+{-# 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.
module Grid (
cube_at,
grid_tests,
- make_grid,
slow_tests,
zoom
)
where
import qualified Data.Array.Repa as R
-import Test.HUnit
+import Test.HUnit (Assertion, assertEqual)
import Test.Framework (Test, testGroup)
import Test.Framework.Providers.HUnit (testCase)
import Test.Framework.Providers.QuickCheck2 (testProperty)
Positive(..),
Property,
choose)
-import Assertions
-import Comparisons
+import Assertions (assertAlmostEqual, assertTrue)
+import Comparisons ((~=))
import Cube (Cube(Cube),
find_containing_tetrahedron,
tetrahedra,
tetrahedron)
-import Examples
-import FunctionValues
-import Point (Point)
-import ScaleFactor
-import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
-import ThreeDimensional
+import Examples (trilinear, trilinear9x9x9, zeros)
+import FunctionValues (make_values, value_at)
+import Point (Point(..))
+import ScaleFactor (ScaleFactor)
+import Tetrahedron (
+ Tetrahedron(v0,v1,v2,v3),
+ c,
+ polynomial,
+ )
import Values (Values3D, dims, empty3d, zoom_shape)
-- another in each direction (x,y,z).
data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
function_values :: Values3D }
- deriving (Eq, Show)
+ deriving (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 -> Values3D -> Grid
-make_grid grid_size values
- | grid_size <= 0 = error "grid size must be positive"
- | otherwise = Grid grid_size values
+ return $ Grid h' 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 throw an error.
+-- centered on that position. If there is no cube there, well, you
+-- shouldn't have done that. The omitted "otherwise" case actually
+-- does improve performance.
cube_at :: Grid -> Int -> Int -> Int -> Cube
-cube_at g i j k
- | i < 0 = error "i < 0 in cube_at"
- | i >= xsize = error "i >= xsize in cube_at"
- | j < 0 = error "j < 0 in cube_at"
- | 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 = 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))
+cube_at !g !i !j !k =
+ Cube delta 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))
+
-- 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.
-- Since our grid is rectangular, we can figure this out without having
-- to check every cube.
find_containing_cube :: Grid -> Point -> Cube
-find_containing_cube g p =
+find_containing_cube g (Point x y z) =
cube_at g i j k
where
- (x, y, z) = p
i = calculate_containing_cube_coordinate g x
j = calculate_containing_cube_coordinate g y
k = calculate_containing_cube_coordinate g z
zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
f p
where
- g = make_grid 1 v3d
+ g = 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
+ p = Point m' n' o'
cube = find_containing_cube g p
t = find_containing_tetrahedron cube p
f = polynomial t
zoom v3d scale_factor
| xsize == 0 || ysize == 0 || zsize == 0 = empty3d
| otherwise =
- R.force $ R.unsafeTraverse v3d transExtent f
+ R.compute $ R.unsafeTraverse v3d transExtent f
where
(xsize, ysize, zsize) = dims v3d
transExtent = zoom_shape scale_factor
testCase "v3 is correct" test_trilinear_f0_t0_v3]
]
where
- g = make_grid 1 trilinear
+ g = Grid 1 trilinear
cube = cube_at g 1 1 1
t = tetrahedron cube 0
test_trilinear_f0_t0_v0 :: Assertion
test_trilinear_f0_t0_v0 =
- assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+ assertEqual "v0 is correct" (v0 t) (Point 1 1 1)
test_trilinear_f0_t0_v1 :: Assertion
test_trilinear_f0_t0_v1 =
- assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+ assertEqual "v1 is correct" (v1 t) (Point 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)
+ assertEqual "v2 is correct" (v2 t) (Point 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)
+ assertEqual "v3 is correct" (v3 t) (Point 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
+ and [p (Point i' j' k') ~= value_at trilinear i j k
| i <- [0..2],
j <- [0..2],
k <- [0..2],
let j' = fromIntegral j,
let k' = fromIntegral k]
where
- g = make_grid 1 trilinear
+ g = Grid 1 trilinear
cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
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
+ and [p (Point i' j' k') ~= value_at zeros i j k
| i <- [0..2],
j <- [0..2],
k <- [0..2],
t0 <- tetrahedra c0,
let p = polynomial t0 ]
where
- g = make_grid 1 zeros
+ g = Grid 1 zeros
cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
test_trilinear9x9x9_reproduced :: Assertion
test_trilinear9x9x9_reproduced =
assertTrue "trilinear 9x9x9 is reproduced correctly" $
- and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
+ and [p (Point i' j' k') ~= value_at trilinear9x9x9 i j k
| i <- [0..8],
j <- [0..8],
k <- [0..8],
let j' = (fromIntegral j) * 0.5,
let k' = (fromIntegral k) * 0.5]
where
- g = make_grid 1 trilinear
+ g = 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 =
testGroup "Grid Tests" [
trilinear_c0_t0_tests,
p80_29_properties,
- testCase "tetrahedra collision test isn't too sensitive"
- test_tetrahedra_collision_sensitivity,
testProperty "cube indices within bounds"
prop_cube_indices_never_go_out_of_bounds ]
projects / spline3.git / blobdiff