+{-# LANGUAGE BangPatterns #-}
+
-- | The FunctionValues module contains the 'FunctionValues' type and
-- the functions used to manipulate it.
+--
module FunctionValues (
- FunctionValues,
+ FunctionValues(..),
empty_values,
eval,
make_values,
rotate,
function_values_tests,
function_values_properties,
- value_at
- )
+ 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 Assertions (assertTrue)
-import Cardinal ( Cardinal(..), cwx, cwy, cwz )
-import Examples (trilinear)
-import Values (Values3D, dims, idx)
+import Prelude hiding ( LT )
+import Test.Tasty ( TestTree, testGroup )
+import Test.Tasty.HUnit ( Assertion, testCase )
+import Test.Tasty.QuickCheck ( Arbitrary( arbitrary ), choose, testProperty )
+
+import Assertions ( assertTrue )
+import Cardinal (
+ Cardinal(F, B, L, R, D, T, FL, FR, FD, FT, BL, BR, BD, BT, LD, LT, RD,
+ RT, FLD, FLT, FRD, FRT, BLD, BLT, BRD, BRT, I, Scalar, Sum,
+ Difference, Product, Quotient ),
+ 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
-- cube. Each value of f can be accessed by the name of its
-- direction.
+--
data FunctionValues =
- FunctionValues { front :: Double,
- back :: Double,
- left :: Double,
- right :: Double,
- top :: Double,
- down :: Double,
- front_left :: Double,
- front_right :: Double,
- front_down :: Double,
- front_top :: Double,
- back_left :: Double,
- back_right :: Double,
- back_down :: Double,
- back_top :: Double,
- left_down :: Double,
- left_top :: Double,
- right_down :: Double,
- right_top :: Double,
- front_left_down :: Double,
- front_left_top :: Double,
- front_right_down :: Double,
- front_right_top :: Double,
- back_left_down :: Double,
- back_left_top :: Double,
- back_right_down :: Double,
- back_right_top :: Double,
- interior :: Double }
+ FunctionValues { front :: !Double,
+ back :: !Double,
+ left :: !Double,
+ right :: !Double,
+ top :: !Double,
+ down :: !Double,
+ front_left :: !Double,
+ front_right :: !Double,
+ front_down :: !Double,
+ front_top :: !Double,
+ back_left :: !Double,
+ back_right :: !Double,
+ back_down :: !Double,
+ back_top :: !Double,
+ left_down :: !Double,
+ left_top :: !Double,
+ right_down :: !Double,
+ right_top :: !Double,
+ front_left_down :: !Double,
+ front_left_top :: !Double,
+ front_right_down :: !Double,
+ front_right_top :: !Double,
+ back_left_down :: !Double,
+ back_left_top :: !Double,
+ back_right_down :: !Double,
+ back_right_top :: !Double,
+ interior :: !Double }
deriving (Eq, Show)
empty_values =
FunctionValues 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+
-- | The eval function is where the magic happens for the
-- FunctionValues type. Given a 'Cardinal' direction and a
-- 'FunctionValues' object, eval will return the value of the
eval f (Product x y) = (eval f x) * (eval f y)
eval f (Quotient x y) = (eval f x) / (eval f y)
+
-- | 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 calculate one
-- 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
+value_at v3d !i !j !k
-- Put the most common case first!
- | (i >= 0) && (j >= 0) && (k >= 0) =
+ | (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).
- | (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)
+ -- 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 (dim_i == 1)
+ then
+ -- We're one-dimensional in our first coordinate, so just
+ -- return the data point that we do have. If we try to use
+ -- the formula from remark 7.3, we go into an infinite loop.
+ value_at v3d 0 j k
+ else
+ 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 (dim_j == 1)
+ then
+ -- We're one-dimensional in our second coordinate, so just
+ -- return the data point that we do have. If we try to use
+ -- the formula from remark 7.3, we go into an infinite loop.
+ value_at v3d i 0 k
+ else
+ 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 (dim_k == 1)
+ then
+ -- We're one-dimensional in our third coordinate, so just
+ -- return the data point that we do have. If we try to use
+ -- the formula from remark 7.3, we go into an infinite loop.
+ value_at v3d i j 0
+ else
+ 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))
+ where
+ (dim_i, dim_j, dim_k) = dims v3d
- | (i == xsize) && (j == -1) && (k >= 0) =
- 2*(value_at v3d (xsize - 1) j k) - (value_at v3d (xsize - 2) j k)
+ valid_i :: Int -> Bool
+ valid_i i' = (i' >= 0) && (i' < dim_i)
- -- 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)
+ valid_j :: Int -> Bool
+ valid_j j' = (j' >= 0) && (j' < dim_j)
- | (i == xsize) && (j == ysize) && (k == zsize) =
- 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2))
+ valid_k :: Int -> Bool
+ valid_k k' = (k' >= 0) && (k' < dim_k)
- | 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 :: Values3D -> Int -> Int -> Int -> FunctionValues
-make_values values i j k =
+make_values values !i !j !k =
empty_values { front = value_at values (i-1) j k,
back = value_at values (i+1) j k,
left = value_at values i (j-1) k,
back_right_top fvs == 15]
-function_values_tests :: Test.Framework.Test
+function_values_tests :: TestTree
function_values_tests =
- testGroup "FunctionValues Tests"
+ testGroup "FunctionValues tests"
[ testCase "test directions" test_directions ]
expr2 = top fv1
-function_values_properties :: Test.Framework.Test
+function_values_properties :: TestTree
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 ]
+ testGroup "FunctionValues properties" [
+ testProperty
+ "x rotation doesn't affect front"
+ prop_x_rotation_doesnt_affect_front,
+ testProperty
+ "x rotation doesn't affect back"
+ prop_x_rotation_doesnt_affect_back,
+ testProperty
+ "y rotation doesn't affect left"
+ prop_y_rotation_doesnt_affect_left,
+ testProperty
+ "y rotation doesn't affect right"
+ prop_y_rotation_doesnt_affect_right,
+ testProperty
+ "z rotation doesn't affect top"
+ prop_z_rotation_doesnt_affect_top,
+ testProperty
+ "z rotation doesn't affect down"
+ prop_z_rotation_doesnt_affect_down ]
projects / spline3.git / blobdiff