Convert the zoom function to use Values3D.

[spline3.git] / src / Grid.hs

diff --git a/src/Grid.hs b/src/Grid.hs
index 6d360e2c103d61cc6b41a9cc3873f52db756e169..3d636b53a780f465b515c6e45f8ee53b6e7f10ba 100644 (file)
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -4,21 +4,37 @@
 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, zoom_shape)
+
+import qualified Data.Array.Repa as R
 
 -- | 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
@@ -26,22 +42,65 @@ 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'.
+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
+
+
+zoom :: Grid -> Int -> Values3D
+zoom g scale_factor
+    | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+    | otherwise =
+        R.traverse arr transExtent (\_ -> newlookup)
+          where
+            fvs = function_values g
+            (xsize, ysize, zsize) = dims fvs
+            arr = fvs
+            transExtent = zoom_shape scale_factor
+            newlookup :: R.DIM3 -> Double
+            newlookup (R.Z R.:. i R.:. j R.:. k) =
+                f p
+                  where
+                    i' = fromIntegral i
+                    j' = fromIntegral j
+                    k' = fromIntegral k
+                    p = (i', j', k') :: Point
+                    c = head (find_containing_cubes g p)
+                    t = head (find_containing_tetrahedra c p)
+                    f = polynomial t