{-# 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,
- make_grid,
slow_tests,
zoom
)
where
import qualified Data.Array.Repa as R
+import qualified Data.Array.Repa.Operators.Traversal as R (unsafeTraverse)
import Test.HUnit (Assertion, assertEqual)
import Test.Framework (Test, testGroup)
import Test.Framework.Providers.HUnit (testCase)
import Test.QuickCheck ((==>),
Arbitrary(..),
Gen,
- Positive(..),
Property,
- choose)
+ choose,
+ vectorOf)
import Assertions (assertAlmostEqual, assertTrue)
import Comparisons ((~=))
import Cube (Cube(Cube),
find_containing_tetrahedron,
tetrahedra,
tetrahedron)
-import Examples (trilinear, trilinear9x9x9, zeros, naturals_1d)
+import Examples (trilinear, trilinear9x9x9, zeros)
import FunctionValues (make_values, value_at)
import Point (Point(..))
import ScaleFactor (ScaleFactor)
-import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
-import ThreeDimensional (ThreeDimensional(..))
+import Tetrahedron (
+ Tetrahedron(v0,v1,v2,v3),
+ c,
+ polynomial,
+ )
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 }
- deriving (Eq, Show)
+-- 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 (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
+ x_dim <- choose (1, 27)
+ y_dim <- choose (1, 27)
+ z_dim <- choose (1, 27)
+ elements <- vectorOf (x_dim * y_dim * z_dim) (arbitrary :: Gen Double)
+ let new_shape = (R.Z R.:. x_dim R.:. y_dim R.:. z_dim)
+ let fvs = R.fromListUnboxed new_shape elements
+ return $ Grid 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))
-
--- 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.
+cube_at !g !i !j !k =
+ Cube i j k fvs' tet_vol
+ where
+ fvs = function_values g
+ fvs' = make_values fvs i j k
+ tet_vol = 1/24
+
+
+-- 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
-- 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'.
zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
f p
where
- g = make_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
f = polynomial t
-zoom :: Values3D -> ScaleFactor -> Values3D
+--
+-- Instead of IO, we could get away with a generic monad 'm'
+-- here. However, /we/ only call this function from within IO.
+--
+zoom :: Values3D -> ScaleFactor -> IO Values3D
zoom v3d scale_factor
- | xsize == 0 || ysize == 0 || zsize == 0 = empty3d
+ | xsize == 0 || ysize == 0 || zsize == 0 = return empty3d
| otherwise =
- R.force $ R.unsafeTraverse v3d transExtent f
- where
- (xsize, ysize, zsize) = dims v3d
- transExtent = zoom_shape scale_factor
- f = zoom_lookup v3d scale_factor
+ R.computeUnboxedP $ R.unsafeTraverse v3d transExtent f
+ where
+ (xsize, ysize, zsize) = dims v3d
+ transExtent = zoom_shape scale_factor
+ f = zoom_lookup v3d scale_factor
-- | Check all coefficients of tetrahedron0 belonging to the cube
testCase "v3 is correct" test_trilinear_f0_t0_v3]
]
where
- g = make_grid 1 trilinear
+ g = Grid trilinear
cube = cube_at g 1 1 1
t = tetrahedron cube 0
let j' = fromIntegral j,
let k' = fromIntegral k]
where
- g = make_grid 1 trilinear
+ g = Grid trilinear
cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
t0 <- tetrahedra c0,
let p = polynomial t0 ]
where
- g = make_grid 1 zeros
+ g = Grid zeros
cs = [ cube_at g ci cj ck | ci <- [0..2], cj <- [0..2], ck <- [0..2] ]
let j' = (fromIntegral j) * 0.5,
let k' = (fromIntegral k) * 0.5]
where
- g = make_grid 1 trilinear
+ g = Grid 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 = Point 0 17.5 0.5
- 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 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)
-- in opposite directions, one of them has to have negative volume!
prop_c0120_identity :: Grid -> Property
prop_c0120_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 1 2 0 ~= (c t0 1 0 2 0 + c t10 1 0 0 2) / 2
where
fvs = function_values g
-- 'prop_c0120_identity'.
prop_c0111_identity :: Grid -> Property
prop_c0111_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 1 1 1 ~= (c t0 1 0 1 1 + c t10 1 0 1 1) / 2
where
fvs = function_values g
-- 'prop_c0120_identity'.
prop_c0201_identity :: Grid -> Property
prop_c0201_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t10 1 1 1 0) / 2
where
fvs = function_values g
-- 'prop_c0120_identity'.
prop_c0102_identity :: Grid -> Property
prop_c0102_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 1 0 2 ~= (c t0 1 0 0 2 + c t10 1 0 2 0) / 2
where
fvs = function_values g
-- 'prop_c0120_identity'.
prop_c0210_identity :: Grid -> Property
prop_c0210_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t10 1 1 0 1) / 2
where
fvs = function_values g
-- 'prop_c0120_identity'.
prop_c0300_identity :: Grid -> Property
prop_c0300_identity g =
- and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ xsize >= 3 && ysize >= 3 && zsize >= 3 ==>
c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t10 1 2 0 0) / 2
where
fvs = function_values 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