-- | The Grid module just contains the Grid type and two constructors
-- for it. We hide the main Grid constructor because we don't want
-- to allow instantiation of a grid with h <= 0.
-module Grid
+module Grid (
+ grid_tests,
+ make_grid,
+ slow_tests,
+ zoom
+ )
where
import Data.Array (Array, array, (!))
import qualified Data.Array.Repa as R
-import Test.QuickCheck (Arbitrary(..), Gen, Positive(..))
+import Test.HUnit
+import Test.Framework (Test, testGroup)
+import Test.Framework.Providers.HUnit (testCase)
+import Test.Framework.Providers.QuickCheck2 (testProperty)
+import Test.QuickCheck (Arbitrary(..), Gen, Positive(..), choose)
-import Cube (Cube(Cube), find_containing_tetrahedron)
+import Assertions
+import Comparisons
+import Cube (Cube(Cube),
+ find_containing_tetrahedron,
+ tetrahedra,
+ tetrahedron0,
+ tetrahedron15)
+import Examples
import FunctionValues
import Point (Point)
import ScaleFactor
-import Tetrahedron (polynomial)
+import Tetrahedron (c, polynomial, v0, v1, v2, v3)
+import ThreeDimensional
import Values (Values3D, dims, empty3d, zoom_shape)
| otherwise = Grid grid_size values (cubes grid_size values)
--- | Creates an empty grid with grid size 1.
-empty_grid :: Grid
-empty_grid = make_grid 1 empty3d
-
-
-- | Returns a three-dimensional array of cubes centered on the grid
-- points (h*i, h*j, h*k) with the appropriate 'FunctionValues'.
cubes :: Double -> Values3D -> CubeGrid
j' = (fromIntegral j) / (fromIntegral sfy) - offset
k' = (fromIntegral k) / (fromIntegral sfz) - offset
p = (i', j', k') :: Point
- c = find_containing_cube g p
- t = find_containing_tetrahedron c p
+ cube = find_containing_cube g p
+ t = find_containing_tetrahedron cube p
f = polynomial t
arr = function_values g
(xsize, ysize, zsize) = dims arr
transExtent = zoom_shape scale_factor
+
+
+
+
+-- | Check all coefficients of tetrahedron0 belonging to the cube
+-- centered on (1,1,1) with a grid constructed from the trilinear
+-- values. See example one in the paper.
+--
+-- We also verify that the four vertices on face0 of the cube are
+-- in the correct location.
+--
+trilinear_c0_t0_tests :: Test.Framework.Test
+trilinear_c0_t0_tests =
+ testGroup "trilinear c0 t0"
+ [testGroup "coefficients"
+ [testCase "c0030 is correct" test_trilinear_c0030,
+ testCase "c0003 is correct" test_trilinear_c0003,
+ testCase "c0021 is correct" test_trilinear_c0021,
+ testCase "c0012 is correct" test_trilinear_c0012,
+ testCase "c0120 is correct" test_trilinear_c0120,
+ testCase "c0102 is correct" test_trilinear_c0102,
+ testCase "c0111 is correct" test_trilinear_c0111,
+ testCase "c0210 is correct" test_trilinear_c0210,
+ testCase "c0201 is correct" test_trilinear_c0201,
+ testCase "c0300 is correct" test_trilinear_c0300,
+ testCase "c1020 is correct" test_trilinear_c1020,
+ testCase "c1002 is correct" test_trilinear_c1002,
+ testCase "c1011 is correct" test_trilinear_c1011,
+ testCase "c1110 is correct" test_trilinear_c1110,
+ testCase "c1101 is correct" test_trilinear_c1101,
+ testCase "c1200 is correct" test_trilinear_c1200,
+ testCase "c2010 is correct" test_trilinear_c2010,
+ testCase "c2001 is correct" test_trilinear_c2001,
+ testCase "c2100 is correct" test_trilinear_c2100,
+ testCase "c3000 is correct" test_trilinear_c3000],
+
+ testGroup "face0 vertices"
+ [testCase "v0 is correct" test_trilinear_f0_t0_v0,
+ testCase "v1 is correct" test_trilinear_f0_t0_v1,
+ testCase "v2 is correct" test_trilinear_f0_t0_v2,
+ testCase "v3 is correct" test_trilinear_f0_t0_v3]
+ ]
+ where
+ g = make_grid 1 trilinear
+ cube = cube_at g 1 1 1
+ t = tetrahedron0 cube
+
+ test_trilinear_c0030 :: Assertion
+ test_trilinear_c0030 =
+ assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
+
+ test_trilinear_c0003 :: Assertion
+ test_trilinear_c0003 =
+ assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
+
+ test_trilinear_c0021 :: Assertion
+ test_trilinear_c0021 =
+ assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
+
+ test_trilinear_c0012 :: Assertion
+ test_trilinear_c0012 =
+ assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
+
+ test_trilinear_c0120 :: Assertion
+ test_trilinear_c0120 =
+ assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
+
+ test_trilinear_c0102 :: Assertion
+ test_trilinear_c0102 =
+ assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
+
+ test_trilinear_c0111 :: Assertion
+ test_trilinear_c0111 =
+ assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
+
+ test_trilinear_c0210 :: Assertion
+ test_trilinear_c0210 =
+ assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
+
+ test_trilinear_c0201 :: Assertion
+ test_trilinear_c0201 =
+ assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
+
+ test_trilinear_c0300 :: Assertion
+ test_trilinear_c0300 =
+ assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
+
+ test_trilinear_c1020 :: Assertion
+ test_trilinear_c1020 =
+ assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
+
+ test_trilinear_c1002 :: Assertion
+ test_trilinear_c1002 =
+ assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
+
+ test_trilinear_c1011 :: Assertion
+ test_trilinear_c1011 =
+ assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
+
+ test_trilinear_c1110 :: Assertion
+ test_trilinear_c1110 =
+ assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
+
+ test_trilinear_c1101 :: Assertion
+ test_trilinear_c1101 =
+ assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
+
+ test_trilinear_c1200 :: Assertion
+ test_trilinear_c1200 =
+ assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
+
+ test_trilinear_c2010 :: Assertion
+ test_trilinear_c2010 =
+ assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
+
+ test_trilinear_c2001 :: Assertion
+ test_trilinear_c2001 =
+ assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
+
+ test_trilinear_c2100 :: Assertion
+ test_trilinear_c2100 =
+ assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
+
+ test_trilinear_c3000 :: Assertion
+ test_trilinear_c3000 =
+ assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
+
+ test_trilinear_f0_t0_v0 :: Assertion
+ test_trilinear_f0_t0_v0 =
+ assertEqual "v0 is correct" (v0 t) (1, 1, 1)
+
+ test_trilinear_f0_t0_v1 :: Assertion
+ test_trilinear_f0_t0_v1 =
+ assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
+
+ test_trilinear_f0_t0_v2 :: Assertion
+ test_trilinear_f0_t0_v2 =
+ assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
+
+ test_trilinear_f0_t0_v3 :: Assertion
+ test_trilinear_f0_t0_v3 =
+ assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
+
+
+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 = 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 = 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 = cube_at g 1 1 1
+
+
+-- | 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 (tetrahedron15 c) p
+-- -3.4694469519536365e-18
+--
+test_tetrahedra_collision_sensitivity :: Assertion
+test_tetrahedra_collision_sensitivity =
+ assertTrue "tetrahedron collision tests isn't too sensitive" $
+ contains_point t15 p
+ where
+ g = make_grid 1 naturals_1d
+ cube = cube_at g 0 17 1
+ p = (0, 16.75, 0.5) :: Point
+ t15 = tetrahedron15 cube
+
+
+prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
+prop_cube_indices_never_go_out_of_bounds g =
+ do
+ let delta = Grid.h g
+ let coordmin = negate (delta/2)
+
+ let (xsize, ysize, zsize) = dims $ function_values g
+ let xmax = delta*(fromIntegral xsize) - (delta/2)
+ let ymax = delta*(fromIntegral ysize) - (delta/2)
+ let zmax = delta*(fromIntegral zsize) - (delta/2)
+
+ x <- choose (coordmin, xmax)
+ y <- choose (coordmin, ymax)
+ z <- choose (coordmin, zmax)
+
+ let idx_x = calculate_containing_cube_coordinate g x
+ let idx_y = calculate_containing_cube_coordinate g y
+ let idx_z = calculate_containing_cube_coordinate g z
+
+ return $
+ idx_x >= 0 &&
+ idx_x <= xsize - 1 &&
+ idx_y >= 0 &&
+ idx_y <= ysize - 1 &&
+ idx_z >= 0 &&
+ idx_z <= zsize - 1
+
+
+
+grid_tests :: Test.Framework.Test
+grid_tests =
+ testGroup "Grid Tests" [
+ trilinear_c0_t0_tests,
+ testCase "tetrahedra collision test isn't too sensitive"
+ test_tetrahedra_collision_sensitivity,
+ testCase "trilinear reproduced" test_trilinear_reproduced,
+ testCase "zeros reproduced" test_zeros_reproduced ]
+
+
+-- Do the slow tests last so we can stop paying attention.
+slow_tests :: Test.Framework.Test
+slow_tests =
+ testGroup "Slow Tests" [
+ testProperty "cube indices within bounds"
+ prop_cube_indices_never_go_out_of_bounds,
+ testCase "trilinear9x9x9 reproduced" test_trilinear9x9x9_reproduced ]
+++ /dev/null
-module Tests.Grid
-where
-
-import Test.Framework (Test, testGroup)
-import Test.Framework.Providers.HUnit (testCase)
-import Test.HUnit
-import Test.QuickCheck
-
-
-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
-import Values (dims)
-
-
--- | Check all coefficients of tetrahedron0 belonging to the cube
--- centered on (1,1,1) with a grid constructed from the trilinear
--- values. See example one in the paper.
---
--- We also verify that the four vertices on face0 of the cube are
--- in the correct location.
---
-trilinear_c0_t0_tests :: Test.Framework.Test
-trilinear_c0_t0_tests =
- testGroup "trilinear c0 t0"
- [testGroup "coefficients"
- [testCase "c0030 is correct" test_trilinear_c0030,
- testCase "c0003 is correct" test_trilinear_c0003,
- testCase "c0021 is correct" test_trilinear_c0021,
- testCase "c0012 is correct" test_trilinear_c0012,
- testCase "c0120 is correct" test_trilinear_c0120,
- testCase "c0102 is correct" test_trilinear_c0102,
- testCase "c0111 is correct" test_trilinear_c0111,
- testCase "c0210 is correct" test_trilinear_c0210,
- testCase "c0201 is correct" test_trilinear_c0201,
- testCase "c0300 is correct" test_trilinear_c0300,
- testCase "c1020 is correct" test_trilinear_c1020,
- testCase "c1002 is correct" test_trilinear_c1002,
- testCase "c1011 is correct" test_trilinear_c1011,
- testCase "c1110 is correct" test_trilinear_c1110,
- testCase "c1101 is correct" test_trilinear_c1101,
- testCase "c1200 is correct" test_trilinear_c1200,
- testCase "c2010 is correct" test_trilinear_c2010,
- testCase "c2001 is correct" test_trilinear_c2001,
- testCase "c2100 is correct" test_trilinear_c2100,
- testCase "c3000 is correct" test_trilinear_c3000],
-
- testGroup "face0 vertices"
- [testCase "v0 is correct" test_trilinear_f0_t0_v0,
- testCase "v1 is correct" test_trilinear_f0_t0_v1,
- testCase "v2 is correct" test_trilinear_f0_t0_v2,
- testCase "v3 is correct" test_trilinear_f0_t0_v3]
- ]
- where
- g = make_grid 1 trilinear
- cube = cube_at g 1 1 1
- t = tetrahedron0 cube
-
- test_trilinear_c0030 :: Assertion
- test_trilinear_c0030 =
- assertAlmostEqual "c0030 is correct" (c t 0 0 3 0) (17/8)
-
- test_trilinear_c0003 :: Assertion
- test_trilinear_c0003 =
- assertAlmostEqual "c0003 is correct" (c t 0 0 0 3) (27/8)
-
- test_trilinear_c0021 :: Assertion
- test_trilinear_c0021 =
- assertAlmostEqual "c0021 is correct" (c t 0 0 2 1) (61/24)
-
- test_trilinear_c0012 :: Assertion
- test_trilinear_c0012 =
- assertAlmostEqual "c0012 is correct" (c t 0 0 1 2) (71/24)
-
- test_trilinear_c0120 :: Assertion
- test_trilinear_c0120 =
- assertAlmostEqual "c0120 is correct" (c t 0 1 2 0) (55/24)
-
- test_trilinear_c0102 :: Assertion
- test_trilinear_c0102 =
- assertAlmostEqual "c0102 is correct" (c t 0 1 0 2) (73/24)
-
- test_trilinear_c0111 :: Assertion
- test_trilinear_c0111 =
- assertAlmostEqual "c0111 is correct" (c t 0 1 1 1) (8/3)
-
- test_trilinear_c0210 :: Assertion
- test_trilinear_c0210 =
- assertAlmostEqual "c0210 is correct" (c t 0 2 1 0) (29/12)
-
- test_trilinear_c0201 :: Assertion
- test_trilinear_c0201 =
- assertAlmostEqual "c0201 is correct" (c t 0 2 0 1) (11/4)
-
- test_trilinear_c0300 :: Assertion
- test_trilinear_c0300 =
- assertAlmostEqual "c0300 is correct" (c t 0 3 0 0) (5/2)
-
- test_trilinear_c1020 :: Assertion
- test_trilinear_c1020 =
- assertAlmostEqual "c1020 is correct" (c t 1 0 2 0) (8/3)
-
- test_trilinear_c1002 :: Assertion
- test_trilinear_c1002 =
- assertAlmostEqual "c1002 is correct" (c t 1 0 0 2) (23/6)
-
- test_trilinear_c1011 :: Assertion
- test_trilinear_c1011 =
- assertAlmostEqual "c1011 is correct" (c t 1 0 1 1) (13/4)
-
- test_trilinear_c1110 :: Assertion
- test_trilinear_c1110 =
- assertAlmostEqual "c1110 is correct" (c t 1 1 1 0) (23/8)
-
- test_trilinear_c1101 :: Assertion
- test_trilinear_c1101 =
- assertAlmostEqual "c1101 is correct" (c t 1 1 0 1) (27/8)
-
- test_trilinear_c1200 :: Assertion
- test_trilinear_c1200 =
- assertAlmostEqual "c1200 is correct" (c t 1 2 0 0) 3
-
- test_trilinear_c2010 :: Assertion
- test_trilinear_c2010 =
- assertAlmostEqual "c2010 is correct" (c t 2 0 1 0) (10/3)
-
- test_trilinear_c2001 :: Assertion
- test_trilinear_c2001 =
- assertAlmostEqual "c2001 is correct" (c t 2 0 0 1) 4
-
- test_trilinear_c2100 :: Assertion
- test_trilinear_c2100 =
- assertAlmostEqual "c2100 is correct" (c t 2 1 0 0) (7/2)
-
- test_trilinear_c3000 :: Assertion
- test_trilinear_c3000 =
- assertAlmostEqual "c3000 is correct" (c t 3 0 0 0) 4
-
- test_trilinear_f0_t0_v0 :: Assertion
- test_trilinear_f0_t0_v0 =
- assertEqual "v0 is correct" (v0 t) (1, 1, 1)
-
- test_trilinear_f0_t0_v1 :: Assertion
- test_trilinear_f0_t0_v1 =
- assertEqual "v1 is correct" (v1 t) (0.5, 1, 1)
-
- test_trilinear_f0_t0_v2 :: Assertion
- test_trilinear_f0_t0_v2 =
- assertEqual "v2 is correct" (v2 t) (0.5, 0.5, 1.5)
-
- test_trilinear_f0_t0_v3 :: Assertion
- test_trilinear_f0_t0_v3 =
- assertClose "v3 is correct" (v3 t) (0.5, 1.5, 1.5)
-
-
-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 = 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 = 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 = cube_at g 1 1 1
-
-
--- | 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 (tetrahedron15 c) p
--- -3.4694469519536365e-18
---
-test_tetrahedra_collision_sensitivity :: Assertion
-test_tetrahedra_collision_sensitivity =
- assertTrue "tetrahedron collision tests isn't too sensitive" $
- contains_point t15 p
- where
- g = make_grid 1 naturals_1d
- c = cube_at g 0 17 1
- p = (0, 16.75, 0.5) :: Point
- t15 = tetrahedron15 c
-
-
-prop_cube_indices_never_go_out_of_bounds :: Grid -> Gen Bool
-prop_cube_indices_never_go_out_of_bounds g =
- do
- let delta = Grid.h g
- let coordmin = negate (delta/2)
-
- let (xsize, ysize, zsize) = dims $ function_values g
- let xmax = delta*(fromIntegral xsize) - (delta/2)
- let ymax = delta*(fromIntegral ysize) - (delta/2)
- let zmax = delta*(fromIntegral zsize) - (delta/2)
-
- x <- choose (coordmin, xmax)
- y <- choose (coordmin, ymax)
- z <- choose (coordmin, zmax)
-
- let p = (x,y,z) :: Point
- let idx_x = calculate_containing_cube_coordinate g x
- let idx_y = calculate_containing_cube_coordinate g y
- let idx_z = calculate_containing_cube_coordinate g z
-
- return $
- idx_x >= 0 &&
- idx_x <= xsize - 1 &&
- idx_y >= 0 &&
- idx_y <= ysize - 1 &&
- idx_z >= 0 &&
- idx_z <= zsize - 1
projects / spline3.git / commitdiff