Remove the 'h' parameter from the model entirely by defining h=1.

[spline3.git] / src / Grid.hs

diff --git a/src/Grid.hs b/src/Grid.hs
index 66275491fd5c58d64fd0db110c15702211862b1a..26f44251d4a5f08612317788afa223cb723a24e2 100644 (file)
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -1,7 +1,6 @@
 {-# LANGUAGE BangPatterns #-}
--- | 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.
+-- | The Grid module contains the Grid type, its tests, and the 'zoom'
+--   function used to build the interpolation.
 module Grid (
   cube_at,
   grid_tests,
@@ -18,7 +17,6 @@ import Test.Framework.Providers.QuickCheck2 (testProperty)
 import Test.QuickCheck ((==>),
                         Arbitrary(..),
                         Gen,
-                        Positive(..),
                         Property,
                         choose)
 import Assertions (assertAlmostEqual, assertTrue)
@@ -40,19 +38,18 @@ import Values (Values3D, dims, empty3d, zoom_shape)
 
 
 -- | 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 :: Values3D }
+--   positive number h, which we have defined to always be 1 for
+--   performance reasons (and simplicity). The function values are the
+--   values of the function at the grid points, which are distance h=1
+--   from one another in each direction (x,y,z).
+data Grid = Grid { function_values :: Values3D }
           deriving (Show)
 
 
 instance Arbitrary Grid where
     arbitrary = do
-      (Positive h') <- arbitrary :: Gen (Positive Double)
       fvs <- arbitrary :: Gen Values3D
-      return $ Grid h' fvs
+      return $ Grid fvs
 
 
 
@@ -62,19 +59,18 @@ instance Arbitrary Grid where
 --   does improve performance.
 cube_at :: Grid -> Int -> Int -> Int -> Cube
 cube_at !g !i !j !k =
-   Cube delta i j k fvs' tet_vol
+   Cube i j k fvs' tet_vol
    where
      fvs = function_values g
      fvs' = make_values fvs i j k
-     delta = h g
-     tet_vol = (1/24)*(delta^(3::Int))
+     tet_vol = 1/24
 
 
---   The first cube along any axis covers (-h/2, h/2). The second
---   covers (h/2, 3h/2).  The third, (3h/2, 5h/2), and so on.
+--   The first cube along any axis covers (-1/2, 1/2). The second
+--   covers (1/2, 3/2).  The third, (3/2, 5/2), and so on.
 --
---   We translate the (x,y,z) coordinates forward by 'h/2' so that the
---   first covers (0, h), the second covers (h, 2h), etc. This makes
+--   We translate the (x,y,z) coordinates forward by 1/2 so that the
+--   first covers (0, 1), the second covers (1, 2), etc. This makes
 --   it easy to figure out which cube contains the given point.
 calculate_containing_cube_coordinate :: Grid -> Double -> Int
 calculate_containing_cube_coordinate g coord
@@ -83,11 +79,10 @@ calculate_containing_cube_coordinate g coord
     -- exists.
     | coord < offset = 0
     | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 1
-    | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
+    | otherwise = (ceiling (coord + offset)) - 1
     where
       (xsize, ysize, zsize) = dims (function_values g)
-      cube_width = (h g)
-      offset = cube_width / 2
+      offset = 1/2
 
 
 -- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'.
@@ -111,8 +106,8 @@ zoom_result :: Values3D -> ScaleFactor -> R.DIM3 -> Double
 zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
   f p
   where
-    g = Grid 1 v3d
-    offset = (h g)/2
+    g = Grid v3d
+    offset = 1/2
     m' = (fromIntegral m) / (fromIntegral sfx) - offset
     n' = (fromIntegral n) / (fromIntegral sfy) - offset
     o' = (fromIntegral o) / (fromIntegral sfz) - offset
@@ -172,7 +167,7 @@ trilinear_c0_t0_tests =
        testCase "v3 is correct" test_trilinear_f0_t0_v3]
     ]
   where
-    g = Grid 1 trilinear
+    g = Grid trilinear
     cube = cube_at g 1 1 1
     t = tetrahedron cube 0
 
@@ -287,7 +282,7 @@ test_trilinear_reproduced =
                       let j' = fromIntegral j,
                       let k' = fromIntegral k]
     where
-      g = Grid 1 trilinear
+      g = Grid trilinear
       cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
@@ -305,7 +300,7 @@ test_zeros_reproduced =
                       t0 <- tetrahedra c0,
                       let p = polynomial t0 ]
     where
-      g = Grid 1 zeros
+      g = Grid zeros
       cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
 
 
@@ -323,7 +318,7 @@ test_trilinear9x9x9_reproduced =
               let j' = (fromIntegral j) * 0.5,
               let k' = (fromIntegral k) * 0.5]
     where
-      g = Grid 1 trilinear
+      g = Grid trilinear
       c0 = cube_at g 1 1 1
 
 
@@ -331,13 +326,12 @@ test_trilinear9x9x9_reproduced =
 prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
 prop_cube_indices_never_go_out_of_bounds g =
   do
-    let delta = Grid.h g
-    let coordmin = negate (delta/2)
+    let coordmin = negate (1/2)
 
     let (xsize, ysize, zsize) = dims $ function_values g
-    let xmax = delta*(fromIntegral xsize) - (delta/2)
-    let ymax = delta*(fromIntegral ysize) - (delta/2)
-    let zmax = delta*(fromIntegral zsize) - (delta/2)
+    let xmax = (fromIntegral xsize) - (1/2)
+    let ymax = (fromIntegral ysize) - (1/2)
+    let zmax = (fromIntegral zsize) - (1/2)
 
     x <- choose (coordmin, xmax)
     y <- choose (coordmin, ymax)