X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=6e67d4cd4d6d3c7311a7c095e4b43be9387ba69b;hb=fa764bc6679c8fe62341918c271df287365eaa04;hp=8f22266049538cc697d3c0cbd83eb492654f28d3;hpb=a06c2cdbc189c6b16add4ca06856f0727c12a617;p=spline3.git diff --git a/src/Cube.hs b/src/Cube.hs index 8f22266..6e67d4c 100644 --- a/src/Cube.hs +++ b/src/Cube.hs @@ -28,15 +28,7 @@ import qualified Face (Face(Face, v0, v1, v2, v3)) import FunctionValues import Misc (all_equal, disjoint) import Point -import Tetrahedron ( - Tetrahedron(..), - c, - b0, - b1, - b2, - b3, - volume - ) +import Tetrahedron (Tetrahedron(..), c, volume) import ThreeDimensional data Cube = Cube { h :: Double, @@ -72,8 +64,7 @@ instance Show Cube where " ymin: " ++ (show (ymin cube)) ++ "\n" ++ " ymax: " ++ (show (ymax cube)) ++ "\n" ++ " zmin: " ++ (show (zmin cube)) ++ "\n" ++ - " zmax: " ++ (show (zmax cube)) ++ "\n" ++ - " fv: " ++ (show (Cube.fv cube)) ++ "\n" + " zmax: " ++ (show (zmax cube)) ++ "\n" where subscript = (show (i cube)) ++ "," ++ (show (j cube)) ++ "," ++ (show (k cube)) @@ -82,7 +73,7 @@ instance Show Cube where -- | The left-side boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. xmin :: Cube -> Double -xmin cube = (2*i' - 1)*delta / 2 +xmin cube = (i' - 1/2)*delta where i' = fromIntegral (i cube) :: Double delta = h cube @@ -90,7 +81,7 @@ xmin cube = (2*i' - 1)*delta / 2 -- | The right-side boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. xmax :: Cube -> Double -xmax cube = (2*i' + 1)*delta / 2 +xmax cube = (i' + 1/2)*delta where i' = fromIntegral (i cube) :: Double delta = h cube @@ -98,7 +89,7 @@ xmax cube = (2*i' + 1)*delta / 2 -- | The front boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. ymin :: Cube -> Double -ymin cube = (2*j' - 1)*delta / 2 +ymin cube = (j' - 1/2)*delta where j' = fromIntegral (j cube) :: Double delta = h cube @@ -106,7 +97,7 @@ ymin cube = (2*j' - 1)*delta / 2 -- | The back boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. ymax :: Cube -> Double -ymax cube = (2*j' + 1)*delta / 2 +ymax cube = (j' + 1/2)*delta where j' = fromIntegral (j cube) :: Double delta = h cube @@ -114,7 +105,7 @@ ymax cube = (2*j' + 1)*delta / 2 -- | The bottom boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. zmin :: Cube -> Double -zmin cube = (2*k' - 1)*delta / 2 +zmin cube = (k' - 1/2)*delta where k' = fromIntegral (k cube) :: Double delta = h cube @@ -122,7 +113,7 @@ zmin cube = (2*k' - 1)*delta / 2 -- | The top boundary of the cube. See Sorokina and Zeilfelder, -- p. 76. zmax :: Cube -> Double -zmax cube = (2*k' + 1)*delta / 2 +zmax cube = (k' + 1/2)*delta where k' = fromIntegral (k cube) :: Double delta = h cube @@ -673,15 +664,15 @@ prop_opposite_octant_tetrahedra_disjoint6 cube = -- | Since the grid size is necessarily positive, all tetrahedra --- (which comprise cubes of positive volume) must have positive volume --- as well. +-- (which comprise cubes of positive volume) must have positive +-- volume as well. prop_all_volumes_positive :: Cube -> Bool prop_all_volumes_positive cube = - null nonpositive_volumes + all (>= 0) volumes where ts = tetrahedra cube volumes = map volume ts - nonpositive_volumes = filter (<= 0) volumes + -- | In fact, since all of the tetrahedra are identical, we should -- already know their volumes. There's 24 tetrahedra to a cube, so @@ -701,7 +692,7 @@ prop_v0_all_equal cube = (v0 t0) == (v0 t1) -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Note that the --- third and fourth indices of c-t1 have been switched. This is +-- third and fourth indices of c-t3 have been switched. This is -- because we store the triangles oriented such that their volume is -- positive. If T and T-tilde share \ and v3,v3-tilde point -- in opposite directions, one of them has to have negative volume! @@ -750,8 +741,8 @@ prop_c0120_identity5 cube = t4 = tetrahedron cube 4 t5 = tetrahedron cube 5 --- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats --- -- 'prop_c0120_identity1' with tetrahedrons 5 and 6. +-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats +-- 'prop_c0120_identity1' with tetrahedrons 5 and 6. prop_c0120_identity6 :: Cube -> Bool prop_c0120_identity6 cube = c t6 0 1 2 0 ~= (c t6 0 0 2 1 + c t5 0 0 1 2) / 2 @@ -760,8 +751,8 @@ prop_c0120_identity6 cube = t6 = tetrahedron cube 6 --- -- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats --- -- 'prop_c0120_identity1' with tetrahedrons 6 and 7. +-- | Given in Sorokina and Zeilfelder, p. 79, (2.6). Repeats +-- 'prop_c0120_identity1' with tetrahedrons 6 and 7. prop_c0120_identity7 :: Cube -> Bool prop_c0120_identity7 cube = c t7 0 1 2 0 ~= (c t7 0 0 2 1 + c t6 0 0 1 2) / 2 @@ -955,23 +946,6 @@ prop_c1011_identity cube = t6 = tetrahedron cube 6 - --- | Given in Sorokina and Zeilfelder, p. 78. -prop_cijk1_identity :: Cube -> Bool -prop_cijk1_identity cube = - and [ c t0 i j k 1 ~= - (c t1 (i+1) j k 0) * ((b0 t0) (v3 t1)) + - (c t1 i (j+1) k 0) * ((b1 t0) (v3 t1)) + - (c t1 i j (k+1) 0) * ((b2 t0) (v3 t1)) + - (c t1 i j k 1) * ((b3 t0) (v3 t1)) | i <- [0..2], - j <- [0..2], - k <- [0..2], - i + j + k == 2] - where - t0 = tetrahedron cube 0 - t1 = tetrahedron cube 1 - - -- | The function values at the interior should be the same for all -- tetrahedra. prop_interior_values_all_identical :: Cube -> Bool @@ -1139,14 +1113,6 @@ prop_t7_shares_edge_with_t20 cube = t20 = tetrahedron cube 20 - - - -p78_25_properties :: Test.Framework.Test -p78_25_properties = - testGroup "p. 78, Section (2.5) Properties" [ - testProperty "c_ijk1 identity" prop_cijk1_identity ] - p79_26_properties :: Test.Framework.Test p79_26_properties = testGroup "p. 79, Section (2.6) Properties" [ @@ -1207,7 +1173,6 @@ edge_incidence_tests = cube_properties :: Test.Framework.Test cube_properties = testGroup "Cube Properties" [ - p78_25_properties, p79_26_properties, p79_27_properties, p79_28_properties,