X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTests%2FGrid.hs;h=92ba20efbce2aa1c9f7bb843ec06806cb3e5d631;hb=ac0e94e82605a5fd1e3ee724cd597f48614689e4;hp=e22557b6e396f4951e208aa097f122c3463c5523;hpb=89b8b6e94fcc944a1f4611811265f3c6217af850;p=spline3.git

diff --git a/src/Tests/Grid.hs b/src/Tests/Grid.hs
index e22557b..92ba20e 100644
--- a/src/Tests/Grid.hs
+++ b/src/Tests/Grid.hs
@@ -1,11 +1,379 @@
 module Tests.Grid
 where
 
-import Test.QuickCheck
+import Data.Maybe (fromJust)
+import Test.HUnit
+
+import Assertions
+import Comparisons
+import Cube hiding (i, j, k)
+import Examples
+import FunctionValues (value_at)
 import Grid
+import Point (Point)
+import Tetrahedron
+import ThreeDimensional
+
+
+-- | Check the value of c0030 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0030 :: Assertion
+test_trilinear_c0030 =
+    assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0003 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0003 :: Assertion
+test_trilinear_c0003 =
+    assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0021 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0021 :: Assertion
+test_trilinear_c0021 =
+    assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0012 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0012 :: Assertion
+test_trilinear_c0012 =
+    assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0120 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0120 :: Assertion
+test_trilinear_c0120 =
+    assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0102 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0102 :: Assertion
+test_trilinear_c0102 =
+    assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0111 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0111 :: Assertion
+test_trilinear_c0111 =
+    assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0210 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0210 :: Assertion
+test_trilinear_c0210 =
+    assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0201 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0201 :: Assertion
+test_trilinear_c0201 =
+    assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c0300 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c0300 :: Assertion
+test_trilinear_c0300 =
+    assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1020 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1020 :: Assertion
+test_trilinear_c1020 =
+    assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1002 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1002 :: Assertion
+test_trilinear_c1002 =
+    assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1011 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1011 :: Assertion
+test_trilinear_c1011 =
+    assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1110 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1110 :: Assertion
+test_trilinear_c1110 =
+    assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1101 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1101 :: Assertion
+test_trilinear_c1101 =
+    assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c1200 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c1200 :: Assertion
+test_trilinear_c1200 =
+    assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c2010 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c2010 :: Assertion
+test_trilinear_c2010 =
+    assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c2001 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c2001 :: Assertion
+test_trilinear_c2001 =
+    assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c2100 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c2100 :: Assertion
+test_trilinear_c2100 =
+    assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Check the value of c3000 for tetrahedron0 belonging to the
+--   cube centered on (1,1,1) with a grid constructed from the
+--   trilinear values. See example one in the paper.
+test_trilinear_c3000 :: Assertion
+test_trilinear_c3000 =
+    assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Make sure that v0 of tetrahedron0 belonging to the cube centered
+--   on (1,1,1) with a grid constructed from the trilinear values
+--   winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v0 :: Assertion
+test_trilinear_f0_t0_v0 =
+    assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Make sure that v1 of tetrahedron0 belonging to the cube centered
+--   on (1,1,1) with a grid constructed from the trilinear values
+--   winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v1 :: Assertion
+test_trilinear_f0_t0_v1 =
+    assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Make sure that v2 of tetrahedron0 belonging to the cube centered
+--   on (1,1,1) with a grid constructed from the trilinear values
+--   winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v2 :: Assertion
+test_trilinear_f0_t0_v2 =
+    assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+-- | Make sure that v3 of tetrahedron0 belonging to the cube centered
+--   on (1,1,1) with a grid constructed from the trilinear values
+--   winds up in the right place. See example one in the paper.
+test_trilinear_f0_t0_v3 :: Assertion
+test_trilinear_f0_t0_v3 =
+    assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+      where
+        g = make_grid 1 trilinear
+        cube = fromJust $ cube_at g 1 1 1
+        t = tetrahedron0 cube
+
+
+test_trilinear_reproduced :: Assertion
+test_trilinear_reproduced =
+    assertTrue "trilinears are reproduced correctly" $
+             and [p (i', j', k') ~= value_at trilinear i j k
+                    | i <- [0..2],
+                      j <- [0..2],
+                      k <- [0..2],
+                      t <- tetrahedra c0,
+                      let p = polynomial t,
+                      let i' = fromIntegral i,
+                      let j' = fromIntegral j,
+                      let k' = fromIntegral k]
+    where
+      g = make_grid 1 trilinear
+      c0 = fromJust $ cube_at g 1 1 1
+
+
+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
+                    | i <- [0..2],
+                      j <- [0..2],
+                      k <- [0..2],
+                      let i' = fromIntegral i,
+                      let j' = fromIntegral j,
+                      let k' = fromIntegral k]
+    where
+      g = make_grid 1 zeros
+      c0 = fromJust $ cube_at g 1 1 1
+      t0 = tetrahedron0 c0
+      p = polynomial t0
+
+
+-- | Make sure we can reproduce a 9x9x9 trilinear from the 3x3x3 one.
+test_trilinear9x9x9_reproduced :: Assertion
+test_trilinear9x9x9_reproduced =
+    assertTrue "trilinear 9x9x9 is reproduced correctly" $
+      and [p (i', j', k') ~= value_at trilinear9x9x9 i j k
+            | i <- [0..8],
+              j <- [0..8],
+              k <- [0..8],
+              t <- tetrahedra c0,
+              let p = polynomial t,
+              let i' = (fromIntegral i) * 0.5,
+              let j' = (fromIntegral j) * 0.5,
+              let k' = (fromIntegral k) * 0.5]
+    where
+      g = make_grid 1 trilinear
+      c0 = fromJust $ cube_at g 1 1 1
+
 
-instance Arbitrary Grid where
-    arbitrary = do
-      (Positive h') <- arbitrary :: Gen (Positive Double)
-      fv <- arbitrary :: Gen [[[Double]]]
-      return (make_grid h' fv)
+-- | The point 'p' in this test lies on the boundary of tetrahedra 12 and 15.
+--   However, the 'contains_point' test fails due to some numerical innacuracy.
+--   This bug should have been fixed by setting a positive tolerance level.
+--
+--   Example from before the fix:
+--
+--   > b0 (tetrahedron12 c) p
+--   -2.168404344971019e-18
+--   > b0 (tetrahedron15 c) p
+--   -3.4694469519536365e-18
+--
+test_tetrahedra_collision_sensitivity :: Assertion
+test_tetrahedra_collision_sensitivity =
+  assertTrue "tetrahedron collision tests aren't too sensitive" $
+             contains_point t12 p &&
+             contains_point t15 p
+  where
+    g = make_grid 1 trilinear
+    c = cube_at g 0 17 1
+    p = (0, 16.75, 0.5) :: Point
+    t12 = tetrahedron12 c
+    t15 = tetrahedron15 c