HALFEDGE: make 'indirectToDirect' a safe function

We had to add NoFace/NoEdge/NoVert constructors to our half-edge
data structures, because using "Maybe HeEdge a" as the result value
of 'indirectToDirect' causes an infinite recursion, since the whole
data structure (which is cyclic and infinite) has to be evaluated
in order to know which constructor to use.

Unfortunately this makes the code quite hard to read.

TODO: add pseudo-code

Graphics/HalfEdge.hs

@@ -24,9 +24,11 @@ module Graphics.HalfEdge (
 ) where
 
 import Algebra.Vector
+import Control.Applicative
+import Control.Monad
 import qualified Data.ByteString.Char8 as B
-import Data.Functor
 import qualified Data.IntMap.Lazy as Map
+import Data.Maybe
 import Parser.Meshparser
 import Safe
 
@@ -35,21 +37,21 @@ import Safe
 data HeVert a = HeVert {
     vcoord  :: a        -- the coordinates of the vertex
   , emedge  :: HeEdge a -- one of the half-edges emanating from the vertex
+} | NoVert
 
-}
 
 -- |The face data structure for the half-edge.
 data HeFace a = HeFace {
   bordedge :: HeEdge a -- one of the half-edges bordering the face
-}
+} | NoFace
 
 -- |The actual half-edge data structure.
 data HeEdge a = HeEdge {
-    startvert :: HeVert a         -- start-vertex of the half-edge
-  , oppedge   :: Maybe (HeEdge a) -- oppositely oriented adjacent half-edge
-  , edgeface  :: HeFace a         -- face the half-edge borders
-  , nextedge  :: HeEdge a         -- next half-edge around the face
-}
+    startvert :: HeVert a  -- start-vertex of the half-edge
+  , oppedge   :: HeEdge a  -- oppositely oriented adjacent half-edge
+  , edgeface  :: HeFace a  -- face the half-edge borders
+  , nextedge  :: HeEdge a  -- next half-edge around the face
+} | NoEdge
 
 -- This is a helper data structure of half-edge edges
 -- for tying the knots in 'indirectToDirect'.
@@ -132,8 +134,7 @@ indirectHeVerts hes' = go hes' Map.empty 0
 -- |Tie the knots!
 -- It is assumed that the list of points is indexed in order of their
 -- appearance in the obj mesh file.
--- TODO: make this function safe.
-indirectToDirect :: [a]                      -- ^ list of points
+indirectToDirect :: [a]                       -- ^ list of points
                  -> [IndirectHeEdge]
                  -> [IndirectHeFace]
                  -> Map.IntMap IndirectHeVert -- ^ assumed to start at index 1
@@ -142,22 +143,32 @@ indirectToDirect pts pe@(e:_) fs vertarr
   = thisEdge e
   where
     thisEdge (IndirectHeEdge ei sv _ fi off)
-      = HeEdge (thisVert (vertarr Map.! sv) sv)
-               (getOppEdge sv fi)
-               (thisFace (fs !! fi))
-               (thisEdge . (!!) pe $ (ei + off))
+      = case (fs `atMay` fi, pe `atMay` (ei + off), Map.lookup sv vertarr) of
+          (Just x, Just y, Just z) -> HeEdge (thisVert z sv)
+                                             (getOppEdge sv fi)
+                                             (thisFace x)
+                                             (thisEdge y)
+          _                        -> NoEdge
     thisFace (IndirectHeFace (_, vi:_))
-      = HeFace (thisEdge (pe !! vi))
+      = case pe `atMay` vi of
+          Just x  -> HeFace (thisEdge x)
+          Nothing -> NoFace
+    thisFace (IndirectHeFace _) = NoFace
     thisVert (IndirectHeVert eedg _) coordi
-      = HeVert (pts !! (coordi - 1))
-               (thisEdge (pe !! (eedg - 1)))
+      = case (pts `atMay` (coordi - 1), pe `atMay` (eedg - 1)) of
+          (Just x, Just y) -> HeVert x (thisEdge y)
+          _                -> NoVert
     getOppEdge sv fi
-      = (\x -> thisEdge (pe !! x))
-        <$>
-        (headMay
-          . filter (\x -> (/=) fi . indexf $ (pe !! x))
-          . edgelist
-          $ (vertarr Map.! sv))
+      = case join
+               $ headMay
+               . filter ((/=) fi . indexf)
+               . catMaybes
+               . fmap (pe `atMay`)
+               . edgelist
+               <$> Map.lookup sv vertarr of
+        Just x  -> thisEdge x
+        Nothing -> NoEdge
+indirectToDirect _ _ _ _ = NoEdge
 
 
 -- |Build the half-edge data structure from a list of points