X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FFunctionValues.hs;h=8eb5bdb0d375ffdfe72eabb81097cc99c121e563;hb=178804214397f6bc04370192aa3006b93d6fa0ef;hp=e9ff0647f413b3f530757725f3bab382ac33a730;hpb=6fb9ab6b6068870323e996da931fc04c7710e3e4;p=spline3.git diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index e9ff064..8eb5bdb 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -1,10 +1,18 @@ +-- | 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 +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 +22,110 @@ 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 +160,27 @@ 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 choose a nearby +-- point and use its value. +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 j k + | ysize <= j = value_at v3d i ysize k + | zsize <= k = value_at v3d i j zsize + | otherwise = idx v3d i j k + where + (xsize, ysize, zsize) = dims v3d + -make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues +-- | 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, @@ -95,14 +198,48 @@ 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 }