X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFunctionValues.hs;h=9d5232334bc5ad805f449faa3d51249644689b4e;hb=2f1d864660ff740773ea2c36ab79a837000f6452;hp=9fd3c7862516cc404220b66e172201685c18ea35;hpb=cd45e5bb439301e3610d986ece0346a2e7e5c36d;p=spline3.git diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index 9fd3c78..9d52323 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -1,10 +1,33 @@ -module FunctionValues +-- | The FunctionValues module contains the 'FunctionValues' type and +-- the functions used to manipulate it. +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 +-- cube. Each value of f can be accessed by the name of its +-- direction. data FunctionValues = FunctionValues { front :: Double, back :: Double, @@ -14,31 +37,110 @@ data FunctionValues = down :: Double, front_left :: Double, front_right :: Double, - front_top :: Double, front_down :: Double, + front_top :: Double, back_left :: Double, back_right :: Double, - back_top :: Double, back_down :: Double, - left_top :: Double, + back_top :: Double, left_down :: Double, - right_top :: Double, + left_top :: Double, right_down :: Double, - front_left_top :: Double, + right_top :: Double, front_left_down :: Double, - front_right_top :: Double, + front_left_top :: Double, front_right_down :: Double, - back_left_top :: Double, + front_right_top :: Double, back_left_down :: Double, - back_right_top :: Double, + back_left_top :: Double, back_right_down :: Double, + back_right_top :: Double, interior :: Double } deriving (Eq, Show) + +instance Arbitrary FunctionValues where + arbitrary = do + front' <- choose (min_double, max_double) + back' <- choose (min_double, max_double) + left' <- choose (min_double, max_double) + right' <- choose (min_double, max_double) + top' <- choose (min_double, max_double) + down' <- choose (min_double, max_double) + front_left' <- choose (min_double, max_double) + front_right' <- choose (min_double, max_double) + front_top' <- choose (min_double, max_double) + front_down' <- choose (min_double, max_double) + back_left' <- choose (min_double, max_double) + back_right' <- choose (min_double, max_double) + back_top' <- choose (min_double, max_double) + back_down' <- choose (min_double, max_double) + left_top' <- choose (min_double, max_double) + left_down' <- choose (min_double, max_double) + right_top' <- choose (min_double, max_double) + right_down' <- choose (min_double, max_double) + front_left_top' <- choose (min_double, max_double) + front_left_down' <- choose (min_double, max_double) + front_right_top' <- choose (min_double, max_double) + front_right_down' <- choose (min_double, max_double) + back_left_top' <- choose (min_double, max_double) + back_left_down' <- choose (min_double, max_double) + back_right_top' <- choose (min_double, max_double) + back_right_down' <- choose (min_double, max_double) + interior' <- choose (min_double, max_double) + + return empty_values { front = front', + back = back', + left = left', + right = right', + top = top', + down = down', + front_left = front_left', + front_right = front_right', + front_top = front_top', + front_down = front_down', + back_left = back_left', + back_right = back_right', + back_top = back_top', + back_down = back_down', + left_top = left_top', + left_down = left_down', + right_top = right_top', + right_down = right_down', + front_left_top = front_left_top', + front_left_down = front_left_down', + front_right_top = front_right_top', + front_right_down = front_right_down', + back_left_top = back_left_top', + back_left_down = back_left_down', + back_right_top = back_right_top', + back_right_down = back_right_down', + interior = interior' } + where + -- | We perform addition with the function values contained in a + -- FunctionValues object. If we choose random doubles near the machine + -- min/max, we risk overflowing or underflowing the 'Double'. This + -- places a reasonably safe limit on the maximum size of our generated + -- 'Double' members. + max_double :: Double + max_double = 10000.0 + + -- | See 'max_double'. + min_double :: Double + min_double = (-1) * max_double + + +-- | Return a 'FunctionValues' with a bunch of zeros for data points. empty_values :: FunctionValues 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 +-- function f in that 'Cardinal' direction. Note that 'Cardinal' can +-- be a composite type; eval is what performs the \"arithmetic\" on +-- 'Cardinal' directions. eval :: FunctionValues -> Cardinal -> Double eval f F = front f eval f B = back f @@ -73,11 +175,87 @@ eval f (Difference x y) = (eval f x) - (eval f y) eval f (Product x y) = (eval f x) * (eval f y) eval f (Quotient x y) = (eval f x) / (eval f y) -value_at :: [[[Double]]] -> Int -> Int -> Int -> Double -value_at values i j k = - ((values !! k) !! j) !! i +-- | 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 +-- 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) -make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues + | (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 :: 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, @@ -95,20 +273,24 @@ make_values values i j k = back_top = value_at values (i+1) j (k+1), left_down = value_at values i (j-1) (k-1), left_top = value_at values i (j-1) (k+1), - right_top = value_at values i (j+1) (k+1), right_down = value_at values i (j+1) (k-1), + right_top = value_at values i (j+1) (k+1), front_left_down = value_at values (i-1) (j-1) (k-1), front_left_top = value_at values (i-1) (j-1) (k+1), front_right_down = value_at values (i-1) (j+1) (k-1), front_right_top = value_at values (i-1) (j+1) (k+1), - back_left_down = value_at values (i-1) (j-1) (k-1), + back_left_down = value_at values (i+1) (j-1) (k-1), back_left_top = value_at values (i+1) (j-1) (k+1), back_right_down = value_at values (i+1) (j+1) (k-1), back_right_top = value_at values (i+1) (j+1) (k+1), interior = value_at values i j k } -rotate :: FunctionValues -> (Cardinal -> Cardinal) -> FunctionValues -rotate fv rotation = +-- | Takes a 'FunctionValues' and a function that transforms one +-- 'Cardinal' to another (called a rotation). Then it applies the +-- rotation to each element of the 'FunctionValues' object, and +-- returns the result. +rotate :: (Cardinal -> Cardinal) -> FunctionValues -> FunctionValues +rotate rotation fv = FunctionValues { front = eval fv (rotation F), back = eval fv (rotation B), left = eval fv (rotation L), @@ -136,3 +318,111 @@ rotate fv rotation = 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 ]