X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=8e9acd38c8b9a0b858f56287fc8aa0c637fd8beb;hb=d6dd574714648c0703175b5b2d3ccdd5198bb552;hp=4c7abed0fe78e282ec1096c410cae41c15300129;hpb=35bc3798d28ed65ab970cf158082bf8d68e2c480;p=spline3.git

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index 4c7abed..8e9acd3 100644
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -1,36 +1,32 @@
 {-# LANGUAGE BangPatterns #-}
+
 module Tetrahedron (
   Tetrahedron(..),
   b0, -- Cube test
   b1, -- Cube test
   b2, -- Cube test
   b3, -- Cube test
+  barycenter,
   c,
   polynomial,
   tetrahedron_properties,
   tetrahedron_tests,
-  volume -- Cube test
-  )
+  volume ) -- Cube test
 where
 
-import qualified Data.Vector as V (
-  singleton,
-  snoc,
-  sum
-  )
-
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.HUnit (testCase)
-import Test.Framework.Providers.QuickCheck2 (testProperty)
+import Data.Vector ( singleton, snoc )
+import qualified Data.Vector as V ( sum )
+import Test.Framework ( Test, testGroup )
+import Test.Framework.Providers.HUnit ( testCase )
+import Test.Framework.Providers.QuickCheck2 ( testProperty )
 import Test.HUnit (Assertion, assertEqual)
-import Test.QuickCheck (Arbitrary(..), Gen, Property, (==>))
+import Test.QuickCheck ( Arbitrary(..), Gen, Property, (==>) )
 
-import Comparisons ((~=), nearly_ge)
-import FunctionValues (FunctionValues(..), empty_values)
-import Misc (factorial)
-import Point (Point, scale)
-import RealFunction (RealFunction, cmult, fexp)
-import ThreeDimensional (ThreeDimensional(..))
+import Comparisons ( (~=) )
+import FunctionValues ( FunctionValues(..), empty_values )
+import Misc ( factorial )
+import Point ( Point(..), scale )
+import RealFunction ( RealFunction, cmult, fexp )
 
 data Tetrahedron =
   Tetrahedron { function_values :: FunctionValues,
@@ -67,57 +63,36 @@ 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 is only used in tests.
-    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 inner_tetrahedron = t { v0 = 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 }
+-- | 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)
 
-        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`
-            ((c t 0 0 1 2) `cmult` (beta t 0 0 1 2)) `V.snoc`
-            ((c t 0 0 2 1) `cmult` (beta t 0 0 2 1)) `V.snoc`
-            ((c t 0 0 3 0) `cmult` (beta t 0 0 3 0)) `V.snoc`
-            ((c t 0 1 0 2) `cmult` (beta t 0 1 0 2)) `V.snoc`
-            ((c t 0 1 1 1) `cmult` (beta t 0 1 1 1)) `V.snoc`
-            ((c t 0 1 2 0) `cmult` (beta t 0 1 2 0)) `V.snoc`
-            ((c t 0 2 0 1) `cmult` (beta t 0 2 0 1)) `V.snoc`
-            ((c t 0 2 1 0) `cmult` (beta t 0 2 1 0)) `V.snoc`
-            ((c t 0 3 0 0) `cmult` (beta t 0 3 0 0)) `V.snoc`
-            ((c t 1 0 0 2) `cmult` (beta t 1 0 0 2)) `V.snoc`
-            ((c t 1 0 1 1) `cmult` (beta t 1 0 1 1)) `V.snoc`
-            ((c t 1 0 2 0) `cmult` (beta t 1 0 2 0)) `V.snoc`
-            ((c t 1 1 0 1) `cmult` (beta t 1 1 0 1)) `V.snoc`
-            ((c t 1 1 1 0) `cmult` (beta t 1 1 1 0)) `V.snoc`
-            ((c t 1 2 0 0) `cmult` (beta t 1 2 0 0)) `V.snoc`
-            ((c t 2 0 0 1) `cmult` (beta t 2 0 0 1)) `V.snoc`
-            ((c t 2 0 1 0) `cmult` (beta t 2 0 1 0)) `V.snoc`
-            ((c t 2 1 0 0) `cmult` (beta t 2 1 0 0)) `V.snoc`
+    V.sum $ singleton ((c t 0 0 0 3) `cmult` (beta t 0 0 0 3)) `snoc`
+            ((c t 0 0 1 2) `cmult` (beta t 0 0 1 2)) `snoc`
+            ((c t 0 0 2 1) `cmult` (beta t 0 0 2 1)) `snoc`
+            ((c t 0 0 3 0) `cmult` (beta t 0 0 3 0)) `snoc`
+            ((c t 0 1 0 2) `cmult` (beta t 0 1 0 2)) `snoc`
+            ((c t 0 1 1 1) `cmult` (beta t 0 1 1 1)) `snoc`
+            ((c t 0 1 2 0) `cmult` (beta t 0 1 2 0)) `snoc`
+            ((c t 0 2 0 1) `cmult` (beta t 0 2 0 1)) `snoc`
+            ((c t 0 2 1 0) `cmult` (beta t 0 2 1 0)) `snoc`
+            ((c t 0 3 0 0) `cmult` (beta t 0 3 0 0)) `snoc`
+            ((c t 1 0 0 2) `cmult` (beta t 1 0 0 2)) `snoc`
+            ((c t 1 0 1 1) `cmult` (beta t 1 0 1 1)) `snoc`
+            ((c t 1 0 2 0) `cmult` (beta t 1 0 2 0)) `snoc`
+            ((c t 1 1 0 1) `cmult` (beta t 1 1 0 1)) `snoc`
+            ((c t 1 1 1 0) `cmult` (beta t 1 1 1 0)) `snoc`
+            ((c t 1 2 0 0) `cmult` (beta t 1 2 0 0)) `snoc`
+            ((c t 2 0 0 1) `cmult` (beta t 2 0 0 1)) `snoc`
+            ((c t 2 0 1 0) `cmult` (beta t 2 0 1 0)) `snoc`
+            ((c t 2 1 0 0) `cmult` (beta t 2 1 0 0)) `snoc`
             ((c t 3 0 0 0) `cmult` (beta t 3 0 0 0))
 
 
@@ -125,10 +100,8 @@ polynomial t =
 -- | 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)
@@ -141,8 +114,8 @@ 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 =
   coefficient i j k l
@@ -271,8 +244,6 @@ 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,
@@ -294,10 +265,10 @@ 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
@@ -308,23 +279,13 @@ 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
-       | 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
-
+volume (Tetrahedron _ v0' v1' v2' v3' _) =
+  (1/6)*(det v0' v1' v2' v3')
 
 -- | 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
@@ -332,6 +293,7 @@ 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
@@ -339,6 +301,7 @@ 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
@@ -346,6 +309,7 @@ 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
@@ -354,23 +318,18 @@ b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
 
 
 
--- Tests
-
-
 -- | Check the volume of a particular tetrahedron (computed by hand)
---   and whether or not it contains a specific point chosen to be
---   outside of it. Its vertices are in clockwise order, so the volume
---   should be negative.
+--   Its vertices are in clockwise order, so the volume should be
+--   negative.
 tetrahedron1_geometry_tests :: Test.Framework.Test
 tetrahedron1_geometry_tests =
   testGroup "tetrahedron1 geometry"
-              [ testCase "volume1" volume1,
-                testCase "doesn't contain point1" doesnt_contain_point1]
+              [ testCase "volume1" volume1 ]
   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,
@@ -384,28 +343,19 @@ tetrahedron1_geometry_tests =
       where
         vol = volume t
 
-    doesnt_contain_point1 :: Assertion
-    doesnt_contain_point1 =
-      assertEqual "doesn't contain an exterior point" False contained
-      where
-        exterior_point = (5, 2, -9.0212)
-        contained = contains_point t exterior_point
-
 
 -- | Check the volume of a particular tetrahedron (computed by hand)
---   and whether or not it contains a specific point chosen to be
---   inside of it. Its vertices are in counter-clockwise order, so the
---   volume should be positive.
+--   Its vertices are in counter-clockwise order, so the volume should
+--   be positive.
 tetrahedron2_geometry_tests :: Test.Framework.Test
 tetrahedron2_geometry_tests =
   testGroup "tetrahedron2 geometry"
-              [ testCase "volume1" volume1,
-                testCase "contains point1" contains_point1]
+              [ testCase "volume1" volume1 ]
   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,
@@ -418,85 +368,6 @@ tetrahedron2_geometry_tests =
       where
         vol = volume t
 
-    contains_point1 :: Assertion
-    contains_point1 = assertEqual "contains an inner point" True contained
-        where
-          inner_point = (1, 0, 0.5)
-          contained = contains_point t inner_point
-
-
--- | Ensure that tetrahedra do not contain a particular point chosen to
---   be outside of them.
-containment_tests :: Test.Framework.Test
-containment_tests =
-  testGroup "containment tests"
-              [ testCase "doesn't contain point2" doesnt_contain_point2,
-                testCase "doesn't contain point3" doesnt_contain_point3,
-                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)
-
-    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)
-        t = Tetrahedron { v0 = p0,
-                          v1 = p1,
-                          v2 = p2,
-                          v3 = p3,
-                          function_values = empty_values,
-                          precomputed_volume = 0 }
-        contained = contains_point t exterior_point
-
-
-    doesnt_contain_point3 :: Assertion
-    doesnt_contain_point3 =
-      assertEqual "doesn't contain an exterior point" False contained
-      where
-        p0 = (1, 1, 1)
-        p1 = (1, 0, 1)
-        t = Tetrahedron { v0 = p0,
-                          v1 = p1,
-                          v2 = p2,
-                          v3 = p3,
-                          function_values = empty_values,
-                          precomputed_volume = 0 }
-        contained = contains_point t exterior_point
-
-
-    doesnt_contain_point4 :: Assertion
-    doesnt_contain_point4 =
-      assertEqual "doesn't contain an exterior point" False contained
-      where
-        p0 = (1, 0, 1)
-        p1 = (0, 0, 1)
-        t = Tetrahedron { v0 = p0,
-                          v1 = p1,
-                          v2 = p2,
-                          v3 = p3,
-                          function_values = empty_values,
-                          precomputed_volume = 0 }
-        contained = contains_point t exterior_point
-
-
-    doesnt_contain_point5 :: Assertion
-    doesnt_contain_point5 =
-      assertEqual "doesn't contain an exterior point" False contained
-      where
-        p0 = (0, 0, 1)
-        p1 = (0, 1, 1)
-        t = Tetrahedron { v0 = p0,
-                          v1 = p1,
-                          v2 = p2,
-                          v3 = p3,
-                          function_values = empty_values,
-                          precomputed_volume = 0 }
-        contained = contains_point t exterior_point
 
 
 -- | The barycentric coordinate of v0 with respect to itself should
@@ -627,8 +498,7 @@ tetrahedron_tests :: Test.Framework.Test
 tetrahedron_tests =
     testGroup "Tetrahedron Tests" [
       tetrahedron1_geometry_tests,
-      tetrahedron2_geometry_tests,
-      containment_tests ]
+      tetrahedron2_geometry_tests ]
 
 
 
@@ -641,9 +511,8 @@ p78_24_properties =
   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
-      | i + j + k + l == 3 = weighted_sum `scale` (1/3)
-      | otherwise = error "domain point index out of bounds"
+    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)
@@ -707,11 +576,11 @@ tetrahedron_properties =
     testProperty "b3_v0_always_zero" prop_b3_v0_always_zero,
     testProperty "b3_v1_always_zero" prop_b3_v1_always_zero,
     testProperty "b3_v2_always_zero" prop_b3_v2_always_zero,
-    testProperty "swapping_vertices_doesnt_affect_coefficients1" $
+    testProperty "swapping_vertices_doesnt_affect_coefficients1"
       prop_swapping_vertices_doesnt_affect_coefficients1,
-    testProperty "swapping_vertices_doesnt_affect_coefficients2" $
+    testProperty "swapping_vertices_doesnt_affect_coefficients2"
       prop_swapping_vertices_doesnt_affect_coefficients2,
-    testProperty "swapping_vertices_doesnt_affect_coefficients3" $
+    testProperty "swapping_vertices_doesnt_affect_coefficients3"
       prop_swapping_vertices_doesnt_affect_coefficients3,
-    testProperty "swapping_vertices_doesnt_affect_coefficients4" $
+    testProperty "swapping_vertices_doesnt_affect_coefficients4"
       prop_swapping_vertices_doesnt_affect_coefficients4 ]