+{-# LANGUAGE BangPatterns #-}
module Tetrahedron (
Tetrahedron(..),
b0, -- Cube test
sum
)
-import Prelude hiding (LT)
import Test.Framework (Test, testGroup)
import Test.Framework.Providers.HUnit (testCase)
import Test.Framework.Providers.QuickCheck2 (testProperty)
-import Test.HUnit
+import Test.HUnit (Assertion, assertEqual)
import Test.QuickCheck (Arbitrary(..), Gen, Property, (==>))
import Comparisons ((~=), nearly_ge)
import FunctionValues (FunctionValues(..), empty_values)
import Misc (factorial)
-import Point
-import RealFunction
-import ThreeDimensional
+import Point (Point, scale)
+import RealFunction (RealFunction, cmult, fexp)
+import ThreeDimensional (ThreeDimensional(..))
data Tetrahedron =
Tetrahedron { function_values :: FunctionValues,
- v0 :: Point,
- v1 :: Point,
- v2 :: Point,
- v3 :: Point,
- precomputed_volume :: Double
+ v0 :: !Point,
+ v1 :: !Point,
+ v2 :: !Point,
+ v3 :: !Point,
+ precomputed_volume :: !Double
}
deriving (Eq)
((c t 3 0 0 0) `cmult` (beta t 3 0 0 0))
--- | Returns the domain point of t with indices i,j,k,l.
--- Simply an alias for the domain_point function.
-xi :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
-xi = domain_point
-
--- | Returns the domain point of t with indices i,j,k,l.
-domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
-domain_point t i j k l
- | i + j + k + l == 3 = weighted_sum `scale` (1/3)
- | otherwise = error "domain point index out of bounds"
- where
- v0' = (v0 t) `scale` (fromIntegral i)
- v1' = (v1 t) `scale` (fromIntegral j)
- v2' = (v2 t) `scale` (fromIntegral k)
- v3' = (v3 t) `scale` (fromIntegral l)
- weighted_sum = v0' + v1' + v2' + v3'
-
-- | The Bernstein polynomial on t with indices i,j,k,l. Denoted by a
-- capital 'B' in the Sorokina/Zeilfelder paper.
-- Zeilfelder, pp. 84-86. If incorrect indices are supplied, the
-- function will simply error.
c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-c t i j k l =
+c !t !i !j !k !l =
coefficient i j k l
where
fvs = function_values 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
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]
+ 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]
+ where
+ -- | Returns the domain point of t with indices i,j,k,l.
+ domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point
+ domain_point t i j k l
+ | i + j + k + l == 3 = weighted_sum `scale` (1/3)
+ | otherwise = error "domain point index out of bounds"
+ where
+ v0' = (v0 t) `scale` (fromIntegral i)
+ v1' = (v1 t) `scale` (fromIntegral j)
+ v2' = (v2 t) `scale` (fromIntegral k)
+ v3' = (v3 t) `scale` (fromIntegral l)
+ weighted_sum = v0' + v1' + v2' + v3'
+
+
+ -- | Used for convenience in the next few tests.
+ p :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
+ p t i j k l = (polynomial t) (domain_point 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))
+
tetrahedron_properties :: Test.Framework.Test
projects / spline3.git / blobdiff