X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFunctionValues.hs;h=1fbc044909d4ba28de0b74fcc1c494e754a6829d;hb=ecb77f944fcba8c8cfe60ca782bc5d9c8ab68cf9;hp=28f596b618e5dcd3c3c8acfb92103c2208691818;hpb=58cf11569acb270995d2de924dda03ef526647e2;p=spline3.git diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index 28f596b..1fbc044 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -4,12 +4,14 @@ module FunctionValues where import Prelude hiding (LT) +import Test.QuickCheck (Arbitrary(..), choose) import Cardinal -- | The FunctionValues type represents the value of our function f at --- the 27 points surrounding the center of a cube. Each value of f --- can be accessed by the name of its direction. +-- 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, @@ -19,27 +21,99 @@ 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 = @@ -49,7 +123,7 @@ empty_values = -- 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 +-- be a composite type; eval is what performs the \"arithmetic\" on -- 'Cardinal' directions. eval :: FunctionValues -> Cardinal -> Double eval f F = front f @@ -120,13 +194,13 @@ 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), @@ -136,8 +210,8 @@ make_values values i j k = -- 'Cardinal' to another (called a rotation). Then it applies the -- rotation to each element of the 'FunctionValues' object, and -- returns the result. -rotate :: FunctionValues -> (Cardinal -> Cardinal) -> FunctionValues -rotate fv rotation = +rotate :: (Cardinal -> Cardinal) -> FunctionValues -> FunctionValues +rotate rotation fv = FunctionValues { front = eval fv (rotation F), back = eval fv (rotation B), left = eval fv (rotation L),