X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=6e33423d2da3a828257b21ab85055db58b681af8;hb=7cee33b2fa4789525a12685923edf1f38924a7f4;hp=11762a5efeb0b1366d0455da5e97198f82ece0fc;hpb=71c69c67074e6eb6ce7520739bc729691525b20b;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index 11762a5..6e33423 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -3,11 +3,10 @@ module Cube (
   cube_properties,
   find_containing_tetrahedron,
   tetrahedra,
-  tetrahedron
-  )
+  tetrahedron )
 where
 
-import Data.Maybe (fromJust)
+import Data.Maybe ( fromJust )
 import qualified Data.Vector as V (
   Vector,
   findIndex,
@@ -15,24 +14,28 @@ import qualified Data.Vector as V (
   minimum,
   singleton,
   snoc,
-  unsafeIndex
-  )
-import Prelude hiding (LT)
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
-
-import Cardinal
-import Comparisons ((~=), (~~=))
-import qualified Face (Face(Face, v0, v1, v2, v3))
-import FunctionValues (FunctionValues, eval, rotate)
-import Misc (all_equal, disjoint)
-import Point (Point(..), dot)
-import Tetrahedron (Tetrahedron(..), c, volume)
-import ThreeDimensional
-
-data Cube = Cube { h  :: !Double,
-                   i  :: !Int,
+  unsafeIndex)
+import Prelude hiding ( LT )
+import Test.Framework ( Test, testGroup )
+import Test.Framework.Providers.QuickCheck2 ( testProperty )
+import Test.QuickCheck ( Arbitrary(..), Gen, Positive(..), choose )
+
+import Cardinal (
+  Cardinal(..),
+  ccwx,
+  ccwy,
+  ccwz,
+  cwx,
+  cwy,
+  cwz )
+import Comparisons ( (~=), (~~=) )
+import qualified Face ( Face(..), center )
+import FunctionValues ( FunctionValues, eval, rotate )
+import Misc ( all_equal, disjoint )
+import Point ( Point(..), dot )
+import Tetrahedron ( Tetrahedron(..), barycenter, c, volume )
+
+data Cube = Cube { i  :: !Int,
                    j  :: !Int,
                    k  :: !Int,
                    fv :: !FunctionValues,
@@ -42,13 +45,12 @@ data Cube = Cube { h  :: !Double,
 
 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
       (Positive tet_vol) <- arbitrary :: Gen (Positive Double)
-      return (Cube h' i' j' k' fv' tet_vol)
+      return (Cube i' j' k' fv' tet_vol)
       where
         -- The idea here is that, when cubed in the volume formula,
         -- these numbers don't overflow 64 bits. This number is not
@@ -61,7 +63,6 @@ instance Arbitrary Cube where
 instance Show Cube where
     show cube =
         "Cube_" ++ subscript ++ "\n" ++
-        " h: " ++ (show (h cube)) ++ "\n" ++
         " Center: " ++ (show (center cube)) ++ "\n" ++
         " xmin: " ++ (show (xmin cube)) ++ "\n" ++
         " xmax: " ++ (show (xmax cube)) ++ "\n" ++
@@ -77,76 +78,56 @@ instance Show Cube where
 -- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 xmin :: Cube -> Double
-xmin cube = (i' - 1/2)*delta
+xmin cube = (i' - 1/2)
     where
       i' = fromIntegral (i cube) :: Double
-      delta = h cube
 
 -- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 xmax :: Cube -> Double
-xmax cube = (i' + 1/2)*delta
+xmax cube = (i' + 1/2)
     where
       i' = fromIntegral (i cube) :: Double
-      delta = h cube
 
 -- | The front boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 ymin :: Cube -> Double
-ymin cube = (j' - 1/2)*delta
+ymin cube = (j' - 1/2)
     where
       j' = fromIntegral (j cube) :: Double
-      delta = h cube
 
 -- | The back boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 ymax :: Cube -> Double
-ymax cube = (j' + 1/2)*delta
+ymax cube = (j' + 1/2)
     where
       j' = fromIntegral (j cube) :: Double
-      delta = h cube
 
 -- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 zmin :: Cube -> Double
-zmin cube = (k' - 1/2)*delta
+zmin cube = (k' - 1/2)
     where
       k' = fromIntegral (k cube) :: Double
-      delta = h cube
 
 -- | The top boundary of the cube. See Sorokina and Zeilfelder,
 --   p. 76.
 zmax :: Cube -> Double
-zmax cube = (k' + 1/2)*delta
+zmax cube = (k' + 1/2)
     where
       k' = fromIntegral (k cube) :: Double
-      delta = h cube
-
-instance ThreeDimensional Cube where
-    -- | The center of Cube_ijk coincides with v_ijk at
-    --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
-    center cube = Point x y z
-           where
-             delta = h cube
-             i' = fromIntegral (i cube) :: Double
-             j' = fromIntegral (j cube) :: Double
-             k' = fromIntegral (k cube) :: Double
-             x = delta * i'
-             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 cube (Point x y z)
-        | x < (xmin cube) = False
-        | x > (xmax cube) = False
-        | y < (ymin cube) = False
-        | y > (ymax cube) = False
-        | z < (zmin cube) = False
-        | z > (zmax cube) = False
-        | otherwise = True
 
 
+-- | The center of Cube_ijk coincides with v_ijk at
+--   (i, j, k). See Sorokina and Zeilfelder, p. 76.
+center :: Cube -> Point
+center cube =
+  Point x y z
+  where
+    x = fromIntegral (i cube) :: Double
+    y = fromIntegral (j cube) :: Double
+    z = fromIntegral (k cube) :: Double
+
 
 -- Face stuff.
 
@@ -154,7 +135,7 @@ instance ThreeDimensional Cube where
 top_face :: Cube -> Face.Face
 top_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point delta (-delta) delta )
       v1' = cc + ( Point delta delta delta )
@@ -167,7 +148,7 @@ top_face cube = Face.Face v0' v1' v2' v3'
 back_face :: Cube -> Face.Face
 back_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point delta (-delta) (-delta) )
       v1' = cc + ( Point delta delta (-delta) )
@@ -179,7 +160,7 @@ back_face cube = Face.Face v0' v1' v2' v3'
 down_face :: Cube -> Face.Face
 down_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point (-delta) (-delta) (-delta) )
       v1' = cc + ( Point (-delta) delta (-delta) )
@@ -192,7 +173,7 @@ down_face cube = Face.Face v0' v1' v2' v3'
 front_face :: Cube -> Face.Face
 front_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point (-delta) (-delta) delta )
       v1' = cc + ( Point (-delta) delta delta )
@@ -203,7 +184,7 @@ front_face cube = Face.Face v0' v1' v2' v3'
 left_face :: Cube -> Face.Face
 left_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point delta (-delta) delta )
       v1' = cc + ( Point (-delta) (-delta) delta )
@@ -215,7 +196,7 @@ left_face cube = Face.Face v0' v1' v2' v3'
 right_face :: Cube -> Face.Face
 right_face cube = Face.Face v0' v1' v2' v3'
     where
-      delta = (1/2)*(h cube)
+      delta = 1/2
       cc  = center cube
       v0' = cc + ( Point (-delta) delta delta)
       v1' = cc + ( Point delta  delta delta )
@@ -230,7 +211,7 @@ tetrahedron cube 0 =
     where
       v0' = center cube
       ff  = front_face cube
-      v1' = center ff
+      v1' = Face.center ff
       v2' = Face.v0 ff
       v3' = Face.v1 ff
       vol = tetrahedra_volume cube
@@ -240,7 +221,7 @@ tetrahedron cube 1 =
     where
       v0' = center cube
       ff  = front_face cube
-      v1' = center ff
+      v1' = Face.center ff
       v2' = Face.v1 ff
       v3' = Face.v2 ff
       fv' = rotate ccwx (fv cube)
@@ -251,7 +232,7 @@ tetrahedron cube 2 =
     where
       v0' = center cube
       ff  = front_face cube
-      v1' = center ff
+      v1' = Face.center ff
       v2' = Face.v2 ff
       v3' = Face.v3 ff
       fv' = rotate ccwx $ rotate ccwx $ fv cube
@@ -262,7 +243,7 @@ tetrahedron cube 3 =
     where
       v0' = center cube
       ff  = front_face cube
-      v1' = center ff
+      v1' = Face.center ff
       v2' = Face.v3 ff
       v3' = Face.v0 ff
       fv' = rotate cwx (fv cube)
@@ -273,7 +254,7 @@ tetrahedron cube 4 =
     where
       v0' = center cube
       tf  = top_face cube
-      v1' = center tf
+      v1' = Face.center tf
       v2' = Face.v0 tf
       v3' = Face.v1 tf
       fv' = rotate cwy (fv cube)
@@ -284,7 +265,7 @@ tetrahedron cube 5 =
     where
       v0' = center cube
       tf  = top_face cube
-      v1' = center tf
+      v1' = Face.center tf
       v2' = Face.v1 tf
       v3' = Face.v2 tf
       fv' = rotate cwy $ rotate cwz $ fv cube
@@ -295,7 +276,7 @@ tetrahedron cube 6 =
     where
       v0' = center cube
       tf  = top_face cube
-      v1' = center tf
+      v1' = Face.center tf
       v2' = Face.v2 tf
       v3' = Face.v3 tf
       fv' = rotate cwy $ rotate cwz
@@ -308,7 +289,7 @@ tetrahedron cube 7 =
     where
       v0' = center cube
       tf  = top_face cube
-      v1' = center tf
+      v1' = Face.center tf
       v2' = Face.v3 tf
       v3' = Face.v0 tf
       fv' = rotate cwy $ rotate ccwz $ fv cube
@@ -319,7 +300,7 @@ tetrahedron cube 8 =
     where
       v0' = center cube
       bf  = back_face cube
-      v1' = center bf
+      v1' = Face.center bf
       v2' = Face.v0 bf
       v3' = Face.v1 bf
       fv' = rotate cwy $ rotate cwy $ fv cube
@@ -330,7 +311,7 @@ tetrahedron cube 9 =
     where
       v0' = center cube
       bf  = back_face cube
-      v1' = center bf
+      v1' = Face.center bf
       v2' = Face.v1 bf
       v3' = Face.v2 bf
       fv' = rotate cwy $ rotate cwy
@@ -343,7 +324,7 @@ tetrahedron cube 10 =
     where
       v0' = center cube
       bf  = back_face cube
-      v1' = center bf
+      v1' = Face.center bf
       v2' = Face.v2 bf
       v3' = Face.v3 bf
       fv' = rotate cwy $ rotate cwy
@@ -358,7 +339,7 @@ tetrahedron cube 11 =
     where
       v0' = center cube
       bf  = back_face cube
-      v1' = center bf
+      v1' = Face.center bf
       v2' = Face.v3 bf
       v3' = Face.v0 bf
       fv' = rotate cwy $ rotate cwy
@@ -371,7 +352,7 @@ tetrahedron cube 12 =
     where
       v0' = center cube
       df  = down_face cube
-      v1' = center df
+      v1' = Face.center df
       v2' = Face.v0 df
       v3' = Face.v1 df
       fv' = rotate ccwy $ fv cube
@@ -382,7 +363,7 @@ tetrahedron cube 13 =
     where
       v0' = center cube
       df  = down_face cube
-      v1' = center df
+      v1' = Face.center df
       v2' = Face.v1 df
       v3' = Face.v2 df
       fv' = rotate ccwy $ rotate ccwz $ fv cube
@@ -393,7 +374,7 @@ tetrahedron cube 14 =
     where
       v0' = center cube
       df  = down_face cube
-      v1' = center df
+      v1' = Face.center df
       v2' = Face.v2 df
       v3' = Face.v3 df
       fv' = rotate ccwy $ rotate ccwz
@@ -406,7 +387,7 @@ tetrahedron cube 15 =
     where
       v0' = center cube
       df  = down_face cube
-      v1' = center df
+      v1' = Face.center df
       v2' = Face.v3 df
       v3' = Face.v0 df
       fv' = rotate ccwy $ rotate cwz $ fv cube
@@ -417,7 +398,7 @@ tetrahedron cube 16 =
     where
       v0' = center cube
       rf  = right_face cube
-      v1' = center rf
+      v1' = Face.center rf
       v2' = Face.v0 rf
       v3' = Face.v1 rf
       fv' = rotate ccwz $ fv cube
@@ -428,7 +409,7 @@ tetrahedron cube 17 =
     where
       v0' = center cube
       rf  = right_face cube
-      v1' = center rf
+      v1' = Face.center rf
       v2' = Face.v1 rf
       v3' = Face.v2 rf
       fv' = rotate ccwz $ rotate cwy $ fv cube
@@ -439,7 +420,7 @@ tetrahedron cube 18 =
     where
       v0' = center cube
       rf  = right_face cube
-      v1' = center rf
+      v1' = Face.center rf
       v2' = Face.v2 rf
       v3' = Face.v3 rf
       fv' = rotate ccwz $ rotate cwy
@@ -452,7 +433,7 @@ tetrahedron cube 19 =
     where
       v0' = center cube
       rf  = right_face cube
-      v1' = center rf
+      v1' = Face.center rf
       v2' = Face.v3 rf
       v3' = Face.v0 rf
       fv' = rotate ccwz $ rotate ccwy
@@ -464,7 +445,7 @@ tetrahedron cube 20 =
     where
       v0' = center cube
       lf  = left_face cube
-      v1' = center lf
+      v1' = Face.center lf
       v2' = Face.v0 lf
       v3' = Face.v1 lf
       fv' = rotate cwz $ fv cube
@@ -475,7 +456,7 @@ tetrahedron cube 21 =
     where
       v0' = center cube
       lf  = left_face cube
-      v1' = center lf
+      v1' = Face.center lf
       v2' = Face.v1 lf
       v3' = Face.v2 lf
       fv' = rotate cwz $ rotate ccwy $ fv cube
@@ -486,7 +467,7 @@ tetrahedron cube 22 =
     where
       v0' = center cube
       lf  = left_face cube
-      v1' = center lf
+      v1' = Face.center lf
       v2' = Face.v2 lf
       v3' = Face.v3 lf
       fv' = rotate cwz $ rotate ccwy
@@ -499,16 +480,13 @@ tetrahedron cube 23 =
     where
       v0' = center cube
       lf  = left_face cube
-      v1' = center lf
+      v1' = Face.center lf
       v2' = Face.v3 lf
       v3' = Face.v0 lf
       fv' = rotate cwz $ rotate cwy
                        $ fv cube
       vol = tetrahedra_volume cube
 
--- Feels dirty, but whatever.
-tetrahedron _ _ = error "asked for a nonexistent tetrahedron"
-
 
 -- Only used in tests, so we don't need the added speed
 -- of Data.Vector.
@@ -629,9 +607,9 @@ find_containing_tetrahedron cube p =
     top_half = in_top_half cube p
     left_half = in_left_half cube p
 
-    candidates =
-      if front_half then
-
+    candidates :: V.Vector Tetrahedron
+    candidates
+      | front_half =
         if left_half then
           if top_half then
             front_left_top_tetrahedra cube
@@ -643,8 +621,7 @@ find_containing_tetrahedron cube p =
           else
             front_right_down_tetrahedra cube
 
-      else -- bottom half
-
+      | otherwise = -- back half
         if left_half then
           if top_half then
             back_left_top_tetrahedra cube
@@ -659,10 +636,20 @@ find_containing_tetrahedron cube p =
     -- Use the dot product instead of Euclidean distance here to save
     -- a sqrt(). So, "distances" below really means "distances
     -- squared."
-    distances = V.map ((dot p) . center) candidates
+    distances :: V.Vector Double
+    distances = V.map ((dot p) . barycenter) candidates
+
+    shortest_distance :: Double
     shortest_distance = V.minimum distances
+
+    -- Compute the index of the tetrahedron with the center closest to
+    -- p. This is a bad algorithm, but don't change it! If you make it
+    -- smarter by finding the index of shortest_distance in distances
+    -- (this should give the same answer and avoids recomputing the
+    -- dot product), the program gets slower. Seriously!
+    lucky_idx :: Maybe Int
     lucky_idx = V.findIndex
-                  (\t -> (center t) `dot` p == shortest_distance)
+                  (\t -> (barycenter t) `dot` p == shortest_distance)
                   candidates
 
 
@@ -712,14 +699,13 @@ prop_all_volumes_positive cube =
 
 -- | In fact, since all of the tetrahedra are identical, we should
 --   already know their volumes. There's 24 tetrahedra to a cube, so
---   we'd expect the volume of each one to be (1/24)*h^3.
+--   we'd expect the volume of each one to be 1/24.
 prop_all_volumes_exact :: Cube -> Bool
 prop_all_volumes_exact cube =
-    and [volume t ~~= (1/24)*(delta^(3::Int)) | t <- tetrahedra cube]
-    where
-      delta = h cube
+    and [volume t ~~= 1/24 | t <- tetrahedra cube]
 
--- | All tetrahedron should have their v0 located at the center of the cube.
+-- | All tetrahedron should have their v0 located at the center of the
+--   cube.
 prop_v0_all_equal :: Cube -> Bool
 prop_v0_all_equal cube = (v0 t0) == (v0 t1)
     where
@@ -993,7 +979,7 @@ prop_interior_values_all_identical cube =
 --   This test checks the rotation works as expected.
 prop_c_tilde_2100_rotation_correct :: Cube -> Bool
 prop_c_tilde_2100_rotation_correct cube =
-    expr1 == expr2
+    expr1 ~= expr2
     where
       t0 = tetrahedron cube 0
       t6 = tetrahedron cube 6
@@ -1027,7 +1013,7 @@ prop_c_tilde_2100_rotation_correct cube =
 --   even meaningful!
 prop_c_tilde_2100_correct :: Cube -> Bool
 prop_c_tilde_2100_correct cube =
-    c t6 2 1 0 0 == expected
+    c t6 2 1 0 0 ~= expected
     where
       t0 = tetrahedron cube 0
       t6 = tetrahedron cube 6