restrict
|
||||||
, ddist, closestPoint
|
, ddist, closestPoint
|
||||||
, interpolate
|
, interpolate
|
||||||
, extrema
|
, extrema
|
||||||
|
|
@ -141,6 +141,17 @@ subdivide ( Bezier {..} ) t = ( Bezier p0 q1 pt, Bezier pt r1 p2 )
|
||||||
pt = lerp @v t q1 r1
|
pt = lerp @v t q1 r1
|
||||||
{-# INLINEABLE subdivide #-}
|
{-# INLINEABLE subdivide #-}
|
||||||
|
|
||||||
|
-- | Restrict a quadratic Bézier curve to a sub-interval, re-parametrising
|
||||||
|
-- to \( [0,1] \).
|
||||||
|
restrict :: forall v r p. ( Torsor v p, Ring.Field r, Module r v ) => Bezier p -> ( r , r ) -> Bezier p
|
||||||
|
restrict bez ( a, b ) = fst $ ( flip ( subdivide @v ) b' ) $ snd $ subdivide @v bez a
|
||||||
|
where
|
||||||
|
b' = ( b Ring.- a ) Ring./ ( Ring.fromInteger 1 Ring.- a )
|
||||||
|
-- TODO: this could be made more efficient.
|
||||||
|
-- See e.g. "https://math.stackexchange.com/questions/4172835/cubic-b%C3%A9zier-spline-multiple-split"
|
||||||
|
-- or the paper "On the numerical condition of Bernstein-Bézier subdivision process".
|
||||||
|
{-# INLINEABLE restrict #-}
|
||||||
|
|
||||||
-- | Polynomial coefficients of the derivative of the distance to a quadratic Bézier curve.
|
-- | Polynomial coefficients of the derivative of the distance to a quadratic Bézier curve.
|
||||||
ddist :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> [ r ]
|
ddist :: forall v r p. ( Torsor v p, Inner r v, RealFloat r ) => Bezier p -> p -> [ r ]
|
||||||
ddist ( Bezier {..} ) c = [ a3, a2, a1, a0 ]
|
ddist ( Bezier {..} ) c = [ a3, a2, a1, a0 ]
|
||||||
|
|
@ -148,6 +148,7 @@ import Math.Orientation
|
||||||
( Orientation(..), splineOrientation
|
( Orientation(..), splineOrientation
|
||||||
, between
|
, between
|
||||||
)
|
)
|
||||||
|
import qualified Math.Ring as Ring
|
||||||
import Math.Roots
|
import Math.Roots
|
||||||
|
|
||||||
import Debug.Utils
|
import Debug.Utils
|
||||||
|
|
@ -600,7 +601,7 @@ outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||||
|
|
||||||
( newtTrees, ( newtDunno, newtSols ) ) =
|
( newtTrees, ( newtDunno, newtSols ) ) =
|
||||||
intervalNewtonGS
|
intervalNewtonGS
|
||||||
NoPreconditioning --InverseMidJacobian
|
InverseMidJacobian
|
||||||
1e-7
|
1e-7
|
||||||
curvesI
|
curvesI
|
||||||
|
|
||||||
|
|
@ -634,7 +635,7 @@ outlineFunction rootAlgo ptParams toBrushParams brushFromParams = \ sp0 crv ->
|
||||||
logContents = unlines $ functionDataLines ++ treeLines
|
logContents = unlines $ functionDataLines ++ treeLines
|
||||||
|
|
||||||
in trace (unlines solLines) $
|
in trace (unlines solLines) $
|
||||||
logToFile cuspFindingMVar logContents `seq`
|
--logToFile cuspFindingMVar logContents `seq`
|
||||||
OutlineInfo
|
OutlineInfo
|
||||||
{ outlineFn = fwdBwd
|
{ outlineFn = fwdBwd
|
||||||
, outlineDefiniteCusps = map ( cuspCoords curves ) newtSols
|
, outlineDefiniteCusps = map ( cuspCoords curves ) newtSols
|
||||||
|
|
@ -1112,7 +1113,7 @@ solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strok
|
||||||
++ "}"
|
++ "}"
|
||||||
]
|
]
|
||||||
|
|
||||||
in logToFile rootSolvingMVar logContents `seq`
|
in --logToFile rootSolvingMVar logContents `seq`
|
||||||
( good, ds, dcdt )
|
( good, ds, dcdt )
|
||||||
|
|
||||||
(runSolveMethod, methodName) = case rootAlgo of
|
(runSolveMethod, methodName) = case rootAlgo of
|
||||||
|
|
@ -1206,7 +1207,7 @@ brushStrokeData co1 co2 path params brush =
|
||||||
splines :: Seq ( D k ( I i brushParams ) ( I i ( ℝ 1 ) `arr` I i ( ℝ 2 ) ) )
|
splines :: Seq ( D k ( I i brushParams ) ( I i ( ℝ 1 ) `arr` I i ( ℝ 2 ) ) )
|
||||||
!splines = getZipSeq $ traverse ( ZipSeq . splineCurveFns @k @i co2 ) dbrush_params
|
!splines = getZipSeq $ traverse ( ZipSeq . splineCurveFns @k @i co2 ) dbrush_params
|
||||||
dbrushes_t :: Seq ( I i ( ℝ 1 ) -> D k ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) ) )
|
dbrushes_t :: Seq ( I i ( ℝ 1 ) -> D k ( I i ( ℝ 2 ) ) ( I i ( ℝ 2 ) ) )
|
||||||
!dbrushes_t = force $ fmap ( uncurryD @k . chain @(I i Double) @k dparams_t ) splines
|
!dbrushes_t = force $ fmap ( uncurryD @k . chain @( I i Double ) @k dparams_t ) splines
|
||||||
-- This is the crucial use of the chain rule.
|
-- This is the crucial use of the chain rule.
|
||||||
|
|
||||||
in fmap ( mkStrokeDatum dpath_t ) dbrushes_t
|
in fmap ( mkStrokeDatum dpath_t ) dbrushes_t
|
||||||
|
|
@ -1274,6 +1275,115 @@ gaussSeidel
|
||||||
return ( ( 𝕀 ( ℝ1 x1'_lo ) ( ℝ1 x1'_hi ), 𝕀 ( ℝ1 x2'_lo ) ( ℝ1 x2'_hi ) )
|
return ( ( 𝕀 ( ℝ1 x1'_lo ) ( ℝ1 x1'_hi ), 𝕀 ( ℝ1 x2'_lo ) ( ℝ1 x2'_hi ) )
|
||||||
, sub_x1 && sub_x2 )
|
, sub_x1 && sub_x2 )
|
||||||
|
|
||||||
|
{-
|
||||||
|
gaussSeidel2 :: Int
|
||||||
|
-> Double
|
||||||
|
-> Double
|
||||||
|
-> ( 𝕀ℝ 2, 𝕀ℝ 2 ) -- ^ columns of \( A \)
|
||||||
|
-> 𝕀ℝ 2 -- ^ \( B \)
|
||||||
|
-> ( 𝕀ℝ 1, 𝕀ℝ 1 ) -- ^ initial box \( X \)
|
||||||
|
-> [ ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool ) ]
|
||||||
|
gaussSeidel2 maxIters eps_abs eps_rel
|
||||||
|
( 𝕀 ( ℝ2 a11_lo a21_lo ) ( ℝ2 a11_hi a21_hi )
|
||||||
|
, 𝕀 ( ℝ2 a12_lo a22_lo ) ( ℝ2 a12_hi a22_hi ) )
|
||||||
|
( 𝕀 ( ℝ2 b1_lo b2_lo ) ( ℝ2 b1_hi b2_hi ) )
|
||||||
|
x0
|
||||||
|
= let !a11 = 𝕀 a11_lo a11_hi
|
||||||
|
!a12 = 𝕀 a12_lo a12_hi
|
||||||
|
!a21 = 𝕀 a21_lo a21_hi
|
||||||
|
!a22 = 𝕀 a22_lo a22_hi
|
||||||
|
!b1 = 𝕀 b1_lo b1_hi
|
||||||
|
!b2 = 𝕀 b2_lo b2_hi
|
||||||
|
|
||||||
|
-- See "Algorithm 2" in
|
||||||
|
-- "Using interval unions to solve linear systems of equations with uncertainties"
|
||||||
|
iter ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) ) = do
|
||||||
|
let
|
||||||
|
!x1 = 𝕀 x1_lo x1_hi
|
||||||
|
!x2 = 𝕀 x2_lo x2_hi
|
||||||
|
blah1 = do
|
||||||
|
let s = b1 - a12 * x2
|
||||||
|
let s1 = s `monus` ( a11 * x1 )
|
||||||
|
y1 <-
|
||||||
|
if not $ containsZero ( s1 - a11 * x1 )
|
||||||
|
then []
|
||||||
|
else
|
||||||
|
if containsZero s1 && containsZero a11
|
||||||
|
then [ ( x1, False ) ]
|
||||||
|
else do
|
||||||
|
x1'' <- s1 `extendedDivide` a11
|
||||||
|
x1'' `intersect` x1
|
||||||
|
|
||||||
|
let s2 = s `monus` ( a12 * x2 )
|
||||||
|
y2 <-
|
||||||
|
if not $ containsZero ( s2 - a11 * x1 )
|
||||||
|
then []
|
||||||
|
else
|
||||||
|
if containsZero s2 && containsZero a11
|
||||||
|
then [ ( x1, False ) ]
|
||||||
|
else do
|
||||||
|
x1'' <- s2 `extendedDivide` a12
|
||||||
|
x1'' `intersect` x1
|
||||||
|
return ( y1 `cart` y2 )
|
||||||
|
|
||||||
|
blah2 = do
|
||||||
|
let s = b2 - a21 * x1
|
||||||
|
let s1 = s `monus` ( a21 * x1 )
|
||||||
|
y1 <-
|
||||||
|
if not $ containsZero ( s1 - a22 * x2 )
|
||||||
|
then []
|
||||||
|
else
|
||||||
|
if containsZero s1 && containsZero a22
|
||||||
|
then [ ( x1, False ) ]
|
||||||
|
else do
|
||||||
|
x1'' <- s1 `extendedDivide` a21
|
||||||
|
x1'' `intersect` x1
|
||||||
|
|
||||||
|
let s2 = s `monus` ( a12 * x2 )
|
||||||
|
y2 <-
|
||||||
|
if not $ containsZero ( s2 - a22 * x2 )
|
||||||
|
then []
|
||||||
|
else
|
||||||
|
if containsZero s2 && containsZero a22
|
||||||
|
then [ ( x1, False ) ]
|
||||||
|
else do
|
||||||
|
x1'' <- s2 `extendedDivide` a22
|
||||||
|
x1'' `intersect` x1
|
||||||
|
return ( y1 `cart` y2 )
|
||||||
|
|
||||||
|
blah1 ++ blah2
|
||||||
|
|
||||||
|
go :: Int -> ( 𝕀ℝ 1, 𝕀ℝ 1 ) -> [ ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool ) ]
|
||||||
|
go !i x
|
||||||
|
= do { nxt@( x', sub ) <- iter x
|
||||||
|
; let dw_abs = maxWidth x - maxWidth x'
|
||||||
|
dw_rel = 1 - ( maxWidth x' / maxWidth x )
|
||||||
|
; if sub
|
||||||
|
|| i >= maxIters
|
||||||
|
|| dw_abs < eps_abs
|
||||||
|
|| dw_rel < eps_rel
|
||||||
|
then return nxt
|
||||||
|
else go ( i + 1 ) x'
|
||||||
|
}
|
||||||
|
|
||||||
|
in go 1 x0
|
||||||
|
where
|
||||||
|
maxWidth :: ( 𝕀ℝ 1, 𝕀ℝ 1 ) -> Double
|
||||||
|
maxWidth ( 𝕀 ( ℝ1 x1_lo ) ( ℝ1 x1_hi ), 𝕀 ( ℝ1 x2_lo ) ( ℝ1 x2_hi ) )
|
||||||
|
= max ( x1_hi - x1_lo ) ( x2_hi - x2_lo )
|
||||||
|
containsZero :: 𝕀 Double -> Bool
|
||||||
|
containsZero ( 𝕀 lo hi ) = lo <= 0 && hi >= 0
|
||||||
|
monus :: 𝕀 Double -> 𝕀 Double -> 𝕀 Double
|
||||||
|
monus ( 𝕀 lo1 hi1 ) ( 𝕀 lo2 hi2 )
|
||||||
|
| hi1 - lo1 >= hi2 - lo2
|
||||||
|
= 𝕀 ( lo1 - lo2 ) ( hi1 - hi2 )
|
||||||
|
| otherwise
|
||||||
|
= 𝕀 ( hi1 - hi2 ) ( lo1 - lo2 )
|
||||||
|
cart :: ( 𝕀 Double, Bool ) -> ( 𝕀 Double, Bool ) -> ( ( 𝕀ℝ 1, 𝕀ℝ 1 ), Bool )
|
||||||
|
cart ( 𝕀 lo1 hi1, sub1 ) ( 𝕀 lo2 hi2, sub2 ) =
|
||||||
|
( ( 𝕀 ( ℝ1 lo1 ) ( ℝ1 hi1 ), 𝕀 ( ℝ1 lo2 ) ( ℝ1 hi2 ) ), sub1 && sub2 )
|
||||||
|
-}
|
||||||
|
|
||||||
-- | Compute the intersection of two intervals.
|
-- | Compute the intersection of two intervals.
|
||||||
--
|
--
|
||||||
-- Returns whether the first interval is a strict subset of the second interval,
|
-- Returns whether the first interval is a strict subset of the second interval,
|
||||||
|
|
@ -1342,7 +1452,7 @@ data IntervalNewtonLeaf d
|
||||||
showIntervalNewtonTree :: Box -> IntervalNewtonTree Box -> Tree String
|
showIntervalNewtonTree :: Box -> IntervalNewtonTree Box -> Tree String
|
||||||
showIntervalNewtonTree cand (IntervalNewtonLeaf l) = Node (show cand ++ " " ++ showArea (boxArea cand) ++ " " ++ show l) []
|
showIntervalNewtonTree cand (IntervalNewtonLeaf l) = Node (show cand ++ " " ++ showArea (boxArea cand) ++ " " ++ show l) []
|
||||||
showIntervalNewtonTree cand (IntervalNewtonStep s ts)
|
showIntervalNewtonTree cand (IntervalNewtonStep s ts)
|
||||||
= Node (show cand ++ " " ++ showArea (boxArea cand) ++ " " ++ show s) $ map (\ (c,t) -> showIntervalNewtonTree c t) ts
|
= Node (show cand ++ " abc " ++ showArea (boxArea cand) ++ " " ++ show s) $ map (\ (c,t) -> showIntervalNewtonTree c t) ts
|
||||||
|
|
||||||
boxArea :: Box -> Double
|
boxArea :: Box -> Double
|
||||||
boxArea ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), _, 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
boxArea ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ), _, 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||||
|
|
@ -1383,96 +1493,152 @@ intervalNewtonGSFrom
|
||||||
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
-> ( [ ( Box, IntervalNewtonTree Box ) ], ( [ Box ], [ Box ] ) )
|
||||||
intervalNewtonGSFrom precondMethod minWidth eqs initBox =
|
intervalNewtonGSFrom precondMethod minWidth eqs initBox =
|
||||||
runWriter $
|
runWriter $
|
||||||
map ( initBox , ) <$> go initBox
|
map ( initBox , ) <$> evalStrokeDataAndGo initBox
|
||||||
|
|
||||||
where
|
where
|
||||||
|
|
||||||
recur f cands = do
|
recur :: ( cand -> Writer ( [ Box ], [ Box ] ) [ IntervalNewtonTree Box ] )
|
||||||
rest <- traverse ( \ c -> do { trees <- go c; return [ (c, tree) | tree <- trees ] } ) cands
|
-> ( [ ( cand, IntervalNewtonTree Box ) ] -> IntervalNewtonTree Box )
|
||||||
|
-> [ cand ]
|
||||||
|
-> Writer ( [Box], [Box] ) [ IntervalNewtonTree Box ]
|
||||||
|
recur r f cands = do
|
||||||
|
rest <- traverse ( \ c -> do { trees <- r c; return [ (c, tree) | tree <- trees ] } ) cands
|
||||||
return [ f $ concat rest ]
|
return [ f $ concat rest ]
|
||||||
|
|
||||||
go :: Box -- box to work on
|
evalStrokeDataAndGo :: Box -> Writer ( [Box], [Box] ) [ IntervalNewtonTree Box ]
|
||||||
|
evalStrokeDataAndGo box@( t, i, s ) = go ( box, ( eqs t `Seq.index` i ) s )
|
||||||
|
|
||||||
|
go :: ( Box, StrokeDatum 3 𝕀 ) -- box to work on
|
||||||
-> Writer ( [ Box ], [ Box ] )
|
-> Writer ( [ Box ], [ Box ] )
|
||||||
[ IntervalNewtonTree Box ]
|
[ IntervalNewtonTree Box ]
|
||||||
go cand@( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
go ( cand@( t@( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_hi ) )
|
||||||
, i
|
, i
|
||||||
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
, s@( 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_hi ) )
|
||||||
)
|
)
|
||||||
|
, sd@( StrokeDatum { ee = D22 _ ( T ee_t ) (T ee_s ) _ _ _
|
||||||
|
, 𝛿E𝛿sdcdt = D12 _ ( T ( T f_t ) ) ( T ( T f_s ) ) })
|
||||||
|
)
|
||||||
-- Box is small: stop processing it.
|
-- Box is small: stop processing it.
|
||||||
| t_hi - t_lo < minWidth && s_hi - s_lo < minWidth
|
| t_hi - t_lo < minWidth && s_hi - s_lo < minWidth
|
||||||
= do let res = TooSmall cand
|
= do let res = TooSmall cand
|
||||||
tell ( [ cand ], [] )
|
tell ( [ cand ], [] )
|
||||||
return [ IntervalNewtonLeaf res ]
|
return [ IntervalNewtonLeaf res ]
|
||||||
|
| -- Check the envelope equation interval contains zero.
|
||||||
| StrokeDatum { ee = D22 ee ( T _ee_t ) ( T _ee_s ) _ _ _
|
ee_potential_zero sd
|
||||||
, 𝛿E𝛿sdcdt = D12 ( T f ) ( T ( T f_t ) ) ( T ( T f_s ) ) }
|
-- Check the 𝛿E𝛿sdcdt interval contains zero.
|
||||||
<- ( eqs t `Seq.index` i ) s
|
, 𝛿E𝛿sdcdt_potential_zero sd
|
||||||
|
|
||||||
, StrokeDatum { ee = D22 _ee_mid _ _ _ _ _
|
, StrokeDatum { ee = D22 _ee_mid _ _ _ _ _
|
||||||
, 𝛿E𝛿sdcdt = D12 ( T f_mid ) ( T ( T _f_t_mid ) ) ( T ( T _f_s_mid ) ) }
|
, 𝛿E𝛿sdcdt = D12 ( T f_mid ) ( T ( T _f_t_mid ) ) ( T ( T _f_s_mid ) ) }
|
||||||
<- ( eqs i_t_mid `Seq.index` i ) i_s_mid
|
<- ( eqs i_t_mid `Seq.index` i ) i_s_mid
|
||||||
, let ee_potential_zero = inf ee <= ℝ1 0 && sup ee >= ℝ1 0
|
= let -- Interval Newton method: take one Gauss–Seidel step
|
||||||
𝛿E𝛿sdcdt_potential_zero = cmpℝ2 (<=) ( inf f ) ( ℝ2 0 0 ) && cmpℝ2 (>=) ( sup f ) ( ℝ2 0 0 )
|
-- for the equation f'(x) v = - f(x_mid),
|
||||||
= if | -- Check the envelope equation interval contains zero.
|
-- where f = 𝛿E/𝛿s * dc/dt
|
||||||
ee_potential_zero
|
!( a, b ) = precondition precondMethod
|
||||||
-- Check the 𝛿E𝛿sdcdt interval contains zero.
|
( midI f_t, midI f_s )
|
||||||
, 𝛿E𝛿sdcdt_potential_zero
|
( f_t, f_s ) ( neg f_mid )
|
||||||
-> let -- Interval Newton method: take one Gauss–Seidel step
|
--(a, b)
|
||||||
-- for the equation f'(x) v = - f(x_mid),
|
-- | 𝕀 (ℝ1 ee_lo) (ℝ1 ee_hi) <- ee_mid
|
||||||
-- where f = 𝛿E/𝛿s * dc/dt
|
-- , 𝕀 (ℝ1 ee_t_lo) (ℝ1 ee_t_hi) <- ee_t
|
||||||
!( a, b ) = precondition precondMethod
|
-- , 𝕀 (ℝ1 ee_s_lo) (ℝ1 ee_s_hi) <- ee_s
|
||||||
( midI f_t, midI f_s )
|
-- , 𝕀 (ℝ2 fx_lo fy_lo) (ℝ2 fx_hi fy_hi) <- f_mid
|
||||||
( f_t, f_s ) ( neg f_mid )
|
-- , 𝕀 (ℝ2 f_tx_lo f_ty_lo) (ℝ2 f_tx_hi f_ty_hi) <- f_t
|
||||||
--(a, b)
|
-- , 𝕀 (ℝ2 f_sx_lo f_sy_lo) (ℝ2 f_sx_hi f_sy_hi) <- f_s
|
||||||
-- | 𝕀 (ℝ1 ee_lo) (ℝ1 ee_hi) <- ee_mid
|
-- = ( ( 𝕀 (ℝ2 f_tx_lo ee_t_lo) (ℝ2 f_tx_hi ee_t_hi)
|
||||||
-- , 𝕀 (ℝ1 ee_t_lo) (ℝ1 ee_t_hi) <- ee_t
|
-- , 𝕀 (ℝ2 f_sx_lo ee_s_lo) (ℝ2 f_sx_hi ee_s_hi)
|
||||||
-- , 𝕀 (ℝ1 ee_s_lo) (ℝ1 ee_s_hi) <- ee_s
|
-- )
|
||||||
-- , 𝕀 (ℝ2 fx_lo fy_lo) (ℝ2 fx_hi fy_hi) <- f_mid
|
-- , neg $ 𝕀 (ℝ2 fx_lo ee_lo) (ℝ2 fx_hi ee_hi)
|
||||||
-- , 𝕀 (ℝ2 f_tx_lo f_ty_lo) (ℝ2 f_tx_hi f_ty_hi) <- f_t
|
-- )
|
||||||
-- , 𝕀 (ℝ2 f_sx_lo f_sy_lo) (ℝ2 f_sx_hi f_sy_hi) <- f_s
|
|
||||||
-- = ( ( 𝕀 (ℝ2 f_tx_lo ee_t_lo) (ℝ2 f_tx_hi ee_t_hi)
|
|
||||||
-- , 𝕀 (ℝ2 f_sx_lo ee_s_lo) (ℝ2 f_sx_hi ee_s_hi)
|
|
||||||
-- )
|
|
||||||
-- , neg $ 𝕀 (ℝ2 fx_lo ee_lo) (ℝ2 fx_hi ee_hi)
|
|
||||||
-- )
|
|
||||||
|
|
||||||
!gsGuesses = gaussSeidel a b
|
!gsGuesses = gaussSeidel a b
|
||||||
( coerce ( (-) @( 𝕀 Double ) ) t i_t_mid
|
( coerce ( (-) @( 𝕀 Double ) ) t i_t_mid
|
||||||
, coerce ( (-) @( 𝕀 Double ) ) s i_s_mid )
|
, coerce ( (-) @( 𝕀 Double ) ) s i_s_mid )
|
||||||
in if all ( smaller . fst ) gsGuesses
|
in if any ( smaller . fst ) gsGuesses
|
||||||
then
|
then
|
||||||
-- If the Gauss–Seidel step was a contraction, then the box
|
-- If the Gauss–Seidel step was a contraction, then the box
|
||||||
-- contains a unique solution (by the Banach fixed point theorem).
|
-- contains a unique solution (by the Banach fixed point theorem).
|
||||||
--
|
--
|
||||||
-- These boxes can thus be directly added to the solution set:
|
-- These boxes can thus be directly added to the solution set:
|
||||||
-- Newton's method is guaranteed to converge to the unique solution.
|
-- Newton's method is guaranteed to converge to the unique solution.
|
||||||
let !(done, todo) = bimap ( map ( mkGuess . fst ) ) ( map ( mkGuess . fst ) )
|
let !(done, todo) = bimap ( map ( mkGuess . fst ) ) ( map ( mkGuess . fst ) )
|
||||||
$ partition snd gsGuesses
|
$ partition snd gsGuesses
|
||||||
in do tell ([], done)
|
in do tell ([], done)
|
||||||
case todo of
|
case todo of
|
||||||
[] -> return [ IntervalNewtonLeaf $ NoSolution "GaussSeidel" cand ]
|
[] -> return [ IntervalNewtonLeaf $ NoSolution "GaussSeidel" cand ]
|
||||||
_ -> recur (IntervalNewtonStep (IntervalNewtonContraction done)) todo
|
_ -> recur evalStrokeDataAndGo ( IntervalNewtonStep ( IntervalNewtonContraction done ) )
|
||||||
else
|
todo
|
||||||
-- Gauss–Seidel failed to shrink the boxes.
|
else
|
||||||
-- Bisect along the widest dimension instead.
|
-- Gauss–Seidel failed to shrink the boxes, so bisect instead.
|
||||||
let (bisGuesses, whatBis)
|
-- We have to pick along which dimension to bisect:
|
||||||
| t_hi - t_lo > s_hi - s_lo
|
-- - if bisecting along a particular dimension discards one of
|
||||||
= ( [ ( 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_mid ), i, s )
|
-- the boxes, do that;
|
||||||
, ( 𝕀 ( ℝ1 t_mid ) ( ℝ1 t_hi ), i, s ) ]
|
-- - otherwise, bisect along the dimension j that maximises
|
||||||
, ("t", t_mid) )
|
-- width(x_j) * || J_j ||.
|
||||||
| otherwise
|
let l_t = 𝕀 ( ℝ1 t_lo ) ( ℝ1 t_mid )
|
||||||
= ( [ ( t, i, 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_mid ) )
|
r_t = 𝕀 ( ℝ1 t_mid ) ( ℝ1 t_hi )
|
||||||
, ( t, i, 𝕀 ( ℝ1 s_mid ) ( ℝ1 s_hi ) ) ]
|
d_s = 𝕀 ( ℝ1 s_lo ) ( ℝ1 s_mid )
|
||||||
, ("s", s_mid) )
|
u_s = 𝕀 ( ℝ1 s_mid ) ( ℝ1 s_hi )
|
||||||
in recur (IntervalNewtonStep (IntervalNewtonBisection whatBis)) bisGuesses
|
l = ( l_t, i, s )
|
||||||
|
r = ( r_t, i, s )
|
||||||
|
d = ( t, i, d_s )
|
||||||
|
u = ( t, i, u_s )
|
||||||
|
l_dat = ( eqs l_t `Seq.index` i ) s
|
||||||
|
r_dat = ( eqs r_t `Seq.index` i ) s
|
||||||
|
d_dat = ( eqs t `Seq.index` i ) d_s
|
||||||
|
u_dat = ( eqs t `Seq.index` i ) u_s
|
||||||
|
l_skip =
|
||||||
|
not ( ee_potential_zero l_dat )
|
||||||
|
|| not ( 𝛿E𝛿sdcdt_potential_zero l_dat )
|
||||||
|
r_skip =
|
||||||
|
not ( ee_potential_zero r_dat )
|
||||||
|
|| not ( 𝛿E𝛿sdcdt_potential_zero r_dat )
|
||||||
|
d_skip =
|
||||||
|
not ( ee_potential_zero d_dat )
|
||||||
|
|| not ( 𝛿E𝛿sdcdt_potential_zero d_dat )
|
||||||
|
u_skip =
|
||||||
|
not ( ee_potential_zero u_dat )
|
||||||
|
|| not ( 𝛿E𝛿sdcdt_potential_zero u_dat )
|
||||||
|
tJWidth = ( t_hi - t_lo ) * normVI3 ee_t f_t
|
||||||
|
sJWidth = ( s_hi - s_lo ) * normVI3 ee_s f_s
|
||||||
|
( bisGuesses, whatBis )
|
||||||
|
| l_skip && r_skip
|
||||||
|
= ( [], ( "lr", t_mid ) )
|
||||||
|
| d_skip && u_skip
|
||||||
|
= ( [], ( "du", s_mid ) )
|
||||||
|
| l_skip
|
||||||
|
= ( [ ( r, r_dat ) ], ( "r", t_mid ) )
|
||||||
|
| r_skip
|
||||||
|
= ( [ ( l, l_dat ) ], ( "l", t_mid ) )
|
||||||
|
| d_skip
|
||||||
|
= ( [ ( u, u_dat ) ], ( "u", s_mid ) )
|
||||||
|
| u_skip
|
||||||
|
= ( [ ( d, d_dat ) ], ( "d", s_mid ) )
|
||||||
|
| tJWidth >= sJWidth
|
||||||
|
-- t_hi - t_lo >= s_hi - s_lo
|
||||||
|
= ( [ ( l, l_dat ), ( r, r_dat ) ], ( "t", t_mid ) )
|
||||||
|
| otherwise
|
||||||
|
= ( [ ( d, d_dat ), ( u, u_dat ) ], ( "s", s_mid ) )
|
||||||
|
in recur go ( IntervalNewtonStep ( IntervalNewtonBisection whatBis ) . map (first fst) )
|
||||||
|
bisGuesses
|
||||||
|
|
||||||
-- Box doesn't contain a solution: discard it.
|
-- Box doesn't contain a solution: discard it.
|
||||||
| otherwise
|
| otherwise
|
||||||
-> return [ IntervalNewtonLeaf $ NoSolution (if ee_potential_zero then "dc/dt" else "ee") cand ]
|
= return [ IntervalNewtonLeaf $ NoSolution ( if ee_potential_zero sd then "dc/dt" else "ee" ) cand ]
|
||||||
where
|
where
|
||||||
midI :: 𝕀ℝ 2 -> 𝕀ℝ 2
|
midI :: 𝕀ℝ 2 -> 𝕀ℝ 2
|
||||||
midI ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
|
midI ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
|
||||||
singleton $ ℝ2 ( 0.5 * ( x_lo + x_hi ) ) ( 0.5 * ( y_lo + y_hi ) )
|
singleton $ ℝ2 ( 0.5 * ( x_lo + x_hi ) ) ( 0.5 * ( y_lo + y_hi ) )
|
||||||
|
--width :: 𝕀ℝ 1 -> Double
|
||||||
|
--width ( 𝕀 ( ℝ1 lo ) ( ℝ1 hi ) ) = hi - lo
|
||||||
|
--normI :: 𝕀ℝ 1 -> Double
|
||||||
|
--normI ( 𝕀 ( ℝ1 lo ) ( ℝ1 hi ) ) = sqrt $ sup $ ( 𝕀 lo hi ) Ring.^ 2
|
||||||
|
--normVI :: 𝕀ℝ 2 -> Double
|
||||||
|
--normVI ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) ) =
|
||||||
|
-- sqrt $ sup $ ( 𝕀 x_lo x_hi ) Ring.^ 2 + ( 𝕀 y_lo y_hi ) Ring.^ 2
|
||||||
|
normVI3 :: 𝕀ℝ 1 -> 𝕀ℝ 2 -> Double
|
||||||
|
normVI3 ( 𝕀 ( ℝ1 lo ) ( ℝ1 hi ) ) ( 𝕀 ( ℝ2 x_lo y_lo ) ( ℝ2 x_hi y_hi ) )
|
||||||
|
= sqrt $ max ( abs lo ) ( abs hi ) Ring.^ 2
|
||||||
|
+ max ( abs x_lo ) ( abs x_hi ) Ring.^ 2
|
||||||
|
+ max ( abs y_lo ) ( abs y_hi ) Ring.^ 2
|
||||||
t_mid = 0.5 * ( t_lo + t_hi )
|
t_mid = 0.5 * ( t_lo + t_hi )
|
||||||
s_mid = 0.5 * ( s_lo + s_hi )
|
s_mid = 0.5 * ( s_lo + s_hi )
|
||||||
i_t_mid = singleton ( ℝ1 t_mid )
|
i_t_mid = singleton ( ℝ1 t_mid )
|
||||||
|
|
@ -1490,6 +1656,16 @@ intervalNewtonGSFrom precondMethod minWidth eqs initBox =
|
||||||
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
!( 𝕀 y'_lo y'_hi ) = negate $ 𝕀 y_lo y_hi
|
||||||
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
in 𝕀 ( ℝ2 x'_lo y'_lo ) ( ℝ2 x'_hi y'_hi )
|
||||||
|
|
||||||
|
ee_potential_zero :: StrokeDatum 3 𝕀 -> Bool
|
||||||
|
ee_potential_zero dat =
|
||||||
|
inf ( _D22_v $ ee dat ) <= ℝ1 0
|
||||||
|
&& sup ( _D22_v $ ee dat ) >= ℝ1 0
|
||||||
|
𝛿E𝛿sdcdt_potential_zero :: StrokeDatum 3 𝕀 -> Bool
|
||||||
|
𝛿E𝛿sdcdt_potential_zero dat =
|
||||||
|
cmpℝ2 (<=) ( inf $ unT $ _D12_v $ 𝛿E𝛿sdcdt dat ) ( ℝ2 0 0 )
|
||||||
|
&& cmpℝ2 (>=) ( sup $ unT $ _D12_v $ 𝛿E𝛿sdcdt dat ) ( ℝ2 0 0 )
|
||||||
|
|
||||||
|
|
||||||
zero, one :: Double
|
zero, one :: Double
|
||||||
zero = 1e-6
|
zero = 1e-6
|
||||||
one = 1 - zero
|
one = 1 - zero
|
||||||
|
|
@ -332,3 +332,31 @@ evaluateQuadratic bez t =
|
||||||
maxs = fmap (Quadratic.bezier @( T Double ) sup_bez)
|
maxs = fmap (Quadratic.bezier @( T Double ) sup_bez)
|
||||||
$ inf t :| ( sup t : filter ( inside t ) ( Quadratic.extrema sup_bez ) )
|
$ inf t :| ( sup t : filter ( inside t ) ( Quadratic.extrema sup_bez ) )
|
||||||
in 𝕀 ( minimum mins ) ( maximum maxs )
|
in 𝕀 ( minimum mins ) ( maximum maxs )
|
||||||
|
|
||||||
|
{-
|
||||||
|
|
||||||
|
evaluateCubic :: Cubic.Bezier ( 𝕀 Double ) -> 𝕀 Double -> 𝕀 Double
|
||||||
|
evaluateCubic bez t =
|
||||||
|
-- assert (inf t >= 0 && sup t <= 1) "evaluateCubic: t ⊊ [0,1]" $ -- Requires t ⊆ [0,1]
|
||||||
|
let inf_bez = Cubic.restrict @( T Double ) ( fmap inf bez ) ( inf t, sup t )
|
||||||
|
sup_bez = Cubic.restrict @( T Double ) ( fmap sup bez ) ( inf t, sup t )
|
||||||
|
mins = fmap (Cubic.bezier @( T Double ) inf_bez)
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||||||
|
$ 0 :| ( 1 : Cubic.extrema inf_bez )
|
||||||
|
maxs = fmap (Cubic.bezier @( T Double ) sup_bez)
|
||||||
|
$ 0 :| ( 1 : Cubic.extrema sup_bez )
|
||||||
|
in 𝕀 ( minimum mins ) ( maximum maxs )
|
||||||
|
|
||||||
|
-- | Evaluate a quadratic Bézier curve, when both the coefficients and the
|
||||||
|
-- parameter are intervals.
|
||||||
|
evaluateQuadratic :: Quadratic.Bezier ( 𝕀 Double ) -> 𝕀 Double -> 𝕀 Double
|
||||||
|
evaluateQuadratic bez t =
|
||||||
|
-- assert (inf t >= 0 && sup t <= 1) "evaluateCubic: t ⊊ [0,1]" $ -- Requires t ⊆ [0,1]
|
||||||
|
let inf_bez = Quadratic.restrict @( T Double ) ( fmap inf bez ) ( inf t, sup t )
|
||||||
|
sup_bez = Quadratic.restrict @( T Double ) ( fmap sup bez ) ( inf t, sup t )
|
||||||
|
mins = fmap (Quadratic.bezier @( T Double ) inf_bez)
|
||||||
|
$ 0 :| ( 1 : Quadratic.extrema inf_bez )
|
||||||
|
maxs = fmap (Quadratic.bezier @( T Double ) sup_bez)
|
||||||
|
$ 0 :| ( 1 : Quadratic.extrema sup_bez )
|
||||||
|
in 𝕀 ( minimum mins ) ( maximum maxs )
|
||||||
|
|
||||||
|
-}
|
||||||
|
|
@ -120,19 +120,7 @@ instance Prelude.Fractional ( 𝕀 Double ) where
|
||||||
| otherwise
|
| otherwise
|
||||||
= error "BAD interval recip; should use extendedRecip instead"
|
= error "BAD interval recip; should use extendedRecip instead"
|
||||||
-- #endif
|
-- #endif
|
||||||
𝕀 x_lo x_hi / 𝕀 y_lo y_hi
|
p / q = p * recip q
|
||||||
-- #ifdef ASSERTS
|
|
||||||
| y_lo == 0
|
|
||||||
= 𝕀 ( fst $ divI x_lo y_hi ) ( 1 / 0 )
|
|
||||||
| y_hi == 0
|
|
||||||
= 𝕀 ( -1 / 0 ) ( snd $ divI x_hi y_lo )
|
|
||||||
| y_lo > 0 || y_hi < 0
|
|
||||||
-- #endif
|
|
||||||
= 𝕀 ( fst $ divI x_lo y_hi ) ( snd $ divI x_hi y_lo )
|
|
||||||
-- #ifdef ASSERTS
|
|
||||||
| otherwise
|
|
||||||
= error "BAD interval division; should use extendedRecip instead"
|
|
||||||
-- #endif
|
|
||||||
|
|
||||||
instance Floating ( 𝕀 Double ) where
|
instance Floating ( 𝕀 Double ) where
|
||||||
sqrt = withHW Prelude.sqrt
|
sqrt = withHW Prelude.sqrt
|
||||||
|
|
@ -158,7 +158,7 @@ runApplication application = do
|
||||||
{ strokeName = "Stroke 1"
|
{ strokeName = "Stroke 1"
|
||||||
, strokeVisible = True
|
, strokeVisible = True
|
||||||
, strokeUnique = strokeUnique
|
, strokeUnique = strokeUnique
|
||||||
, strokeBrush = Just Asset.Brushes.tearDrop
|
, strokeBrush = Just Asset.Brushes.ellipse --tearDrop
|
||||||
, strokeSpline =
|
, strokeSpline =
|
||||||
-- Spline
|
-- Spline
|
||||||
-- { splineStart = mkPoint ( ℝ2 -20 -20 ) 5
|
-- { splineStart = mkPoint ( ℝ2 -20 -20 ) 5
|
||||||
|
|
@ -169,7 +169,7 @@ runApplication application = do
|
||||||
Spline
|
Spline
|
||||||
{ splineStart = mkPoint ( ℝ2 0 0 ) 10 25 0
|
{ splineStart = mkPoint ( ℝ2 0 0 ) 10 25 0
|
||||||
, splineCurves = OpenCurves $ Seq.fromList
|
, splineCurves = OpenCurves $ Seq.fromList
|
||||||
[ LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 100 0 ) 15 40 pi ), curveData = invalidateCache undefined }
|
[ LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 100 0 ) 15 40 (0.1 * pi) ), curveData = invalidateCache undefined }
|
||||||
--, LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 -10 10 ) 8 5 ( pi / 4 ) ), curveData = invalidateCache undefined }
|
--, LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 -10 10 ) 8 5 ( pi / 4 ) ), curveData = invalidateCache undefined }
|
||||||
--, LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 -10 -20 ) 10 7 ( pi / 2 ) ), curveData = invalidateCache undefined }
|
--, LineTo { curveEnd = NextPoint ( mkPoint ( ℝ2 -10 -20 ) 10 7 ( pi / 2 ) ), curveData = invalidateCache undefined }
|
||||||
]
|
]
|
||||||
|
|
@ -179,12 +179,12 @@ runApplication application = do
|
||||||
)
|
)
|
||||||
]
|
]
|
||||||
where
|
where
|
||||||
--mkPoint :: ℝ 2 -> Double -> Double -> Double -> PointData ( Record Asset.Brushes.EllipseBrushFields )
|
mkPoint :: ℝ 2 -> Double -> Double -> Double -> PointData ( Record Asset.Brushes.EllipseBrushFields )
|
||||||
--mkPoint pt a b phi = PointData pt Normal ( MkR $ ℝ3 a b phi )
|
mkPoint pt a b phi = PointData pt Normal ( MkR $ ℝ3 a b phi )
|
||||||
--mkPoint :: ℝ 2 -> Double -> PointData ( Record Asset.Brushes.CircleBrushFields )
|
--mkPoint :: ℝ 2 -> Double -> PointData ( Record Asset.Brushes.CircleBrushFields )
|
||||||
--mkPoint pt r = PointData pt Normal ( MkR $ ℝ1 r )
|
--mkPoint pt r = PointData pt Normal ( MkR $ ℝ1 r )
|
||||||
mkPoint :: ℝ 2 -> Double -> Double -> Double -> PointData ( Record Asset.Brushes.TearDropBrushFields )
|
--mkPoint :: ℝ 2 -> Double -> Double -> Double -> PointData ( Record Asset.Brushes.TearDropBrushFields )
|
||||||
mkPoint pt w h phi = PointData pt Normal ( MkR $ ℝ3 w h phi )
|
--mkPoint pt w h phi = PointData pt Normal ( MkR $ ℝ3 w h phi )
|
||||||
|
|
||||||
recomputeStrokesTVar <- STM.newTVarIO @Bool False
|
recomputeStrokesTVar <- STM.newTVarIO @Bool False
|
||||||
documentRenderTVar <- STM.newTVarIO @( ( Int32, Int32 ) -> Cairo.Render () ) ( const $ pure () )
|
documentRenderTVar <- STM.newTVarIO @( ( Int32, Int32 ) -> Cairo.Render () ) ( const $ pure () )
|
||||||
|
|
|
||||||
|
|
@ -139,12 +139,8 @@ instance ( Torsor ( T ( 𝕀ℝ ( Length ks ) ) ) ( 𝕀ℝ ( Length ks ) )
|
||||||
T ( 𝕀 ( MkR c_lo ) ( MkR c_hi ) )
|
T ( 𝕀 ( MkR c_lo ) ( MkR c_hi ) )
|
||||||
|
|
||||||
type instance RepDim ( Record ks ) = Length ks
|
type instance RepDim ( Record ks ) = Length ks
|
||||||
instance Representable r ( ℝ ( Length ks ) )
|
deriving newtype instance Representable r ( ℝ ( Length ks ) )
|
||||||
=> Representable r ( Record ks ) where
|
=> Representable r ( Record ks )
|
||||||
tabulate f = Record $ tabulate f
|
|
||||||
{-# INLINE tabulate #-}
|
|
||||||
index f (Record r) = index f r
|
|
||||||
{-# INLINE index #-}
|
|
||||||
|
|
||||||
type instance D k ( Record ks ) = D k ( ℝ ( Length ks ) )
|
type instance D k ( Record ks ) = D k ( ℝ ( Length ks ) )
|
||||||
deriving newtype instance HasChainRule Double 2 ( ℝ ( Length ks ) )
|
deriving newtype instance HasChainRule Double 2 ( ℝ ( Length ks ) )
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue