X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=6e31f1911cdef2ed70fe7fcdf836d0bed541c3d8;hb=899320830ae421d98fd9cdc09468409350cd3715;hp=1e83a3e690d4a6b0f39cdc0b0025526650aa81db;hpb=2da1ed2fd5929baa129812632068540a3c38a253;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index 1e83a3e..6e31f19 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -15,7 +15,8 @@ data Cube = Cube { h :: Double,
                    i :: Int,
                    j :: Int,
                    k :: Int,
-                   fv :: FunctionValues }
+                   fv :: FunctionValues,
+                   tetrahedra_volume :: Double }
             deriving (Eq)
 
 
@@ -26,7 +27,8 @@ instance Arbitrary Cube where
       j' <- choose (coordmin, coordmax)
       k' <- choose (coordmin, coordmax)
       fv' <- arbitrary :: Gen FunctionValues
-      return (Cube h' i' j' k' fv')
+      (Positive tet_vol) <- arbitrary :: Gen (Positive Double)
+      return (Cube h' i' j' k' fv' tet_vol)
         where
           coordmin = -268435456 -- -(2^29 / 2)
           coordmax = 268435456  -- +(2^29 / 2)
@@ -51,7 +53,7 @@ instance Show Cube where
 
 -- | Returns an empty 'Cube'.
 empty_cube :: Cube
-empty_cube = Cube 0 0 0 0 empty_values
+empty_cube = Cube 0 0 0 0 empty_values 0
 
 
 -- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
@@ -197,74 +199,69 @@ right_face c = Face.Face v0' v1' v2' v3'
       v3' = (center c) + (-delta, delta, -delta)
 
 
-tetrahedron0 :: Cube -> Tetrahedron
-tetrahedron0 c =
-    Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol
+tetrahedron :: Cube -> Int -> Tetrahedron
+
+tetrahedron c 0 =
+    Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol 0
     where
       v0' = center c
       v1' = center (front_face c)
       v2' = Face.v0 (front_face c)
       v3' = Face.v1 (front_face c)
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron1 :: Cube -> Tetrahedron
-tetrahedron1 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 1 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 1
     where
       v0' = center c
       v1' = center (front_face c)
       v2' = Face.v1 (front_face c)
       v3' = Face.v2 (front_face c)
       fv' = rotate ccwx (Cube.fv c)
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron2 :: Cube -> Tetrahedron
-tetrahedron2 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 2 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 2
     where
       v0' = center c
       v1' = center (front_face c)
       v2' = Face.v2 (front_face c)
       v3' = Face.v3 (front_face c)
       fv' = rotate ccwx $ rotate ccwx $ Cube.fv c
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron3 :: Cube -> Tetrahedron
-tetrahedron3 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 3 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 3
     where
       v0' = center c
       v1' = center (front_face c)
       v2' = Face.v3 (front_face c)
       v3' = Face.v0 (front_face c)
       fv' = rotate cwx (Cube.fv c)
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron4 :: Cube -> Tetrahedron
-tetrahedron4 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 4 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 4
     where
       v0' = center c
       v1' = center (top_face c)
       v2' = Face.v0 (top_face c)
       v3' = Face.v1 (top_face c)
       fv' = rotate cwy (Cube.fv c)
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron5 :: Cube -> Tetrahedron
-tetrahedron5 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 5 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 5
     where
       v0' = center c
       v1' = center (top_face c)
       v2' = Face.v1 (top_face c)
       v3' = Face.v2 (top_face c)
-      fv' = rotate cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      fv' = rotate cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron6 :: Cube -> Tetrahedron
-tetrahedron6 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 6 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 6
     where
       v0' = center c
       v1' = center (top_face c)
@@ -272,34 +269,31 @@ tetrahedron6 c =
       v3' = Face.v3 (top_face c)
       fv' = rotate cwy $ rotate cwz
                        $ rotate cwz
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron7 :: Cube -> Tetrahedron
-tetrahedron7 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 7 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 7
     where
       v0' = center c
       v1' = center (top_face c)
       v2' = Face.v3 (top_face c)
       v3' = Face.v0 (top_face c)
-      fv' = rotate cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      fv' = rotate cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron8 :: Cube -> Tetrahedron
-tetrahedron8 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 8 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 8
     where
       v0' = center c
       v1' = center (back_face c)
       v2' = Face.v0 (back_face c)
       v3' = Face.v1 (back_face c)
-      fv' = rotate cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      fv' = rotate cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron9 :: Cube -> Tetrahedron
-tetrahedron9 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 9 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 9
     where
       v0' = center c
       v1' = center (back_face c)
@@ -307,12 +301,11 @@ tetrahedron9 c =
       v3' = Face.v2 (back_face c)
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron10 :: Cube -> Tetrahedron
-tetrahedron10 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 10 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 10
     where
       v0' = center c
       v1' = center (back_face c)
@@ -321,13 +314,12 @@ tetrahedron10 c =
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ rotate cwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
+                       $ Tetrahedron.fv (tetrahedron c 0)
 
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron11 :: Cube -> Tetrahedron
-tetrahedron11 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 11 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 11
     where
       v0' = center c
       v1' = center (back_face c)
@@ -335,37 +327,31 @@ tetrahedron11 c =
       v3' = Face.v0 (back_face c)
       fv' = rotate cwy $ rotate cwy
                        $ rotate ccwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron12 :: Cube -> Tetrahedron
-tetrahedron12 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 12 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 12
     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))
-      vol = 0
-
+      fv' = rotate ccwy (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-tetrahedron13 :: Cube -> Tetrahedron
-tetrahedron13 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 13 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 13
     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)
-      vol = 0
+      fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-
-tetrahedron14 :: Cube -> Tetrahedron
-tetrahedron14 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 14 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 14
     where
       v0' = center c
       v1' = center (down_face c)
@@ -373,49 +359,41 @@ tetrahedron14 c =
       v3' = Face.v3 (down_face c)
       fv' = rotate ccwy $ rotate ccwz
                         $ rotate ccwz
-                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron15 :: Cube -> Tetrahedron
-tetrahedron15 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 15 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 15
     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)
-      vol = 0
-
+      fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron16 :: Cube -> Tetrahedron
-tetrahedron16 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 16 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 16
     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))
-      vol = 0
+      fv' = rotate ccwz (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-
-tetrahedron17 :: Cube -> Tetrahedron
-tetrahedron17 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 17 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 17
     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)
-      vol = 0
-
+      fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron18 :: Cube -> Tetrahedron
-tetrahedron18 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 18 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 18
     where
       v0' = center c
       v1' = center (right_face c)
@@ -423,50 +401,42 @@ tetrahedron18 c =
       v3' = Face.v3 (right_face c)
       fv' = rotate ccwz $ rotate cwy
                         $ rotate cwy
-                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron19 :: Cube -> Tetrahedron
-tetrahedron19 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 19 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 19
     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)
-      vol = 0
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-
-tetrahedron20 :: Cube -> Tetrahedron
-tetrahedron20 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 20 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 20
     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))
-      vol = 0
-
+      fv' = rotate cwz (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-tetrahedron21 :: Cube -> Tetrahedron
-tetrahedron21 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 21 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 21
     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)
-      vol = 0
+      fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-
-tetrahedron22 :: Cube -> Tetrahedron
-tetrahedron22 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 22 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 22
     where
       v0' = center c
       v1' = center (left_face c)
@@ -474,127 +444,57 @@ tetrahedron22 c =
       v3' = Face.v3 (left_face c)
       fv' = rotate cwz $ rotate ccwy
                        $ rotate ccwy
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron23 :: Cube -> Tetrahedron
-tetrahedron23 c =
-    Tetrahedron fv' v0' v1' v2' v3' vol
+tetrahedron c 23 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 23
     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)
-      vol = 0
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
+
+-- Feels dirty, but whatever.
+tetrahedron _ _ = error "asked for a nonexistent tetrahedron"
 
 
 tetrahedra :: Cube -> [Tetrahedron]
 tetrahedra 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,
-     tetrahedron22 c,
-     tetrahedron23 c]
+    [ tetrahedron c n | n <- [0..23] ]
 
 -- | All completely contained in the front half of the cube.
 front_half_tetrahedra :: Cube -> [Tetrahedron]
 front_half_tetrahedra c =
-  [tetrahedron0 c,
-   tetrahedron1 c,
-   tetrahedron2 c,
-   tetrahedron3 c,
-   tetrahedron6 c,
-   tetrahedron12 c,
-   tetrahedron19 c,
-   tetrahedron21 c]
-
+  [ tetrahedron c n | n <- [0,1,2,3,6,12,19,21] ]
 
 -- | All tetrahedra completely contained in the top half of the cube.
 top_half_tetrahedra :: Cube -> [Tetrahedron]
 top_half_tetrahedra c =
-  [tetrahedron4 c,
-   tetrahedron5 c,
-   tetrahedron6 c,
-   tetrahedron7 c,
-   tetrahedron0 c,
-   tetrahedron10 c,
-   tetrahedron16 c,
-   tetrahedron20 c]
-
+  [ tetrahedron c n | n <- [4,5,6,7,0,10,16,20] ]
 
 -- | All tetrahedra completely contained in the back half of the cube.
 back_half_tetrahedra :: Cube -> [Tetrahedron]
 back_half_tetrahedra c =
-  [tetrahedron8 c,
-   tetrahedron9 c,
-   tetrahedron10 c,
-   tetrahedron11 c,
-   tetrahedron4 c,
-   tetrahedron14 c,
-   tetrahedron17 c,
-   tetrahedron23 c]
-
+  [ tetrahedron c n | n <- [8,9,10,11,4,14,17,23] ]
 
 -- | All tetrahedra completely contained in the down half of the cube.
 down_half_tetrahedra :: Cube -> [Tetrahedron]
 down_half_tetrahedra c =
-  [tetrahedron12 c,
-   tetrahedron13 c,
-   tetrahedron14 c,
-   tetrahedron15 c,
-   tetrahedron2 c,
-   tetrahedron8 c,
-   tetrahedron18 c,
-   tetrahedron22 c]
-
+  [ tetrahedron c n | n <- [12,13,14,15,2,8,18,22] ]
 
 -- | All tetrahedra completely contained in the right half of the cube.
 right_half_tetrahedra :: Cube -> [Tetrahedron]
 right_half_tetrahedra c =
-  [tetrahedron16 c,
-   tetrahedron17 c,
-   tetrahedron18 c,
-   tetrahedron19 c,
-   tetrahedron1 c,
-   tetrahedron5 c,
-   tetrahedron9 c,
-   tetrahedron13 c]
-
+  [ tetrahedron c n | n <- [16,17,18,19,1,5,9,13] ]
 
 -- | All tetrahedra completely contained in the left half of the cube.
 left_half_tetrahedra :: Cube -> [Tetrahedron]
 left_half_tetrahedra c =
-  [tetrahedron20 c,
-   tetrahedron21 c,
-   tetrahedron22 c,
-   tetrahedron23 c,
-   tetrahedron3 c,
-   tetrahedron7 c,
-   tetrahedron11 c,
-   tetrahedron15 c]
-
+  [ tetrahedron c n | n <- [20,21,22,23,3,7,11,15] ]
 
 in_top_half :: Cube -> Point -> Bool
 in_top_half c (_,_,z) =
@@ -660,3 +560,4 @@ find_containing_tetrahedron c p =
 
     contains_our_point = flip contains_point p
     containing_tetrahedra = filter contains_our_point candidates_xyz
+