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https://gitlab.com/sheaf/metabrush.git
synced 2024-11-05 14:53:37 +00:00
Fix issues in withTangent & strictlyParallel function
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sheaf
parent
63b9703faf
commit
2a21980ffc
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@ -230,7 +230,8 @@ executable MetaBrush
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, MetaBrush.Time
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ghc-options:
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-threaded -rtsopts
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-threaded
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-rtsopts
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build-depends:
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metabrushes
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@ -283,3 +283,7 @@ benchmark cusps
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default-language:
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Haskell2010
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ghc-options:
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-threaded
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-rtsopts
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@ -56,8 +56,7 @@ import Data.Proxy
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import Data.Semigroup
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( sconcat )
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import GHC.Exts
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( newMutVar#, runRW#, inline
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)
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( newMutVar#, runRW# )
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import GHC.STRef
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( STRef(..), readSTRef, writeSTRef )
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import GHC.Generics
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@ -145,8 +144,6 @@ import Math.Orientation
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import Math.Roots
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import Math.Root.Isolation
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--import Debug.Utils
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--------------------------------------------------------------------------------
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data Offset
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@ -278,8 +275,8 @@ computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams bru
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endPt :: ptData
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endPt = openCurveEnd lastCurve
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startTgtFwd, startTgtBwd, endTgtFwd, endTgtBwd :: T ( ℝ 2 )
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( ( _, startTgtFwd), ( _, startTgtBwd ) ) = outlineFn firstOutlineFn $ ℝ1 0
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( ( _, endTgtFwd ), ( _, endTgtBwd ) ) = outlineFn lastOutlineFn $ ℝ1 1
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( ( _, startTgtFwd), ( _, startTgtBwd ) ) = outlineFn firstOutlineFn $ ℝ1 1e-4
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( ( _, endTgtFwd ), ( _, endTgtBwd ) ) = outlineFn lastOutlineFn $ ℝ1 (1 - 1e-4)
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startBrush, endBrush :: SplinePts Closed
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startBrush = brushShape spt0
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endBrush = brushShape endPt
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@ -342,8 +339,8 @@ computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams bru
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endTgt = case prevCurves of
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Empty -> endTangent spt0 spt0 lastCurve
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_ :|> lastPrev -> endTangent spt0 ( openCurveEnd lastPrev ) lastCurve
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( ( _, startTgtFwd), ( _, startTgtBwd ) ) = outlineFn firstOutlineFn $ ℝ1 0
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( ( _, endTgtFwd ), ( _, endTgtBwd ) ) = outlineFn lastOutlineFn $ ℝ1 1
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( ( _, startTgtFwd), ( _, startTgtBwd ) ) = outlineFn firstOutlineFn $ ℝ1 1e-9
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( ( _, endTgtFwd ), ( _, endTgtBwd ) ) = outlineFn lastOutlineFn $ ℝ1 (1 - 1e-9)
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fwdStartCap, bwdStartCap :: SplinePts Open
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OutlineData ( fmap fst -> TwoSided fwdStartCap bwdStartCap ) _
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= snd . runWriter
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@ -368,7 +365,7 @@ computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams bru
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where
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outlineInfo :: ptData -> Curve Open crvData ptData -> OutlineInfo
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outlineInfo = inline ( outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams brush )
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outlineInfo = outlineFunction rootAlgo mbCuspOptions ptParams toBrushParams brush
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outlineFns :: Seq OutlineInfo
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outlineFns = go spt0 ( openCurves $ splineCurves ( adjustSplineType @Open spline ) )
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@ -407,8 +404,8 @@ computeStrokeOutline rootAlgo mbCuspOptions fitParams ptParams toBrushParams bru
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tgt, next_tgt, tgtFwd, next_tgtFwd, tgtBwd, next_tgtBwd :: T ( ℝ 2 )
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tgt = startTangent spt0 ptData curve
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next_tgt = endTangent spt0 ptData curve
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( ( _, tgtFwd ), ( _, tgtBwd ) ) = outlineFn fwdBwd $ ℝ1 0
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( ( _, next_tgtFwd ), ( _, next_tgtBwd ) ) = outlineFn fwdBwd $ ℝ1 1
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( ( _, tgtFwd ), ( _, tgtBwd ) ) = outlineFn fwdBwd $ ℝ1 1e-9
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( ( _, next_tgtFwd ), ( _, next_tgtBwd ) ) = outlineFn fwdBwd $ ℝ1 (1 - 1e-9)
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lift $ tellBrushJoin ( prevTgt, prev_tgtFwd, tgtBwd ) ptData ( tgt, tgtFwd, prev_tgtBwd )
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lift $ updateCurveData ( curveData curve ) fwdBwd
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put ( next_tgt, next_tgtFwd, next_tgtBwd )
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@ -857,7 +854,8 @@ withTangent tgt_wanted spline@( Spline { splineStart } )
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-- only allow well-defined query tangent vectors
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, not (badTangent tgt_wanted)
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= case runExcept . ( `runStateT` tgt_last ) $ ibifoldSpline go ( \ _ -> pure () ) $ adjustSplineType @Open spline of
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Left off -> off
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Left off ->
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off
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Right _ ->
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error $
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"withTangent: could not find any point with given tangent vector\n\
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@ -910,12 +908,12 @@ withTangent tgt_wanted spline@( Spline { splineStart } )
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let
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tgt1 :: T ( ℝ 2 )
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tgt1 = p1 --> p2
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in for_ ( convexCombination tgt0 tgt1 tgt_wanted ) \ t ->
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in for_ ( convexCombination tgt0 tgt1 tgt_wanted ) \ s ->
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throwE $
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Offset
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{ offsetIndex = i
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, offsetParameter = Just t
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, offset = T $ Quadratic.bezier @( T ( ℝ 2 ) ) ( Quadratic.Bezier {..} ) t
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, offsetParameter = Just s
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, offset = T $ Quadratic.bezier @( T ( ℝ 2 ) ) ( Quadratic.Bezier {..} ) s
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}
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handleSegment i p0 ( Bezier3To p1 p2 ( NextPoint p3 ) _ ) tgt0 =
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let
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@ -929,10 +927,10 @@ withTangent tgt_wanted spline@( Spline { splineStart } )
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c12 = tgt_wanted × tgt1
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c23 = tgt_wanted × tgt2
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correctTangentParam :: Double -> Maybe Double
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correctTangentParam t
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| t > -epsilon && t < 1 + epsilon
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, tgt_wanted ^.^ Cubic.bezier' bez t > epsilon
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= Just ( max 0 ( min 1 t ) )
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correctTangentParam s
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| s > -epsilon && s < 1 + epsilon
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, tgt_wanted ^.^ Cubic.bezier' bez s > epsilon
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= Just ( max 0 ( min 1 s ) )
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| otherwise
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= Nothing
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in
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@ -941,12 +939,12 @@ withTangent tgt_wanted spline@( Spline { splineStart } )
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mbParam = listToMaybe
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. mapMaybe correctTangentParam
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$ solveQuadratic c01 ( 2 * ( c12 - c01 ) ) ( c01 + c23 - 2 * c12 )
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in for_ mbParam \ t ->
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in for_ mbParam \ s ->
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throwE $
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Offset
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{ offsetIndex = i
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, offsetParameter = Just t
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, offset = T $ Cubic.bezier @( T ( ℝ 2 ) ) bez t
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, offsetParameter = Just s
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, offset = T $ Cubic.bezier @( T ( ℝ 2 ) ) bez s
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}
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--------------------------------------------------------------------------------
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@ -1101,7 +1099,7 @@ solveEnvelopeEquations :: RootSolvingAlgorithm
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-> ( Offset, Offset )
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-> Seq ( ℝ 1 -> StrokeDatum 2 () )
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-> ( ( ℝ 2, T ( ℝ 2 ) ), ( ℝ 2, T ( ℝ 2 ) ) )
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solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strokeData
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solveEnvelopeEquations rootAlgo ( ℝ1 _t ) path_t path'_t ( fwdOffset, bwdOffset ) strokeData
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= ( fwdSol, ( bwdPt, -1 *^ bwdTgt ) )
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where
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@ -1118,23 +1116,23 @@ solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strok
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go is0 =
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case sol desc strokeData is0 of
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( goodSoln, pt, tgt )
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| goodSoln && plausibleTangent tgt
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| goodSoln
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-> ( pt, tgt )
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| otherwise
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-> ( off • path_t, path'_t )
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plausibleTangent :: T ( ℝ 2 ) -> Bool
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plausibleTangent tgt = path'_t ^.^ tgt > 0
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sol :: String -> Seq ( ℝ 1 -> StrokeDatum 2 () ) -> Double -> ( Bool, ℝ 2, T ( ℝ 2 ) )
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sol _desc f is0 =
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sol desc f is0 =
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let ( solRes, _solSteps ) = runSolveMethod ( eqn f ) is0
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( good, is ) =
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case solRes of
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Nothing -> ( False, is0 )
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Just is1 -> ( True , is1 )
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( ds, dcdt ) = finish f is
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Just is1 -> ( if desc == "fwd"
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then sgn >= 0
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else sgn <= 0
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, is1
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)
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( sgn, ds, dcdt ) = finish f is
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in ( good, ds, dcdt )
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runSolveMethod = case rootAlgo of
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@ -1143,18 +1141,21 @@ solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strok
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NewtonRaphson { maxIters, precision } ->
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newtonRaphson maxIters precision domain
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finish :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> Double -> ( ℝ 2, T ( ℝ 2 ) )
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finish :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> Double -> ( Double, ℝ 2, T ( ℝ 2 ) )
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finish fs is =
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let (i, s) = fromDomain is in
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case evalStrokeDatum fs is of -- TODO: a bit redundant to have to compute this again...
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StrokeDatum
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{ stroke
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, mbRotation
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, ee = D12 ( ℝ1 _ee ) _ ( T ( ℝ1 𝛿E𝛿s ) )
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, du = D12 u _ _
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, dv = D12 v _ _
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, 𝛿E𝛿sdcdt = D0 𝛿E𝛿sdcdt
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} ->
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-- The total derivative dc/dt is computed by dividing by ∂E/∂s,
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-- so check it isn't zero first. This corresponds to cusps in the envelope.
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let dcdt
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let unrot_dcdt
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| abs 𝛿E𝛿s < epsilon
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, let s' = if s >= 0.5 then s - 1e-6 else s + 1e-6
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= case ( fs `Seq.index` i ) ( ℝ1 s' ) of
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@ -1162,7 +1163,16 @@ solveEnvelopeEquations rootAlgo _t path_t path'_t ( fwdOffset, bwdOffset ) strok
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-> recip 𝛿E𝛿s' *^ 𝛿E𝛿sdcdt'
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| otherwise
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= recip 𝛿E𝛿s *^ 𝛿E𝛿sdcdt
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in ( stroke, dcdt )
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dcdt = case mbRotation of
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Nothing -> unrot_dcdt
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Just ( D21 θ _ _ ) ->
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let cosθ = cos θ
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sinθ = sin θ
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in rotate cosθ sinθ $ unrot_dcdt
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in ( T u ^.^ T v, stroke, dcdt )
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-- Compute the dot product of u and v (which are rotated versions of ∂c/∂t and ∂c/∂s).
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-- The sign of this quantity determines which side of the envelope
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-- we are on.
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evalStrokeDatum :: Seq ( ℝ 1 -> StrokeDatum 2 () ) -> ( Double -> StrokeDatum 2 () )
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evalStrokeDatum fs is =
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@ -129,11 +129,13 @@ instance Cross Double ( T ( ℝ 2 ) ) where
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-- | Compute whether two vectors point in the same direction,
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-- that is, whether each vector is a (strictly) positive multiple of the other.
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--
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-- Returns @False@ if either of the vectors is zero.
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-- Returns @False@ if either of the vectors is zero (or very close to zero).
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strictlyParallel :: T ( ℝ 2 ) -> T ( ℝ 2 ) -> Bool
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strictlyParallel u v
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= abs ( u × v ) < epsilon -- vectors are collinear
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&& u ^.^ v > epsilon -- vectors point in the same direction (parallel and not anti-parallel)
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= abs ( u × v ) < tol -- vectors are collinear
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&& u ^.^ v > tol -- vectors point in the same direction (parallel and not anti-parallel)
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where
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tol = norm u * norm v * epsilon
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-- | Finds whether the query vector @ u @ is a convex combination of the two provided vectors @ v0 @, @ v1 @.
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--
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