-- | The FunctionValues module contains the 'FunctionValues' type and
-- the functions used to manipulate it.
-module FunctionValues
+module FunctionValues (
+ FunctionValues,
+ empty_values,
+ eval,
+ make_values,
+ rotate,
+ function_values_tests,
+ function_values_properties,
+ value_at
+ )
where
import Prelude hiding (LT)
+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 Cardinal
+import Assertions (assertTrue)
+import Cardinal ( Cardinal(..), cwx, cwy, cwz )
+import Examples (trilinear)
+import Values (Values3D, dims, idx)
-- | The FunctionValues type represents the value of our function f at
-- the 27 points surrounding (and including) the center of a
-- | 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, zero is returned.
-value_at :: [[[Double]]] -> Int -> Int -> Int -> Double
-value_at values i j k
- | i < 0 = 0
- | j < 0 = 0
- | k < 0 = 0
- | length values <= k = 0
- | length (values !! k) <= j = 0
- | length ((values !! k) !! j) <= i = 0
- | otherwise = ((values !! k) !! j) !! i
+-- 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:
+--
+-- >>> value_at Examples.trilinear 0 0 0
+-- 1.0
+--
+-- >>> value_at Examples.trilinear (-1) 0 0
+-- 0.0
+--
+-- >>> value_at Examples.trilinear 0 0 4
+-- 1.0
+--
+-- >>> value_at Examples.trilinear 1 3 0
+-- 4.0
+--
+value_at :: Values3D -> Int -> Int -> Int -> Double
+value_at v3d i j k
+ -- Put the most common case first!
+ | (i >= 0) && (j >= 0) && (k >= 0) =
+ idx v3d i j k
+
+ -- The next three are from the first line in (7.3).
+ | (i == -1) && (j >= 0) && (k >= 0) =
+ 2*(value_at v3d 0 j k) - (value_at v3d 1 j k)
+
+ | (i >= 0) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+
+ | (i >= 0) && (j >= 0) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ -- The next two are from the second line in (7.3).
+ | (i == -1) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d i 0 k) - (value_at v3d i 1 k)
+
+ | (i == -1) && (j == ysize) && (k >= 0) =
+ 2*(value_at v3d i (ysize - 1) k) - (value_at v3d i (ysize - 2) k)
+
+ -- The next two are from the third line in (7.3).
+ | (i == -1) && (j >= 0) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == -1) && (j >= 0) && (k == zsize) =
+ 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
+
+ -- Repeat the above (j and k) cases for i >= 0.
+ | (i >= 0) && (j == -1) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == xsize) && (j == -1) && (k >= 0) =
+ 2*(value_at v3d (xsize - 1) j k) - (value_at v3d (xsize - 2) j k)
+
+ -- These two cases I made up.
+ | (i == -1) && (j == -1) && (k == -1) =
+ 2*(value_at v3d i j 0) - (value_at v3d i j 1)
+
+ | (i == xsize) && (j == ysize) && (k == zsize) =
+ 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 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
-- | Given a three-dimensional list of 'Double' and a set of 3D
-- coordinates (i,j,k), constructs and returns the 'FunctionValues'
-- object centered at (i,j,k)
-make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues
+make_values :: Values3D -> Int -> Int -> Int -> FunctionValues
make_values values i j k =
empty_values { front = value_at values (i-1) j k,
back = value_at values (i+1) j k,
back_right_down = eval fv (rotation BRD),
back_right_top = eval fv (rotation BRT),
interior = interior fv }
+
+
+
+-- | Ensure that the trilinear values wind up where we think they
+-- should.
+test_directions :: Assertion
+test_directions =
+ assertTrue "all direction functions work" (and equalities)
+ where
+ fvs = make_values trilinear 1 1 1
+ equalities = [ interior fvs == 4,
+ front fvs == 1,
+ back fvs == 7,
+ left fvs == 2,
+ right fvs == 6,
+ down fvs == 3,
+ top fvs == 5,
+ front_left fvs == 1,
+ front_right fvs == 1,
+ front_down fvs == 1,
+ front_top fvs == 1,
+ back_left fvs == 3,
+ back_right fvs == 11,
+ back_down fvs == 5,
+ back_top fvs == 9,
+ left_down fvs == 2,
+ left_top fvs == 2,
+ right_down fvs == 4,
+ right_top fvs == 8,
+ front_left_down fvs == 1,
+ front_left_top fvs == 1,
+ front_right_down fvs == 1,
+ front_right_top fvs == 1,
+ back_left_down fvs == 3,
+ back_left_top fvs == 3,
+ back_right_down fvs == 7,
+ back_right_top fvs == 15]
+
+
+function_values_tests :: Test.Framework.Test
+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 ]
projects / spline3.git / blobdiff