(show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c))
+-- | Returns an empty 'Cube'.
empty_cube :: Cube
empty_cube = Cube 0 0 0 0 empty_values
instance ThreeDimensional Cube where
-- | The center of Cube_ijk coincides with v_ijk at
- -- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
+ -- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
center c = (x, y, z)
where
delta = h c
y = delta * j'
z = delta * k'
+ -- | It's easy to tell if a point is within a cube; just make sure
+ -- that it falls on the proper side of each of the cube's faces.
contains_point c p
| (x_coord p) < (xmin c) = False
| (x_coord p) > (xmax c) = False
back_face c = Face.Face v0' v1' v2' v3'
where
delta = (1/2)*(h c)
- v0' = (center c) + (delta, delta, delta)
+ v0' = (center c) + (delta, -delta, -delta)
v1' = (center c) + (delta, delta, -delta)
- v2' = (center c) + (delta, -delta, -delta)
+ v2' = (center c) + (delta, delta, delta)
v3' = (center c) + (delta, -delta, delta)
down_face c = Face.Face v0' v1' v2' v3'
where
delta = (1/2)*(h c)
- v0' = (center c) + (delta, delta, -delta)
+ v0' = (center c) + (-delta, -delta, -delta)
v1' = (center c) + (-delta, delta, -delta)
- v2' = (center c) + (-delta, -delta, -delta)
+ v2' = (center c) + (delta, delta, -delta)
v3' = (center c) + (delta, -delta, -delta)
left_face c = Face.Face v0' v1' v2' v3'
where
delta = (1/2)*(h c)
- v0' = (center c) + (-delta, -delta, delta)
- v1' = (center c) + (delta, -delta, delta)
- v2' = (center c) + (delta, -delta, -delta)
- v3' = (center c) + (-delta, -delta, -delta)
+ v0' = (center c) + (delta, -delta, delta)
+ v1' = (center c) + (-delta, -delta, delta)
+ v2' = (center c) + (-delta, -delta, -delta)
+ v3' = (center c) + (delta, -delta, -delta)
-- | The right (in the direction of y) face of the cube.
right_face c = Face.Face v0' v1' v2' v3'
where
delta = (1/2)*(h c)
- v0' = (center c) + (-delta, delta, -delta)
- v1' = (center c) + (delta, delta, -delta)
- v2' = (center c) + (delta, delta, delta)
- v3' = (center c) + (-delta, delta, delta)
-
+ v0' = (center c) + (-delta, delta, delta)
+ v1' = (center c) + (delta, delta, delta)
+ v2' = (center c) + (delta, delta, -delta)
+ v3' = (center c) + (-delta, delta, -delta)
-reorient :: Tetrahedron -> Tetrahedron
-reorient t = t
--- | volume t > 0 = t
--- | otherwise = t { v2 = (v3 t),
--- v3 = (v2 t) }
tetrahedron0 :: Cube -> Tetrahedron
tetrahedron0 c =
- reorient $ Tetrahedron (Cube.fv c) v0' v1' v2' v3'
+ Tetrahedron (Cube.fv c) v0' v1' v2' v3'
where
v0' = center c
v1' = center (front_face c)
tetrahedron1 :: Cube -> Tetrahedron
tetrahedron1 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (front_face c)
v2' = Face.v1 (front_face c)
v3' = Face.v2 (front_face c)
- fv' = rotate (Cube.fv c) ccwx
+ fv' = rotate (Cube.fv c) cwx
tetrahedron2 :: Cube -> Tetrahedron
tetrahedron2 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (front_face c)
v2' = Face.v2 (front_face c)
v3' = Face.v3 (front_face c)
- fv' = rotate (Cube.fv c) (ccwx . ccwx)
+ fv' = rotate (Cube.fv c) (cwx . cwx)
tetrahedron3 :: Cube -> Tetrahedron
tetrahedron3 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (front_face c)
v2' = Face.v3 (front_face c)
v3' = Face.v0 (front_face c)
- fv' = rotate (Cube.fv c) cwx
+ fv' = rotate (Cube.fv c) ccwx
tetrahedron4 :: Cube -> Tetrahedron
tetrahedron4 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (top_face c)
v2' = Face.v0 (top_face c)
v3' = Face.v1 (top_face c)
- fv' = rotate (Cube.fv c) cwy
+ fv' = rotate (Cube.fv c) ccwy
tetrahedron5 :: Cube -> Tetrahedron
tetrahedron5 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (top_face c)
v2' = Face.v1 (top_face c)
v3' = Face.v2 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwx
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz
tetrahedron6 :: Cube -> Tetrahedron
tetrahedron6 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (top_face c)
v2' = Face.v2 (top_face c)
v3' = Face.v3 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) (ccwx . ccwx)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (cwz . cwz)
tetrahedron7 :: Cube -> Tetrahedron
tetrahedron7 c =
- reorient $ Tetrahedron fv' v0' v1' v2' v3'
+ Tetrahedron fv' v0' v1' v2' v3'
where
v0' = center c
v1' = center (top_face c)
v2' = Face.v3 (top_face c)
v3' = Face.v0 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwx
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz
+
+tetrahedron8 :: Cube -> Tetrahedron
+tetrahedron8 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v0 (back_face c)
+ v3' = Face.v1 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwy
+
+tetrahedron9 :: Cube -> Tetrahedron
+tetrahedron9 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v1 (back_face c)
+ v3' = Face.v2 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwx
+
+tetrahedron10 :: Cube -> Tetrahedron
+tetrahedron10 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v2 (back_face c)
+ v3' = Face.v3 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) (cwx . cwx)
+
+
+tetrahedron11 :: Cube -> Tetrahedron
+tetrahedron11 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (back_face c)
+ v2' = Face.v3 (back_face c)
+ v3' = Face.v0 (back_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwx
+
+
+tetrahedron12 :: Cube -> Tetrahedron
+tetrahedron12 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v0 (down_face c)
+ v3' = Face.v1 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwy
+
+
+tetrahedron13 :: Cube -> Tetrahedron
+tetrahedron13 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v1 (down_face c)
+ v3' = Face.v2 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) cwz
+
+
+tetrahedron14 :: Cube -> Tetrahedron
+tetrahedron14 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v2 (down_face c)
+ v3' = Face.v3 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron13 c)) (cwz . cwz)
+
+
+tetrahedron15 :: Cube -> Tetrahedron
+tetrahedron15 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (down_face c)
+ v2' = Face.v3 (down_face c)
+ v3' = Face.v0 (down_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) ccwz
+
+
+tetrahedron16 :: Cube -> Tetrahedron
+tetrahedron16 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v0 (right_face c)
+ v3' = Face.v1 (right_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwz
+
+
+tetrahedron17 :: Cube -> Tetrahedron
+tetrahedron17 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v1 (right_face c)
+ v3' = Face.v2 (right_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) cwy
+
+
+tetrahedron18 :: Cube -> Tetrahedron
+tetrahedron18 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v2 (right_face c)
+ v3' = Face.v3 (right_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) (cwy . cwy)
+
+
+tetrahedron19 :: Cube -> Tetrahedron
+tetrahedron19 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (right_face c)
+ v2' = Face.v3 (right_face c)
+ v3' = Face.v0 (right_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron16 c)) ccwy
+
+
+tetrahedron20 :: Cube -> Tetrahedron
+tetrahedron20 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v0 (left_face c)
+ v3' = Face.v1 (left_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwz
+
+
+tetrahedron21 :: Cube -> Tetrahedron
+tetrahedron21 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v1 (left_face c)
+ v3' = Face.v2 (left_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) cwy
+
+
+tetrahedron22 :: Cube -> Tetrahedron
+tetrahedron22 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v2 (left_face c)
+ v3' = Face.v3 (left_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) (cwy . cwy)
+
+
+tetrahedron23 :: Cube -> Tetrahedron
+tetrahedron23 c =
+ Tetrahedron fv' v0' v1' v2' v3'
+ where
+ v0' = center c
+ v1' = center (left_face c)
+ v2' = Face.v3 (left_face c)
+ v3' = Face.v0 (left_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) ccwy
+
tetrahedrons :: Cube -> [Tetrahedron]
tetrahedrons c =
tetrahedron4 c,
tetrahedron5 c,
tetrahedron6 c,
- tetrahedron7 c
- -- ,
- -- tetrahedron8 c,
- -- tetrahedron9 c,
- -- tetrahedron10 c,
- -- tetrahedron11 c,
- -- tetrahedron12 c,
- -- tetrahedron13 c,
- -- tetrahedron14 c,
- -- tetrahedron15 c,
- -- tetrahedron16 c,
- -- tetrahedron17 c,
- -- tetrahedron18 c,
- -- tetrahedron19 c,
- -- tetrahedron20 c,
- -- tetrahedron21 c,
- -- tetrahedron21 c,
- -- tetrahedron22 c,
- -- tetrahedron23 c,
- -- tetrahedron24 c
- ]
+ tetrahedron7 c,
+ tetrahedron8 c,
+ tetrahedron9 c,
+ tetrahedron10 c,
+ tetrahedron11 c,
+ tetrahedron12 c,
+ tetrahedron13 c,
+ tetrahedron14 c,
+ tetrahedron15 c,
+ tetrahedron16 c,
+ tetrahedron17 c,
+ tetrahedron18 c,
+ tetrahedron19 c,
+ tetrahedron20 c,
+ tetrahedron21 c,
+ tetrahedron22 c,
+ tetrahedron23 c]
projects / spline3.git / blobdiff