+-- | 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,
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
eval f R = right f
eval f T = top f
eval f D = down f
+eval f FL = front_left f
+eval f FR = front_right f
+eval f FD = front_down f
+eval f FT = front_top f
+eval f BL = back_left f
+eval f BR = back_right f
+eval f BD = back_down f
+eval f BT = back_top f
+eval f LD = left_down f
+eval f LT = left_top f
+eval f RD = right_down f
+eval f RT = right_top f
+eval f FLD = front_left_down f
+eval f FLT = front_left_top f
+eval f FRD = front_right_down f
+eval f FRT = front_right_top f
+eval f BLD = back_left_down f
+eval f BLT = back_left_top f
+eval f BRD = back_right_down f
+eval f BRT = back_right_top f
+eval f I = interior f
+eval _ (Scalar x) = x
eval f (Sum x y) = (eval f x) + (eval f y)
eval f (Difference x y) = (eval f x) - (eval f y)
eval f (Product x y) = (eval f x) * (eval f y)
-eval f (ScalarProduct x y) = 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.
+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
+
+
+-- | 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,
+ left = value_at values i (j-1) k,
+ right = value_at values i (j+1) k,
+ down = value_at values i j (k-1),
+ top = value_at values i j (k+1),
+ front_left = value_at values (i-1) (j-1) k,
+ front_right = value_at values (i-1) (j+1) k,
+ front_down =value_at values (i-1) j (k-1),
+ front_top = value_at values (i-1) j (k+1),
+ back_left = value_at values (i+1) (j-1) k,
+ back_right = value_at values (i+1) (j+1) k,
+ back_down = value_at values (i+1) j (k-1),
+ 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_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_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 }
projects / spline3.git / blobdiff