+-- supplied list. If there is no such value, we calculate one
+-- according to Sorokina and Zeilfelder, remark 7.3, p. 99.
+--
+-- We specifically do not consider values more than one unit away
+-- from our grid.
+--
+-- Examples:
+--
+-- >>> value_at Examples.trilinear 0 0 0
+-- 1.0
+--
+-- >>> value_at Examples.trilinear (-1) 0 0
+-- 0.0
+--
+-- >>> value_at Examples.trilinear 0 0 4
+-- 1.0
+--
+-- >>> value_at Examples.trilinear 1 3 0
+-- 4.0
+--
+value_at :: Values3D -> Int -> Int -> Int -> Double
+value_at v3d i j k
+ -- Put the most common case first!
+ | (i >= 0) && (j >= 0) && (k >= 0) =
+ idx v3d i j k
+
+ -- The next three are from the first line in (7.3).
+ | (i == -1) && (j >= 0) && (k >= 0) =
+ 2*(value_at v3d 0 j k) - (value_at v3d 1 j k)
+
+ | (i >= 0) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+
+ | (i >= 0) && (j >= 0) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ -- The next two are from the second line in (7.3).
+ | (i == -1) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+
+ | (i == -1) && (j == ysize) && (k >= 0) =
+ 2*(value_at v3d i (ysize - 1) k) - (value_at v3d i (ysize - 2) k)
+
+ -- The next two are from the third line in (7.3).
+ | (i == -1) && (j >= 0) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == -1) && (j >= 0) && (k == zsize) =
+ 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
+
+ -- Repeat the above (j and k) cases for i >= 0.
+ | (i >= 0) && (j == -1) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == xsize) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d (xsize - 1) j k) - (value_at v3d (xsize - 2) j k)
+
+ -- These two cases I made up.
+ | (i == -1) && (j == -1) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == xsize) && (j == ysize) && (k == zsize) =
+ 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
+
+ | otherwise =
+ let istr = show i
+ jstr = show j
+ kstr = show k
+ coordstr = "(" ++ istr ++ "," ++ jstr ++ "," ++ kstr ++ ")"
+ in
+ error $ "value_at called outside of domain: " ++ coordstr
+ where
+ (xsize, ysize, zsize) = dims v3d