X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=b0b153e782e3fd6ab98b4856d7f0cf589ee60c40;hb=4d695b8d0b05a02d562bdee3d2a1b98ce6a5e747;hp=1e83a3e690d4a6b0f39cdc0b0025526650aa81db;hpb=2da1ed2fd5929baa129812632068540a3c38a253;p=spline3.git

diff --git a/src/Cube.hs b/src/Cube.hs
index 1e83a3e..b0b153e 100644
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -1,21 +1,31 @@
 module Cube
 where
 
-import Data.List ( (\\) )
+import Data.Maybe (fromJust)
+import qualified Data.Vector as V (
+  Vector,
+  findIndex,
+  map,
+  minimum,
+  singleton,
+  snoc,
+  unsafeIndex
+  )
 import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
 
 import Cardinal
 import qualified Face (Face(Face, v0, v1, v2, v3))
 import FunctionValues
 import Point
-import Tetrahedron hiding (c)
+import Tetrahedron hiding (c, fv)
 import ThreeDimensional
 
 data Cube = Cube { h :: Double,
                    i :: Int,
                    j :: Int,
                    k :: Int,
-                   fv :: FunctionValues }
+                   fv :: FunctionValues,
+                   tetrahedra_volume :: Double }
             deriving (Eq)
 
 
@@ -26,7 +36,8 @@ 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 +62,7 @@ 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,
@@ -197,18 +208,18 @@ right_face c = Face.Face v0' v1' v2' v3'
       v3' = (center c) + (-delta, delta, -delta)
 
 
-tetrahedron0 :: Cube -> Tetrahedron
-tetrahedron0 c =
+tetrahedron :: Cube -> Int -> Tetrahedron
+
+tetrahedron c 0 =
     Tetrahedron (Cube.fv c) v0' v1' v2' v3' vol
     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 c 1 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -216,10 +227,9 @@ tetrahedron1 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 c 2 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -227,10 +237,9 @@ tetrahedron2 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 c 3 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -238,10 +247,9 @@ tetrahedron3 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 c 4 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -249,21 +257,19 @@ tetrahedron4 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 c 5 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron6 :: Cube -> Tetrahedron
-tetrahedron6 c =
+tetrahedron c 6 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -272,33 +278,30 @@ tetrahedron6 c =
       v3' = Face.v3 (top_face c)
       fv' = rotate cwy $ rotate cwz
                        $ rotate cwz
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                       $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron7 :: Cube -> Tetrahedron
-tetrahedron7 c =
+tetrahedron c 7 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron8 :: Cube -> Tetrahedron
-tetrahedron8 c =
+tetrahedron c 8 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron9 :: Cube -> Tetrahedron
-tetrahedron9 c =
+tetrahedron c 9 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -307,11 +310,10 @@ tetrahedron9 c =
       v3' = Face.v2 (back_face c)
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                       $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron10 :: Cube -> Tetrahedron
-tetrahedron10 c =
+tetrahedron c 10 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -321,12 +323,11 @@ tetrahedron10 c =
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ rotate cwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
+                       $ fv c
 
-      vol = 0
+      vol = tetrahedra_volume c
 
-tetrahedron11 :: Cube -> Tetrahedron
-tetrahedron11 c =
+tetrahedron c 11 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -335,36 +336,30 @@ tetrahedron11 c =
       v3' = Face.v0 (back_face c)
       fv' = rotate cwy $ rotate cwy
                        $ rotate ccwx
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                       $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron12 :: Cube -> Tetrahedron
-tetrahedron12 c =
+tetrahedron c 12 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron13 :: Cube -> Tetrahedron
-tetrahedron13 c =
+tetrahedron c 13 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-
-tetrahedron14 :: Cube -> Tetrahedron
-tetrahedron14 c =
+tetrahedron c 14 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -373,48 +368,40 @@ tetrahedron14 c =
       v3' = Face.v3 (down_face c)
       fv' = rotate ccwy $ rotate ccwz
                         $ rotate ccwz
-                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                        $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron15 :: Cube -> Tetrahedron
-tetrahedron15 c =
+tetrahedron c 15 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron16 :: Cube -> Tetrahedron
-tetrahedron16 c =
+tetrahedron c 16 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-
-tetrahedron17 :: Cube -> Tetrahedron
-tetrahedron17 c =
+tetrahedron c 17 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron18 :: Cube -> Tetrahedron
-tetrahedron18 c =
+tetrahedron c 18 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -423,12 +410,10 @@ tetrahedron18 c =
       v3' = Face.v3 (right_face c)
       fv' = rotate ccwz $ rotate cwy
                         $ rotate cwy
-                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                        $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron19 :: Cube -> Tetrahedron
-tetrahedron19 c =
+tetrahedron c 19 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -436,36 +421,30 @@ tetrahedron19 c =
       v2' = Face.v3 (right_face c)
       v3' = Face.v0 (right_face c)
       fv' = rotate ccwz $ rotate ccwy
-                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                        $ fv c
+      vol = tetrahedra_volume c
 
-
-tetrahedron20 :: Cube -> Tetrahedron
-tetrahedron20 c =
+tetrahedron c 20 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron21 :: Cube -> Tetrahedron
-tetrahedron21 c =
+tetrahedron c 21 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     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 $ fv c
+      vol = tetrahedra_volume c
 
-
-tetrahedron22 :: Cube -> Tetrahedron
-tetrahedron22 c =
+tetrahedron c 22 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -474,12 +453,10 @@ tetrahedron22 c =
       v3' = Face.v3 (left_face c)
       fv' = rotate cwz $ rotate ccwy
                        $ rotate ccwy
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
-
+                       $ fv c
+      vol = tetrahedra_volume c
 
-tetrahedron23 :: Cube -> Tetrahedron
-tetrahedron23 c =
+tetrahedron c 23 =
     Tetrahedron fv' v0' v1' v2' v3' vol
     where
       v0' = center c
@@ -487,114 +464,89 @@ tetrahedron23 c =
       v2' = Face.v3 (left_face c)
       v3' = Face.v0 (left_face c)
       fv' = rotate cwz $ rotate cwy
-                       $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+                       $ fv c
+      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]
-
--- | 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]
-
-
--- | 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]
-
-
--- | 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]
-
-
--- | 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]
-
-
--- | 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]
-
-
--- | 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]
 
+-- Only used in tests, so we don't need the added speed
+-- of Data.Vector.
+tetrahedra :: Cube -> [Tetrahedron]
+tetrahedra c = [ tetrahedron c n | n <- [0..23] ]
+
+front_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_left_top_tetrahedra  c =
+  V.singleton (tetrahedron c 0) `V.snoc`
+    (tetrahedron c 3) `V.snoc`
+    (tetrahedron c 6) `V.snoc`
+    (tetrahedron c 7) `V.snoc`
+    (tetrahedron c 20) `V.snoc`
+    (tetrahedron c 21)
+
+front_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_left_down_tetrahedra  c =
+  V.singleton (tetrahedron c 0) `V.snoc`
+    (tetrahedron c 2) `V.snoc`
+    (tetrahedron c 3) `V.snoc`
+    (tetrahedron c 12) `V.snoc`
+    (tetrahedron c 15) `V.snoc`
+    (tetrahedron c 21)
+
+front_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_right_top_tetrahedra  c =
+  V.singleton (tetrahedron c 0) `V.snoc`
+    (tetrahedron c 1) `V.snoc`
+    (tetrahedron c 5) `V.snoc`
+    (tetrahedron c 6) `V.snoc`
+    (tetrahedron c 16) `V.snoc`
+    (tetrahedron c 19)
+
+front_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+front_right_down_tetrahedra  c =
+  V.singleton (tetrahedron c 1) `V.snoc`
+    (tetrahedron c 2) `V.snoc`
+    (tetrahedron c 12) `V.snoc`
+    (tetrahedron c 13) `V.snoc`
+    (tetrahedron c 18) `V.snoc`
+    (tetrahedron c 19)
+
+back_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_left_top_tetrahedra  c =
+  V.singleton (tetrahedron c 0) `V.snoc`
+    (tetrahedron c 3) `V.snoc`
+    (tetrahedron c 6) `V.snoc`
+    (tetrahedron c 7) `V.snoc`
+    (tetrahedron c 20) `V.snoc`
+    (tetrahedron c 21)
+
+back_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_left_down_tetrahedra  c =
+  V.singleton (tetrahedron c 8) `V.snoc`
+    (tetrahedron c 11) `V.snoc`
+    (tetrahedron c 14) `V.snoc`
+    (tetrahedron c 15) `V.snoc`
+    (tetrahedron c 22) `V.snoc`
+    (tetrahedron c 23)
+
+back_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_right_top_tetrahedra  c =
+  V.singleton (tetrahedron c 4) `V.snoc`
+    (tetrahedron c 5) `V.snoc`
+    (tetrahedron c 9) `V.snoc`
+    (tetrahedron c 10) `V.snoc`
+    (tetrahedron c 16) `V.snoc`
+    (tetrahedron c 17)
+
+back_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
+back_right_down_tetrahedra  c =
+  V.singleton (tetrahedron c 8) `V.snoc`
+    (tetrahedron c 9) `V.snoc`
+    (tetrahedron c 13) `V.snoc`
+    (tetrahedron c 14) `V.snoc`
+    (tetrahedron c 17) `V.snoc`
+    (tetrahedron c 18)
 
 in_top_half :: Cube -> Point -> Bool
 in_top_half c (_,_,z) =
@@ -631,32 +583,43 @@ in_left_half c (_,y,_) =
 --
 find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
 find_containing_tetrahedron c p =
-  head containing_tetrahedra
+  candidates `V.unsafeIndex` (fromJust lucky_idx)
   where
-    candidates = tetrahedra c
-    non_candidates_x =
-        if (in_front_half c p) then
-          back_half_tetrahedra c
+    front_half = in_front_half c p
+    top_half = in_top_half c p
+    left_half = in_left_half c p
+
+    candidates =
+      if front_half then
+
+        if left_half then
+          if top_half then
+            front_left_top_tetrahedra c
+          else
+            front_left_down_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
+          if top_half then
+            front_right_top_tetrahedra c
+          else
+            front_right_down_tetrahedra c
+
+      else -- bottom half
+
+        if left_half then
+          if top_half then
+            back_left_top_tetrahedra c
+          else
+            back_left_down_tetrahedra c
+        else
+          if top_half then
+            back_right_top_tetrahedra c
+          else
+            back_right_down_tetrahedra c
+
+    -- 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
+    shortest_distance = V.minimum distances
+    lucky_idx = V.findIndex
+                  (\t -> (center t) `dot` p == shortest_distance)
+                  candidates