X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=6da41945dd6ad01b521acb2d0349c01390c7bd54;hb=993490fd9d940f5e8dea4f934c07c1a5a6c1f8ff;hp=9f68364042e7563a3b10d23f01e72f2845ba74af;hpb=ec2bcae0167bcc09c30e7618a5d7601510593610;p=spline3.git diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs index 9f68364..6da4194 100644 --- a/src/Tetrahedron.hs +++ b/src/Tetrahedron.hs @@ -1,4 +1,15 @@ -module Tetrahedron +module Tetrahedron ( + Tetrahedron(..), + b0, -- Cube test + b1, -- Cube test + b2, -- Cube test + b3, -- Cube test + c, + polynomial, + tetrahedron_properties, + tetrahedron_tests, + volume -- Cube test + ) where import qualified Data.Vector as V ( @@ -8,10 +19,14 @@ import qualified Data.Vector as V ( ) import Numeric.LinearAlgebra hiding (i, scale) import Prelude hiding (LT) -import Test.QuickCheck (Arbitrary(..), Gen) +import Test.Framework (Test, testGroup) +import Test.Framework.Providers.HUnit (testCase) +import Test.Framework.Providers.QuickCheck2 (testProperty) +import Test.HUnit +import Test.QuickCheck (Arbitrary(..), Gen, Property, (==>)) import Cardinal -import Comparisons (nearly_ge) +import Comparisons ((~=), nearly_ge) import FunctionValues import Misc (factorial) import Point @@ -319,3 +334,354 @@ b3 :: Tetrahedron -> (RealFunction Point) b3 t point = (volume inner_tetrahedron) / (precomputed_volume t) where inner_tetrahedron = t { v3 = point } + + + + +-- Tests + + +-- | Check the volume of a particular tetrahedron (computed by hand) +-- and whether or not it contains a specific point chosen to be +-- outside of it. Its vertices are in clockwise order, so the volume +-- should be negative. +tetrahedron1_geometry_tests :: Test.Framework.Test +tetrahedron1_geometry_tests = + testGroup "tetrahedron1 geometry" + [ testCase "volume1" volume1, + testCase "doesn't contain point1" doesnt_contain_point1] + where + p0 = (0, -0.5, 0) + p1 = (0, 0.5, 0) + p2 = (2, 0, 0) + p3 = (1, 0, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + + volume1 :: Assertion + volume1 = + assertEqual "volume is correct" True (vol ~= (-1/3)) + where + vol = volume t + + doesnt_contain_point1 :: Assertion + doesnt_contain_point1 = + assertEqual "doesn't contain an exterior point" False contained + where + exterior_point = (5, 2, -9.0212) + contained = contains_point t exterior_point + + +-- | Check the volume of a particular tetrahedron (computed by hand) +-- and whether or not it contains a specific point chosen to be +-- inside of it. Its vertices are in counter-clockwise order, so the +-- volume should be positive. +tetrahedron2_geometry_tests :: Test.Framework.Test +tetrahedron2_geometry_tests = + testGroup "tetrahedron2 geometry" + [ testCase "volume1" volume1, + testCase "contains point1" contains_point1] + where + p0 = (0, -0.5, 0) + p1 = (2, 0, 0) + p2 = (0, 0.5, 0) + p3 = (1, 0, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + + volume1 :: Assertion + volume1 = assertEqual "volume1 is correct" True (vol ~= (1/3)) + where + vol = volume t + + contains_point1 :: Assertion + contains_point1 = assertEqual "contains an inner point" True contained + where + inner_point = (1, 0, 0.5) + contained = contains_point t inner_point + + +-- | Ensure that tetrahedra do not contain a particular point chosen to +-- be outside of them. +containment_tests :: Test.Framework.Test +containment_tests = + testGroup "containment tests" + [ testCase "doesn't contain point2" doesnt_contain_point2, + testCase "doesn't contain point3" doesnt_contain_point3, + testCase "doesn't contain point4" doesnt_contain_point4, + testCase "doesn't contain point5" doesnt_contain_point5] + where + p2 = (0.5, 0.5, 1) + p3 = (0.5, 0.5, 0.5) + exterior_point = (0, 0, 0) + + doesnt_contain_point2 :: Assertion + doesnt_contain_point2 = + assertEqual "doesn't contain an exterior point" False contained + where + p0 = (0, 1, 1) + p1 = (1, 1, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + contained = contains_point t exterior_point + + + doesnt_contain_point3 :: Assertion + doesnt_contain_point3 = + assertEqual "doesn't contain an exterior point" False contained + where + p0 = (1, 1, 1) + p1 = (1, 0, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + contained = contains_point t exterior_point + + + doesnt_contain_point4 :: Assertion + doesnt_contain_point4 = + assertEqual "doesn't contain an exterior point" False contained + where + p0 = (1, 0, 1) + p1 = (0, 0, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + contained = contains_point t exterior_point + + + doesnt_contain_point5 :: Assertion + doesnt_contain_point5 = + assertEqual "doesn't contain an exterior point" False contained + where + p0 = (0, 0, 1) + p1 = (0, 1, 1) + t = Tetrahedron { v0 = p0, + v1 = p1, + v2 = p2, + v3 = p3, + fv = empty_values, + precomputed_volume = 0 } + contained = contains_point t exterior_point + + +-- | The barycentric coordinate of v0 with respect to itself should +-- be one. +prop_b0_v0_always_unity :: Tetrahedron -> Property +prop_b0_v0_always_unity t = + (volume t) > 0 ==> (b0 t) (v0 t) ~= 1.0 + +-- | The barycentric coordinate of v1 with respect to v0 should +-- be zero. +prop_b0_v1_always_zero :: Tetrahedron -> Property +prop_b0_v1_always_zero t = + (volume t) > 0 ==> (b0 t) (v1 t) ~= 0 + +-- | The barycentric coordinate of v2 with respect to v0 should +-- be zero. +prop_b0_v2_always_zero :: Tetrahedron -> Property +prop_b0_v2_always_zero t = + (volume t) > 0 ==> (b0 t) (v2 t) ~= 0 + +-- | The barycentric coordinate of v3 with respect to v0 should +-- be zero. +prop_b0_v3_always_zero :: Tetrahedron -> Property +prop_b0_v3_always_zero t = + (volume t) > 0 ==> (b0 t) (v3 t) ~= 0 + +-- | The barycentric coordinate of v1 with respect to itself should +-- be one. +prop_b1_v1_always_unity :: Tetrahedron -> Property +prop_b1_v1_always_unity t = + (volume t) > 0 ==> (b1 t) (v1 t) ~= 1.0 + +-- | The barycentric coordinate of v0 with respect to v1 should +-- be zero. +prop_b1_v0_always_zero :: Tetrahedron -> Property +prop_b1_v0_always_zero t = + (volume t) > 0 ==> (b1 t) (v0 t) ~= 0 + +-- | The barycentric coordinate of v2 with respect to v1 should +-- be zero. +prop_b1_v2_always_zero :: Tetrahedron -> Property +prop_b1_v2_always_zero t = + (volume t) > 0 ==> (b1 t) (v2 t) ~= 0 + +-- | The barycentric coordinate of v3 with respect to v1 should +-- be zero. +prop_b1_v3_always_zero :: Tetrahedron -> Property +prop_b1_v3_always_zero t = + (volume t) > 0 ==> (b1 t) (v3 t) ~= 0 + +-- | The barycentric coordinate of v2 with respect to itself should +-- be one. +prop_b2_v2_always_unity :: Tetrahedron -> Property +prop_b2_v2_always_unity t = + (volume t) > 0 ==> (b2 t) (v2 t) ~= 1.0 + +-- | The barycentric coordinate of v0 with respect to v2 should +-- be zero. +prop_b2_v0_always_zero :: Tetrahedron -> Property +prop_b2_v0_always_zero t = + (volume t) > 0 ==> (b2 t) (v0 t) ~= 0 + +-- | The barycentric coordinate of v1 with respect to v2 should +-- be zero. +prop_b2_v1_always_zero :: Tetrahedron -> Property +prop_b2_v1_always_zero t = + (volume t) > 0 ==> (b2 t) (v1 t) ~= 0 + +-- | The barycentric coordinate of v3 with respect to v2 should +-- be zero. +prop_b2_v3_always_zero :: Tetrahedron -> Property +prop_b2_v3_always_zero t = + (volume t) > 0 ==> (b2 t) (v3 t) ~= 0 + +-- | The barycentric coordinate of v3 with respect to itself should +-- be one. +prop_b3_v3_always_unity :: Tetrahedron -> Property +prop_b3_v3_always_unity t = + (volume t) > 0 ==> (b3 t) (v3 t) ~= 1.0 + +-- | The barycentric coordinate of v0 with respect to v3 should +-- be zero. +prop_b3_v0_always_zero :: Tetrahedron -> Property +prop_b3_v0_always_zero t = + (volume t) > 0 ==> (b3 t) (v0 t) ~= 0 + +-- | The barycentric coordinate of v1 with respect to v3 should +-- be zero. +prop_b3_v1_always_zero :: Tetrahedron -> Property +prop_b3_v1_always_zero t = + (volume t) > 0 ==> (b3 t) (v1 t) ~= 0 + +-- | The barycentric coordinate of v2 with respect to v3 should +-- be zero. +prop_b3_v2_always_zero :: Tetrahedron -> Property +prop_b3_v2_always_zero t = + (volume t) > 0 ==> (b3 t) (v2 t) ~= 0 + + +-- | Used for convenience in the next few tests; not a test itself. +p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double +p t i j k l = (polynomial t) (xi t i j k l) + +-- | Given in Sorokina and Zeilfelder, p. 78. +prop_c3000_identity :: Tetrahedron -> Property +prop_c3000_identity t = + (volume t) > 0 ==> + c t 3 0 0 0 ~= p t 3 0 0 0 + +-- | Given in Sorokina and Zeilfelder, p. 78. +prop_c2100_identity :: Tetrahedron -> Property +prop_c2100_identity t = + (volume t) > 0 ==> + c t 2 1 0 0 ~= (term1 - term2 + term3 - term4) + where + term1 = (1/3)*(p t 0 3 0 0) + term2 = (5/6)*(p t 3 0 0 0) + term3 = 3*(p t 2 1 0 0) + term4 = (3/2)*(p t 1 2 0 0) + +-- | Given in Sorokina and Zeilfelder, p. 78. +prop_c1110_identity :: Tetrahedron -> Property +prop_c1110_identity t = + (volume t) > 0 ==> + c t 1 1 1 0 ~= (term1 + term2 - term3 - term4) + where + term1 = (1/3)*((p t 3 0 0 0) + (p t 0 3 0 0) + (p t 0 0 3 0)) + term2 = (9/2)*(p t 1 1 1 0) + term3 = (3/4)*((p t 2 1 0 0) + (p t 1 2 0 0) + (p t 2 0 1 0)) + term4 = (3/4)*((p t 1 0 2 0) + (p t 0 2 1 0) + (p t 0 1 2 0)) + + +prop_swapping_vertices_doesnt_affect_coefficients1 :: Tetrahedron -> Bool +prop_swapping_vertices_doesnt_affect_coefficients1 t = + c t 0 0 1 2 == c t' 0 0 1 2 + where + t' = t { v0 = (v1 t), v1 = (v0 t) } + +prop_swapping_vertices_doesnt_affect_coefficients2 :: Tetrahedron -> Bool +prop_swapping_vertices_doesnt_affect_coefficients2 t = + c t 0 1 1 1 == c t' 0 1 1 1 + where + t' = t { v2 = (v3 t), v3 = (v2 t) } + +prop_swapping_vertices_doesnt_affect_coefficients3 :: Tetrahedron -> Bool +prop_swapping_vertices_doesnt_affect_coefficients3 t = + c t 2 1 0 0 == c t' 2 1 0 0 + where + t' = t { v2 = (v3 t), v3 = (v2 t) } + +prop_swapping_vertices_doesnt_affect_coefficients4 :: Tetrahedron -> Bool +prop_swapping_vertices_doesnt_affect_coefficients4 t = + c t 2 0 0 1 == c t' 2 0 0 1 + where + t' = t { v0 = (v3 t), v3 = (v0 t) } + + + + +tetrahedron_tests :: Test.Framework.Test +tetrahedron_tests = + testGroup "Tetrahedron Tests" [ + tetrahedron1_geometry_tests, + tetrahedron2_geometry_tests, + containment_tests ] + + + +p78_24_properties :: Test.Framework.Test +p78_24_properties = + testGroup "p. 78, Section (2.4) Properties" [ + testProperty "c3000 identity" prop_c3000_identity, + testProperty "c2100 identity" prop_c2100_identity, + testProperty "c1110 identity" prop_c1110_identity] + + +tetrahedron_properties :: Test.Framework.Test +tetrahedron_properties = + testGroup "Tetrahedron Properties" [ + p78_24_properties, + testProperty "b0_v0_always_unity" prop_b0_v0_always_unity, + testProperty "b0_v1_always_zero" prop_b0_v1_always_zero, + testProperty "b0_v2_always_zero" prop_b0_v2_always_zero, + testProperty "b0_v3_always_zero" prop_b0_v3_always_zero, + testProperty "b1_v1_always_unity" prop_b1_v1_always_unity, + testProperty "b1_v0_always_zero" prop_b1_v0_always_zero, + testProperty "b1_v2_always_zero" prop_b1_v2_always_zero, + testProperty "b1_v3_always_zero" prop_b1_v3_always_zero, + testProperty "b2_v2_always_unity" prop_b2_v2_always_unity, + testProperty "b2_v0_always_zero" prop_b2_v0_always_zero, + testProperty "b2_v1_always_zero" prop_b2_v1_always_zero, + testProperty "b2_v3_always_zero" prop_b2_v3_always_zero, + testProperty "b3_v3_always_unity" prop_b3_v3_always_unity, + testProperty "b3_v0_always_zero" prop_b3_v0_always_zero, + testProperty "b3_v1_always_zero" prop_b3_v1_always_zero, + testProperty "b3_v2_always_zero" prop_b3_v2_always_zero, + testProperty "swapping_vertices_doesnt_affect_coefficients1" $ + prop_swapping_vertices_doesnt_affect_coefficients1, + testProperty "swapping_vertices_doesnt_affect_coefficients2" $ + prop_swapping_vertices_doesnt_affect_coefficients2, + testProperty "swapping_vertices_doesnt_affect_coefficients3" $ + prop_swapping_vertices_doesnt_affect_coefficients3, + testProperty "swapping_vertices_doesnt_affect_coefficients4" $ + prop_swapping_vertices_doesnt_affect_coefficients4 ]