Define a custom 'Point' type instead of a 3-tuple so that its constructor can be...

Updated all 'Point' references to use the new constructor.

diff --git a/src/Cube.hs b/src/Cube.hs
index 1c654ffd72763010bbb56352022160f61a0257c6..3c82f67e285f611ba64a11092d61c86cc890724a 100644 (file)
--- a/src/Cube.hs
+++ b/src/Cube.hs
@@ -27,7 +27,7 @@ import Comparisons ((~=), (~~=))
 import qualified Face (Face(Face, v0, v1, v2, v3))
 import FunctionValues (FunctionValues, eval, rotate)
 import Misc (all_equal, disjoint)
 import qualified Face (Face(Face, v0, v1, v2, v3))
 import FunctionValues (FunctionValues, eval, rotate)
 import Misc (all_equal, disjoint)

-import Point
+import Point (Point(..), dot)

 import Tetrahedron (Tetrahedron(..), c, volume)
 import ThreeDimensional
 
 import Tetrahedron (Tetrahedron(..), c, volume)
 import ThreeDimensional
 


@@ -125,7 +125,7 @@ zmax cube = (k' + 1/2)*delta
 instance ThreeDimensional Cube where
     -- | The center of Cube_ijk coincides with v_ijk at
     --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
 instance ThreeDimensional Cube where
     -- | The center of Cube_ijk coincides with v_ijk at
     --   (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.

-    center cube = (x, y, z)
+    center cube = Point x y z

            where
              delta = h cube
              i' = fromIntegral (i cube) :: Double
            where
              delta = h cube
              i' = fromIntegral (i cube) :: Double


@@ -137,7 +137,7 @@ instance ThreeDimensional Cube where
 
     -- | It's easy to tell if a point is within a cube; just make sure
     --   that it falls on the proper side of each of the cube's faces.
 
     -- | It's easy to tell if a point is within a cube; just make sure
     --   that it falls on the proper side of each of the cube's faces.

-    contains_point cube (x, y, z)
+    contains_point cube (Point x y z)

         | x < (xmin cube) = False
         | x > (xmax cube) = False
         | y < (ymin cube) = False
         | x < (xmin cube) = False
         | x > (xmax cube) = False
         | y < (ymin cube) = False


@@ -156,10 +156,10 @@ top_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (delta, -delta, delta)
-      v1' = cc + (delta, delta, delta)
-      v2' = cc + (-delta, delta, delta)
-      v3' = cc + (-delta, -delta, delta)
+      v0' = cc + ( Point delta (-delta) delta )
+      v1' = cc + ( Point delta delta delta )
+      v2' = cc + ( Point (-delta) delta delta )
+      v3' = cc + ( Point (-delta) (-delta) delta )

 
 
 
 
 
 


@@ -169,10 +169,10 @@ back_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (delta, -delta, -delta)
-      v1' = cc + (delta, delta, -delta)
-      v2' = cc + (delta, delta, delta)
-      v3' = cc + (delta, -delta, delta)
+      v0' = cc + ( Point delta (-delta) (-delta) )
+      v1' = cc + ( Point delta delta (-delta) )
+      v2' = cc + ( Point delta delta delta )
+      v3' = cc + ( Point delta (-delta) delta )

 
 
 -- The bottom face (in the direction of -z) of the cube.
 
 
 -- The bottom face (in the direction of -z) of the cube.


@@ -181,10 +181,10 @@ down_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (-delta, -delta, -delta)
-      v1' = cc + (-delta, delta, -delta)
-      v2' = cc + (delta, delta, -delta)
-      v3' = cc + (delta, -delta, -delta)
+      v0' = cc + ( Point (-delta) (-delta) (-delta) )
+      v1' = cc + ( Point (-delta) delta (-delta) )
+      v2' = cc + ( Point delta delta (-delta) )
+      v3' = cc + ( Point delta (-delta) (-delta) )

 
 
 
 
 
 


@@ -194,10 +194,10 @@ front_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (-delta, -delta, delta)
-      v1' = cc + (-delta, delta, delta)
-      v2' = cc + (-delta, delta, -delta)
-      v3' = cc + (-delta, -delta, -delta)
+      v0' = cc + ( Point (-delta) (-delta) delta )
+      v1' = cc + ( Point (-delta) delta delta )
+      v2' = cc + ( Point (-delta) delta (-delta) )
+      v3' = cc + ( Point (-delta) (-delta) (-delta) )

 
 -- | The left (in the direction of -y) face of the cube.
 left_face :: Cube -> Face.Face
 
 -- | The left (in the direction of -y) face of the cube.
 left_face :: Cube -> Face.Face


@@ -205,10 +205,10 @@ left_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (delta, -delta, delta)
-      v1' = cc + (-delta, -delta, delta)
-      v2' = cc + (-delta, -delta, -delta)
-      v3' = cc + (delta, -delta, -delta)
+      v0' = cc + ( Point delta (-delta) delta )
+      v1' = cc + ( Point (-delta) (-delta) delta )
+      v2' = cc + ( Point (-delta) (-delta) (-delta) )
+      v3' = cc + ( Point delta (-delta) (-delta) )

 
 
 -- | The right (in the direction of y) face of the cube.
 
 
 -- | The right (in the direction of y) face of the cube.


@@ -217,10 +217,10 @@ right_face cube = Face.Face v0' v1' v2' v3'
     where
       delta = (1/2)*(h cube)
       cc  = center cube
     where
       delta = (1/2)*(h cube)
       cc  = center cube

-      v0' = cc + (-delta, delta, delta)
-      v1' = cc + (delta, delta, delta)
-      v2' = cc + (delta, delta, -delta)
-      v3' = cc + (-delta, delta, -delta)
+      v0' = cc + ( Point (-delta) delta delta)
+      v1' = cc + ( Point delta  delta delta )
+      v2' = cc + ( Point delta delta (-delta) )
+      v3' = cc + ( Point (-delta) delta (-delta) )

 
 
 tetrahedron :: Cube -> Int -> Tetrahedron
 
 
 tetrahedron :: Cube -> Int -> Tetrahedron


@@ -588,14 +588,14 @@ back_right_down_tetrahedra  cube =
     (tetrahedron cube 18)
 
 in_top_half :: Cube -> Point -> Bool
     (tetrahedron cube 18)
 
 in_top_half :: Cube -> Point -> Bool

-in_top_half cube (_,_,z) =
+in_top_half cube (Point _ _ z) =

   distance_from_top <= distance_from_bottom
   where
     distance_from_top = abs $ (zmax cube) - z
     distance_from_bottom = abs $ (zmin cube) - z
 
 in_front_half :: Cube -> Point -> Bool
   distance_from_top <= distance_from_bottom
   where
     distance_from_top = abs $ (zmax cube) - z
     distance_from_bottom = abs $ (zmin cube) - z
 
 in_front_half :: Cube -> Point -> Bool

-in_front_half cube (x,_,_) =
+in_front_half cube (Point x _ _) =

     distance_from_front <= distance_from_back
   where
     distance_from_front = abs $ (xmin cube) - x
     distance_from_front <= distance_from_back
   where
     distance_from_front = abs $ (xmin cube) - x


@@ -603,7 +603,7 @@ in_front_half cube (x,_,_) =
 
 
 in_left_half :: Cube -> Point -> Bool
 
 
 in_left_half :: Cube -> Point -> Bool

-in_left_half cube (_,y,_) =
+in_left_half cube (Point _ y _) =

     distance_from_left <= distance_from_right
   where
     distance_from_left = abs $ (ymin cube) - y
     distance_from_left <= distance_from_right
   where
     distance_from_left = abs $ (ymin cube) - y

diff --git a/src/Grid.hs b/src/Grid.hs
index d5553b426fc6c18c38438afec5d3039ee1c2a4cc..de5f76ac326ff6d4d169125284a3d8a9b7b381a2 100644 (file)
--- a/src/Grid.hs
+++ b/src/Grid.hs
@@ -30,7 +30,7 @@ import Cube (Cube(Cube),
              tetrahedron)
 import Examples (trilinear, trilinear9x9x9, zeros, naturals_1d)
 import FunctionValues (make_values, value_at)
              tetrahedron)
 import Examples (trilinear, trilinear9x9x9, zeros, naturals_1d)
 import FunctionValues (make_values, value_at)

-import Point (Point)
+import Point (Point(..))

 import ScaleFactor (ScaleFactor)
 import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
 import ThreeDimensional (ThreeDimensional(..))
 import ScaleFactor (ScaleFactor)
 import Tetrahedron (Tetrahedron, c, polynomial, v0, v1, v2, v3)
 import ThreeDimensional (ThreeDimensional(..))


@@ -105,10 +105,9 @@ calculate_containing_cube_coordinate g coord
 --   Since our grid is rectangular, we can figure this out without having
 --   to check every cube.
 find_containing_cube :: Grid -> Point -> Cube
 --   Since our grid is rectangular, we can figure this out without having
 --   to check every cube.
 find_containing_cube :: Grid -> Point -> Cube

-find_containing_cube g p =
+find_containing_cube g (Point x y z) =

     cube_at g i j k
     where
     cube_at g i j k
     where

-      (x, y, z) = p

       i = calculate_containing_cube_coordinate g x
       j = calculate_containing_cube_coordinate g y
       k = calculate_containing_cube_coordinate g z
       i = calculate_containing_cube_coordinate g x
       j = calculate_containing_cube_coordinate g y
       k = calculate_containing_cube_coordinate g z


@@ -128,7 +127,7 @@ zoom_result v3d (sfx, sfy, sfz) (R.Z R.:. m R.:. n R.:. o) =
     m' = (fromIntegral m) / (fromIntegral sfx) - offset
     n' = (fromIntegral n) / (fromIntegral sfy) - offset
     o' = (fromIntegral o) / (fromIntegral sfz) - offset
     m' = (fromIntegral m) / (fromIntegral sfx) - offset
     n' = (fromIntegral n) / (fromIntegral sfy) - offset
     o' = (fromIntegral o) / (fromIntegral sfz) - offset

-    p  = (m', n', o') :: Point
+    p  = Point m' n' o'

     cube = find_containing_cube g p
     t = find_containing_tetrahedron cube p
     f = polynomial t
     cube = find_containing_cube g p
     t = find_containing_tetrahedron cube p
     f = polynomial t


@@ -270,25 +269,25 @@ trilinear_c0_t0_tests =
 
     test_trilinear_f0_t0_v0 :: Assertion
     test_trilinear_f0_t0_v0 =
 
     test_trilinear_f0_t0_v0 :: Assertion
     test_trilinear_f0_t0_v0 =

-      assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+      assertEqual "v0 is correct" (v0 t) (Point 1 1 1)

 
     test_trilinear_f0_t0_v1 :: Assertion
     test_trilinear_f0_t0_v1 =
 
     test_trilinear_f0_t0_v1 :: Assertion
     test_trilinear_f0_t0_v1 =

-      assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+      assertEqual "v1 is correct" (v1 t) (Point 0.5 1 1)

 
     test_trilinear_f0_t0_v2 :: Assertion
     test_trilinear_f0_t0_v2 =
 
     test_trilinear_f0_t0_v2 :: Assertion
     test_trilinear_f0_t0_v2 =

-      assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+      assertEqual "v2 is correct" (v2 t) (Point 0.5 0.5 1.5)

 
     test_trilinear_f0_t0_v3 :: Assertion
     test_trilinear_f0_t0_v3 =
 
     test_trilinear_f0_t0_v3 :: Assertion
     test_trilinear_f0_t0_v3 =

-      assertEqual "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+      assertEqual "v3 is correct" (v3 t) (Point 0.5 1.5 1.5)

 
 
 test_trilinear_reproduced :: Assertion
 test_trilinear_reproduced =
     assertTrue "trilinears are reproduced correctly" $
 
 
 test_trilinear_reproduced :: Assertion
 test_trilinear_reproduced =
     assertTrue "trilinears are reproduced correctly" $

-             and [p (i', j', k') ~= value_at trilinear i j k
+             and [p (Point i' j' k') ~= value_at trilinear i j k

                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],
                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],


@@ -306,7 +305,7 @@ test_trilinear_reproduced =
 test_zeros_reproduced :: Assertion
 test_zeros_reproduced =
     assertTrue "the zero function is reproduced correctly" $
 test_zeros_reproduced :: Assertion
 test_zeros_reproduced =
     assertTrue "the zero function is reproduced correctly" $

-             and [p (i', j', k') ~= value_at zeros i j k
+             and [p (Point i' j' k') ~= value_at zeros i j k

                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],
                     | i <- [0..2],
                       j <- [0..2],
                       k <- [0..2],


@@ -325,7 +324,7 @@ test_zeros_reproduced =
 test_trilinear9x9x9_reproduced :: Assertion
 test_trilinear9x9x9_reproduced =
     assertTrue "trilinear 9x9x9 is reproduced correctly" $
 test_trilinear9x9x9_reproduced :: Assertion
 test_trilinear9x9x9_reproduced =
     assertTrue "trilinear 9x9x9 is reproduced correctly" $

-      and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
+      and [p (Point i' j' k') ~= value_at trilinear9x9x9 i j k

             | i <- [0..8],
               j <- [0..8],
               k <- [0..8],
             | i <- [0..8],
               j <- [0..8],
               k <- [0..8],


@@ -355,7 +354,7 @@ test_tetrahedra_collision_sensitivity =
   where
     g = make_grid 1 naturals_1d
     cube = cube_at g 0 18 0
   where
     g = make_grid 1 naturals_1d
     cube = cube_at g 0 18 0

-    p = (0, 17.5, 0.5) :: Point
+    p = Point 0 17.5 0.5

     t20 = tetrahedron cube 20
 
 
     t20 = tetrahedron cube 20
 
 

diff --git a/src/Point.hs b/src/Point.hs
index fd3ac58dec3ceef5dfd5c8aa1615e25a9bc0af53..a334c5c95642ae1f06dea200d03546aa82418316 100644 (file)
--- a/src/Point.hs
+++ b/src/Point.hs
@@ -1,30 +1,47 @@
 {-# LANGUAGE FlexibleInstances #-}
 
 module Point (
 {-# LANGUAGE FlexibleInstances #-}
 
 module Point (

-  Point,
+  Point(..),

   dot,
   scale
   )
 where
 
   dot,
   scale
   )
 where
 

-type Point = (Double, Double, Double)
+import Test.QuickCheck (Arbitrary(..))
+
+
+-- | Represents a point in three dimensions. We use a custom type (as
+--   opposed to a 3-tuple) so that we can make the coordinates strict.
+data Point =
+  Point !Double !Double !Double
+  deriving (Eq, Show)
+
+
+instance Arbitrary Point where
+  arbitrary = do
+    (x,y,z) <- arbitrary
+    return $ Point x y z
+

 
 instance Num Point where
 
 instance Num Point where

-    (x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)
-    (x1,y1,z1) - (x2,y2,z2) = (x1-x2, y1-y2, z1-z2)
-    (x1,y1,z1) * (x2,y2,z2) = (x1*x2, y1*y2, z1*z2)
-    abs (x, y, z) = (abs x, abs y, abs z)
-    signum (x, y, z) = (signum x, signum y, signum z)
-    fromInteger n = (fromInteger n, fromInteger n, fromInteger n)
+  (Point x1 y1 z1) + (Point x2 y2 z2) = Point (x1+x2) (y1+y2) (z1+z2)
+  (Point x1 y1 z1) - (Point x2 y2 z2) = Point (x1-x2) (y1-y2) (z1-z2)
+  (Point x1 y1 z1) * (Point x2 y2 z2) = Point (x1*x2) (y1*y2) (z1*z2)
+  abs (Point x y z) = Point (abs x) (abs y) (abs z)
+  signum (Point x y z) = Point (signum x) (signum y) (signum z)
+  fromInteger n =
+    Point coord coord coord
+    where
+      coord = fromInteger n

 
 
 -- | Scale a point by a constant.
 scale :: Point -> Double -> Point
 
 
 -- | Scale a point by a constant.
 scale :: Point -> Double -> Point

-scale (x, y, z) d = (x*d, y*d, z*d)
+scale (Point x y z) d = Point (x*d) (y*d) (z*d)

 
 
 -- | Returns the dot product of two points (taken as three-vectors).
 {-# INLINE dot #-}
 dot :: Point -> Point -> Double
 
 
 -- | Returns the dot product of two points (taken as three-vectors).
 {-# INLINE dot #-}
 dot :: Point -> Point -> Double

-dot (x1, y1, z1) (x2, y2, z2) =
+dot (Point x1 y1 z1) (Point x2 y2 z2) =

     (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)
     (x2 - x1)^(2::Int) + (y2 - y1)^(2::Int) + (z2 - z1)^(2::Int)

diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs
index 4c7abed0fe78e282ec1096c410cae41c15300129..f1614f9004b8a984b8e29ff3095072f1c16a72a4 100644 (file)
--- a/src/Tetrahedron.hs
+++ b/src/Tetrahedron.hs
@@ -28,7 +28,7 @@ import Test.QuickCheck (Arbitrary(..), Gen, Property, (==>))
 import Comparisons ((~=), nearly_ge)
 import FunctionValues (FunctionValues(..), empty_values)
 import Misc (factorial)
 import Comparisons ((~=), nearly_ge)
 import FunctionValues (FunctionValues(..), empty_values)
 import Misc (factorial)

-import Point (Point, scale)
+import Point (Point(..), scale)

 import RealFunction (RealFunction, cmult, fexp)
 import ThreeDimensional (ThreeDimensional(..))
 
 import RealFunction (RealFunction, cmult, fexp)
 import ThreeDimensional (ThreeDimensional(..))
 


@@ -294,10 +294,10 @@ det :: Point -> Point -> Point -> Point -> Double
 det p0 p1 p2 p3 =
   term5 + term6
   where
 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
     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


@@ -367,10 +367,10 @@ tetrahedron1_geometry_tests =
               [ testCase "volume1" volume1,
                 testCase "doesn't contain point1" doesnt_contain_point1]
   where
               [ 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,
     t = Tetrahedron { v0 = p0,
                       v1 = p1,
                       v2 = p2,


@@ -388,7 +388,7 @@ tetrahedron1_geometry_tests =
     doesnt_contain_point1 =
       assertEqual "doesn't contain an exterior point" False contained
       where
     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
 
 
         contained = contains_point t exterior_point
 
 


@@ -402,10 +402,10 @@ tetrahedron2_geometry_tests =
               [ testCase "volume1" volume1,
                 testCase "contains point1" contains_point1]
   where
               [ 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,
     t = Tetrahedron { v0 = p0,
                       v1 = p1,
                       v2 = p2,


@@ -421,7 +421,7 @@ tetrahedron2_geometry_tests =
     contains_point1 :: Assertion
     contains_point1 = assertEqual "contains an inner point" True contained
         where
     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
 
 
           contained = contains_point t inner_point
 
 


@@ -435,16 +435,16 @@ containment_tests =
                 testCase "doesn't contain point4" doesnt_contain_point4,
                 testCase "doesn't contain point5" doesnt_contain_point5]
   where
                 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
 
     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,
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,


@@ -458,8 +458,8 @@ containment_tests =
     doesnt_contain_point3 =
       assertEqual "doesn't contain an exterior point" False contained
       where
     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,
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,


@@ -473,8 +473,8 @@ containment_tests =
     doesnt_contain_point4 =
       assertEqual "doesn't contain an exterior point" False contained
       where
     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,
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,


@@ -488,8 +488,8 @@ containment_tests =
     doesnt_contain_point5 =
       assertEqual "doesn't contain an exterior point" False contained
       where
     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,
         t = Tetrahedron { v0 = p0,
                           v1 = p1,
                           v2 = p2,