+-- | 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
+