From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 2 Sep 2011 15:03:12 +0000 (-0400)
Subject: Finish the precomputed_volume optimization.
X-Git-Tag: 0.0.1~175
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=b2e1c440b9b1bb99ae564d6600230bbd1f7d204c;p=spline3.git

Finish the precomputed_volume optimization.
---

diff --git a/src/Cube.hs b/src/Cube.hs
index 1e83a3e..ef2d9ce 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,
@@ -205,7 +207,7 @@ tetrahedron0 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 =
@@ -216,7 +218,7 @@ 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 =
@@ -227,7 +229,7 @@ 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 =
@@ -238,7 +240,7 @@ 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 =
@@ -249,7 +251,7 @@ 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 =
@@ -260,7 +262,7 @@ tetrahedron5 c =
       v2' = Face.v1 (top_face c)
       v3' = Face.v2 (top_face c)
       fv' = rotate cwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron6 :: Cube -> Tetrahedron
 tetrahedron6 c =
@@ -273,7 +275,7 @@ tetrahedron6 c =
       fv' = rotate cwy $ rotate cwz
                        $ rotate cwz
                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron7 :: Cube -> Tetrahedron
 tetrahedron7 c =
@@ -284,7 +286,7 @@ tetrahedron7 c =
       v2' = Face.v3 (top_face c)
       v3' = Face.v0 (top_face c)
       fv' = rotate cwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron8 :: Cube -> Tetrahedron
 tetrahedron8 c =
@@ -295,7 +297,7 @@ tetrahedron8 c =
       v2' = Face.v0 (back_face c)
       v3' = Face.v1 (back_face c)
       fv' = rotate cwy $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron9 :: Cube -> Tetrahedron
 tetrahedron9 c =
@@ -308,7 +310,7 @@ tetrahedron9 c =
       fv' = rotate cwy $ rotate cwy
                        $ rotate cwx
                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron10 :: Cube -> Tetrahedron
 tetrahedron10 c =
@@ -323,7 +325,7 @@ tetrahedron10 c =
                        $ rotate cwx
                        $ Tetrahedron.fv (tetrahedron0 c)
 
-      vol = 0
+      vol = tetrahedra_volume c
 
 tetrahedron11 :: Cube -> Tetrahedron
 tetrahedron11 c =
@@ -336,7 +338,7 @@ tetrahedron11 c =
       fv' = rotate cwy $ rotate cwy
                        $ rotate ccwx
                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron12 :: Cube -> Tetrahedron
@@ -348,7 +350,7 @@ tetrahedron12 c =
       v2' = Face.v0 (down_face c)
       v3' = Face.v1 (down_face c)
       fv' = rotate ccwy (Tetrahedron.fv (tetrahedron0 c))
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron13 :: Cube -> Tetrahedron
@@ -360,7 +362,7 @@ tetrahedron13 c =
       v2' = Face.v1 (down_face c)
       v3' = Face.v2 (down_face c)
       fv' = rotate ccwy $ rotate ccwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron14 :: Cube -> Tetrahedron
@@ -374,7 +376,7 @@ tetrahedron14 c =
       fv' = rotate ccwy $ rotate ccwz
                         $ rotate ccwz
                         $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron15 :: Cube -> Tetrahedron
@@ -386,7 +388,7 @@ tetrahedron15 c =
       v2' = Face.v3 (down_face c)
       v3' = Face.v0 (down_face c)
       fv' = rotate ccwy $ rotate cwz $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron16 :: Cube -> Tetrahedron
@@ -398,7 +400,7 @@ tetrahedron16 c =
       v2' = Face.v0 (right_face c)
       v3' = Face.v1 (right_face c)
       fv' = rotate ccwz (Tetrahedron.fv (tetrahedron0 c))
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron17 :: Cube -> Tetrahedron
@@ -410,7 +412,7 @@ tetrahedron17 c =
       v2' = Face.v1 (right_face c)
       v3' = Face.v2 (right_face c)
       fv' = rotate ccwz $ rotate cwy $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron18 :: Cube -> Tetrahedron
@@ -424,7 +426,7 @@ tetrahedron18 c =
       fv' = rotate ccwz $ rotate cwy
                         $ rotate cwy
                         $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron19 :: Cube -> Tetrahedron
@@ -437,7 +439,7 @@ tetrahedron19 c =
       v3' = Face.v0 (right_face c)
       fv' = rotate ccwz $ rotate ccwy
                         $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron20 :: Cube -> Tetrahedron
@@ -449,7 +451,7 @@ tetrahedron20 c =
       v2' = Face.v0 (left_face c)
       v3' = Face.v1 (left_face c)
       fv' = rotate cwz (Tetrahedron.fv (tetrahedron0 c))
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron21 :: Cube -> Tetrahedron
@@ -461,7 +463,7 @@ tetrahedron21 c =
       v2' = Face.v1 (left_face c)
       v3' = Face.v2 (left_face c)
       fv' = rotate cwz $ rotate ccwy $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron22 :: Cube -> Tetrahedron
@@ -475,7 +477,7 @@ tetrahedron22 c =
       fv' = rotate cwz $ rotate ccwy
                        $ rotate ccwy
                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedron23 :: Cube -> Tetrahedron
@@ -488,7 +490,7 @@ tetrahedron23 c =
       v3' = Face.v0 (left_face c)
       fv' = rotate cwz $ rotate cwy
                        $ Tetrahedron.fv (tetrahedron0 c)
-      vol = 0
+      vol = tetrahedra_volume c
 
 
 tetrahedra :: Cube -> [Tetrahedron]
diff --git a/src/Grid.hs b/src/Grid.hs
index 7325d2b..d9fa975 100644
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -57,7 +57,10 @@ cubes g
                  | i <- [0..xmax],
                    j <- [0..ymax],
                    k <- [0..zmax],
-                   let cube_ijk = Cube (h g) i j k (make_values fvs i j k)]
+                   let delta = h g,
+                   let tet_vol = (1/24)*(delta^(3::Int)),
+                   let cube_ijk =
+                         Cube delta i j k (make_values fvs i j k) tet_vol]
      where
        xmax = xsize - 1
        ymax = ysize - 1
diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index eef1656..1f7c22b 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -29,8 +29,11 @@ instance Arbitrary Tetrahedron where
       rnd_v2 <- arbitrary :: Gen Point
       rnd_v3 <- arbitrary :: Gen Point
       rnd_fv <- arbitrary :: Gen FunctionValues
-      rnd_vol <- arbitrary :: Gen Double
-      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 rnd_vol)
+      -- We can't assign an incorrect precomputed volume,
+      -- so we have to calculate the correct one here.
+      let t' = Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 0
+      let vol = volume t'
+      return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 vol)
 
 
 instance Show Tetrahedron where
@@ -267,27 +270,27 @@ volume t
 
 -- | The barycentric coordinates of a point with respect to v0.
 b0 :: Tetrahedron -> (RealFunction Point)
-b0 t point = (volume inner_tetrahedron) / (volume t)
+b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v0 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v1.
 b1 :: Tetrahedron -> (RealFunction Point)
-b1 t point = (volume inner_tetrahedron) / (volume t)
+b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v1 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v2.
 b2 :: Tetrahedron -> (RealFunction Point)
-b2 t point = (volume inner_tetrahedron) / (volume t)
+b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v2 = point }
 
 
 -- | The barycentric coordinates of a point with respect to v3.
 b3 :: Tetrahedron -> (RealFunction Point)
-b3 t point = (volume inner_tetrahedron) / (volume t)
+b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
                inner_tetrahedron = t { v3 = point }