src/FunctionValues.hs

   1 -- | The FunctionValues module contains the 'FunctionValues' type and
   2 --   the functions used to manipulate it.
   3 module FunctionValues
   4 where
   5
   6 import Prelude hiding (LT)
   7
   8 import Cardinal
   9
  10 -- | The FunctionValues type represents the value of our function f at
  11 --   the 27 points surrounding the center of a cube. Each value of f
  12 --   can be accessed by the name of its direction.
  13 data FunctionValues =
  14     FunctionValues { front  :: Double,
  15                      back   :: Double,
  16                      left   :: Double,
  17                      right  :: Double,
  18                      top    :: Double,
  19                      down   :: Double,
  20                      front_left :: Double,
  21                      front_right :: Double,
  22                      front_top :: Double,
  23                      front_down :: Double,
  24                      back_left :: Double,
  25                      back_right :: Double,
  26                      back_top :: Double,
  27                      back_down :: Double,
  28                      left_top :: Double,
  29                      left_down :: Double,
  30                      right_top :: Double,
  31                      right_down :: Double,
  32                      front_left_top :: Double,
  33                      front_left_down :: Double,
  34                      front_right_top :: Double,
  35                      front_right_down :: Double,
  36                      back_left_top :: Double,
  37                      back_left_down :: Double,
  38                      back_right_top :: Double,
  39                      back_right_down :: Double,
  40                      interior :: Double }
  41       deriving (Eq, Show)
  42
  43 -- | Return a 'FunctionValues' with a bunch of zeros for data points.
  44 empty_values :: FunctionValues
  45 empty_values =
  46     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
  47
  48 -- | The eval function is where the magic happens for the
  49 --   FunctionValues type. Given a 'Cardinal' direction and a
  50 --   'FunctionValues' object, eval will return the value of the
  51 --   function f in that 'Cardinal' direction. Note that 'Cardinal' can
  52 --   be a composite type; eval is what performs the "arithmetic" on
  53 --   'Cardinal' directions.
  54 eval :: FunctionValues -> Cardinal -> Double
  55 eval f F = front f
  56 eval f B = back f
  57 eval f L = left f
  58 eval f R = right f
  59 eval f T = top f
  60 eval f D = down f
  61 eval f FL = front_left f
  62 eval f FR = front_right f
  63 eval f FD = front_down f
  64 eval f FT = front_top f
  65 eval f BL = back_left f
  66 eval f BR = back_right f
  67 eval f BD = back_down f
  68 eval f BT = back_top f
  69 eval f LD = left_down f
  70 eval f LT = left_top f
  71 eval f RD = right_down f
  72 eval f RT = right_top f
  73 eval f FLD = front_left_down f
  74 eval f FLT = front_left_top f
  75 eval f FRD = front_right_down f
  76 eval f FRT = front_right_top f
  77 eval f BLD = back_left_down f
  78 eval f BLT = back_left_top f
  79 eval f BRD = back_right_down f
  80 eval f BRT = back_right_top f
  81 eval f I   = interior f
  82 eval _ (Scalar x) = x
  83 eval f (Sum x y) = (eval f x) + (eval f y)
  84 eval f (Difference x y) = (eval f x) - (eval f y)
  85 eval f (Product x y) = (eval f x) * (eval f y)
  86 eval f (Quotient x y) = (eval f x) / (eval f y)
  87
  88 -- | Takes a three-dimensional list of 'Double' and a set of 3D
  89 --   coordinates (i,j,k), and returns the value at (i,j,k) in the
  90 --   supplied list. If there is no such value, zero is returned.
  91 value_at :: [[[Double]]] -> Int -> Int -> Int -> Double
  92 value_at values i j k
  93          | i < 0 = 0
  94          | j < 0 = 0
  95          | k < 0 = 0
  96          | length values <= k = 0
  97          | length (values !! k) <= j = 0
  98          | length ((values !! k) !! j) <= i = 0
  99          | otherwise = ((values !! k) !! j) !! i
 100
 101
 102 -- | Given a three-dimensional list of 'Double' and a set of 3D
 103 --   coordinates (i,j,k), constructs and returns the 'FunctionValues'
 104 --   object centered at (i,j,k)
 105 make_values :: [[[Double]]] -> Int -> Int -> Int -> FunctionValues
 106 make_values values i j k =
 107     empty_values { front  = value_at values (i-1) j k,
 108                    back   = value_at values (i+1) j k,
 109                    left   = value_at values i (j-1) k,
 110                    right  = value_at values i (j+1) k,
 111                    down   = value_at values i j (k-1),
 112                    top    = value_at values i j (k+1),
 113                    front_left = value_at values (i-1) (j-1) k,
 114                    front_right = value_at values (i-1) (j+1) k,
 115                    front_down =value_at values (i-1) j (k-1),
 116                    front_top = value_at values (i-1) j (k+1),
 117                    back_left = value_at values (i+1) (j-1) k,
 118                    back_right = value_at values (i+1) (j+1) k,
 119                    back_down = value_at values (i+1) j (k-1),
 120                    back_top = value_at values (i+1) j (k+1),
 121                    left_down = value_at values i (j-1) (k-1),
 122                    left_top = value_at values i (j-1) (k+1),
 123                    right_top = value_at values i (j+1) (k+1),
 124                    right_down = value_at values i (j+1) (k-1),
 125                    front_left_down = value_at values (i-1) (j-1) (k-1),
 126                    front_left_top = value_at values (i-1) (j-1) (k+1),
 127                    front_right_down = value_at values (i-1) (j+1) (k-1),
 128                    front_right_top = value_at values (i-1) (j+1) (k+1),
 129                    back_left_down = value_at values (i-1) (j-1) (k-1),
 130                    back_left_top = value_at values (i+1) (j-1) (k+1),
 131                    back_right_down = value_at values (i+1) (j+1) (k-1),
 132                    back_right_top = value_at values (i+1) (j+1) (k+1),
 133                    interior = value_at values i j k }
 134
 135 -- | Takes a 'FunctionValues' and a function that transforms one
 136 --   'Cardinal' to another (called a rotation). Then it applies the
 137 --   rotation to each element of the 'FunctionValues' object, and
 138 --   returns the result.
 139 rotate :: FunctionValues -> (Cardinal -> Cardinal) -> FunctionValues
 140 rotate fv rotation =
 141     FunctionValues { front  = eval fv (rotation F),
 142                      back   = eval fv (rotation B),
 143                      left   = eval fv (rotation L),
 144                      right  = eval fv (rotation R),
 145                      down   = eval fv (rotation D),
 146                      top    = eval fv (rotation T),
 147                      front_left = eval fv (rotation FL),
 148                      front_right = eval fv (rotation FR),
 149                      front_down = eval fv (rotation FD),
 150                      front_top = eval fv (rotation FT),
 151                      back_left = eval fv (rotation BL),
 152                      back_right = eval fv (rotation BR),
 153                      back_down = eval fv (rotation BD),
 154                      back_top = eval fv (rotation BT),
 155                      left_down = eval fv (rotation LD),
 156                      left_top = eval fv (rotation LT),
 157                      right_down = eval fv (rotation RD),
 158                      right_top = eval fv (rotation RT),
 159                      front_left_down = eval fv (rotation FLD),
 160                      front_left_top = eval fv (rotation FLT),
 161                      front_right_down = eval fv (rotation FRD),
 162                      front_right_top = eval fv (rotation FRT),
 163                      back_left_down = eval fv (rotation BLD),
 164                      back_left_top = eval fv (rotation BLT),
 165                      back_right_down = eval fv (rotation BRD),
 166                      back_right_top = eval fv (rotation BRT),
 167                      interior = interior fv }