return list of traces

src/Diagrams/ThreeD/Shapes.hs

@@ -1,8 +1,6 @@
-{-# LANGUAGE TypeFamilies
-           , FlexibleContexts
-           , MultiParamTypeClasses
-           , ViewPatterns
-  #-}
+{-# LANGUAGE FlexibleContexts      #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE TypeFamilies          #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Diagrams.ThreeD.Shapes
@@ -20,17 +18,16 @@ module Diagrams.ThreeD.Shapes
        , sphere
        ) where
 
-import Prelude hiding (minimum)
-import Data.Semigroup
+import           Data.Semigroup
+import           Prelude
 
-import Data.AffineSpace
-import Data.Monoid.Inf (minimum)
-import Data.VectorSpace
+import           Data.AffineSpace
+import           Data.VectorSpace
 
-import Diagrams.Core
+import           Diagrams.Core
 
-import Diagrams.ThreeD.Types
-import Diagrams.Solve
+import           Diagrams.Solve
+import           Diagrams.ThreeD.Types
 
 data Ellipsoid = Ellipsoid T3
 
@@ -51,7 +48,7 @@ sphere = mkQD (Prim $ Ellipsoid mempty)
               mempty
               (Query sphereQuery)
   where sphereEnv v = 1 / magnitude v
-        sphereTrace p v = minimum (quadForm a b c)
+        sphereTrace p v = mkSortedList $ quadForm a b c
           where a = v <.> v
                 b = 2 *^ p' <.> v
                 c = p' <.> p' - 1

src/Diagrams/TwoD/Segment.hs

@@ -24,7 +24,6 @@ module Diagrams.TwoD.Segment where
 import           Control.Applicative     (liftA2)
 
 import           Data.AffineSpace
-import           Data.Monoid.Inf         hiding (minimum)
 import           Data.VectorSpace
 
 import           Diagrams.Core
@@ -38,6 +37,10 @@ import           Diagrams.TwoD.Types
 import           Diagrams.TwoD.Vector
 import           Diagrams.Util
 
+{- All instances of Traced should maintain the invariant that the list of
+   traces is sorted in increasing order.
+-}
+
 instance Traced (Segment Closed R2) where
   getTrace = getTrace . mkFixedSeg . (`at` origin)
 
@@ -73,8 +76,8 @@ instance Traced (FixedSegment R2) where
       t1     = (perp v0 <.> p) / det
     in
       if det == 0 || t0 < 0 || t0 > 1
-        then Infinity
-        else Finite t1
+        then mkSortedList []
+        else mkSortedList [t1]
 
 {- To do intersection of a line with a cubic Bezier, we first rotate
    and scale everything so that the line has parameters (origin, unitX);
@@ -100,7 +103,5 @@ instance Traced (FixedSegment R2) where
       ts = filter (liftA2 (&&) (>= 0) (<= 1)) (cubForm a b c d)
       xs = map (fst . unp2 . atParam bez') ts
     in
-      case xs of
-        [] -> Infinity
-        _  -> Finite (minimum xs)
+      mkSortedList xs