X-Git-Url: https://gitweb.michael.orlitzky.com/?p=spline3.git;a=blobdiff_plain;f=src%2FFunctionValues.hs;h=dc1f0d00f6fd7cc4a6bc36fa67b54efd5d2037d7;hp=895f9253a42506398c5594a3bd8b864baa32099a;hb=83ef0aaeae074756e4ee90d72d3e27e74e136061;hpb=7cb11540c2b74991a117ee0b30b878b4411acb67 diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index 895f925..dc1f0d0 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -1,46 +1,68 @@ +{-# LANGUAGE BangPatterns #-} + -- | 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.QuickCheck (Arbitrary(..), choose) +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 Values (Values3D, dims, idx) +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) @@ -120,6 +142,7 @@ 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 @@ -160,10 +183,14 @@ 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) + -- | 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: -- @@ -171,32 +198,83 @@ eval f (Quotient x y) = (eval f x) / (eval f y) -- 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 +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 - (xsize, ysize, zsize) = dims v3d + (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 = +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, @@ -258,3 +336,121 @@ rotate rotation fv = 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 ]