make_values,
rotate,
function_values_tests,
+ function_values_properties,
value_at
)
where
import Test.HUnit
import Test.Framework (Test, testGroup)
import Test.Framework.Providers.HUnit (testCase)
+import Test.Framework.Providers.QuickCheck2 (testProperty)
import Test.QuickCheck (Arbitrary(..), choose)
import Assertions (assertTrue)
-import Cardinal ( Cardinal(..) )
+import Cardinal ( Cardinal(..), cwx, cwy, cwz )
import Examples (trilinear)
import Values (Values3D, dims, idx)
-- | Takes a three-dimensional list of 'Double' and a set of 3D
-- coordinates (i,j,k), and returns the value at (i,j,k) in the
--- supplied list. If there is no such value, we choose a nearby
--- point and use its value.
+-- supplied list. If there is no such value, we calculate one
+-- according to Sorokina and Zeilfelder, remark 7.3, p. 99.
+--
+-- We specifically do not consider values more than one unit away
+-- from our grid.
--
-- Examples:
--
-- 1.0
--
-- >>> value_at Examples.trilinear (-1) 0 0
--- 1.0
+-- 0.0
--
-- >>> value_at Examples.trilinear 0 0 4
-- 1.0
--
-- >>> value_at Examples.trilinear 1 3 0
--- 4.0
+-- 5.0
--
value_at :: Values3D -> Int -> Int -> Int -> Double
value_at v3d i j k
- | i < 0 = value_at v3d 0 j k
- | j < 0 = value_at v3d i 0 k
- | k < 0 = value_at v3d i j 0
- | xsize <= i = value_at v3d (xsize - 1) j k
- | ysize <= j = value_at v3d i (ysize - 1) k
- | zsize <= k = value_at v3d i j (zsize - 1)
- | otherwise = idx v3d i j k
+ -- Put the most common case first!
+ | (valid_i i) && (valid_j j) && (valid_k k) =
+ idx v3d i j k
+
+ -- The next three are from the first line in (7.3). Analogous cases
+ -- have been added where the indices are one-too-big. These are the
+ -- "one index is bad" cases.
+ | not (valid_i i) =
+ if (i == -1)
+ then
+ 2*(value_at v3d 0 j k) - (value_at v3d 1 j k)
+ else
+ 2*(value_at v3d (i-1) j k) - (value_at v3d (i-2) j k)
+
+ | not (valid_j j) =
+ if (j == -1)
+ then
+ 2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+ else
+ 2*(value_at v3d i (j-1) k) - (value_at v3d i (j-2) k)
+
+ | not (valid_k k) =
+ if (k == -1)
+ then
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+ else
+ 2*(value_at v3d i j (k-1)) - (value_at v3d i j (k-2))
+
+ | otherwise =
+ let istr = show i
+ jstr = show j
+ kstr = show k
+ coordstr = "(" ++ istr ++ "," ++ jstr ++ "," ++ kstr ++ ")"
+ in
+ error $ "value_at called outside of domain: " ++ coordstr
where
(xsize, ysize, zsize) = dims v3d
+ valid_i :: Int -> Bool
+ valid_i i' = (i' >= 0) && (i' < xsize)
+
+ valid_j :: Int -> Bool
+ valid_j j' = (j' >= 0) && (j' < ysize)
+
+ valid_k :: Int -> Bool
+ valid_k k' = (k' >= 0) && (k' < zsize)
+
+
-- | Given a three-dimensional list of 'Double' and a set of 3D
-- coordinates (i,j,k), constructs and returns the 'FunctionValues'
function_values_tests =
testGroup "FunctionValues Tests"
[ testCase "test directions" test_directions ]
+
+
+prop_x_rotation_doesnt_affect_front :: FunctionValues -> Bool
+prop_x_rotation_doesnt_affect_front fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwx fv0
+ expr1 = front fv0
+ expr2 = front fv1
+
+prop_x_rotation_doesnt_affect_back :: FunctionValues -> Bool
+prop_x_rotation_doesnt_affect_back fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwx fv0
+ expr1 = back fv0
+ expr2 = back fv1
+
+
+prop_y_rotation_doesnt_affect_left :: FunctionValues -> Bool
+prop_y_rotation_doesnt_affect_left fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwy fv0
+ expr1 = left fv0
+ expr2 = left fv1
+
+prop_y_rotation_doesnt_affect_right :: FunctionValues -> Bool
+prop_y_rotation_doesnt_affect_right fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwy fv0
+ expr1 = right fv0
+ expr2 = right fv1
+
+
+prop_z_rotation_doesnt_affect_down :: FunctionValues -> Bool
+prop_z_rotation_doesnt_affect_down fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwz fv0
+ expr1 = down fv0
+ expr2 = down fv1
+
+
+prop_z_rotation_doesnt_affect_top :: FunctionValues -> Bool
+prop_z_rotation_doesnt_affect_top fv0 =
+ expr1 == expr2
+ where
+ fv1 = rotate cwz fv0
+ expr1 = top fv0
+ expr2 = top fv1
+
+
+function_values_properties :: Test.Framework.Test
+function_values_properties =
+ let tp = testProperty
+ in
+ testGroup "FunctionValues Properties" [
+ tp "x rotation doesn't affect front" prop_x_rotation_doesnt_affect_front,
+ tp "x rotation doesn't affect back" prop_x_rotation_doesnt_affect_back,
+ tp "y rotation doesn't affect left" prop_y_rotation_doesnt_affect_left,
+ tp "y rotation doesn't affect right" prop_y_rotation_doesnt_affect_right,
+ tp "z rotation doesn't affect top" prop_z_rotation_doesnt_affect_top,
+ tp "z rotation doesn't affect down" prop_z_rotation_doesnt_affect_down ]