X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=d863c290f2084ef8c79c0dc944dbb7c0c5c6c191;hb=5f01596d42cca3ec2b8236d697adb468cfcdb055;hp=bec49b4086a09947697ec183ff97459e76f43122;hpb=e0bc55b3ed14d49a1745d71cd8dcd0fe58cc7867;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index bec49b4..d863c29 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -24,12 +24,11 @@ import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
 
 import Cardinal
 import Comparisons ((~=), (~~=))
-import qualified Face (Face(Face, v0, v1, v2, v3))
+import qualified Face (Face(..), center)
 import FunctionValues (FunctionValues, eval, rotate)
 import Misc (all_equal, disjoint)
-import Point
-import Tetrahedron (Tetrahedron(..), c, volume)
-import ThreeDimensional
+import Point (Point(..), dot)
+import Tetrahedron (Tetrahedron(..), barycenter, c, volume)
 
 data Cube = Cube { h  :: !Double,
                    i  :: !Int,
@@ -122,30 +121,20 @@ zmax cube = (k' + 1/2)*delta
       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 = (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 (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
+--   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
+center :: Cube -> Point
+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'
 
 
 -- Face stuff.
@@ -155,10 +144,11 @@ top_face :: Cube -> Face.Face
 top_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (delta, -delta, delta)
-      v1' = (center cube) + (delta, delta, delta)
-      v2' = (center cube) + (-delta, delta, delta)
-      v3' = (center cube) + (-delta, -delta, delta)
+      cc  = center cube
+      v0' = cc + ( Point delta (-delta) delta )
+      v1' = cc + ( Point delta delta delta )
+      v2' = cc + ( Point (-delta) delta delta )
+      v3' = cc + ( Point (-delta) (-delta) delta )
 
 
 
@@ -167,10 +157,11 @@ back_face :: Cube -> Face.Face
 back_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (delta, -delta, -delta)
-      v1' = (center cube) + (delta, delta, -delta)
-      v2' = (center cube) + (delta, delta, delta)
-      v3' = (center cube) + (delta, -delta, delta)
+      cc  = center cube
+      v0' = cc + ( Point delta (-delta) (-delta) )
+      v1' = cc + ( Point delta delta (-delta) )
+      v2' = cc + ( Point delta delta delta )
+      v3' = cc + ( Point delta (-delta) delta )
 
 
 -- The bottom face (in the direction of -z) of the cube.
@@ -178,10 +169,11 @@ down_face :: Cube -> Face.Face
 down_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (-delta, -delta, -delta)
-      v1' = (center cube) + (-delta, delta, -delta)
-      v2' = (center cube) + (delta, delta, -delta)
-      v3' = (center cube) + (delta, -delta, -delta)
+      cc  = center cube
+      v0' = cc + ( Point (-delta) (-delta) (-delta) )
+      v1' = cc + ( Point (-delta) delta (-delta) )
+      v2' = cc + ( Point delta delta (-delta) )
+      v3' = cc + ( Point delta (-delta) (-delta) )
 
 
 
@@ -190,20 +182,22 @@ front_face :: Cube -> Face.Face
 front_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (-delta, -delta, delta)
-      v1' = (center cube) + (-delta, delta, delta)
-      v2' = (center cube) + (-delta, delta, -delta)
-      v3' = (center cube) + (-delta, -delta, -delta)
+      cc  = center cube
+      v0' = cc + ( Point (-delta) (-delta) delta )
+      v1' = cc + ( Point (-delta) delta delta )
+      v2' = cc + ( Point (-delta) delta (-delta) )
+      v3' = cc + ( Point (-delta) (-delta) (-delta) )
 
 -- | The left (in the direction of -y) face of the cube.
 left_face :: Cube -> Face.Face
 left_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (delta, -delta, delta)
-      v1' = (center cube) + (-delta, -delta, delta)
-      v2' = (center cube) + (-delta, -delta, -delta)
-      v3' = (center cube) + (delta, -delta, -delta)
+      cc  = center cube
+      v0' = cc + ( Point delta (-delta) delta )
+      v1' = cc + ( Point (-delta) (-delta) delta )
+      v2' = cc + ( Point (-delta) (-delta) (-delta) )
+      v3' = cc + ( Point delta (-delta) (-delta) )
 
 
 -- | The right (in the direction of y) face of the cube.
@@ -211,10 +205,11 @@ right_face :: Cube -> Face.Face
 right_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
-      v0' = (center cube) + (-delta, delta, delta)
-      v1' = (center cube) + (delta, delta, delta)
-      v2' = (center cube) + (delta, delta, -delta)
-      v3' = (center cube) + (-delta, delta, -delta)
+      cc  = center cube
+      v0' = cc + ( Point (-delta) delta delta)
+      v1' = cc + ( Point delta  delta delta )
+      v2' = cc + ( Point delta delta (-delta) )
+      v3' = cc + ( Point (-delta) delta (-delta) )
 
 
 tetrahedron :: Cube -> Int -> Tetrahedron
@@ -223,18 +218,20 @@ tetrahedron cube 0 =
     Tetrahedron (fv cube) v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (front_face cube)
-      v2' = Face.v0 (front_face cube)
-      v3' = Face.v1 (front_face cube)
+      ff  = front_face cube
+      v1' = Face.center ff
+      v2' = Face.v0 ff
+      v3' = Face.v1 ff
       vol = tetrahedra_volume cube
 
 tetrahedron cube 1 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (front_face cube)
-      v2' = Face.v1 (front_face cube)
-      v3' = Face.v2 (front_face cube)
+      ff  = front_face cube
+      v1' = Face.center ff
+      v2' = Face.v1 ff
+      v3' = Face.v2 ff
       fv' = rotate ccwx (fv cube)
       vol = tetrahedra_volume cube
 
@@ -242,9 +239,10 @@ tetrahedron cube 2 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (front_face cube)
-      v2' = Face.v2 (front_face cube)
-      v3' = Face.v3 (front_face cube)
+      ff  = front_face cube
+      v1' = Face.center ff
+      v2' = Face.v2 ff
+      v3' = Face.v3 ff
       fv' = rotate ccwx $ rotate ccwx $ fv cube
       vol = tetrahedra_volume cube
 
@@ -252,9 +250,10 @@ tetrahedron cube 3 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (front_face cube)
-      v2' = Face.v3 (front_face cube)
-      v3' = Face.v0 (front_face cube)
+      ff  = front_face cube
+      v1' = Face.center ff
+      v2' = Face.v3 ff
+      v3' = Face.v0 ff
       fv' = rotate cwx (fv cube)
       vol = tetrahedra_volume cube
 
@@ -262,9 +261,10 @@ tetrahedron cube 4 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (top_face cube)
-      v2' = Face.v0 (top_face cube)
-      v3' = Face.v1 (top_face cube)
+      tf  = top_face cube
+      v1' = Face.center tf
+      v2' = Face.v0 tf
+      v3' = Face.v1 tf
       fv' = rotate cwy (fv cube)
       vol = tetrahedra_volume cube
 
@@ -272,9 +272,10 @@ tetrahedron cube 5 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (top_face cube)
-      v2' = Face.v1 (top_face cube)
-      v3' = Face.v2 (top_face cube)
+      tf  = top_face cube
+      v1' = Face.center tf
+      v2' = Face.v1 tf
+      v3' = Face.v2 tf
       fv' = rotate cwy $ rotate cwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -282,9 +283,10 @@ tetrahedron cube 6 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (top_face cube)
-      v2' = Face.v2 (top_face cube)
-      v3' = Face.v3 (top_face cube)
+      tf  = top_face cube
+      v1' = Face.center tf
+      v2' = Face.v2 tf
+      v3' = Face.v3 tf
       fv' = rotate cwy $ rotate cwz
                        $ rotate cwz
                        $ fv cube
@@ -294,9 +296,10 @@ tetrahedron cube 7 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (top_face cube)
-      v2' = Face.v3 (top_face cube)
-      v3' = Face.v0 (top_face cube)
+      tf  = top_face cube
+      v1' = Face.center tf
+      v2' = Face.v3 tf
+      v3' = Face.v0 tf
       fv' = rotate cwy $ rotate ccwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -304,9 +307,10 @@ tetrahedron cube 8 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (back_face cube)
-      v2' = Face.v0 (back_face cube)
-      v3' = Face.v1 (back_face cube)
+      bf  = back_face cube
+      v1' = Face.center bf
+      v2' = Face.v0 bf
+      v3' = Face.v1 bf
       fv' = rotate cwy $ rotate cwy $ fv cube
       vol = tetrahedra_volume cube
 
@@ -314,9 +318,10 @@ tetrahedron cube 9 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (back_face cube)
-      v2' = Face.v1 (back_face cube)
-      v3' = Face.v2 (back_face cube)
+      bf  = back_face cube
+      v1' = Face.center bf
+      v2' = Face.v1 bf
+      v3' = Face.v2 bf
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ fv cube
@@ -326,9 +331,10 @@ tetrahedron cube 10 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (back_face cube)
-      v2' = Face.v2 (back_face cube)
-      v3' = Face.v3 (back_face cube)
+      bf  = back_face cube
+      v1' = Face.center bf
+      v2' = Face.v2 bf
+      v3' = Face.v3 bf
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ rotate cwx
@@ -340,9 +346,10 @@ tetrahedron cube 11 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (back_face cube)
-      v2' = Face.v3 (back_face cube)
-      v3' = Face.v0 (back_face cube)
+      bf  = back_face cube
+      v1' = Face.center bf
+      v2' = Face.v3 bf
+      v3' = Face.v0 bf
       fv' = rotate cwy $ rotate cwy
                        $ rotate ccwx
                        $ fv cube
@@ -352,9 +359,10 @@ tetrahedron cube 12 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (down_face cube)
-      v2' = Face.v0 (down_face cube)
-      v3' = Face.v1 (down_face cube)
+      df  = down_face cube
+      v1' = Face.center df
+      v2' = Face.v0 df
+      v3' = Face.v1 df
       fv' = rotate ccwy $ fv cube
       vol = tetrahedra_volume cube
 
@@ -362,9 +370,10 @@ tetrahedron cube 13 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (down_face cube)
-      v2' = Face.v1 (down_face cube)
-      v3' = Face.v2 (down_face cube)
+      df  = down_face cube
+      v1' = Face.center df
+      v2' = Face.v1 df
+      v3' = Face.v2 df
       fv' = rotate ccwy $ rotate ccwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -372,9 +381,10 @@ tetrahedron cube 14 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (down_face cube)
-      v2' = Face.v2 (down_face cube)
-      v3' = Face.v3 (down_face cube)
+      df  = down_face cube
+      v1' = Face.center df
+      v2' = Face.v2 df
+      v3' = Face.v3 df
       fv' = rotate ccwy $ rotate ccwz
                         $ rotate ccwz
                         $ fv cube
@@ -384,9 +394,10 @@ tetrahedron cube 15 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (down_face cube)
-      v2' = Face.v3 (down_face cube)
-      v3' = Face.v0 (down_face cube)
+      df  = down_face cube
+      v1' = Face.center df
+      v2' = Face.v3 df
+      v3' = Face.v0 df
       fv' = rotate ccwy $ rotate cwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -394,9 +405,10 @@ tetrahedron cube 16 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (right_face cube)
-      v2' = Face.v0 (right_face cube)
-      v3' = Face.v1 (right_face cube)
+      rf  = right_face cube
+      v1' = Face.center rf
+      v2' = Face.v0 rf
+      v3' = Face.v1 rf
       fv' = rotate ccwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -404,9 +416,10 @@ tetrahedron cube 17 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (right_face cube)
-      v2' = Face.v1 (right_face cube)
-      v3' = Face.v2 (right_face cube)
+      rf  = right_face cube
+      v1' = Face.center rf
+      v2' = Face.v1 rf
+      v3' = Face.v2 rf
       fv' = rotate ccwz $ rotate cwy $ fv cube
       vol = tetrahedra_volume cube
 
@@ -414,9 +427,10 @@ tetrahedron cube 18 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (right_face cube)
-      v2' = Face.v2 (right_face cube)
-      v3' = Face.v3 (right_face cube)
+      rf  = right_face cube
+      v1' = Face.center rf
+      v2' = Face.v2 rf
+      v3' = Face.v3 rf
       fv' = rotate ccwz $ rotate cwy
                         $ rotate cwy
                         $ fv cube
@@ -426,9 +440,10 @@ tetrahedron cube 19 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (right_face cube)
-      v2' = Face.v3 (right_face cube)
-      v3' = Face.v0 (right_face cube)
+      rf  = right_face cube
+      v1' = Face.center rf
+      v2' = Face.v3 rf
+      v3' = Face.v0 rf
       fv' = rotate ccwz $ rotate ccwy
                         $ fv cube
       vol = tetrahedra_volume cube
@@ -437,9 +452,10 @@ tetrahedron cube 20 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (left_face cube)
-      v2' = Face.v0 (left_face cube)
-      v3' = Face.v1 (left_face cube)
+      lf  = left_face cube
+      v1' = Face.center lf
+      v2' = Face.v0 lf
+      v3' = Face.v1 lf
       fv' = rotate cwz $ fv cube
       vol = tetrahedra_volume cube
 
@@ -447,9 +463,10 @@ tetrahedron cube 21 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (left_face cube)
-      v2' = Face.v1 (left_face cube)
-      v3' = Face.v2 (left_face cube)
+      lf  = left_face cube
+      v1' = Face.center lf
+      v2' = Face.v1 lf
+      v3' = Face.v2 lf
       fv' = rotate cwz $ rotate ccwy $ fv cube
       vol = tetrahedra_volume cube
 
@@ -457,9 +474,10 @@ tetrahedron cube 22 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (left_face cube)
-      v2' = Face.v2 (left_face cube)
-      v3' = Face.v3 (left_face cube)
+      lf  = left_face cube
+      v1' = Face.center lf
+      v2' = Face.v2 lf
+      v3' = Face.v3 lf
       fv' = rotate cwz $ rotate ccwy
                        $ rotate ccwy
                        $ fv cube
@@ -469,16 +487,14 @@ tetrahedron cube 23 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center cube
-      v1' = center (left_face cube)
-      v2' = Face.v3 (left_face cube)
-      v3' = Face.v0 (left_face cube)
+      lf  = left_face cube
+      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.
@@ -558,14 +574,14 @@ back_right_down_tetrahedra  cube =
     (tetrahedron cube 18)
 
 in_top_half :: Cube -> Point -> Bool
-in_top_half cube (_,_,z) =
+in_top_half cube (Point _ _ z) =
   distance_from_top <= distance_from_bottom
   where
     distance_from_top = abs $ (zmax cube) - z
     distance_from_bottom = abs $ (zmin cube) - z
 
 in_front_half :: Cube -> Point -> Bool
-in_front_half cube (x,_,_) =
+in_front_half cube (Point x _ _) =
     distance_from_front <= distance_from_back
   where
     distance_from_front = abs $ (xmin cube) - x
@@ -573,7 +589,7 @@ in_front_half cube (x,_,_) =
 
 
 in_left_half :: Cube -> Point -> Bool
-in_left_half cube (_,y,_) =
+in_left_half cube (Point _ y _) =
     distance_from_left <= distance_from_right
   where
     distance_from_left = abs $ (ymin cube) - y
@@ -590,6 +606,7 @@ in_left_half cube (_,y,_) =
 --   This can throw an exception, but the use of 'head' might
 --   save us some unnecessary computations.
 --
+{-# INLINE find_containing_tetrahedron #-}
 find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
 find_containing_tetrahedron cube p =
   candidates `V.unsafeIndex` (fromJust lucky_idx)
@@ -598,6 +615,7 @@ find_containing_tetrahedron cube p =
     top_half = in_top_half cube p
     left_half = in_left_half cube p
 
+    candidates :: V.Vector Tetrahedron
     candidates =
       if front_half then
 
@@ -625,12 +643,23 @@ find_containing_tetrahedron cube p =
           else
             back_right_down_tetrahedra cube
 
-    -- Use the dot product instead of 'distance' here to save a
-    -- sqrt(). So, "distances" below really means "distances squared."
-    distances = V.map ((dot p) . center) candidates
+    -- Use the dot product instead of Euclidean distance here to save
+    -- a sqrt(). So, "distances" below really means "distances
+    -- squared."
+    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
 
 
@@ -687,7 +716,8 @@ prop_all_volumes_exact cube =
     where
       delta = h 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