+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). Note that the
+-- third and fourth indices of c-t10 have been switched. This is
+-- because we store the triangles oriented such that their volume is
+-- positive. If T and T-tilde share \<v1,v2,v3\> and v0,v0-tilde point
+-- in opposite directions, one of them has to have negative volume!
+prop_c0120_identity :: Grid -> Property
+prop_c0120_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 1 2 0 ~= (c t0 1 0 2 0 + c t10 1 0 0 2) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+-- 'prop_c0120_identity'.
+prop_c0111_identity :: Grid -> Property
+prop_c0111_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 1 1 1 ~= (c t0 1 0 1 1 + c t10 1 0 1 1) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+-- 'prop_c0120_identity'.
+prop_c0201_identity :: Grid -> Property
+prop_c0201_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 2 0 1 ~= (c t0 1 1 0 1 + c t10 1 1 1 0) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+-- 'prop_c0120_identity'.
+prop_c0102_identity :: Grid -> Property
+prop_c0102_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 1 0 2 ~= (c t0 1 0 0 2 + c t10 1 0 2 0) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+-- 'prop_c0120_identity'.
+prop_c0210_identity :: Grid -> Property
+prop_c0210_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 2 1 0 ~= (c t0 1 1 1 0 + c t10 1 1 0 1) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | Given in Sorokina and Zeilfelder, p. 80, (2.9). See
+-- 'prop_c0120_identity'.
+prop_c0300_identity :: Grid -> Property
+prop_c0300_identity g =
+ and [xsize >= 3, ysize >= 3, zsize >= 3] ==>
+ c t0 0 3 0 0 ~= (c t0 1 2 0 0 + c t10 1 2 0 0) / 2
+ where
+ fvs = function_values g
+ (xsize, ysize, zsize) = dims fvs
+ cube0 = cube_at g 1 1 1
+ cube1 = cube_at g 0 1 1
+ t0 = tetrahedron cube0 0 -- These two tetrahedra share a face.
+ t10 = tetrahedron cube1 10
+
+
+-- | All of the properties from Section (2.9), p. 80. These require a
+-- grid since they refer to two adjacent cubes.
+p80_29_properties :: Test.Framework.Test
+p80_29_properties =
+ testGroup "p. 80, Section (2.9) Properties" [
+ testProperty "c0120 identity" prop_c0120_identity,
+ testProperty "c0111 identity" prop_c0111_identity,
+ testProperty "c0201 identity" prop_c0201_identity,
+ testProperty "c0102 identity" prop_c0102_identity,
+ testProperty "c0210 identity" prop_c0210_identity,
+ testProperty "c0300 identity" prop_c0300_identity ]
+