X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=e84b09103d7ad1bb850bed4b9380aeb47d6bb3b3;hb=525f4e76394c74e5a6f6bcdc7fb50d0dc2b9ec2d;hp=6da41945dd6ad01b521acb2d0349c01390c7bd54;hpb=993490fd9d940f5e8dea4f934c07c1a5a6c1f8ff;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index 6da4194..e84b091 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -17,7 +17,7 @@ import qualified Data.Vector as V (
   snoc,
   sum
   )
-import Numeric.LinearAlgebra hiding (i, scale)
+
 import Prelude hiding (LT)
 import Test.Framework (Test, testGroup)
 import Test.Framework.Providers.HUnit (testCase)
@@ -34,7 +34,7 @@ import RealFunction
 import ThreeDimensional
 
 data Tetrahedron =
-  Tetrahedron { fv :: FunctionValues,
+  Tetrahedron { function_values :: FunctionValues,
                 v0 :: Point,
                 v1 :: Point,
                 v2 :: Point,
@@ -61,7 +61,7 @@ instance Arbitrary Tetrahedron where
 
 instance Show Tetrahedron where
     show t = "Tetrahedron:\n" ++
-             "  fv: " ++ (show (fv t)) ++ "\n" ++
+             "  function_values: " ++ (show (function_values t)) ++ "\n" ++
              "  v0: " ++ (show (v0 t)) ++ "\n" ++
              "  v1: " ++ (show (v1 t)) ++ "\n" ++
              "  v2: " ++ (show (v2 t)) ++ "\n" ++
@@ -72,7 +72,7 @@ instance ThreeDimensional Tetrahedron where
     center (Tetrahedron _ v0' v1' v2' v3' _) =
         (v0' + v1' + v2' + v3') `scale` (1/4)
 
-    contains_point t p =
+    contains_point t p0 =
       b0_unscaled `nearly_ge` 0 &&
       b1_unscaled `nearly_ge` 0 &&
       b2_unscaled `nearly_ge` 0 &&
@@ -82,19 +82,19 @@ instance ThreeDimensional Tetrahedron where
         -- would do if we used the regular b0,..b3 functions.
         b0_unscaled :: Double
         b0_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v0 = p }
+          where inner_tetrahedron = t { v0 = p0 }
 
         b1_unscaled :: Double
         b1_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v1 = p }
+          where inner_tetrahedron = t { v1 = p0 }
 
         b2_unscaled :: Double
         b2_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v2 = p }
+          where inner_tetrahedron = t { v2 = p0 }
 
         b3_unscaled :: Double
         b3_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v3 = p }
+          where inner_tetrahedron = t { v3 = p0 }
 
 
 polynomial :: Tetrahedron -> (RealFunction Point)
@@ -161,73 +161,73 @@ beta t i j k l
 --   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
 --   function will simply error.
 c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-c t 0 0 3 0 = eval (fv t) $
+c t 0 0 3 0 = eval (function_values t) $
               (1/8) * (I + F + L + T + LT + FL + FT + FLT)
 
-c t 0 0 0 3 = eval (fv t) $
+c t 0 0 0 3 = eval (function_values t) $
               (1/8) * (I + F + R + T + RT + FR + FT + FRT)
 
-c t 0 0 2 1 = eval (fv t) $
+c t 0 0 2 1 = eval (function_values t) $
               (5/24)*(I + F + T + FT) +
               (1/24)*(L + FL + LT + FLT)
 
-c t 0 0 1 2 = eval (fv t) $
+c t 0 0 1 2 = eval (function_values t) $
               (5/24)*(I + F + T + FT) +
               (1/24)*(R + FR + RT + FRT)
 
-c t 0 1 2 0 = eval (fv t) $
+c t 0 1 2 0 = eval (function_values t) $
               (5/24)*(I + F) +
               (1/8)*(L + T + FL + FT) +
               (1/24)*(LT + FLT)
 
-c t 0 1 0 2 = eval (fv t) $
+c t 0 1 0 2 = eval (function_values t) $
               (5/24)*(I + F) +
               (1/8)*(R + T + FR + FT) +
               (1/24)*(RT + FRT)
 
-c t 0 1 1 1 = eval (fv t) $
+c t 0 1 1 1 = eval (function_values t) $
           (13/48)*(I + F) +
           (7/48)*(T + FT) +
           (1/32)*(L + R + FL + FR) +
           (1/96)*(LT + RT + FLT + FRT)
 
-c t 0 2 1 0 = eval (fv t) $
+c t 0 2 1 0 = eval (function_values t) $
           (13/48)*(I + F) +
           (17/192)*(L + T + FL + FT) +
           (1/96)*(LT + FLT) +
           (1/64)*(R + D + FR + FD) +
           (1/192)*(RT + LD + FRT + FLD)
 
-c t 0 2 0 1 = eval (fv t) $
+c t 0 2 0 1 = eval (function_values t) $
           (13/48)*(I + F) +
           (17/192)*(R + T + FR + FT) +
           (1/96)*(RT + FRT) +
           (1/64)*(L + D + FL + FD) +
           (1/192)*(RD + LT + FLT + FRD)
 
-c t 0 3 0 0 = eval (fv t) $
+c t 0 3 0 0 = eval (function_values t) $
           (13/48)*(I + F) +
           (5/96)*(L + R + T + D + FL + FR + FT + FD) +
           (1/192)*(RT + RD + LT + LD + FRT + FRD + FLT + FLD)
 
-c t 1 0 2 0 = eval (fv t) $
+c t 1 0 2 0 = eval (function_values t) $
               (1/4)*I +
               (1/6)*(F + L + T) +
               (1/12)*(LT + FL + FT)
 
-c t 1 0 0 2 = eval (fv t) $
+c t 1 0 0 2 = eval (function_values t) $
               (1/4)*I +
               (1/6)*(F + R + T) +
               (1/12)*(RT + FR + FT)
 
-c t 1 0 1 1 = eval (fv t) $
+c t 1 0 1 1 = eval (function_values t) $
           (1/3)*I +
           (5/24)*(F + T) +
           (1/12)*FT +
           (1/24)*(L + R) +
           (1/48)*(LT + RT + FL + FR)
 
-c t 1 1 1 0 = eval (fv t) $
+c t 1 1 1 0 = eval (function_values t) $
           (1/3)*I +
           (5/24)*F +
           (1/8)*(L + T) +
@@ -235,7 +235,7 @@ c t 1 1 1 0 = eval (fv t) $
           (1/48)*(D + R + LT) +
           (1/96)*(FD + LD + RT + FR)
 
-c t 1 1 0 1 = eval (fv t) $
+c t 1 1 0 1 = eval (function_values t) $
           (1/3)*I +
           (5/24)*F +
           (1/8)*(R + T) +
@@ -243,26 +243,26 @@ c t 1 1 0 1 = eval (fv t) $
           (1/48)*(D + L + RT) +
           (1/96)*(FD + LT + RD + FL)
 
-c t 1 2 0 0 = eval (fv t) $
+c t 1 2 0 0 = eval (function_values t) $
           (1/3)*I +
           (5/24)*F +
           (7/96)*(L + R + T + D) +
           (1/32)*(FL + FR + FT + FD) +
           (1/96)*(RT + RD + LT + LD)
 
-c t 2 0 1 0 = eval (fv t) $
+c t 2 0 1 0 = eval (function_values t) $
           (3/8)*I +
           (7/48)*(F + T + L) +
           (1/48)*(R + D + B + LT + FL + FT) +
           (1/96)*(RT + BT + FR + FD + LD + BL)
 
-c t 2 0 0 1 = eval (fv t) $
+c t 2 0 0 1 = eval (function_values t) $
           (3/8)*I +
           (7/48)*(F + T + R) +
           (1/48)*(L + D + B + RT + FR + FT) +
           (1/96)*(LT + BT + FL + FD + RD + BR)
 
-c t 2 1 0 0 = eval (fv t) $
+c t 2 1 0 0 = eval (function_values t) $
           (3/8)*I +
           (1/12)*(T + R + L + D) +
           (1/64)*(FT + FR + FL + FD) +
@@ -271,7 +271,7 @@ c t 2 1 0 0 = eval (fv t) $
           (1/96)*(RT + LD + LT + RD) +
           (1/192)*(BT + BR + BL + BD)
 
-c t 3 0 0 0 = eval (fv t) $
+c t 3 0 0 0 = eval (function_values t) $
           (3/8)*I +
           (1/12)*(T + F + L + R + D + B) +
           (1/96)*(LT + FL + FT + RT + BT + FR) +
@@ -281,31 +281,39 @@ c _ _ _ _ _ = error "coefficient index out of bounds"
 
 
 
--- | The matrix used in the tetrahedron volume calculation as given in
---   Lai & Schumaker, Definition 15.4, page 436.
-vol_matrix :: Tetrahedron -> Matrix Double
-vol_matrix t = (4><4)
-               [1,  1,  1,  1,
-                x1, x2, x3, x4,
-                y1, y2, y3, y4,
-                z1, z2, z3, z4 ]
-    where
-      (x1, y1, z1) = v0 t
-      (x2, y2, z2) = v1 t
-      (x3, y3, z3) = v2 t
-      (x4, y4, z4) = v3 t
+det :: Point -> Point -> Point -> Point -> Double
+det p0 p1 p2 p3 =
+--  Both of these results are just copy/pasted from Sage. One of them
+--  might be more numerically stable, faster, or both.
+--
+--  x1*y2*z4 - x1*y2*z3 + x1*y3*z2 - x1*y3*z4 - x1*y4*z2 + x1*y4*z3 +
+--  x2*y1*z3 - x2*y1*z4 - x2*y3*z1 + x2*y3*z4 +
+--  x2*y4*z1 - x2*y4*z3 - x3*y1*z2 + x3*y1*z4 + x3*y2*z1 - x3*y2*z4 - x3*y4*z1 +
+--  x3*y4*z2 + x4*y1*z2 - x4*y1*z3 - x4*y2*z1 + x4*y2*z3 + x4*y3*z1 - x4*y3*z2
+  -((x2 - x3)*y1 - (x1 - x3)*y2 + (x1 - x2)*y3)*z4 + ((x2 - x4)*y1 - (x1 - x4)*y2 + (x1 - x2)*y4)*z3 + ((x3 - x4)*y2 - (x2 - x4)*y3 + (x2 - x3)*y4)*z1 - ((x3 - x4)*y1 - (x1 - x4)*y3 + (x1 - x3)*y4)*z2
+  where
+    (x1, y1, z1) = p0
+    (x2, y2, z2) = p1
+    (x3, y3, z3) = p2
+    (x4, y4, z4) = p3
+
 
 -- | Computed using the formula from Lai & Schumaker, Definition 15.4,
 --   page 436.
 volume :: Tetrahedron -> Double
 volume t
-       | (v0 t) == (v1 t) = 0
-       | (v0 t) == (v2 t) = 0
-       | (v0 t) == (v3 t) = 0
-       | (v1 t) == (v2 t) = 0
-       | (v1 t) == (v3 t) = 0
-       | (v2 t) == (v3 t) = 0
-       | otherwise = (1/6)*(det (vol_matrix t))
+       | v0' == v1' = 0
+       | v0' == v2' = 0
+       | v0' == v3' = 0
+       | v1' == v2' = 0
+       | v1' == v3' = 0
+       | v2' == v3' = 0
+       | otherwise = (1/6)*(det v0' v1' v2' v3')
+  where
+    v0' = v0 t
+    v1' = v1 t
+    v2' = v2 t
+    v3' = v3 t
 
 
 -- | The barycentric coordinates of a point with respect to v0.
@@ -359,7 +367,7 @@ tetrahedron1_geometry_tests =
                       v1 = p1,
                       v2 = p2,
                       v3 = p3,
-                      fv = empty_values,
+                      function_values = empty_values,
                       precomputed_volume = 0 }
 
     volume1 :: Assertion
@@ -394,7 +402,7 @@ tetrahedron2_geometry_tests =
                       v1 = p1,
                       v2 = p2,
                       v3 = p3,
-                      fv = empty_values,
+                      function_values = empty_values,
                       precomputed_volume = 0 }
 
     volume1 :: Assertion
@@ -433,7 +441,7 @@ containment_tests =
                           v1 = p1,
                           v2 = p2,
                           v3 = p3,
-                          fv = empty_values,
+                          function_values = empty_values,
                           precomputed_volume = 0 }
         contained = contains_point t exterior_point
 
@@ -448,7 +456,7 @@ containment_tests =
                           v1 = p1,
                           v2 = p2,
                           v3 = p3,
-                          fv = empty_values,
+                          function_values = empty_values,
                           precomputed_volume = 0 }
         contained = contains_point t exterior_point
 
@@ -463,7 +471,7 @@ containment_tests =
                           v1 = p1,
                           v2 = p2,
                           v3 = p3,
-                          fv = empty_values,
+                          function_values = empty_values,
                           precomputed_volume = 0 }
         contained = contains_point t exterior_point
 
@@ -478,7 +486,7 @@ containment_tests =
                           v1 = p1,
                           v2 = p2,
                           v3 = p3,
-                          fv = empty_values,
+                          function_values = empty_values,
                           precomputed_volume = 0 }
         contained = contains_point t exterior_point