import Point (Point(..), dot)
import Tetrahedron (Tetrahedron(..), barycenter, c, volume)
-data Cube = Cube { h :: !Double,
- i :: !Int,
+data Cube = Cube { i :: !Int,
j :: !Int,
k :: !Int,
fv :: !FunctionValues,
instance Arbitrary Cube where
arbitrary = do
- (Positive h') <- arbitrary :: Gen (Positive Double)
i' <- choose (coordmin, coordmax)
j' <- choose (coordmin, coordmax)
k' <- choose (coordmin, coordmax)
fv' <- arbitrary :: Gen FunctionValues
(Positive tet_vol) <- arbitrary :: Gen (Positive Double)
- return (Cube h' i' j' k' fv' tet_vol)
+ return (Cube i' j' k' fv' tet_vol)
where
-- The idea here is that, when cubed in the volume formula,
-- these numbers don't overflow 64 bits. This number is not
instance Show Cube where
show cube =
"Cube_" ++ subscript ++ "\n" ++
- " h: " ++ (show (h cube)) ++ "\n" ++
" Center: " ++ (show (center cube)) ++ "\n" ++
" xmin: " ++ (show (xmin cube)) ++ "\n" ++
" xmax: " ++ (show (xmax cube)) ++ "\n" ++
-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmin :: Cube -> Double
-xmin cube = (i' - 1/2)*delta
+xmin cube = (i' - 1/2)
where
i' = fromIntegral (i cube) :: Double
- delta = h cube
-- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmax :: Cube -> Double
-xmax cube = (i' + 1/2)*delta
+xmax cube = (i' + 1/2)
where
i' = fromIntegral (i cube) :: Double
- delta = h cube
-- | The front boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymin :: Cube -> Double
-ymin cube = (j' - 1/2)*delta
+ymin cube = (j' - 1/2)
where
j' = fromIntegral (j cube) :: Double
- delta = h cube
-- | The back boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymax :: Cube -> Double
-ymax cube = (j' + 1/2)*delta
+ymax cube = (j' + 1/2)
where
j' = fromIntegral (j cube) :: Double
- delta = h cube
-- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmin :: Cube -> Double
-zmin cube = (k' - 1/2)*delta
+zmin cube = (k' - 1/2)
where
k' = fromIntegral (k cube) :: Double
- delta = h cube
-- | The top boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmax :: Cube -> Double
-zmax cube = (k' + 1/2)*delta
+zmax cube = (k' + 1/2)
where
k' = fromIntegral (k cube) :: Double
- delta = h cube
-- | The center of Cube_ijk coincides with v_ijk at
--- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
+-- (i, j, k). See Sorokina and Zeilfelder, p. 76.
center :: Cube -> Point
center cube =
Point x y z
where
- delta = h cube
- i' = fromIntegral (i cube) :: Double
- j' = fromIntegral (j cube) :: Double
- k' = fromIntegral (k cube) :: Double
- x = delta * i'
- y = delta * j'
- z = delta * k'
+ x = fromIntegral (i cube) :: Double
+ y = fromIntegral (j cube) :: Double
+ z = fromIntegral (k cube) :: Double
-- Face stuff.
top_face :: Cube -> Face.Face
top_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point delta (-delta) delta )
v1' = cc + ( Point delta delta delta )
back_face :: Cube -> Face.Face
back_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point delta (-delta) (-delta) )
v1' = cc + ( Point delta delta (-delta) )
down_face :: Cube -> Face.Face
down_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point (-delta) (-delta) (-delta) )
v1' = cc + ( Point (-delta) delta (-delta) )
front_face :: Cube -> Face.Face
front_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point (-delta) (-delta) delta )
v1' = cc + ( Point (-delta) delta delta )
left_face :: Cube -> Face.Face
left_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point delta (-delta) delta )
v1' = cc + ( Point (-delta) (-delta) delta )
right_face :: Cube -> Face.Face
right_face cube = Face.Face v0' v1' v2' v3'
where
- delta = (1/2)*(h cube)
+ delta = 1/2
cc = center cube
v0' = cc + ( Point (-delta) delta delta)
v1' = cc + ( Point delta delta delta )
-- | In fact, since all of the tetrahedra are identical, we should
-- already know their volumes. There's 24 tetrahedra to a cube, so
--- we'd expect the volume of each one to be (1/24)*h^3.
+-- we'd expect the volume of each one to be 1/24.
prop_all_volumes_exact :: Cube -> Bool
prop_all_volumes_exact cube =
- and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
- where
- delta = h cube
+ and [volume t ~~= 1/24 | t <- tetrahedra cube]
-- | All tetrahedron should have their v0 located at the center of the
-- cube.
import Cardinal as X
import Comparisons as X
-import Cube as X hiding (h)
import Examples as X
import Face as X hiding (v0,v1,v2,v3)
import FunctionValues as X
{-# 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,
import Test.QuickCheck ((==>),
Arbitrary(..),
Gen,
- Positive(..),
Property,
choose)
import Assertions (assertAlmostEqual, assertTrue)
-- | 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
-- 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
-- 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 = 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
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
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] ]
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] ]
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
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)
projects / spline3.git / commitdiff