+-- | The FunctionValues module contains the 'FunctionValues' type and
+-- the functions used to manipulate it.
module FunctionValues
where
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,
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)
+-- | 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
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, zero is returned.
+value_at :: [[[Double]]] -> Int -> Int -> Int -> Double
+value_at values i j k
+ | i < 0 = 0
+ | j < 0 = 0
+ | k < 0 = 0
+ | length values <= k = 0
+ | length (values !! k) <= j = 0
+ | 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,
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 }