fix issue with incorrect subdivision in fit

* was using `Max ( Arg t sq_dist )` instead of `Max ( Arg sq_dist t )`

app/Main.hs

@@ -215,8 +215,8 @@ main = do
   fitParametersTVar  <- STM.newTVarIO @FitParameters
     ( FitParameters
       { maxSubdiv  = 3
-      , nbSegments = 30
-      , dist_tol   = 5e-4
+      , nbSegments = 13
+      , dist_tol   = 5e-3
       , t_tol      = 1e-4
       , maxIters   = 100
       }

src/lib/Math/Bezier/Cubic/Fit.hs

@@ -134,7 +134,7 @@ fitSpline ( FitParameters {..} ) = go 0
         qs = [ fst $ curve ( dt * fromIntegral j ) | j <- [ 1 .. nbSegments - 1 ] ]
       in
         case fitPiece dist_tol t_tol maxIters p tp qs r tr of
-          ( bez, Max ( Arg t_split sq_d ) )
+          ( bez, Max ( Arg sq_d t_split ) )
             |  subdiv >= maxSubdiv
             || sq_d <= dist_tol ^ ( 2 :: Int )
             -> ( Seq.singleton bez, ( FitTangent p tp :<| Seq.fromList ( map FitPoint qs ) ) :|> FitTangent r tr )
@@ -150,7 +150,7 @@ fitSpline ( FitParameters {..} ) = go 0
 --   * ends at \( r \) with tangent \( \textrm{t}_r \),
 --   * best fits the intermediate sequence of points \( \left ( q_i \right )_{i=1}^n \).
 --
--- This function also returns \( \textrm{ArgMax}\ t_\textrm{max}\ d^2_\textrm{max}: \)
+-- This function also returns \( \textrm{ArgMax}\ d^2_\textrm{max}\ t_\textrm{max}: \)
 -- the parameter and squared distance of the worst-fitting point.
 -- It is guaranteed that all points to fit lie within the tubular neighbourhood
 -- of radius \( d_\textrm{max} \) of the fitted curve.
@@ -254,11 +254,11 @@ fitPiece dist_tol t_tol maxIters p tp qs r tr =
         let
           sq_dist :: Double
           sq_dist = quadrance @( Vector2D Double ) q ( Cubic.bezier @( Vector2D Double ) bez ti' )
-        modify' ( second ( <> Max ( Arg ti' sq_dist ) ) )
+        modify' ( second ( <> Max ( Arg sq_dist ti' ) ) )
         lift ( Unboxed.MVector.unsafeWrite ts i ti' )
 
       case argmax_sq_dist of
-        Max ( Arg _ max_sq_dist )
+        Max ( Arg max_sq_dist _ )
           |  count < maxIters
           && ( dts_changed || max_sq_dist > dist_tol ^ ( 2 :: Int ) )
           -> loop ts ( count + 1 )