X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=d873a379ddfca39eba80bf7cb3022b258addfacc;hb=408f4da9058366cd8047592aa96f97bcc348d329;hp=d741f490c6e7499a309b991c0e5d3ba0a9c6cd55;hpb=551cd4237e70d474ac00125644157f506c367ed5;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index d741f49..d873a37 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -1,52 +1,35 @@
 module Cube
 where
 
-import Grid
+import Cardinal
+import Face (Face(Face, v0, v1, v2, v3))
+import FunctionValues
 import Point
+import Tetrahedron (Tetrahedron(Tetrahedron), fv)
 import ThreeDimensional
 
-class Gridded a where
-    back :: a -> Cube
-    down :: a -> Cube
-    front :: a -> Cube
-    left :: a -> Cube
-    right :: a -> Cube
-    top :: a -> Cube
-
-
-data Cube = Cube { grid :: Grid,
+data Cube = Cube { h :: Double,
                    i :: Int,
                    j :: Int,
                    k :: Int,
-                   datum :: Double }
+                   fv :: FunctionValues }
             deriving (Eq)
 
 
 instance Show Cube where
     show c =
         "Cube_" ++ (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c)) ++
-        " (Grid: " ++ (show (grid c)) ++ ")" ++
         " (Center: " ++ (show (center c)) ++ ")" ++
         " (xmin: " ++ (show (xmin c)) ++ ")" ++
         " (xmax: " ++ (show (xmax c)) ++ ")" ++
         " (ymin: " ++ (show (ymin c)) ++ ")" ++
         " (ymax: " ++ (show (ymax c)) ++ ")" ++
         " (zmin: " ++ (show (zmin c)) ++ ")" ++
-        " (zmax: " ++ (show (zmax c)) ++ ")" ++
-        " (datum: " ++ (show (datum c)) ++ ")\n\n"
+        " (zmax: " ++ (show (zmax c)) ++ ")"
 
 empty_cube :: Cube
-empty_cube = Cube empty_grid 0 0 0 0
-
--- TODO: The paper considers 'i' to be the front/back direction,
--- whereas I have it in the left/right direction.
-instance Gridded Cube where
-    back c = cube_at (grid c) ((i c) + 1) (j c) (k c)
-    down c = cube_at (grid c) (i c) (j c) ((k c) - 1)
-    front c = cube_at (grid c) ((i c) - 1) (j c) (k c)
-    left c = cube_at (grid c) (i c) ((j c) - 1) (k c)
-    right c = cube_at (grid c) (i c) ((j c) + 1) (k c)
-    top c = cube_at (grid c) (i c) (j c) ((k c) + 1)
+empty_cube = Cube 0 0 0 0 empty_values
+
 
 -- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -54,7 +37,7 @@ xmin :: Cube -> Double
 xmin c = (2*i' - 1)*delta / 2
     where
       i' = fromIntegral (i c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 -- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -62,7 +45,7 @@ xmax :: Cube -> Double
 xmax c = (2*i' + 1)*delta / 2
     where
       i' = fromIntegral (i c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 -- | The front boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -70,7 +53,7 @@ ymin :: Cube -> Double
 ymin c = (2*j' - 1)*delta / 2
     where
       j' = fromIntegral (j c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 -- | The back boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -78,7 +61,7 @@ ymax :: Cube -> Double
 ymax c = (2*j' + 1)*delta / 2
     where
       j' = fromIntegral (j c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 -- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -86,7 +69,7 @@ zmin :: Cube -> Double
 zmin c = (2*k' - 1)*delta / 2
     where
       k' = fromIntegral (k c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 -- | The top boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
@@ -94,14 +77,14 @@ zmax :: Cube -> Double
 zmax c = (2*k' + 1)*delta / 2
     where
       k' = fromIntegral (k c) :: Double
-      delta = h (grid c)
+      delta = h c
 
 instance ThreeDimensional Cube where
     -- | The center of Cube_ijk coincides with v_ijk at
     --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
     center c = (x, y, z)
            where
-             delta = h (grid c)
+             delta = h c
              i' = fromIntegral (i c) :: Double
              j' = fromIntegral (j c) :: Double
              k' = fromIntegral (k c) :: Double
@@ -119,69 +102,229 @@ instance ThreeDimensional Cube where
         | otherwise = True
 
 
-instance Num Cube where
-    (Cube g1 i1 j1 k1 d1) + (Cube _ i2 j2 k2 d2) =
-        Cube g1 (i1 + i2) (j1 + j2) (k1 + k2) (d1 + d2)
+-- instance Num Cube where
+--     (Cube g1 i1 j1 k1 d1) + (Cube _ i2 j2 k2 d2) =
+--         Cube g1 (i1 + i2) (j1 + j2) (k1 + k2) (d1 + d2)
+
+--     (Cube g1 i1 j1 k1 d1) - (Cube _ i2 j2 k2 d2) =
+--         Cube g1 (i1 - i2) (j1 - j2) (k1 - k2) (d1 - d2)
+
+--     (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
+--         Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)
+
+--     abs (Cube g1 i1 j1 k1 d1) =
+--         Cube g1 (abs i1) (abs j1) (abs k1) (abs d1)
+
+--     signum (Cube g1 i1 j1 k1 d1) =
+--         Cube g1 (signum i1) (signum j1) (signum k1) (signum d1)
+
+--     fromInteger x = empty_cube { datum = (fromIntegral x) }
+
+-- instance Fractional Cube where
+--     (Cube g1 i1 j1 k1 d1) / (Cube _ _ _ _ d2) =
+--         Cube g1 i1 j1 k1 (d1 / d2)
 
-    (Cube g1 i1 j1 k1 d1) - (Cube _ i2 j2 k2 d2) =
-        Cube g1 (i1 - i2) (j1 - j2) (k1 - k2) (d1 - d2)
+--     recip (Cube g1 i1 j1 k1 d1) =
+--         Cube g1 i1 j1 k1 (recip d1)
 
-    (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
-        Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)
+--     fromRational q = empty_cube { datum = fromRational q }
 
-    abs (Cube g1 i1 j1 k1 d1) =
-        Cube g1 (abs i1) (abs j1) (abs k1) (abs d1)
 
-    signum (Cube g1 i1 j1 k1 d1) =
-        Cube g1 (signum i1) (signum j1) (signum k1) (signum d1)
 
-    fromInteger x = empty_cube { datum = (fromIntegral x) }
+-- | Return the cube corresponding to the grid point i,j,k. The list
+--   of cubes is stored as [z][y][x] but we'll be requesting it by
+--   [x][y][z] so we flip the indices in the last line.
+-- cube_at :: Grid -> Int -> Int -> Int -> Cube
+-- cube_at g i' j' k'
+--         | i' >= length (function_values g) = Cube g i' j' k' 0
+--         | i' < 0                          = Cube g i' j' k' 0
+--         | j' >= length ((function_values g) !! i') = Cube g i' j' k' 0
+--         | j' < 0                                  = Cube g i' j' k' 0
+--         | k' >= length (((function_values g) !! i') !! j') = Cube g i' j' k' 0
+--         | k' < 0                                          = Cube g i' j' k' 0
+--         | otherwise =
+--             (((cubes g) !! k') !! j') !! i'
 
-instance Fractional Cube where
-    (Cube g1 i1 j1 k1 d1) / (Cube _ _ _ _ d2) =
-        Cube g1 i1 j1 k1 (d1 / d2)
 
-    recip (Cube g1 i1 j1 k1 d1) =
-        Cube g1 i1 j1 k1 (recip d1)
 
-    fromRational q = empty_cube { datum = fromRational q }
 
--- | Constructs a cube, switching the i and k axes.
-reverse_cube :: Grid -> Int -> Int -> Int -> Double -> Cube
-reverse_cube g k' j' i' = Cube g i' j' k'
 
 
-cube_at :: Grid -> Int -> Int -> Int -> Cube
-cube_at g i' j' k'
-        | i' >= length (function_values g) = Cube g i' j' k' 0
-        | i' < 0                          = Cube g i' j' k' 0
-        | j' >= length ((function_values g) !! i') = Cube g i' j' k' 0
-        | j' < 0                                  = Cube g i' j' k' 0
-        | k' >= length (((function_values g) !! i') !! j') = Cube g i' j' k' 0
-        | k' < 0                                          = Cube g i' j' k' 0
-        | otherwise =
-            Cube g i' j' k' ((((function_values g) !! i') !! j') !! k')
+-- Face stuff.
+
+-- | The top (in the direction of z) face of the cube.
+top_face :: Cube -> Face
+top_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (delta, delta, delta)
+      v1' = (center c) + (delta, -delta, delta)
+      v2' = (center c) + (-delta, -delta, delta)
+      v3' = (center c) + (-delta, delta, delta)
 
--- These next three functions basically form a 'for' loop, looping
--- through the xs, ys, and zs in that order.
 
--- | The cubes_from_values function will return a function that takes
---   a list of values and returns a list of cubes. It could just as
---   well be written to take the values as a parameter; the omission
---   of the last parameter is known as an eta reduce.
-cubes_from_values :: Grid -> Int -> Int -> ([Double] -> [Cube])
-cubes_from_values g i' j' =
-    zipWith (reverse_cube g i' j') [0..]
 
--- | The cubes_from_planes function will return a function that takes
---   a list of planes and returns a list of cubes. It could just as
---   well be written to take the planes as a parameter; the omission
---   of the last parameter is known as an eta reduce.
-cubes_from_planes :: Grid -> Int -> ([[Double]] -> [[Cube]])
-cubes_from_planes g i' =
-    zipWith (cubes_from_values g i') [0..]
+-- | The back (in the direction of x) face of the cube.
+back_face :: Cube -> Face
+back_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (delta, delta, delta)
+      v1' = (center c) + (delta, delta, -delta)
+      v2' = (center c) + (delta, -delta, -delta)
+      v3' = (center c) + (delta, -delta, delta)
 
--- | Takes a grid as an argument, and returns a three-dimensional list
---   of cubes centered on its grid points.
-cubes :: Grid -> [[[Cube]]]
-cubes g = zipWith (cubes_from_planes g) [0..] (function_values g)
+
+-- The bottom face (in the direction of -z) of the cube.
+down_face :: Cube -> Face
+down_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (delta, delta, -delta)
+      v1' = (center c) + (-delta, delta, -delta)
+      v2' = (center c) + (-delta, -delta, -delta)
+      v3' = (center c) + (delta, -delta, -delta)
+
+
+
+-- | The front (in the direction of -x) face of the cube.
+front_face :: Cube -> Face
+front_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (-delta, -delta, delta)
+      v1' = (center c) + (-delta, delta, delta)
+      v2' = (center c) + (-delta, delta, -delta)
+      v3' = (center c) + (-delta, -delta, -delta)
+
+
+-- | The left (in the direction of -y) face of the cube.
+left_face :: Cube -> Face
+left_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (-delta, -delta, delta)
+      v1' = (center c) + (delta, -delta, delta)
+      v2' = (center c) + (delta, -delta, -delta)
+      v3' = (center c) + (-delta, -delta, -delta)
+
+
+-- | The right (in the direction of y) face of the cube.
+right_face :: Cube -> Face
+right_face c = Face v0' v1' v2' v3'
+    where
+      delta = (1/2)*(h c)
+      v0' = (center c) + (-delta, delta, -delta)
+      v1' = (center c) + (delta, delta, -delta)
+      v2' = (center c) + (delta, delta, delta)
+      v3' = (center c) + (-delta, delta, delta)
+
+
+
+tetrahedron0 :: Cube -> Tetrahedron
+tetrahedron0 c =
+    Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (front_face c)
+      v2' = v0 (front_face c)
+      v3' = v1 (front_face c)
+
+tetrahedron1 :: Cube -> Tetrahedron
+tetrahedron1 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (front_face c)
+      v2' = v1 (front_face c)
+      v3' = v2 (front_face c)
+      fv' = rotate (Cube.fv c) ccwx
+
+tetrahedron2 :: Cube -> Tetrahedron
+tetrahedron2 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (front_face c)
+      v2' = v2 (front_face c)
+      v3' = v3 (front_face c)
+      fv' = rotate (Cube.fv c) (ccwx . ccwx)
+
+tetrahedron3 :: Cube -> Tetrahedron
+tetrahedron3 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (front_face c)
+      v2' = v3 (front_face c)
+      v3' = v1 (front_face c)
+      fv' = rotate (Cube.fv c) cwx
+
+tetrahedron4 :: Cube -> Tetrahedron
+tetrahedron4 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (top_face c)
+      v2' = v0 (front_face c)
+      v3' = v1 (front_face c)
+      fv' = rotate (Cube.fv c) cwy
+
+tetrahedron5 :: Cube -> Tetrahedron
+tetrahedron5 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (top_face c)
+      v2' = v1 (top_face c)
+      v3' = v2 (top_face c)
+      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwx
+
+tetrahedron6 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (top_face c)
+      v2' = v2 (top_face c)
+      v3' = v3 (top_face c)
+      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) (ccwx . ccwx)
+
+tetrahedron7 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (top_face c)
+      v2' = v3 (top_face c)
+      v3' = v1 (top_face c)
+      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwx
+
+tetrahedrons :: Cube -> [Tetrahedron]
+tetrahedrons c =
+    [tetrahedron0 c,
+     tetrahedron1 c,
+     tetrahedron2 c,
+     tetrahedron3 c,
+     tetrahedron4 c,
+     tetrahedron5 c,
+     tetrahedron6 c,
+     tetrahedron7 c
+                -- ,
+                --  tetrahedron8 c,
+                --  tetrahedron9 c,
+                --  tetrahedron10 c,
+                --  tetrahedron11 c,
+                --  tetrahedron12 c,
+                --  tetrahedron13 c,
+                --  tetrahedron14 c,
+                --  tetrahedron15 c,
+                --  tetrahedron16 c,
+                --  tetrahedron17 c,
+                --  tetrahedron18 c,
+                --  tetrahedron19 c,
+                --  tetrahedron20 c,
+                --  tetrahedron21 c,
+                --  tetrahedron21 c,
+                --  tetrahedron22 c,
+                --  tetrahedron23 c,
+                --  tetrahedron24 c
+    ]