X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=6e31f1911cdef2ed70fe7fcdf836d0bed541c3d8;hb=899320830ae421d98fd9cdc09468409350cd3715;hp=2878eb06b76ffb54c0685de2543457faf3d8db29;hpb=f6d0c289ad3397cf392976c24f3afdb17da5d377;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index 2878eb0..6e31f19 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -1,8 +1,9 @@
 module Cube
 where
 
+import Data.List ( (\\) )
 import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
-    
+
 import Cardinal
 import qualified Face (Face(Face, v0, v1, v2, v3))
 import FunctionValues
@@ -14,7 +15,8 @@ data Cube = Cube { h :: Double,
                    i :: Int,
                    j :: Int,
                    k :: Int,
-                   fv :: FunctionValues }
+                   fv :: FunctionValues,
+                   tetrahedra_volume :: Double }
             deriving (Eq)
 
 
@@ -25,7 +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)
@@ -50,7 +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,
@@ -103,7 +106,7 @@ 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
@@ -116,13 +119,13 @@ instance ThreeDimensional Cube where
 
     -- | 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
-        | (y_coord p) < (ymin c) = False
-        | (y_coord p) > (ymax c) = False
-        | (z_coord p) < (zmin c) = False
-        | (z_coord p) > (zmax c) = False
+    contains_point c (x, y, z)
+        | x < (xmin c) = False
+        | x > (xmax c) = False
+        | y < (ymin c) = False
+        | y > (ymax c) = False
+        | z < (zmin c) = False
+        | z > (zmax c) = False
         | otherwise = True
 
 
@@ -196,108 +199,113 @@ 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'
+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 = tetrahedra_volume c
 
-tetrahedron1 :: Cube -> Tetrahedron
-tetrahedron1 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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 = tetrahedra_volume c
 
-tetrahedron2 :: Cube -> Tetrahedron
-tetrahedron2 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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 = tetrahedra_volume c
 
-tetrahedron3 :: Cube -> Tetrahedron
-tetrahedron3 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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 = tetrahedra_volume c
 
-tetrahedron4 :: Cube -> Tetrahedron
-tetrahedron4 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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 = tetrahedra_volume c
 
-tetrahedron5 :: Cube -> Tetrahedron
-tetrahedron5 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
+      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'
+tetrahedron c 6 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 6
     where
       v0' = center c
       v1' = center (top_face c)
       v2' = Face.v2 (top_face c)
       v3' = Face.v3 (top_face c)
-      fv' = rotate cwy $ rotate cwz $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
+      fv' = rotate cwy $ rotate cwz
+                       $ rotate cwz
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron7 :: Cube -> Tetrahedron
-tetrahedron7 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
+      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'
+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))
+      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'
+tetrahedron c 9 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 9
     where
       v0' = center c
       v1' = center (back_face c)
       v2' = Face.v1 (back_face c)
       v3' = Face.v2 (back_face c)
-      fv' = rotate cwy $ rotate cwy $ rotate cwx $ Tetrahedron.fv (tetrahedron0 c)
+      fv' = rotate cwy $ rotate cwy
+                       $ rotate cwx
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron10 :: Cube -> Tetrahedron
-tetrahedron10 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 10 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 10
     where
       v0' = center c
       v1' = center (back_face c)
@@ -306,12 +314,12 @@ tetrahedron10 c =
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ rotate cwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
+                       $ Tetrahedron.fv (tetrahedron c 0)
 
+      vol = tetrahedra_volume c
 
-tetrahedron11 :: Cube -> Tetrahedron
-tetrahedron11 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+tetrahedron c 11 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 11
     where
       v0' = center c
       v1' = center (back_face c)
@@ -319,34 +327,31 @@ tetrahedron11 c =
       v3' = Face.v0 (back_face c)
       fv' = rotate cwy $ rotate cwy
                        $ rotate ccwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
-
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron12 :: Cube -> Tetrahedron
-tetrahedron12 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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))
+      fv' = rotate ccwy (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-
-tetrahedron13 :: Cube -> Tetrahedron
-tetrahedron13 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
-
+      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'
+tetrahedron c 14 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 14
     where
       v0' = center c
       v1' = center (down_face c)
@@ -354,45 +359,41 @@ tetrahedron14 c =
       v3' = Face.v3 (down_face c)
       fv' = rotate ccwy $ rotate ccwz
                         $ rotate ccwz
-                        $ Tetrahedron.fv (tetrahedron0 c)
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-
-tetrahedron15 :: Cube -> Tetrahedron
-tetrahedron15 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
-
+      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'
+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))
+      fv' = rotate ccwz (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-
-tetrahedron17 :: Cube -> Tetrahedron
-tetrahedron17 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
-
+      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'
+tetrahedron c 18 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 18
     where
       v0' = center c
       v1' = center (right_face c)
@@ -400,46 +401,42 @@ tetrahedron18 c =
       v3' = Face.v3 (right_face c)
       fv' = rotate ccwz $ rotate cwy
                         $ rotate cwy
-                        $ Tetrahedron.fv (tetrahedron0 c)
-
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron19 :: Cube -> Tetrahedron
-tetrahedron19 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
+                        $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-
-tetrahedron20 :: Cube -> Tetrahedron
-tetrahedron20 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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))
-
+      fv' = rotate cwz (Tetrahedron.fv (tetrahedron c 0))
+      vol = tetrahedra_volume c
 
-tetrahedron21 :: Cube -> Tetrahedron
-tetrahedron21 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
+      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'
+tetrahedron c 22 =
+    Tetrahedron fv' v0' v1' v2' v3' vol 22
     where
       v0' = center c
       v1' = center (left_face c)
@@ -447,54 +444,120 @@ tetrahedron22 c =
       v3' = Face.v3 (left_face c)
       fv' = rotate cwz $ rotate ccwy
                        $ rotate ccwy
-                       $ Tetrahedron.fv (tetrahedron0 c)
-
+                       $ Tetrahedron.fv (tetrahedron c 0)
+      vol = tetrahedra_volume c
 
-tetrahedron23 :: Cube -> Tetrahedron
-tetrahedron23 c =
-    Tetrahedron fv' v0' v1' v2' v3'
+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)
+                       $ 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]
-
-
--- | 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
+    [ 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 =
+  [ 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 =
+  [ 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 =
+  [ 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 =
+  [ 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 =
+  [ 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 =
+  [ tetrahedron c n | n <- [20,21,22,23,3,7,11,15] ]
+
+in_top_half :: Cube -> Point -> Bool
+in_top_half c (_,_,z) =
+  distance_from_top <= distance_from_bottom
+  where
+    distance_from_top = abs $ (zmax c) - z
+    distance_from_bottom = abs $ (zmin c) - z
+
+in_front_half :: Cube -> Point -> Bool
+in_front_half c (x,_,_) =
+    distance_from_front <= distance_from_back
+  where
+    distance_from_front = abs $ (xmin c) - x
+    distance_from_back = abs $ (xmax c) - x
+
+
+in_left_half :: Cube -> Point -> Bool
+in_left_half c (_,y,_) =
+    distance_from_left <= distance_from_right
+  where
+    distance_from_left = abs $ (ymin c) - y
+    distance_from_right = abs $ (ymax c) - y
+
+
+-- | Takes a 'Cube', and returns the Tetrahedra belonging to it that
+--   contain the given 'Point'. This should be faster than checking
+--   every tetrahedron individually, since we determine which half
+--   (hemisphere?) of the cube the point lies in three times: once in
+--   each dimension. This allows us to eliminate non-candidates
+--   quickly.
+--
+--   This can throw an exception, but the use of 'head' might
+--   save us some unnecessary computations.
+--
+find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
+find_containing_tetrahedron c p =
+  head containing_tetrahedra
+  where
+    candidates = tetrahedra c
+    non_candidates_x =
+        if (in_front_half c p) then
+          back_half_tetrahedra c
+        else
+          front_half_tetrahedra c
+
+    candidates_x = candidates \\ non_candidates_x
+
+    non_candidates_y =
+      if (in_left_half c p) then
+        right_half_tetrahedra c
+      else
+        left_half_tetrahedra c
+
+    candidates_xy = candidates_x \\ non_candidates_y
+
+    non_candidates_z =
+      if (in_top_half c p) then
+        down_half_tetrahedra c
+      else
+        top_half_tetrahedra c
+
+    candidates_xyz = candidates_xy \\ non_candidates_z
+
+    contains_our_point = flip contains_point p
+    containing_tetrahedra = filter contains_our_point candidates_xyz
+