X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFunctionValues.hs;h=1fbc044909d4ba28de0b74fcc1c494e754a6829d;hb=ecb77f944fcba8c8cfe60ca782bc5d9c8ab68cf9;hp=e8bdcb8e2d1f294216d38fa24d3b56fcc4cba786;hpb=d8bb807e89fbb193b373be111217813d5a4222e9;p=spline3.git diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index e8bdcb8..1fbc044 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -1,10 +1,17 @@ +-- | The FunctionValues module contains the 'FunctionValues' type and +-- the functions used to manipulate it. 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 (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 +21,110 @@ 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 @@ -73,6 +159,9 @@ 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, zero is returned. value_at :: [[[Double]]] -> Int -> Int -> Int -> Double value_at values i j k | i < 0 = 0 @@ -83,6 +172,10 @@ value_at values i j k | length ((values !! k) !! j) <= i = 0 | otherwise = ((values !! k) !! j) !! i + +-- | 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 :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues make_values values i j k = empty_values { front = value_at values (i-1) j k, @@ -101,20 +194,24 @@ 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),