X-Git-Url: https://gitweb.michael.orlitzky.com/?p=spline3.git;a=blobdiff_plain;f=src%2FFunctionValues.hs;h=dc1f0d00f6fd7cc4a6bc36fa67b54efd5d2037d7;hp=e9ff0647f413b3f530757725f3bab382ac33a730;hb=83ef0aaeae074756e4ee90d72d3e27e74e136061;hpb=6fb9ab6b6068870323e996da931fc04c7710e3e4 diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index e9ff064..dc1f0d0 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -1,44 +1,154 @@ -module FunctionValues +{-# LANGUAGE BangPatterns #-} + +-- | 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 Prelude hiding ( LT ) +import Test.Tasty ( TestTree, testGroup ) +import Test.Tasty.HUnit ( Assertion, testCase ) +import Test.Tasty.QuickCheck ( Arbitrary( arbitrary ), choose, testProperty ) -import Cardinal +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_top :: Double, - front_down :: Double, - back_left :: Double, - back_right :: Double, - back_top :: Double, - back_down :: Double, - left_top :: Double, - left_down :: Double, - right_top :: Double, - right_down :: Double, - front_left_top :: Double, - front_left_down :: Double, - front_right_top :: Double, - front_right_down :: Double, - back_left_top :: Double, - back_left_down :: Double, - back_right_top :: Double, - back_right_down :: 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) + +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 @@ -73,12 +183,98 @@ 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 -make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues -make_values values i j k = +-- | 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 +-- 5.0 +-- +value_at :: Values3D -> Int -> Int -> Int -> Double +value_at 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 (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 + + valid_i :: Int -> Bool + valid_i i' = (i' >= 0) && (i' < dim_i) + + valid_j :: Int -> Bool + valid_j j' = (j' >= 0) && (j' < dim_j) + + valid_k :: Int -> Bool + valid_k k' = (k' >= 0) && (k' < dim_k) + + + +-- | 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, left = value_at values i (j-1) k, @@ -95,14 +291,166 @@ 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 } + +-- | 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), + right = eval fv (rotation R), + down = eval fv (rotation D), + top = eval fv (rotation T), + front_left = eval fv (rotation FL), + front_right = eval fv (rotation FR), + front_down = eval fv (rotation FD), + front_top = eval fv (rotation FT), + back_left = eval fv (rotation BL), + back_right = eval fv (rotation BR), + back_down = eval fv (rotation BD), + back_top = eval fv (rotation BT), + left_down = eval fv (rotation LD), + left_top = eval fv (rotation LT), + right_down = eval fv (rotation RD), + right_top = eval fv (rotation RT), + front_left_down = eval fv (rotation FLD), + front_left_top = eval fv (rotation FLT), + front_right_down = eval fv (rotation FRD), + front_right_top = eval fv (rotation FRT), + back_left_down = eval fv (rotation BLD), + back_left_top = eval fv (rotation BLT), + 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 :: TestTree +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 :: TestTree +function_values_properties = + 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 ]