X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=2878eb06b76ffb54c0685de2543457faf3d8db29;hb=f6d0c289ad3397cf392976c24f3afdb17da5d377;hp=8287177ed17edf6307a9517d06e11548320fa7da;hpb=51adbba172ccaa70c4832809de334674a8ba6a0f;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index 8287177..2878eb0 100644
--- 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
@@ -139,9 +157,9 @@ down_face :: Cube -> Face.Face
 down_face c = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h c)
-      v0' = (center c) + (delta, delta, -delta)
+      v0' = (center c) + (-delta, -delta, -delta)
       v1' = (center c) + (-delta, delta, -delta)
-      v2' = (center c) + (-delta, -delta, -delta)
+      v2' = (center c) + (delta, delta, -delta)
       v3' = (center c) + (delta, -delta, -delta)
 
 
@@ -161,10 +179,10 @@ left_face :: Cube -> Face.Face
 left_face c = Face.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)
+      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.
@@ -172,10 +190,10 @@ right_face :: Cube -> Face.Face
 right_face c = Face.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)
+      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
@@ -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
@@ -296,11 +317,153 @@ 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
+tetrahedron12 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (down_face c)
+      v2' = Face.v0 (down_face c)
+      v3' = Face.v1 (down_face c)
+      fv' = rotate ccwy (Tetrahedron.fv (tetrahedron0 c))
+
+
+tetrahedron13 :: Cube -> Tetrahedron
+tetrahedron13 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (down_face c)
+      v2' = Face.v1 (down_face c)
+      v3' = Face.v2 (down_face c)
+      fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron14 :: Cube -> Tetrahedron
+tetrahedron14 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (down_face c)
+      v2' = Face.v2 (down_face c)
+      v3' = Face.v3 (down_face c)
+      fv' = rotate ccwy $ rotate ccwz
+                        $ rotate ccwz
+                        $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron15 :: Cube -> Tetrahedron
+tetrahedron15 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (down_face c)
+      v2' = Face.v3 (down_face c)
+      v3' = Face.v0 (down_face c)
+      fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron16 :: Cube -> Tetrahedron
+tetrahedron16 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (right_face c)
+      v2' = Face.v0 (right_face c)
+      v3' = Face.v1 (right_face c)
+      fv' = rotate ccwz (Tetrahedron.fv (tetrahedron0 c))
 
 
-tetrahedrons :: Cube -> [Tetrahedron]
-tetrahedrons c =
+tetrahedron17 :: Cube -> Tetrahedron
+tetrahedron17 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (right_face c)
+      v2' = Face.v1 (right_face c)
+      v3' = Face.v2 (right_face c)
+      fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron18 :: Cube -> Tetrahedron
+tetrahedron18 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (right_face c)
+      v2' = Face.v2 (right_face c)
+      v3' = Face.v3 (right_face c)
+      fv' = rotate ccwz $ rotate cwy
+                        $ rotate cwy
+                        $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron19 :: Cube -> Tetrahedron
+tetrahedron19 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (right_face c)
+      v2' = Face.v3 (right_face c)
+      v3' = Face.v0 (right_face c)
+      fv' = rotate ccwz $ rotate ccwy
+                        $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron20 :: Cube -> Tetrahedron
+tetrahedron20 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (left_face c)
+      v2' = Face.v0 (left_face c)
+      v3' = Face.v1 (left_face c)
+      fv' = rotate cwz (Tetrahedron.fv (tetrahedron0 c))
+
+
+tetrahedron21 :: Cube -> Tetrahedron
+tetrahedron21 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (left_face c)
+      v2' = Face.v1 (left_face c)
+      v3' = Face.v2 (left_face c)
+      fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron22 :: Cube -> Tetrahedron
+tetrahedron22 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (left_face c)
+      v2' = Face.v2 (left_face c)
+      v3' = Face.v3 (left_face c)
+      fv' = rotate cwz $ rotate ccwy
+                       $ rotate ccwy
+                       $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedron23 :: Cube -> Tetrahedron
+tetrahedron23 c =
+    Tetrahedron fv' v0' v1' v2' v3'
+    where
+      v0' = center c
+      v1' = center (left_face c)
+      v2' = Face.v3 (left_face c)
+      v3' = Face.v0 (left_face c)
+      fv' = rotate cwz $ rotate cwy
+                       $ Tetrahedron.fv (tetrahedron0 c)
+
+
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra c =
     [tetrahedron0 c,
      tetrahedron1 c,
      tetrahedron2 c,
@@ -312,19 +475,26 @@ tetrahedrons 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
-    ]
+     tetrahedron11 c,
+     tetrahedron12 c,
+     tetrahedron13 c,
+     tetrahedron14 c,
+     tetrahedron15 c,
+     tetrahedron16 c,
+     tetrahedron17 c,
+     tetrahedron18 c,
+     tetrahedron19 c,
+     tetrahedron20 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 = tetrahedra c