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