v0 :: Point,
v1 :: Point,
v2 :: Point,
- v3 :: Point }
+ v3 :: Point,
+ precomputed_volume :: Double }
deriving (Eq)
rnd_v2 <- arbitrary :: Gen Point
rnd_v3 <- arbitrary :: Gen Point
rnd_fv <- arbitrary :: Gen FunctionValues
- return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3)
+ -- We can't assign an incorrect precomputed volume,
+ -- so we have to calculate the correct one here.
+ let t' = Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 0
+ let vol = volume t'
+ return (Tetrahedron rnd_fv rnd_v0 rnd_v1 rnd_v2 rnd_v3 vol)
instance Show Tetrahedron where
instance ThreeDimensional Tetrahedron where
center t = ((v0 t) + (v1 t) + (v2 t) + (v3 t)) `scale` (1/4)
contains_point t p =
- (b0 t p) `nearly_ge` 0 &&
- (b1 t p) `nearly_ge` 0 &&
- (b2 t p) `nearly_ge` 0 &&
- (b3 t p) `nearly_ge` 0
+ b0_unscaled `nearly_ge` 0 &&
+ b1_unscaled `nearly_ge` 0 &&
+ b2_unscaled `nearly_ge` 0 &&
+ b3_unscaled `nearly_ge` 0
+ where
+ -- Drop the useless division and volume calculation that we
+ -- would do if we used the regular b0,..b3 functions.
+ b0_unscaled :: Double
+ b0_unscaled = volume inner_tetrahedron
+ where inner_tetrahedron = t { v0 = p }
+
+ b1_unscaled :: Double
+ b1_unscaled = volume inner_tetrahedron
+ where inner_tetrahedron = t { v1 = p }
+
+ b2_unscaled :: Double
+ b2_unscaled = volume inner_tetrahedron
+ where inner_tetrahedron = t { v2 = p }
+
+ b3_unscaled :: Double
+ b3_unscaled = volume inner_tetrahedron
+ where inner_tetrahedron = t { v3 = p }
polynomial :: Tetrahedron -> (RealFunction Point)
-- | The barycentric coordinates of a point with respect to v0.
b0 :: Tetrahedron -> (RealFunction Point)
-b0 t point = (volume inner_tetrahedron) / (volume t)
+b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
inner_tetrahedron = t { v0 = point }
-- | The barycentric coordinates of a point with respect to v1.
b1 :: Tetrahedron -> (RealFunction Point)
-b1 t point = (volume inner_tetrahedron) / (volume t)
+b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
inner_tetrahedron = t { v1 = point }
-- | The barycentric coordinates of a point with respect to v2.
b2 :: Tetrahedron -> (RealFunction Point)
-b2 t point = (volume inner_tetrahedron) / (volume t)
+b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
inner_tetrahedron = t { v2 = point }
-- | The barycentric coordinates of a point with respect to v3.
b3 :: Tetrahedron -> (RealFunction Point)
-b3 t point = (volume inner_tetrahedron) / (volume t)
+b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
inner_tetrahedron = t { v3 = point }