where
import Cardinal
-import Face (Face(Face, v0, v1, v2, v3))
+import qualified Face (Face(Face, v0, v1, v2, v3))
import FunctionValues
import Point
-import Tetrahedron (Tetrahedron(Tetrahedron), fv)
+import Tetrahedron hiding (c)
import ThreeDimensional
data Cube = Cube { h :: Double,
instance Show Cube where
show c =
- "Cube_" ++ (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c)) ++
- " (Center: " ++ (show (center c)) ++ ")" ++
- " (xmin: " ++ (show (xmin c)) ++ ")" ++
- " (xmax: " ++ (show (xmax c)) ++ ")" ++
- " (ymin: " ++ (show (ymin c)) ++ ")" ++
- " (ymax: " ++ (show (ymax c)) ++ ")" ++
- " (zmin: " ++ (show (zmin c)) ++ ")" ++
- " (zmax: " ++ (show (zmax c)) ++ ")"
+ "Cube_" ++ subscript ++ "\n" ++
+ " h: " ++ (show (h c)) ++ "\n" ++
+ " Center: " ++ (show (center c)) ++ "\n" ++
+ " xmin: " ++ (show (xmin c)) ++ "\n" ++
+ " xmax: " ++ (show (xmax c)) ++ "\n" ++
+ " ymin: " ++ (show (ymin c)) ++ "\n" ++
+ " ymax: " ++ (show (ymax c)) ++ "\n" ++
+ " zmin: " ++ (show (zmin c)) ++ "\n" ++
+ " zmax: " ++ (show (zmax c)) ++ "\n" ++
+ " fv: " ++ (show (Cube.fv c)) ++ "\n"
+ where
+ subscript =
+ (show (i c)) ++ "," ++ (show (j c)) ++ "," ++ (show (k c))
+
empty_cube :: Cube
empty_cube = Cube 0 0 0 0 empty_values
| otherwise = True
--- instance Num Cube where
--- (Cube g1 i1 j1 k1 d1) + (Cube _ i2 j2 k2 d2) =
--- Cube g1 (i1 + i2) (j1 + j2) (k1 + k2) (d1 + d2)
-
--- (Cube g1 i1 j1 k1 d1) - (Cube _ i2 j2 k2 d2) =
--- Cube g1 (i1 - i2) (j1 - j2) (k1 - k2) (d1 - d2)
-
--- (Cube g1 i1 j1 k1 d1) * (Cube _ i2 j2 k2 d2) =
--- Cube g1 (i1 * i2) (j1 * j2) (k1 * k2) (d1 * d2)
-
--- abs (Cube g1 i1 j1 k1 d1) =
--- Cube g1 (abs i1) (abs j1) (abs k1) (abs d1)
-
--- signum (Cube g1 i1 j1 k1 d1) =
--- Cube g1 (signum i1) (signum j1) (signum k1) (signum d1)
-
--- fromInteger x = empty_cube { datum = (fromIntegral x) }
-
--- instance Fractional Cube where
--- (Cube g1 i1 j1 k1 d1) / (Cube _ _ _ _ d2) =
--- Cube g1 i1 j1 k1 (d1 / d2)
-
--- recip (Cube g1 i1 j1 k1 d1) =
--- Cube g1 i1 j1 k1 (recip d1)
-
--- fromRational q = empty_cube { datum = fromRational q }
-
-
-
--- | Return the cube corresponding to the grid point i,j,k. The list
--- of cubes is stored as [z][y][x] but we'll be requesting it by
--- [x][y][z] so we flip the indices in the last line.
--- cube_at :: Grid -> Int -> Int -> Int -> Cube
--- cube_at g i' j' k'
--- | i' >= length (function_values g) = Cube g i' j' k' 0
--- | i' < 0 = Cube g i' j' k' 0
--- | j' >= length ((function_values g) !! i') = Cube g i' j' k' 0
--- | j' < 0 = Cube g i' j' k' 0
--- | k' >= length (((function_values g) !! i') !! j') = Cube g i' j' k' 0
--- | k' < 0 = Cube g i' j' k' 0
--- | otherwise =
--- (((cubes g) !! k') !! j') !! i'
-
-
-
-
-
-- Face stuff.
-- | The top (in the direction of z) face of the cube.
-top_face :: Cube -> Face
-top_face c = Face v0' v1' v2' v3'
+top_face :: Cube -> Face.Face
+top_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 back (in the direction of x) face of the cube.
-back_face :: Cube -> Face
-back_face c = Face v0' v1' v2' v3'
+back_face :: Cube -> Face.Face
+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)
-- The bottom face (in the direction of -z) of the cube.
-down_face :: Cube -> Face
-down_face c = Face v0' v1' v2' v3'
+down_face :: Cube -> Face.Face
+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)
-- | The front (in the direction of -x) face of the cube.
-front_face :: Cube -> Face
-front_face c = Face v0' v1' v2' v3'
+front_face :: Cube -> Face.Face
+front_face c = Face.Face v0' v1' v2' v3'
where
delta = (1/2)*(h c)
v0' = (center c) + (-delta, -delta, delta)
v2' = (center c) + (-delta, delta, -delta)
v3' = (center c) + (-delta, -delta, -delta)
-
-- | The left (in the direction of -y) face of the cube.
-left_face :: Cube -> Face
-left_face c = Face v0' v1' v2' v3'
+left_face :: Cube -> Face.Face
+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 :: Cube -> Face
-right_face c = Face v0' v1' v2' v3'
+right_face :: Cube -> Face.Face
+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)
tetrahedron0 :: Cube -> Tetrahedron
where
v0' = center c
v1' = center (front_face c)
- v2' = v0 (front_face c)
- v3' = v1 (front_face c)
+ v2' = Face.v0 (front_face c)
+ v3' = Face.v1 (front_face c)
tetrahedron1 :: Cube -> Tetrahedron
tetrahedron1 c =
where
v0' = center c
v1' = center (front_face c)
- v2' = v1 (front_face c)
- v3' = v2 (front_face c)
+ v2' = Face.v1 (front_face c)
+ v3' = Face.v2 (front_face c)
fv' = rotate (Cube.fv c) ccwx
tetrahedron2 :: Cube -> Tetrahedron
where
v0' = center c
v1' = center (front_face c)
- v2' = v2 (front_face c)
- v3' = v3 (front_face c)
+ v2' = Face.v2 (front_face c)
+ v3' = Face.v3 (front_face c)
fv' = rotate (Cube.fv c) (ccwx . ccwx)
tetrahedron3 :: Cube -> Tetrahedron
where
v0' = center c
v1' = center (front_face c)
- v2' = v3 (front_face c)
- v3' = v1 (front_face c)
+ v2' = Face.v3 (front_face c)
+ v3' = Face.v0 (front_face c)
fv' = rotate (Cube.fv c) cwx
tetrahedron4 :: Cube -> Tetrahedron
where
v0' = center c
v1' = center (top_face c)
- v2' = v0 (front_face c)
- v3' = v1 (front_face c)
+ v2' = Face.v0 (top_face c)
+ v3' = Face.v1 (top_face c)
fv' = rotate (Cube.fv c) cwy
tetrahedron5 :: Cube -> Tetrahedron
where
v0' = center c
v1' = center (top_face c)
- v2' = v1 (top_face c)
- v3' = v2 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwx
+ v2' = Face.v1 (top_face c)
+ v3' = Face.v2 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz
tetrahedron6 :: Cube -> Tetrahedron
tetrahedron6 c =
where
v0' = center c
v1' = center (top_face c)
- v2' = v2 (top_face c)
- v3' = v3 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) (ccwx . ccwx)
+ v2' = Face.v2 (top_face c)
+ v3' = Face.v3 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz)
tetrahedron7 :: Cube -> Tetrahedron
tetrahedron7 c =
where
v0' = center c
v1' = center (top_face c)
- v2' = v3 (top_face c)
- v3' = v1 (top_face c)
- fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwx
+ v2' = Face.v3 (top_face c)
+ v3' = Face.v0 (top_face c)
+ fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz
+
+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)) cwy
+
+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)) ccwx
+
+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)) (ccwx . ccwx)
+
+
+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)) cwx
+
+
+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)) cwy
+
+
+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)) ccwz
+
+
+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)) (ccwz . ccwz)
+
+
+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)) cwz
+
+
+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)) ccwz
+
+
+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)) cwz
+
+
+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)) ccwy
+
+
+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)) ccwy
+
+
+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