-- 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,
)
where
-import Data.Array (Array, array, (!))
import qualified Data.Array.Repa as R
import Test.HUnit
import Test.Framework (Test, testGroup)
import Cube (Cube(Cube),
find_containing_tetrahedron,
tetrahedra,
- tetrahedron0,
- tetrahedron15)
+ tetrahedron)
import Examples
import FunctionValues
import Point (Point)
import ScaleFactor
-import Tetrahedron (c, polynomial, v0, v1, v2, v3)
+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
-- another in each direction (x,y,z).
data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO!
- function_values :: Values3D,
- cube_grid :: CubeGrid }
+ function_values :: Values3D }
deriving (Eq, Show)
make_grid :: Double -> Values3D -> Grid
make_grid grid_size values
| grid_size <= 0 = error "grid size must be positive"
- | otherwise = Grid grid_size values (cubes grid_size values)
-
-
--- | Returns a three-dimensional array of cubes centered on the grid
--- points (h*i, h*j, h*k) with the appropriate 'FunctionValues'.
-cubes :: Double -> Values3D -> CubeGrid
-cubes delta fvs
- = array (lbounds, ubounds)
- [ ((i,j,k), cube_ijk)
- | i <- [0..xmax],
- j <- [0..ymax],
- k <- [0..zmax],
- let tet_vol = (1/24)*(delta^(3::Int)),
- let cube_ijk =
- Cube delta i j k (make_values fvs i j k) tet_vol]
- where
- xmax = xsize - 1
- ymax = ysize - 1
- zmax = zsize - 1
- lbounds = (0, 0, 0)
- ubounds = (xmax, ymax, zmax)
- (xsize, ysize, zsize) = dims fvs
+ | otherwise = Grid grid_size values
+
-- | Takes a grid and a position as an argument and returns the cube
| 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_grid 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.
{-# 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
+ g = make_grid 1 v3d
offset = (h g)/2
- i' = (fromIntegral i) / (fromIntegral sfx) - offset
- j' = (fromIntegral j) / (fromIntegral sfy) - offset
- k' = (fromIntegral k) / (fromIntegral sfz) - offset
- p = (i', j', k') :: Point
+ 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.
where
g = make_grid 1 trilinear
cube = cube_at g 1 1 1
- t = tetrahedron0 cube
+ t = tetrahedron cube 0
test_trilinear_c0030 :: Assertion
test_trilinear_c0030 =
where
g = make_grid 1 zeros
c0 = cube_at g 1 1 1
- t0 = tetrahedron0 c0
+ t0 = tetrahedron c0 0
p = polynomial t0
--
-- Example from before the fix:
--
--- > b0 (tetrahedron15 c) p
--- -3.4694469519536365e-18
+-- 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 t15 p
+ contains_point t20 p
where
g = make_grid 1 naturals_1d
- cube = cube_at g 0 17 1
- p = (0, 16.75, 0.5) :: Point
- t15 = tetrahedron15 cube
+ 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
projects / spline3.git / blobdiff