X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=647ec574f08b5338ce58042f9a54c9d3fcec3ff8;hb=3f0b6b7faecc561af0b7312a11c73a44a1b416f6;hp=7325d2b5b0968f5860834e21b809e9b67995dba8;hpb=c4701eee43e313f634d3d76faee681ff28d76b72;p=spline3.git

diff --git a/src/Grid.hs b/src/Grid.hs
index 7325d2b..647ec57 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -1,24 +1,37 @@
 -- | 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
+module Grid (
+  cube_at,
+  grid_tests,
+  make_grid,
+  slow_tests,
+  zoom
+  )
 where
 
-import Data.Array (Array, array, (!))
 import qualified Data.Array.Repa as R
-import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+import Test.HUnit
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.HUnit (testCase)
+import Test.Framework.Providers.QuickCheck2 (testProperty)
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
 
-import Cube (Cube(Cube), find_containing_tetrahedron)
+import Assertions
+import Comparisons
+import Cube (Cube(Cube),
+             find_containing_tetrahedron,
+             tetrahedra,
+             tetrahedron)
+import Examples
 import FunctionValues
 import Point (Point)
 import ScaleFactor
-import Tetrahedron (polynomial)
+import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
+import ThreeDimensional
 import Values (Values3D, dims, empty3d, zoom_shape)
 
 
-type CubeGrid = Array (Int,Int,Int) Cube
-
-
 -- | 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
@@ -43,30 +56,6 @@ make_grid grid_size values
     | otherwise = Grid grid_size values
 
 
--- | Creates an empty grid with grid size 1.
-empty_grid :: Grid
-empty_grid = Grid 1 empty3d
-
-
--- | Returns a three-dimensional array of cubes centered on the grid
---   points of g with the appropriate 'FunctionValues'.
-cubes :: Grid -> CubeGrid
-cubes g
-  = array (lbounds, ubounds)
-           [ ((i,j,k), cube_ijk)
-                 | i <- [0..xmax],
-                   j <- [0..ymax],
-                   k <- [0..zmax],
-                   let cube_ijk = Cube (h g) i j k (make_values fvs i j k)]
-     where
-       xmax = xsize - 1
-       ymax = ysize - 1
-       zmax = zsize - 1
-       lbounds = (0, 0, 0)
-       ubounds = (xmax, ymax, zmax)
-       fvs = function_values g
-       (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
@@ -79,10 +68,13 @@ cube_at g i j k
     | j >= ysize = error "j >= ysize in cube_at"
     | k < 0      = error "k < 0 in cube_at"
     | k >= zsize = error "k >= zsize in cube_at"
-    | otherwise = (cubes g) ! (i,j,k)
-      where
+    | otherwise = Cube delta i j k fvs' tet_vol
+      where        
         fvs = function_values g
         (xsize, ysize, zsize) = dims fvs
+        fvs' = make_values fvs i j k
+        delta = h g
+        tet_vol = (1/24)*(delta^(3::Int))
 
 --   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.
@@ -95,8 +87,8 @@ calculate_containing_cube_coordinate g coord
     -- Don't use a cube on the boundary if we can help it. This
     -- returns cube #1 if we would have returned cube #0 and cube #1
     -- exists.
-    | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1
     | coord < offset = 0
+    | coord == offset && (xsize > 1 && ysize > 1 && zsize > 1) = 1
     | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1
     where
       (xsize, ysize, zsize) = dims (function_values g)
@@ -118,30 +110,293 @@ find_containing_cube g p =
 
 
 {-# INLINE zoom_lookup #-}
-zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double)
-zoom_lookup g scale_factor _ = zoom_result g scale_factor
+zoom_lookup :: Values3D -> ScaleFactor -> a -> (R.DIM3 -> Double)
+zoom_lookup v3d scale_factor _ =
+    zoom_result v3d scale_factor
 
 
 {-# INLINE zoom_result #-}
-zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double
-zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) =
+zoom_result :: Values3D -> ScaleFactor -> R.DIM3 -> Double
+zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
   f p
   where
-    i' = (fromIntegral i) / (fromIntegral sfx)
-    j' = (fromIntegral j) / (fromIntegral sfy)
-    k' = (fromIntegral k) / (fromIntegral sfz)
-    p  = (i', j', k') :: Point
-    c = find_containing_cube g p
-    t = find_containing_tetrahedron c p
+    g = make_grid 1 v3d
+    offset = (h g)/2
+    m' = (fromIntegral m) / (fromIntegral sfx) - offset
+    n' = (fromIntegral n) / (fromIntegral sfy) - offset
+    o' = (fromIntegral o) / (fromIntegral sfz) - offset
+    p  = (m', n', o') :: Point
+    cube = find_containing_cube g p
+    t = find_containing_tetrahedron cube p
     f = polynomial t
 
 
-zoom :: Grid -> ScaleFactor -> Values3D
-zoom g scale_factor
+zoom :: Values3D -> ScaleFactor -> Values3D
+zoom v3d scale_factor
     | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
     | otherwise =
-        R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor)
+        R.force $ R.unsafeTraverse v3d transExtent (zoom_lookup v3d scale_factor)
           where
-            arr = function_values g
-            (xsize, ysize, zsize) = dims arr
+            (xsize, ysize, zsize) = dims v3d
             transExtent = zoom_shape scale_factor
+
+
+
+-- | Check all coefficients of tetrahedron0 belonging to the cube
+--   centered on (1,1,1) with a grid constructed from the trilinear
+--   values. See example one in the paper.
+--
+--   We also verify that the four vertices on face0 of the cube are
+--   in the correct location.
+--
+trilinear_c0_t0_tests :: Test.Framework.Test
+trilinear_c0_t0_tests =
+  testGroup "trilinear c0 t0"
+    [testGroup "coefficients"
+      [testCase "c0030 is correct" test_trilinear_c0030,
+       testCase "c0003 is correct" test_trilinear_c0003,
+       testCase "c0021 is correct" test_trilinear_c0021,
+       testCase "c0012 is correct" test_trilinear_c0012,
+       testCase "c0120 is correct" test_trilinear_c0120,
+       testCase "c0102 is correct" test_trilinear_c0102,
+       testCase "c0111 is correct" test_trilinear_c0111,
+       testCase "c0210 is correct" test_trilinear_c0210,
+       testCase "c0201 is correct" test_trilinear_c0201,
+       testCase "c0300 is correct" test_trilinear_c0300,
+       testCase "c1020 is correct" test_trilinear_c1020,
+       testCase "c1002 is correct" test_trilinear_c1002,
+       testCase "c1011 is correct" test_trilinear_c1011,
+       testCase "c1110 is correct" test_trilinear_c1110,
+       testCase "c1101 is correct" test_trilinear_c1101,
+       testCase "c1200 is correct" test_trilinear_c1200,
+       testCase "c2010 is correct" test_trilinear_c2010,
+       testCase "c2001 is correct" test_trilinear_c2001,
+       testCase "c2100 is correct" test_trilinear_c2100,
+       testCase "c3000 is correct" test_trilinear_c3000],
+
+    testGroup "face0 vertices"
+      [testCase "v0 is correct" test_trilinear_f0_t0_v0,
+       testCase "v1 is correct" test_trilinear_f0_t0_v1,
+       testCase "v2 is correct" test_trilinear_f0_t0_v2,
+       testCase "v3 is correct" test_trilinear_f0_t0_v3]
+    ]
+  where
+    g = make_grid 1 trilinear
+    cube = cube_at g 1 1 1
+    t = tetrahedron cube 0
+
+    test_trilinear_c0030 :: Assertion
+    test_trilinear_c0030 =
+      assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+
+    test_trilinear_c0003 :: Assertion
+    test_trilinear_c0003 =
+      assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+
+    test_trilinear_c0021 :: Assertion
+    test_trilinear_c0021 =
+      assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+
+    test_trilinear_c0012 :: Assertion
+    test_trilinear_c0012 =
+      assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+
+    test_trilinear_c0120 :: Assertion
+    test_trilinear_c0120 =
+      assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+
+    test_trilinear_c0102 :: Assertion
+    test_trilinear_c0102 =
+      assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+
+    test_trilinear_c0111 :: Assertion
+    test_trilinear_c0111 =
+      assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+
+    test_trilinear_c0210 :: Assertion
+    test_trilinear_c0210 =
+      assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+
+    test_trilinear_c0201 :: Assertion
+    test_trilinear_c0201 =
+      assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+
+    test_trilinear_c0300 :: Assertion
+    test_trilinear_c0300 =
+      assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+
+    test_trilinear_c1020 :: Assertion
+    test_trilinear_c1020 =
+      assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+
+    test_trilinear_c1002 :: Assertion
+    test_trilinear_c1002 =
+      assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+
+    test_trilinear_c1011 :: Assertion
+    test_trilinear_c1011 =
+      assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+
+    test_trilinear_c1110 :: Assertion
+    test_trilinear_c1110 =
+      assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+
+    test_trilinear_c1101 :: Assertion
+    test_trilinear_c1101 =
+      assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+
+    test_trilinear_c1200 :: Assertion
+    test_trilinear_c1200 =
+      assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+
+    test_trilinear_c2010 :: Assertion
+    test_trilinear_c2010 =
+      assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+
+    test_trilinear_c2001 :: Assertion
+    test_trilinear_c2001 =
+      assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+
+    test_trilinear_c2100 :: Assertion
+    test_trilinear_c2100 =
+      assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+
+    test_trilinear_c3000 :: Assertion
+    test_trilinear_c3000 =
+      assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+
+    test_trilinear_f0_t0_v0 :: Assertion
+    test_trilinear_f0_t0_v0 =
+      assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+
+    test_trilinear_f0_t0_v1 :: Assertion
+    test_trilinear_f0_t0_v1 =
+      assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+
+    test_trilinear_f0_t0_v2 :: Assertion
+    test_trilinear_f0_t0_v2 =
+      assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+
+    test_trilinear_f0_t0_v3 :: Assertion
+    test_trilinear_f0_t0_v3 =
+      assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+
+
+test_trilinear_reproduced :: Assertion
+test_trilinear_reproduced =
+    assertTrue "trilinears are reproduced correctly" $
+             and [p (i', j', k') ~= value_at trilinear i j k
+                    | i <- [0..2],
+                      j <- [0..2],
+                      k <- [0..2],
+                      t <- tetrahedra c0,
+                      let p = polynomial t,
+                      let i' = fromIntegral i,
+                      let j' = fromIntegral j,
+                      let k' = fromIntegral k]
+    where
+      g = make_grid 1 trilinear
+      c0 = cube_at g 1 1 1
+
+
+test_zeros_reproduced :: Assertion
+test_zeros_reproduced =
+    assertTrue "the zero function is reproduced correctly" $
+             and [p (i', j', k') ~= value_at zeros i j k
+                    | i <- [0..2],
+                      j <- [0..2],
+                      k <- [0..2],
+                      let i' = fromIntegral i,
+                      let j' = fromIntegral j,
+                      let k' = fromIntegral k]
+    where
+      g = make_grid 1 zeros
+      c0 = cube_at g 1 1 1
+      t0 = tetrahedron c0 0
+      p = polynomial t0
+
+
+-- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
+test_trilinear9x9x9_reproduced :: Assertion
+test_trilinear9x9x9_reproduced =
+    assertTrue "trilinear 9x9x9 is reproduced correctly" $
+      and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
+            | i <- [0..8],
+              j <- [0..8],
+              k <- [0..8],
+              t <- tetrahedra c0,
+              let p = polynomial t,
+              let i' = (fromIntegral i) * 0.5,
+              let j' = (fromIntegral j) * 0.5,
+              let k' = (fromIntegral k) * 0.5]
+    where
+      g = make_grid 1 trilinear
+      c0 = cube_at g 1 1 1
+
+
+-- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
+--   However, the 'contains_point' test fails due to some numerical innacuracy.
+--   This bug should have been fixed by setting a positive tolerance level.
+--
+--   Example from before the fix:
+--
+--   b1 (tetrahedron c 20) (0, 17.5, 0.5)
+--   -0.0
+--
+test_tetrahedra_collision_sensitivity :: Assertion
+test_tetrahedra_collision_sensitivity =
+  assertTrue "tetrahedron collision tests isn't too sensitive" $
+             contains_point t20 p
+  where
+    g = make_grid 1 naturals_1d
+    cube = cube_at g 0 18 0
+    p = (0, 17.5, 0.5) :: Point
+    t20 = tetrahedron cube 20
+
+
+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 (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)
+
+    x <- choose (coordmin, xmax)
+    y <- choose (coordmin, ymax)
+    z <- choose (coordmin, zmax)
+
+    let idx_x = calculate_containing_cube_coordinate g x
+    let idx_y = calculate_containing_cube_coordinate g y
+    let idx_z = calculate_containing_cube_coordinate g z
+
+    return $
+      idx_x >= 0 &&
+      idx_x <= xsize - 1 &&
+      idx_y >= 0 &&
+      idx_y <= ysize - 1 &&
+      idx_z >= 0 &&
+      idx_z <= zsize - 1
+
+
+
+grid_tests :: Test.Framework.Test
+grid_tests =
+    testGroup "Grid Tests" [
+      trilinear_c0_t0_tests,
+      testCase "tetrahedra collision test isn't too sensitive"
+         test_tetrahedra_collision_sensitivity,
+      testCase "trilinear reproduced" test_trilinear_reproduced,
+      testCase "zeros reproduced" test_zeros_reproduced ]
+
+
+-- Do the slow tests last so we can stop paying attention.
+slow_tests :: Test.Framework.Test
+slow_tests =
+    testGroup "Slow Tests" [
+      testProperty "cube indices within bounds"
+                   prop_cube_indices_never_go_out_of_bounds,
+      testCase "trilinear9x9x9 reproduced" test_trilinear9x9x9_reproduced ]