Begin updating everything to use Repa arrays (Values3D).

[spline3.git] / src / Grid.hs

diff --git a/src/Grid.hs b/src/Grid.hs
index 3ca66ca7ddbde546bec6080b55637306b5232e8f..1a01ab7eb60bba873e31e087b645eaf8d83a3689 100644 (file)
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,21 +4,35 @@
 module Grid
 where
 
-import Cube (Cube(Cube))
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+
+import Cube (Cube(Cube), find_containing_tetrahedra)
 import FunctionValues
+import Misc (flatten)
+import Point (Point)
+import Tetrahedron (polynomial)
+import ThreeDimensional (contains_point)
+import Values (Values3D, dims, empty3d)
 
 -- | 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
 --   another in each direction (x,y,z).
 data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
-                   function_values :: [[[Double]]] }
+                   function_values :: Values3D }
           deriving (Eq, Show)
 
 
+instance Arbitrary Grid where
+    arbitrary = do
+      (Positive h') <- arbitrary :: Gen (Positive Double)
+      fvs <- arbitrary :: Gen Values3D
+      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
+make_grid :: Double -> Values3D -> Grid
 make_grid grid_size values
     | grid_size <= 0 = error "grid size must be positive"
     | otherwise = Grid grid_size values
@@ -26,30 +40,26 @@ make_grid grid_size values
 
 -- | Creates an empty grid with grid size 1.
 empty_grid :: Grid
-empty_grid = Grid 1 [[[]]]
-
+empty_grid = Grid 1 empty3d
 
 
--- This is how we do a 'for' loop in Haskell.
--- No, seriously.
+-- | 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 == [[]] = [[[]]]
+    | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]]
     | 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
+      (xsize, ysize, zsize) = dims fvs
 
 
 -- | 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.
+--   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
@@ -59,3 +69,40 @@ cube_at g i j k
     | 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
+
+
+
+zoom :: Grid -> Int -> [[[Double]]]
+zoom g scale_factor
+    | xsize == 0 || ysize == 0 || zsize == 0 = []
+    | otherwise =
+        [[[f p | i <- [0..scaled_zsize],
+                 let i' = scale_dimension i,
+                 let j' = scale_dimension j,
+                 let k' = scale_dimension k,
+                 let p = (i', j', k') :: Point,
+                 let c = (find_containing_cubes g p) !! 0,
+                 let t = (find_containing_tetrahedra c p) !! 0,
+                 let f = polynomial t]
+                 | j <- [0..scaled_ysize]]
+                   | k <- [0..scaled_xsize]]
+  where
+    scale_dimension :: Int -> Double
+    scale_dimension x = (fromIntegral x) / (fromIntegral scale_factor)
+
+    fvs = function_values g
+    (xsize, ysize, zsize) = dims fvs
+    scaled_xsize = xsize * scale_factor
+    scaled_ysize = ysize * scale_factor
+    scaled_zsize = zsize * scale_factor
+