Fix all orphan instances.

[spline3.git] / src / Cube.hs

diff --git a/src/Cube.hs b/src/Cube.hs
index b44f0070f5c8be1982584897efdf605884846788..6941425a82be541635168da6d5af85feb1a070b7 100644 (file)
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -1,6 +1,8 @@
 module Cube
 where
 
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
+    
 import Cardinal
 import qualified Face (Face(Face, v0, v1, v2, v3))
 import FunctionValues
@@ -16,6 +18,19 @@ data Cube = Cube { h :: Double,
             deriving (Eq)
 
 
+instance Arbitrary Cube where
+    arbitrary = do
+      (Positive h') <- arbitrary :: Gen (Positive Double)
+      i' <- choose (coordmin, coordmax)
+      j' <- choose (coordmin, coordmax)
+      k' <- choose (coordmin, coordmax)
+      fv' <- arbitrary :: Gen FunctionValues
+      return (Cube h' i' j' k' fv')
+        where
+          coordmin = -268435456 -- -(2^29 / 2)
+          coordmax = 268435456  -- +(2^29 / 2)
+
+
 instance Show Cube where
     show c =
         "Cube_" ++ subscript ++ "\n" ++
@@ -33,6 +48,7 @@ instance Show Cube where
               (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c))
 
 
+-- | Returns an empty 'Cube'.
 empty_cube :: Cube
 empty_cube = Cube 0 0 0 0 empty_values
 
@@ -87,7 +103,7 @@ zmax c = (2*k' + 1)*delta / 2
 
 instance ThreeDimensional Cube where
     -- | The center of Cube_ijk coincides with v_ijk at
-    --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
+    --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.    
     center c = (x, y, z)
            where
              delta = h c
@@ -98,6 +114,8 @@ instance ThreeDimensional Cube where
              y = delta * j'
              z = delta * k'
 
+    -- | It's easy to tell if a point is within a cube; just make sure
+    --   that it falls on the proper side of each of the cube's faces.
     contains_point c p
         | (x_coord p) < (xmin c) = False
         | (x_coord p) > (xmax c) = False
@@ -195,7 +213,7 @@ tetrahedron1 c =
       v1' = center (front_face c)
       v2' = Face.v1 (front_face c)
       v3' = Face.v2 (front_face c)
-      fv' = rotate (Cube.fv c) ccwx
+      fv' = rotate ccwx (Cube.fv c)
 
 tetrahedron2 :: Cube -> Tetrahedron
 tetrahedron2 c =
@@ -205,7 +223,7 @@ tetrahedron2 c =
       v1' = center (front_face c)
       v2' = Face.v2 (front_face c)
       v3' = Face.v3 (front_face c)
-      fv' = rotate (Cube.fv c) (ccwx . ccwx)
+      fv' = rotate ccwx $ rotate ccwx $ Cube.fv c
 
 tetrahedron3 :: Cube -> Tetrahedron
 tetrahedron3 c =
@@ -215,7 +233,7 @@ tetrahedron3 c =
       v1' = center (front_face c)
       v2' = Face.v3 (front_face c)
       v3' = Face.v0 (front_face c)
-      fv' = rotate (Cube.fv c) cwx
+      fv' = rotate cwx (Cube.fv c)
 
 tetrahedron4 :: Cube -> Tetrahedron
 tetrahedron4 c =
@@ -225,7 +243,7 @@ tetrahedron4 c =
       v1' = center (top_face c)
       v2' = Face.v0 (top_face c)
       v3' = Face.v1 (top_face c)
-      fv' = rotate (Cube.fv c) cwy
+      fv' = rotate cwy (Cube.fv c)
 
 tetrahedron5 :: Cube -> Tetrahedron
 tetrahedron5 c =
@@ -235,7 +253,7 @@ tetrahedron5 c =
       v1' = center (top_face c)
       v2' = Face.v1 (top_face c)
       v3' = Face.v2 (top_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz
+      fv' = rotate cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
 
 tetrahedron6 :: Cube -> Tetrahedron
 tetrahedron6 c =
@@ -245,7 +263,7 @@ tetrahedron6 c =
       v1' = center (top_face c)
       v2' = Face.v2 (top_face c)
       v3' = Face.v3 (top_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz)
+      fv' = rotate cwy $ rotate cwz $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
 
 tetrahedron7 :: Cube -> Tetrahedron
 tetrahedron7 c =
@@ -255,7 +273,7 @@ tetrahedron7 c =
       v1' = center (top_face c)
       v2' = Face.v3 (top_face c)
       v3' = Face.v0 (top_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz
+      fv' = rotate cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
 
 tetrahedron8 :: Cube -> Tetrahedron
 tetrahedron8 c =
@@ -265,7 +283,7 @@ tetrahedron8 c =
       v1' = center (back_face c)
       v2' = Face.v0 (back_face c)
       v3' = Face.v1 (back_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwy
+      fv' = rotate cwy $ rotate cwy $ (Tetrahedron.fv (tetrahedron0 c))
 
 tetrahedron9 :: Cube -> Tetrahedron
 tetrahedron9 c =
@@ -275,7 +293,7 @@ tetrahedron9 c =
       v1' = center (back_face c)
       v2' = Face.v1 (back_face c)
       v3' = Face.v2 (back_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwx
+      fv' = rotate cwy $ rotate cwy $ rotate cwx $ Tetrahedron.fv (tetrahedron0 c)
 
 tetrahedron10 :: Cube -> Tetrahedron
 tetrahedron10 c =
@@ -285,7 +303,10 @@ tetrahedron10 c =
       v1' = center (back_face c)
       v2' = Face.v2 (back_face c)
       v3' = Face.v3 (back_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) (ccwx . ccwx)
+      fv' = rotate cwy $ rotate cwy
+                       $ rotate cwx
+                       $ rotate cwx
+                       $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron11 :: Cube -> Tetrahedron
@@ -296,7 +317,9 @@ tetrahedron11 c =
       v1' = center (back_face c)
       v2' = Face.v3 (back_face c)
       v3' = Face.v0 (back_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwx
+      fv' = rotate cwy $ rotate cwy
+                       $ rotate ccwx
+                       $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron12 :: Cube -> Tetrahedron
@@ -307,7 +330,7 @@ tetrahedron12 c =
       v1' = center (down_face c)
       v2' = Face.v0 (down_face c)
       v3' = Face.v1 (down_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwy
+      fv' = rotate ccwy (Tetrahedron.fv (tetrahedron0 c))
 
 
 tetrahedron13 :: Cube -> Tetrahedron
@@ -318,7 +341,7 @@ tetrahedron13 c =
       v1' = center (down_face c)
       v2' = Face.v1 (down_face c)
       v3' = Face.v2 (down_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) ccwz
+      fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron14 :: Cube -> Tetrahedron
@@ -329,7 +352,9 @@ tetrahedron14 c =
       v1' = center (down_face c)
       v2' = Face.v2 (down_face c)
       v3' = Face.v3 (down_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron13 c)) (ccwz . ccwz)
+      fv' = rotate ccwy $ rotate ccwz
+                        $ rotate ccwz
+                        $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron15 :: Cube -> Tetrahedron
@@ -340,7 +365,7 @@ tetrahedron15 c =
       v1' = center (down_face c)
       v2' = Face.v3 (down_face c)
       v3' = Face.v0 (down_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) cwz
+      fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron16 :: Cube -> Tetrahedron
@@ -351,7 +376,7 @@ tetrahedron16 c =
       v1' = center (right_face c)
       v2' = Face.v0 (right_face c)
       v3' = Face.v1 (right_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwz
+      fv' = rotate ccwz (Tetrahedron.fv (tetrahedron0 c))
 
 
 tetrahedron17 :: Cube -> Tetrahedron
@@ -362,7 +387,7 @@ tetrahedron17 c =
       v1' = center (right_face c)
       v2' = Face.v1 (right_face c)
       v3' = Face.v2 (right_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) cwy
+      fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron18 :: Cube -> Tetrahedron
@@ -373,7 +398,9 @@ tetrahedron18 c =
       v1' = center (right_face c)
       v2' = Face.v2 (right_face c)
       v3' = Face.v3 (right_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) (cwy . cwy)
+      fv' = rotate ccwz $ rotate cwy
+                        $ rotate cwy
+                        $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron19 :: Cube -> Tetrahedron
@@ -384,7 +411,8 @@ tetrahedron19 c =
       v1' = center (right_face c)
       v2' = Face.v3 (right_face c)
       v3' = Face.v0 (right_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) ccwy
+      fv' = rotate ccwz $ rotate ccwy
+                        $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron20 :: Cube -> Tetrahedron
@@ -395,7 +423,7 @@ tetrahedron20 c =
       v1' = center (left_face c)
       v2' = Face.v0 (left_face c)
       v3' = Face.v1 (left_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwz
+      fv' = rotate cwz (Tetrahedron.fv (tetrahedron0 c))
 
 
 tetrahedron21 :: Cube -> Tetrahedron
@@ -406,7 +434,7 @@ tetrahedron21 c =
       v1' = center (left_face c)
       v2' = Face.v1 (left_face c)
       v3' = Face.v2 (left_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) ccwy
+      fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron22 :: Cube -> Tetrahedron
@@ -417,7 +445,9 @@ tetrahedron22 c =
       v1' = center (left_face c)
       v2' = Face.v2 (left_face c)
       v3' = Face.v3 (left_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) ccwy
+      fv' = rotate cwz $ rotate ccwy
+                       $ rotate ccwy
+                       $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedron23 :: Cube -> Tetrahedron
@@ -428,7 +458,8 @@ tetrahedron23 c =
       v1' = center (left_face c)
       v2' = Face.v3 (left_face c)
       v3' = Face.v0 (left_face c)
-      fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) ccwy
+      fv' = rotate cwz $ rotate cwy
+                       $ Tetrahedron.fv (tetrahedron0 c)
 
 
 tetrahedrons :: Cube -> [Tetrahedron]
@@ -457,3 +488,13 @@ tetrahedrons c =
      tetrahedron21 c,
      tetrahedron22 c,
      tetrahedron23 c]
+
+
+-- | Takes a 'Cube', and returns all Tetrahedra belonging to it that
+--   contain the given 'Point'.
+find_containing_tetrahedra :: Cube -> Point -> [Tetrahedron]
+find_containing_tetrahedra c p =
+    filter contains_our_point all_tetrahedra
+    where
+      contains_our_point = flip contains_point p
+      all_tetrahedra = tetrahedrons c