import Comparisons ((~=), nearly_ge)
import FunctionValues (FunctionValues(..), empty_values)
import Misc (factorial)
-import Point (Point, scale)
+import Point (Point(..), scale)
import RealFunction (RealFunction, cmult, fexp)
import ThreeDimensional (ThreeDimensional(..))
center (Tetrahedron _ v0' v1' v2' v3' _) =
(v0' + v1' + v2' + v3') `scale` (1/4)
+ -- contains_point is only used in tests.
contains_point t p0 =
b0_unscaled `nearly_ge` 0 &&
b1_unscaled `nearly_ge` 0 &&
det p0 p1 p2 p3 =
term5 + term6
where
- (x1, y1, z1) = p0
- (x2, y2, z2) = p1
- (x3, y3, z3) = p2
- (x4, y4, z4) = p3
+ Point x1 y1 z1 = p0
+ Point x2 y2 z2 = p1
+ Point x3 y3 z3 = p2
+ Point x4 y4 z4 = p3
term1 = ((x2 - x4)*y1 - (x1 - x4)*y2 + (x1 - x2)*y4)*z3
term2 = ((x2 - x3)*y1 - (x1 - x3)*y2 + (x1 - x2)*y3)*z4
term3 = ((x3 - x4)*y2 - (x2 - x4)*y3 + (x2 - x3)*y4)*z1
-- | Computed using the formula from Lai & Schumaker, Definition 15.4,
-- page 436.
+{-# INLINE volume #-}
volume :: Tetrahedron -> Double
volume t
| v0' == v1' = 0
-- | The barycentric coordinates of a point with respect to v0.
+{-# INLINE b0 #-}
b0 :: Tetrahedron -> (RealFunction Point)
b0 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
-- | The barycentric coordinates of a point with respect to v1.
+{-# INLINE b1 #-}
b1 :: Tetrahedron -> (RealFunction Point)
b1 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
-- | The barycentric coordinates of a point with respect to v2.
+{-# INLINE b2 #-}
b2 :: Tetrahedron -> (RealFunction Point)
b2 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
-- | The barycentric coordinates of a point with respect to v3.
+{-# INLINE b3 #-}
b3 :: Tetrahedron -> (RealFunction Point)
b3 t point = (volume inner_tetrahedron) / (precomputed_volume t)
where
[ 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)
+ p0 = Point 0 (-0.5) 0
+ p1 = Point 0 0.5 0
+ p2 = Point 2 0 0
+ p3 = Point 1 0 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
doesnt_contain_point1 =
assertEqual "doesn't contain an exterior point" False contained
where
- exterior_point = (5, 2, -9.0212)
+ exterior_point = Point 5 2 (-9.0212)
contained = contains_point t exterior_point
[ 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)
+ p0 = Point 0 (-0.5) 0
+ p1 = Point 2 0 0
+ p2 = Point 0 0.5 0
+ p3 = Point 1 0 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
contains_point1 :: Assertion
contains_point1 = assertEqual "contains an inner point" True contained
where
- inner_point = (1, 0, 0.5)
+ inner_point = Point 1 0 0.5
contained = contains_point t inner_point
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)
+ p2 = Point 0.5 0.5 1
+ p3 = Point 0.5 0.5 0.5
+ exterior_point = 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)
+ p0 = Point 0 1 1
+ p1 = Point 1 1 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
doesnt_contain_point3 =
assertEqual "doesn't contain an exterior point" False contained
where
- p0 = (1, 1, 1)
- p1 = (1, 0, 1)
+ p0 = Point 1 1 1
+ p1 = Point 1 0 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
doesnt_contain_point4 =
assertEqual "doesn't contain an exterior point" False contained
where
- p0 = (1, 0, 1)
- p1 = (0, 0, 1)
+ p0 = Point 1 0 1
+ p1 = Point 0 0 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,
doesnt_contain_point5 =
assertEqual "doesn't contain an exterior point" False contained
where
- p0 = (0, 0, 1)
- p1 = (0, 1, 1)
+ p0 = Point 0 0 1
+ p1 = Point 0 1 1
t = Tetrahedron { v0 = p0,
v1 = p1,
v2 = p2,