Fix all orphan instances.

[spline3.git] / src / Grid.hs

diff --git a/src/Grid.hs b/src/Grid.hs
index e67ac764022a82ab974593395482ec4d6cfa81fc..efa63418947c308e7bed8c25619dadbc8d9d0a8e 100644 (file)
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -1,13 +1,18 @@
 -- | The Grid module just contains the Grid type and two constructors
 --   for it. We hide the main Grid constructor because we don't want
 --   to allow instantiation of a grid with h <= 0.
-module Grid (empty_grid,
-             function_values,
-             Grid,
-             h,
-             make_grid)
+module Grid
 where
 
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
+import Cube (Cube(Cube))
+import FunctionValues
+import Misc (flatten)
+import Point (Point)
+import ThreeDimensional (contains_point)
+
+
 -- | Our problem is defined on a Grid. The grid size is given by the
 --   positive number h. The function values are the values of the
 --   function at the grid points, which are distance h from one
@@ -17,6 +22,13 @@ data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
           deriving (Eq, Show)
 
 
+instance Arbitrary Grid where
+    arbitrary = do
+      (Positive h') <- arbitrary :: Gen (Positive Double)
+      fvs <- arbitrary :: Gen [[[Double]]]
+      return (make_grid h' fvs)
+
+
 -- | The constructor that we want people to use. If we're passed a
 --   non-positive grid size, we throw an error.
 make_grid :: Double -> [[[Double]]] -> Grid
@@ -28,3 +40,44 @@ make_grid grid_size values
 -- | Creates an empty grid with grid size 1.
 empty_grid :: Grid
 empty_grid = Grid 1 [[[]]]
+
+
+-- | Returns a three-dimensional list of cubes centered on the grid
+--   points of g with the appropriate 'FunctionValues'.
+cubes :: Grid -> [[[Cube]]]
+cubes g
+    | fvs == [[[]]] = [[[]]]
+    | head fvs == [[]] = [[[]]]
+    | otherwise =
+        [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]]
+              | j <- [0..ysize]]
+              | k <- [0..zsize]]
+    where
+      fvs = function_values g
+      zsize = (length fvs) - 1
+      ysize = length (head fvs) - 1
+      xsize = length (head $ head fvs) - 1
+
+
+-- | Takes a grid and a position as an argument and returns the cube
+--   centered on that position. If there is no cube there (i.e. the
+--   position is outside of the grid), it will return 'Nothing'.
+cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube
+cube_at g i j k
+    | i < 0 = Nothing
+    | j < 0 = Nothing
+    | k < 0 = Nothing
+    | i >= length (cubes g) = Nothing
+    | j >= length ((cubes g) !! i) = Nothing
+    | k >= length (((cubes g) !! i) !! j) = Nothing
+    | otherwise = Just $ (((cubes g) !! i) !! j) !! k
+
+
+-- | Takes a 'Grid', and returns all 'Cube's belonging to it that
+--   contain the given 'Point'.
+find_containing_cubes :: Grid -> Point -> [Cube]
+find_containing_cubes g p =
+    filter contains_our_point all_cubes
+    where
+      all_cubes = flatten $ cubes g
+      contains_our_point = flip contains_point p