X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=75957291c4d37ce005448de53fb159785a73361a;hb=5f01596d42cca3ec2b8236d697adb468cfcdb055;hp=f3b53198362768b8fdbe83085cc55b8e6306b7cc;hpb=1cd0b90dae4b2a0ea35447427e7962b6fe053308;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index f3b5319..7595729 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -1,10 +1,13 @@
+{-# LANGUAGE BangPatterns #-}
 module Tetrahedron (
   Tetrahedron(..),
   b0, -- Cube test
   b1, -- Cube test
   b2, -- Cube test
   b3, -- Cube test
+  barycenter,
   c,
+  contains_point,
   polynomial,
   tetrahedron_properties,
   tetrahedron_tests,
@@ -18,27 +21,25 @@ import qualified Data.Vector as V (
   sum
   )
 
-import Prelude hiding (LT)
 import Test.Framework (Test, testGroup)
 import Test.Framework.Providers.HUnit (testCase)
 import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.HUnit
+import Test.HUnit (Assertion, assertEqual)
 import Test.QuickCheck (Arbitrary(..), Gen, Property, (==>))
 
 import Comparisons ((~=), nearly_ge)
 import FunctionValues (FunctionValues(..), empty_values)
 import Misc (factorial)
-import Point
-import RealFunction
-import ThreeDimensional
+import Point (Point(..), scale)
+import RealFunction (RealFunction, cmult, fexp)
 
 data Tetrahedron =
   Tetrahedron { function_values :: FunctionValues,
-                v0 :: Point,
-                v1 :: Point,
-                v2 :: Point,
-                v3 :: Point,
-                precomputed_volume :: Double
+                v0 :: !Point,
+                v1 :: !Point,
+                v2 :: !Point,
+                v3 :: !Point,
+                precomputed_volume :: !Double
               }
     deriving (Eq)
 
@@ -67,35 +68,42 @@ instance Show Tetrahedron where
              "  v3: " ++ (show (v3 t)) ++ "\n"
 
 
-instance ThreeDimensional Tetrahedron where
-    center (Tetrahedron _ v0' v1' v2' v3' _) =
-        (v0' + v1' + v2' + v3') `scale` (1/4)
-
-    contains_point t p0 =
-      b0_unscaled `nearly_ge` 0 &&
-      b1_unscaled `nearly_ge` 0 &&
-      b2_unscaled `nearly_ge` 0 &&
-      b3_unscaled `nearly_ge` 0
+-- | Find the barycenter of the given tetrahedron.
+--   We just average the four vertices.
+barycenter :: Tetrahedron -> Point
+barycenter (Tetrahedron _ v0' v1' v2' v3' _) =
+  (v0' + v1' + v2' + v3') `scale` (1/4)
+
+-- | A point is internal to a tetrahedron if all of its barycentric
+--   coordinates with respect to that tetrahedron are non-negative.
+contains_point :: Tetrahedron -> Point -> Bool
+contains_point t p0 =
+  b0_unscaled `nearly_ge` 0 &&
+  b1_unscaled `nearly_ge` 0 &&
+  b2_unscaled `nearly_ge` 0 &&
+  b3_unscaled `nearly_ge` 0
+  where
+    -- Drop the useless division and volume calculation that we
+    -- would do if we used the regular b0,..b3 functions.
+    b0_unscaled :: Double
+    b0_unscaled = volume inner_tetrahedron
       where
-        -- Drop the useless division and volume calculation that we
-        -- would do if we used the regular b0,..b3 functions.
-        b0_unscaled :: Double
-        b0_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v0 = p0 }
+        inner_tetrahedron = t { v0 = p0 }
 
-        b1_unscaled :: Double
-        b1_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v1 = p0 }
+    b1_unscaled :: Double
+    b1_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v1 = p0 }
 
-        b2_unscaled :: Double
-        b2_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v2 = p0 }
+    b2_unscaled :: Double
+    b2_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v2 = p0 }
 
-        b3_unscaled :: Double
-        b3_unscaled = volume inner_tetrahedron
-          where inner_tetrahedron = t { v3 = p0 }
+    b3_unscaled :: Double
+    b3_unscaled = volume inner_tetrahedron
+      where inner_tetrahedron = t { v3 = p0 }
 
 
+{-# INLINE polynomial #-}
 polynomial :: Tetrahedron -> (RealFunction Point)
 polynomial t =
     V.sum $ V.singleton ((c t 0 0 0 3) `cmult` (beta t 0 0 0 3)) `V.snoc`
@@ -120,31 +128,12 @@ polynomial t =
             ((c t 3 0 0 0) `cmult` (beta t 3 0 0 0))
 
 
--- | Returns the domain point of t with indices i,j,k,l.
---   Simply an alias for the domain_point function.
-xi :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
-xi = domain_point
-
--- | Returns the domain point of t with indices i,j,k,l.
-domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
-domain_point t i j k l
-   | i + j + k + l == 3 = weighted_sum `scale` (1/3)
-   | otherwise = error "domain point index out of bounds"
-   where
-     v0' = (v0 t) `scale` (fromIntegral i)
-     v1' = (v1 t) `scale` (fromIntegral j)
-     v2' = (v2 t) `scale` (fromIntegral k)
-     v3' = (v3 t) `scale` (fromIntegral l)
-     weighted_sum = v0' + v1' + v2' + v3'
-
 
 -- | The Bernstein polynomial on t with indices i,j,k,l. Denoted by a
 --   capital 'B' in the Sorokina/Zeilfelder paper.
 beta :: Tetrahedron -> Int -> Int -> Int -> Int -> (RealFunction Point)
-beta t i j k l
-  | (i + j + k + l == 3) =
-      coefficient `cmult` (b0_term * b1_term * b2_term * b3_term)
-  | otherwise = error "basis function index out of bounds"
+beta t i j k l =
+  coefficient `cmult` (b0_term * b1_term * b2_term * b3_term)
   where
     denominator = (factorial i)*(factorial j)*(factorial k)*(factorial l)
     coefficient = 6 / (fromIntegral denominator)
@@ -157,10 +146,10 @@ beta t i j k l
 -- | The coefficient function. c t i j k l returns the coefficient
 --   c_ijkl with respect to the tetrahedron t. The definition uses
 --   pattern matching to mimic the definitions given in Sorokina and
---   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
---   function will simply error.
+--   Zeilfelder, pp. 84-86. If incorrect indices are supplied, the world
+--   will end. This is for performance reasons.
 c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-c t i j k l =
+c !t !i !j !k !l =
   coefficient i j k l
   where
     fvs = function_values t
@@ -287,8 +276,6 @@ c t i j k l =
                + (1/96)*(lt + fl + ft + rt + bt + fr)
                + (1/96)*(fd + ld + bd + br + rd + bl)
 
-    coefficient _ _ _ _ = error "coefficient index out of bounds"
-
 
 
 -- | Compute the determinant of the 4x4 matrix,
@@ -310,10 +297,10 @@ det :: Point -> Point -> Point -> Point -> Double
 det p0 p1 p2 p3 =
   term5 + term6
   where
-    (x1, y1, z1) = p0
-    (x2, y2, z2) = p1
-    (x3, y3, z3) = p2
-    (x4, y4, z4) = p3
+    Point x1 y1 z1 = p0
+    Point x2 y2 z2 = p1
+    Point x3 y3 z3 = p2
+    Point x4 y4 z4 = p3
     term1 = ((x2 - x4)*y1 - (x1 - x4)*y2 + (x1 - x2)*y4)*z3
     term2 = ((x2 - x3)*y1 - (x1 - x3)*y2 + (x1 - x2)*y3)*z4
     term3 = ((x3 - x4)*y2 - (x2 - x4)*y3 + (x2 - x3)*y4)*z1
@@ -324,6 +311,7 @@ det p0 p1 p2 p3 =
 
 -- | Computed using the formula from Lai & Schumaker, Definition 15.4,
 --   page 436.
+{-# INLINE volume #-}
 volume :: Tetrahedron -> Double
 volume t
        | v0' == v1' = 0
@@ -341,6 +329,7 @@ volume t
 
 
 -- | The barycentric coordinates of a point with respect to v0.
+{-# INLINE b0 #-}
 b0 :: Tetrahedron -> (RealFunction Point)
 b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
@@ -348,6 +337,7 @@ b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
 
 
 -- | The barycentric coordinates of a point with respect to v1.
+{-# INLINE b1 #-}
 b1 :: Tetrahedron -> (RealFunction Point)
 b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
@@ -355,6 +345,7 @@ b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
 
 
 -- | The barycentric coordinates of a point with respect to v2.
+{-# INLINE b2 #-}
 b2 :: Tetrahedron -> (RealFunction Point)
 b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
@@ -362,6 +353,7 @@ b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
 
 
 -- | The barycentric coordinates of a point with respect to v3.
+{-# INLINE b3 #-}
 b3 :: Tetrahedron -> (RealFunction Point)
 b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
              where
@@ -383,10 +375,10 @@ tetrahedron1_geometry_tests =
               [ testCase "volume1" volume1,
                 testCase "doesn't contain point1" doesnt_contain_point1]
   where
-    p0 = (0, -0.5, 0)
-    p1 = (0, 0.5, 0)
-    p2 = (2, 0, 0)
-    p3 = (1, 0, 1)
+    p0 = Point 0 (-0.5) 0
+    p1 = Point 0 0.5 0
+    p2 = Point 2 0 0
+    p3 = Point 1 0 1
     t = Tetrahedron { v0 = p0,
                       v1 = p1,
                       v2 = p2,
@@ -404,7 +396,7 @@ tetrahedron1_geometry_tests =
     doesnt_contain_point1 =
       assertEqual "doesn't contain an exterior point" False contained
       where
-        exterior_point = (5, 2, -9.0212)
+        exterior_point = Point 5 2 (-9.0212)
         contained = contains_point t exterior_point
 
 
@@ -418,10 +410,10 @@ tetrahedron2_geometry_tests =
               [ testCase "volume1" volume1,
                 testCase "contains point1" contains_point1]
   where
-    p0 = (0, -0.5, 0)
-    p1 = (2, 0, 0)
-    p2 = (0, 0.5, 0)
-    p3 = (1, 0, 1)
+    p0 = Point 0 (-0.5) 0
+    p1 = Point 2 0 0
+    p2 = Point 0 0.5 0
+    p3 = Point 1 0 1
     t = Tetrahedron { v0 = p0,
                       v1 = p1,
                       v2 = p2,
@@ -437,7 +429,7 @@ tetrahedron2_geometry_tests =
     contains_point1 :: Assertion
     contains_point1 = assertEqual "contains an inner point" True contained
         where
-          inner_point = (1, 0, 0.5)
+          inner_point = Point 1 0 0.5
           contained = contains_point t inner_point
 
 
@@ -451,16 +443,16 @@ containment_tests =
                 testCase "doesn't contain point4" doesnt_contain_point4,
                 testCase "doesn't contain point5" doesnt_contain_point5]
   where
-    p2 = (0.5, 0.5, 1)
-    p3 = (0.5, 0.5, 0.5)
-    exterior_point = (0, 0, 0)
+    p2 = Point 0.5 0.5 1
+    p3 = Point 0.5 0.5 0.5
+    exterior_point = Point 0 0 0
 
     doesnt_contain_point2 :: Assertion
     doesnt_contain_point2 =
       assertEqual "doesn't contain an exterior point" False contained
       where
-        p0 = (0, 1, 1)
-        p1 = (1, 1, 1)
+        p0 = Point 0 1 1
+        p1 = Point 1 1 1
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,
@@ -474,8 +466,8 @@ containment_tests =
     doesnt_contain_point3 =
       assertEqual "doesn't contain an exterior point" False contained
       where
-        p0 = (1, 1, 1)
-        p1 = (1, 0, 1)
+        p0 = Point 1 1 1
+        p1 = Point 1 0 1
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,
@@ -489,8 +481,8 @@ containment_tests =
     doesnt_contain_point4 =
       assertEqual "doesn't contain an exterior point" False contained
       where
-        p0 = (1, 0, 1)
-        p1 = (0, 0, 1)
+        p0 = Point 1 0 1
+        p1 = Point 0 0 1
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,
@@ -504,8 +496,8 @@ containment_tests =
     doesnt_contain_point5 =
       assertEqual "doesn't contain an exterior point" False contained
       where
-        p0 = (0, 0, 1)
-        p1 = (0, 1, 1)
+        p0 = Point 0 0 1
+        p1 = Point 0 1 1
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,
@@ -612,39 +604,6 @@ prop_b3_v2_always_zero t =
     (volume t) > 0 ==> (b3 t) (v2 t) ~= 0
 
 
--- | Used for convenience in the next few tests; not a test itself.
-p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-p t i j k l = (polynomial t) (xi t i j k l)
-
--- | Given in Sorokina and Zeilfelder, p. 78.
-prop_c3000_identity :: Tetrahedron -> Property
-prop_c3000_identity t =
-    (volume t) > 0 ==>
-               c t 3 0 0 0 ~= p t 3 0 0 0
-
--- | Given in Sorokina and Zeilfelder, p. 78.
-prop_c2100_identity :: Tetrahedron -> Property
-prop_c2100_identity t =
-    (volume t) > 0 ==>
-      c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
-        where
-          term1 = (1/3)*(p t 0 3 0 0)
-          term2 = (5/6)*(p t 3 0 0 0)
-          term3 = 3*(p t 2 1 0 0)
-          term4 = (3/2)*(p t 1 2 0 0)
-
--- | Given in Sorokina and Zeilfelder, p. 78.
-prop_c1110_identity :: Tetrahedron -> Property
-prop_c1110_identity t =
-    (volume t) > 0 ==>
-       c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
-        where
-          term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
-          term2 = (9/2)*(p t 1 1 1 0)
-          term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
-          term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
-
-
 prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool
 prop_swapping_vertices_doesnt_affect_coefficients1 t =
       c t 0 0 1 2 == c t' 0 0 1 2
@@ -683,10 +642,56 @@ tetrahedron_tests =
 
 p78_24_properties :: Test.Framework.Test
 p78_24_properties =
-    testGroup "p. 78, Section (2.4) Properties" [
-      testProperty "c3000 identity" prop_c3000_identity,
-      testProperty "c2100 identity" prop_c2100_identity,
-      testProperty "c1110 identity" prop_c1110_identity]
+  testGroup "p. 78, Section (2.4) Properties" [
+    testProperty "c3000 identity" prop_c3000_identity,
+    testProperty "c2100 identity" prop_c2100_identity,
+    testProperty "c1110 identity" prop_c1110_identity]
+  where
+    -- | Returns the domain point of t with indices i,j,k,l.
+    domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
+    domain_point t i j k l =
+      weighted_sum `scale` (1/3)
+      where
+        v0' = (v0 t) `scale` (fromIntegral i)
+        v1' = (v1 t) `scale` (fromIntegral j)
+        v2' = (v2 t) `scale` (fromIntegral k)
+        v3' = (v3 t) `scale` (fromIntegral l)
+        weighted_sum = v0' + v1' + v2' + v3'
+
+
+    -- | Used for convenience in the next few tests.
+    p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
+    p t i j k l = (polynomial t) (domain_point t i j k l)
+
+
+    -- | Given in Sorokina and Zeilfelder, p. 78.
+    prop_c3000_identity :: Tetrahedron -> Property
+    prop_c3000_identity t =
+      (volume t) > 0 ==>
+        c t 3 0 0 0 ~= p t 3 0 0 0
+
+    -- | Given in Sorokina and Zeilfelder, p. 78.
+    prop_c2100_identity :: Tetrahedron -> Property
+    prop_c2100_identity t =
+      (volume t) > 0 ==>
+        c t 2 1 0 0 ~= (term1 - term2 + term3 - term4)
+        where
+          term1 = (1/3)*(p t 0 3 0 0)
+          term2 = (5/6)*(p t 3 0 0 0)
+          term3 = 3*(p t 2 1 0 0)
+          term4 = (3/2)*(p t 1 2 0 0)
+
+    -- | Given in Sorokina and Zeilfelder, p. 78.
+    prop_c1110_identity :: Tetrahedron -> Property
+    prop_c1110_identity t =
+      (volume t) > 0 ==>
+        c t 1 1 1 0 ~= (term1 + term2 - term3 - term4)
+        where
+          term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0))
+          term2 = (9/2)*(p t 1 1 1 0)
+          term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0))
+          term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0))
+
 
 
 tetrahedron_properties :: Test.Framework.Test