instance Show Cube where
- show c =
+ show cube =
"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"
+ " h: " ++ (show (h cube)) ++ "\n" ++
+ " Center: " ++ (show (center cube)) ++ "\n" ++
+ " xmin: " ++ (show (xmin cube)) ++ "\n" ++
+ " xmax: " ++ (show (xmax cube)) ++ "\n" ++
+ " ymin: " ++ (show (ymin cube)) ++ "\n" ++
+ " ymax: " ++ (show (ymax cube)) ++ "\n" ++
+ " zmin: " ++ (show (zmin cube)) ++ "\n" ++
+ " zmax: " ++ (show (zmax cube)) ++ "\n" ++
+ " fv: " ++ (show (Cube.fv cube)) ++ "\n"
where
subscript =
- (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 0
+ (show (i cube)) ++ "," ++ (show (j cube)) ++ "," ++ (show (k cube))
-- | The left-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmin :: Cube -> Double
-xmin c = (2*i' - 1)*delta / 2
+xmin cube = (2*i' - 1)*delta / 2
where
- i' = fromIntegral (i c) :: Double
- delta = h c
+ i' = fromIntegral (i cube) :: Double
+ delta = h cube
-- | The right-side boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
xmax :: Cube -> Double
-xmax c = (2*i' + 1)*delta / 2
+xmax cube = (2*i' + 1)*delta / 2
where
- i' = fromIntegral (i c) :: Double
- delta = h c
+ i' = fromIntegral (i cube) :: Double
+ delta = h cube
-- | The front boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymin :: Cube -> Double
-ymin c = (2*j' - 1)*delta / 2
+ymin cube = (2*j' - 1)*delta / 2
where
- j' = fromIntegral (j c) :: Double
- delta = h c
+ j' = fromIntegral (j cube) :: Double
+ delta = h cube
-- | The back boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
ymax :: Cube -> Double
-ymax c = (2*j' + 1)*delta / 2
+ymax cube = (2*j' + 1)*delta / 2
where
- j' = fromIntegral (j c) :: Double
- delta = h c
+ j' = fromIntegral (j cube) :: Double
+ delta = h cube
-- | The bottom boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmin :: Cube -> Double
-zmin c = (2*k' - 1)*delta / 2
+zmin cube = (2*k' - 1)*delta / 2
where
- k' = fromIntegral (k c) :: Double
- delta = h c
+ k' = fromIntegral (k cube) :: Double
+ delta = h cube
-- | The top boundary of the cube. See Sorokina and Zeilfelder,
-- p. 76.
zmax :: Cube -> Double
-zmax c = (2*k' + 1)*delta / 2
+zmax cube = (2*k' + 1)*delta / 2
where
- k' = fromIntegral (k c) :: Double
- delta = h c
+ k' = fromIntegral (k cube) :: Double
+ delta = h cube
instance ThreeDimensional Cube where
-- | The center of Cube_ijk coincides with v_ijk at
-- (ih, jh, kh). See Sorokina and Zeilfelder, p. 76.
- center c = (x, y, z)
+ center cube = (x, y, z)
where
- delta = h c
- i' = fromIntegral (i c) :: Double
- j' = fromIntegral (j c) :: Double
- k' = fromIntegral (k c) :: Double
+ delta = h cube
+ i' = fromIntegral (i cube) :: Double
+ j' = fromIntegral (j cube) :: Double
+ k' = fromIntegral (k cube) :: Double
x = delta * i'
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 (x, y, z)
- | x < (xmin c) = False
- | x > (xmax c) = False
- | y < (ymin c) = False
- | y > (ymax c) = False
- | z < (zmin c) = False
- | z > (zmax c) = False
+ contains_point cube (x, y, z)
+ | x < (xmin cube) = False
+ | x > (xmax cube) = False
+ | y < (ymin cube) = False
+ | y > (ymax cube) = False
+ | z < (zmin cube) = False
+ | z > (zmax cube) = False
| otherwise = True
-- | The top (in the direction of z) face of the cube.
top_face :: Cube -> Face.Face
-top_face c = Face.Face v0' v1' v2' v3'
+top_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (delta, -delta, delta)
+ v1' = (center cube) + (delta, delta, delta)
+ v2' = (center cube) + (-delta, delta, delta)
+ v3' = (center cube) + (-delta, -delta, delta)
-- | The back (in the direction of x) face of the cube.
back_face :: Cube -> Face.Face
-back_face c = Face.Face v0' v1' v2' v3'
+back_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (delta, -delta, -delta)
+ v1' = (center cube) + (delta, delta, -delta)
+ v2' = (center cube) + (delta, delta, delta)
+ v3' = (center cube) + (delta, -delta, delta)
-- The bottom face (in the direction of -z) of the cube.
down_face :: Cube -> Face.Face
-down_face c = Face.Face v0' v1' v2' v3'
+down_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (-delta, -delta, -delta)
+ v1' = (center cube) + (-delta, delta, -delta)
+ v2' = (center cube) + (delta, delta, -delta)
+ v3' = (center cube) + (delta, -delta, -delta)
-- | The front (in the direction of -x) face of the cube.
front_face :: Cube -> Face.Face
-front_face c = Face.Face v0' v1' v2' v3'
+front_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (-delta, -delta, delta)
+ v1' = (center cube) + (-delta, delta, delta)
+ v2' = (center cube) + (-delta, delta, -delta)
+ v3' = (center cube) + (-delta, -delta, -delta)
-- | The left (in the direction of -y) face of the cube.
left_face :: Cube -> Face.Face
-left_face c = Face.Face v0' v1' v2' v3'
+left_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (delta, -delta, delta)
+ v1' = (center cube) + (-delta, -delta, delta)
+ v2' = (center cube) + (-delta, -delta, -delta)
+ v3' = (center cube) + (delta, -delta, -delta)
-- | The right (in the direction of y) face of the cube.
right_face :: Cube -> Face.Face
-right_face c = Face.Face v0' v1' v2' v3'
+right_face cube = 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)
+ delta = (1/2)*(h cube)
+ v0' = (center cube) + (-delta, delta, delta)
+ v1' = (center cube) + (delta, delta, delta)
+ v2' = (center cube) + (delta, delta, -delta)
+ v3' = (center cube) + (-delta, delta, -delta)
tetrahedron :: Cube -> Int -> Tetrahedron
-tetrahedron c 0 =
- Tetrahedron (fv c) v0' v1' v2' v3' vol
+tetrahedron cube 0 =
+ Tetrahedron (fv cube) v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (front_face c)
- v2' = Face.v0 (front_face c)
- v3' = Face.v1 (front_face c)
- vol = tetrahedra_volume c
+ v0' = center cube
+ v1' = center (front_face cube)
+ v2' = Face.v0 (front_face cube)
+ v3' = Face.v1 (front_face cube)
+ vol = tetrahedra_volume cube
-tetrahedron c 1 =
+tetrahedron cube 1 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (front_face c)
- v2' = Face.v1 (front_face c)
- v3' = Face.v2 (front_face c)
- fv' = rotate ccwx (fv c)
- vol = tetrahedra_volume c
-
-tetrahedron c 2 =
+ v0' = center cube
+ v1' = center (front_face cube)
+ v2' = Face.v1 (front_face cube)
+ v3' = Face.v2 (front_face cube)
+ fv' = rotate ccwx (fv cube)
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 2 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (front_face c)
- v2' = Face.v2 (front_face c)
- v3' = Face.v3 (front_face c)
- fv' = rotate ccwx $ rotate ccwx $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 3 =
+ v0' = center cube
+ v1' = center (front_face cube)
+ v2' = Face.v2 (front_face cube)
+ v3' = Face.v3 (front_face cube)
+ fv' = rotate ccwx $ rotate ccwx $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 3 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (front_face c)
- v2' = Face.v3 (front_face c)
- v3' = Face.v0 (front_face c)
- fv' = rotate cwx (fv c)
- vol = tetrahedra_volume c
-
-tetrahedron c 4 =
+ v0' = center cube
+ v1' = center (front_face cube)
+ v2' = Face.v3 (front_face cube)
+ v3' = Face.v0 (front_face cube)
+ fv' = rotate cwx (fv cube)
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 4 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (top_face c)
- v2' = Face.v0 (top_face c)
- v3' = Face.v1 (top_face c)
- fv' = rotate cwy (fv c)
- vol = tetrahedra_volume c
-
-tetrahedron c 5 =
+ v0' = center cube
+ v1' = center (top_face cube)
+ v2' = Face.v0 (top_face cube)
+ v3' = Face.v1 (top_face cube)
+ fv' = rotate cwy (fv cube)
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 5 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (top_face c)
- v2' = Face.v1 (top_face c)
- v3' = Face.v2 (top_face c)
- fv' = rotate cwy $ rotate cwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 6 =
+ v0' = center cube
+ v1' = center (top_face cube)
+ v2' = Face.v1 (top_face cube)
+ v3' = Face.v2 (top_face cube)
+ fv' = rotate cwy $ rotate cwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 6 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (top_face c)
- v2' = Face.v2 (top_face c)
- v3' = Face.v3 (top_face c)
+ v0' = center cube
+ v1' = center (top_face cube)
+ v2' = Face.v2 (top_face cube)
+ v3' = Face.v3 (top_face cube)
fv' = rotate cwy $ rotate cwz
$ rotate cwz
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 7 =
+tetrahedron cube 7 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (top_face c)
- v2' = Face.v3 (top_face c)
- v3' = Face.v0 (top_face c)
- fv' = rotate cwy $ rotate ccwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 8 =
+ v0' = center cube
+ v1' = center (top_face cube)
+ v2' = Face.v3 (top_face cube)
+ v3' = Face.v0 (top_face cube)
+ fv' = rotate cwy $ rotate ccwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 8 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (back_face c)
- v2' = Face.v0 (back_face c)
- v3' = Face.v1 (back_face c)
- fv' = rotate cwy $ rotate cwy $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 9 =
+ v0' = center cube
+ v1' = center (back_face cube)
+ v2' = Face.v0 (back_face cube)
+ v3' = Face.v1 (back_face cube)
+ fv' = rotate cwy $ rotate cwy $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 9 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (back_face c)
- v2' = Face.v1 (back_face c)
- v3' = Face.v2 (back_face c)
+ v0' = center cube
+ v1' = center (back_face cube)
+ v2' = Face.v1 (back_face cube)
+ v3' = Face.v2 (back_face cube)
fv' = rotate cwy $ rotate cwy
$ rotate cwx
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 10 =
+tetrahedron cube 10 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (back_face c)
- v2' = Face.v2 (back_face c)
- v3' = Face.v3 (back_face c)
+ v0' = center cube
+ v1' = center (back_face cube)
+ v2' = Face.v2 (back_face cube)
+ v3' = Face.v3 (back_face cube)
fv' = rotate cwy $ rotate cwy
$ rotate cwx
$ rotate cwx
- $ fv c
+ $ fv cube
- vol = tetrahedra_volume c
+ vol = tetrahedra_volume cube
-tetrahedron c 11 =
+tetrahedron cube 11 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (back_face c)
- v2' = Face.v3 (back_face c)
- v3' = Face.v0 (back_face c)
+ v0' = center cube
+ v1' = center (back_face cube)
+ v2' = Face.v3 (back_face cube)
+ v3' = Face.v0 (back_face cube)
fv' = rotate cwy $ rotate cwy
$ rotate ccwx
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 12 =
+tetrahedron cube 12 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (down_face c)
- v2' = Face.v0 (down_face c)
- v3' = Face.v1 (down_face c)
- fv' = rotate ccwy $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 13 =
+ v0' = center cube
+ v1' = center (down_face cube)
+ v2' = Face.v0 (down_face cube)
+ v3' = Face.v1 (down_face cube)
+ fv' = rotate ccwy $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 13 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (down_face c)
- v2' = Face.v1 (down_face c)
- v3' = Face.v2 (down_face c)
- fv' = rotate ccwy $ rotate ccwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 14 =
+ v0' = center cube
+ v1' = center (down_face cube)
+ v2' = Face.v1 (down_face cube)
+ v3' = Face.v2 (down_face cube)
+ fv' = rotate ccwy $ rotate ccwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 14 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (down_face c)
- v2' = Face.v2 (down_face c)
- v3' = Face.v3 (down_face c)
+ v0' = center cube
+ v1' = center (down_face cube)
+ v2' = Face.v2 (down_face cube)
+ v3' = Face.v3 (down_face cube)
fv' = rotate ccwy $ rotate ccwz
$ rotate ccwz
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 15 =
+tetrahedron cube 15 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (down_face c)
- v2' = Face.v3 (down_face c)
- v3' = Face.v0 (down_face c)
- fv' = rotate ccwy $ rotate cwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 16 =
+ v0' = center cube
+ v1' = center (down_face cube)
+ v2' = Face.v3 (down_face cube)
+ v3' = Face.v0 (down_face cube)
+ fv' = rotate ccwy $ rotate cwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 16 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (right_face c)
- v2' = Face.v0 (right_face c)
- v3' = Face.v1 (right_face c)
- fv' = rotate ccwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 17 =
+ v0' = center cube
+ v1' = center (right_face cube)
+ v2' = Face.v0 (right_face cube)
+ v3' = Face.v1 (right_face cube)
+ fv' = rotate ccwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 17 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (right_face c)
- v2' = Face.v1 (right_face c)
- v3' = Face.v2 (right_face c)
- fv' = rotate ccwz $ rotate cwy $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 18 =
+ v0' = center cube
+ v1' = center (right_face cube)
+ v2' = Face.v1 (right_face cube)
+ v3' = Face.v2 (right_face cube)
+ fv' = rotate ccwz $ rotate cwy $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 18 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (right_face c)
- v2' = Face.v2 (right_face c)
- v3' = Face.v3 (right_face c)
+ v0' = center cube
+ v1' = center (right_face cube)
+ v2' = Face.v2 (right_face cube)
+ v3' = Face.v3 (right_face cube)
fv' = rotate ccwz $ rotate cwy
$ rotate cwy
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 19 =
+tetrahedron cube 19 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (right_face c)
- v2' = Face.v3 (right_face c)
- v3' = Face.v0 (right_face c)
+ v0' = center cube
+ v1' = center (right_face cube)
+ v2' = Face.v3 (right_face cube)
+ v3' = Face.v0 (right_face cube)
fv' = rotate ccwz $ rotate ccwy
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 20 =
+tetrahedron cube 20 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (left_face c)
- v2' = Face.v0 (left_face c)
- v3' = Face.v1 (left_face c)
- fv' = rotate cwz $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 21 =
+ v0' = center cube
+ v1' = center (left_face cube)
+ v2' = Face.v0 (left_face cube)
+ v3' = Face.v1 (left_face cube)
+ fv' = rotate cwz $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 21 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (left_face c)
- v2' = Face.v1 (left_face c)
- v3' = Face.v2 (left_face c)
- fv' = rotate cwz $ rotate ccwy $ fv c
- vol = tetrahedra_volume c
-
-tetrahedron c 22 =
+ v0' = center cube
+ v1' = center (left_face cube)
+ v2' = Face.v1 (left_face cube)
+ v3' = Face.v2 (left_face cube)
+ fv' = rotate cwz $ rotate ccwy $ fv cube
+ vol = tetrahedra_volume cube
+
+tetrahedron cube 22 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (left_face c)
- v2' = Face.v2 (left_face c)
- v3' = Face.v3 (left_face c)
+ v0' = center cube
+ v1' = center (left_face cube)
+ v2' = Face.v2 (left_face cube)
+ v3' = Face.v3 (left_face cube)
fv' = rotate cwz $ rotate ccwy
$ rotate ccwy
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-tetrahedron c 23 =
+tetrahedron cube 23 =
Tetrahedron fv' v0' v1' v2' v3' vol
where
- v0' = center c
- v1' = center (left_face c)
- v2' = Face.v3 (left_face c)
- v3' = Face.v0 (left_face c)
+ v0' = center cube
+ v1' = center (left_face cube)
+ v2' = Face.v3 (left_face cube)
+ v3' = Face.v0 (left_face cube)
fv' = rotate cwz $ rotate cwy
- $ fv c
- vol = tetrahedra_volume c
+ $ fv cube
+ vol = tetrahedra_volume cube
-- Feels dirty, but whatever.
tetrahedron _ _ = error "asked for a nonexistent tetrahedron"
-- Only used in tests, so we don't need the added speed
-- of Data.Vector.
tetrahedra :: Cube -> [Tetrahedron]
-tetrahedra c = [ tetrahedron c n | n <- [0..23] ]
+tetrahedra cube = [ tetrahedron cube n | n <- [0..23] ]
front_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
-front_left_top_tetrahedra c =
- V.singleton (tetrahedron c 0) `V.snoc`
- (tetrahedron c 3) `V.snoc`
- (tetrahedron c 6) `V.snoc`
- (tetrahedron c 7) `V.snoc`
- (tetrahedron c 20) `V.snoc`
- (tetrahedron c 21)
+front_left_top_tetrahedra cube =
+ V.singleton (tetrahedron cube 0) `V.snoc`
+ (tetrahedron cube 3) `V.snoc`
+ (tetrahedron cube 6) `V.snoc`
+ (tetrahedron cube 7) `V.snoc`
+ (tetrahedron cube 20) `V.snoc`
+ (tetrahedron cube 21)
front_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
-front_left_down_tetrahedra c =
- V.singleton (tetrahedron c 0) `V.snoc`
- (tetrahedron c 2) `V.snoc`
- (tetrahedron c 3) `V.snoc`
- (tetrahedron c 12) `V.snoc`
- (tetrahedron c 15) `V.snoc`
- (tetrahedron c 21)
+front_left_down_tetrahedra cube =
+ V.singleton (tetrahedron cube 0) `V.snoc`
+ (tetrahedron cube 2) `V.snoc`
+ (tetrahedron cube 3) `V.snoc`
+ (tetrahedron cube 12) `V.snoc`
+ (tetrahedron cube 15) `V.snoc`
+ (tetrahedron cube 21)
front_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
-front_right_top_tetrahedra c =
- V.singleton (tetrahedron c 0) `V.snoc`
- (tetrahedron c 1) `V.snoc`
- (tetrahedron c 5) `V.snoc`
- (tetrahedron c 6) `V.snoc`
- (tetrahedron c 16) `V.snoc`
- (tetrahedron c 19)
+front_right_top_tetrahedra cube =
+ V.singleton (tetrahedron cube 0) `V.snoc`
+ (tetrahedron cube 1) `V.snoc`
+ (tetrahedron cube 5) `V.snoc`
+ (tetrahedron cube 6) `V.snoc`
+ (tetrahedron cube 16) `V.snoc`
+ (tetrahedron cube 19)
front_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
-front_right_down_tetrahedra c =
- V.singleton (tetrahedron c 1) `V.snoc`
- (tetrahedron c 2) `V.snoc`
- (tetrahedron c 12) `V.snoc`
- (tetrahedron c 13) `V.snoc`
- (tetrahedron c 18) `V.snoc`
- (tetrahedron c 19)
+front_right_down_tetrahedra cube =
+ V.singleton (tetrahedron cube 1) `V.snoc`
+ (tetrahedron cube 2) `V.snoc`
+ (tetrahedron cube 12) `V.snoc`
+ (tetrahedron cube 13) `V.snoc`
+ (tetrahedron cube 18) `V.snoc`
+ (tetrahedron cube 19)
back_left_top_tetrahedra :: Cube -> V.Vector Tetrahedron
-back_left_top_tetrahedra c =
- V.singleton (tetrahedron c 0) `V.snoc`
- (tetrahedron c 3) `V.snoc`
- (tetrahedron c 6) `V.snoc`
- (tetrahedron c 7) `V.snoc`
- (tetrahedron c 20) `V.snoc`
- (tetrahedron c 21)
+back_left_top_tetrahedra cube =
+ V.singleton (tetrahedron cube 0) `V.snoc`
+ (tetrahedron cube 3) `V.snoc`
+ (tetrahedron cube 6) `V.snoc`
+ (tetrahedron cube 7) `V.snoc`
+ (tetrahedron cube 20) `V.snoc`
+ (tetrahedron cube 21)
back_left_down_tetrahedra :: Cube -> V.Vector Tetrahedron
-back_left_down_tetrahedra c =
- V.singleton (tetrahedron c 8) `V.snoc`
- (tetrahedron c 11) `V.snoc`
- (tetrahedron c 14) `V.snoc`
- (tetrahedron c 15) `V.snoc`
- (tetrahedron c 22) `V.snoc`
- (tetrahedron c 23)
+back_left_down_tetrahedra cube =
+ V.singleton (tetrahedron cube 8) `V.snoc`
+ (tetrahedron cube 11) `V.snoc`
+ (tetrahedron cube 14) `V.snoc`
+ (tetrahedron cube 15) `V.snoc`
+ (tetrahedron cube 22) `V.snoc`
+ (tetrahedron cube 23)
back_right_top_tetrahedra :: Cube -> V.Vector Tetrahedron
-back_right_top_tetrahedra c =
- V.singleton (tetrahedron c 4) `V.snoc`
- (tetrahedron c 5) `V.snoc`
- (tetrahedron c 9) `V.snoc`
- (tetrahedron c 10) `V.snoc`
- (tetrahedron c 16) `V.snoc`
- (tetrahedron c 17)
+back_right_top_tetrahedra cube =
+ V.singleton (tetrahedron cube 4) `V.snoc`
+ (tetrahedron cube 5) `V.snoc`
+ (tetrahedron cube 9) `V.snoc`
+ (tetrahedron cube 10) `V.snoc`
+ (tetrahedron cube 16) `V.snoc`
+ (tetrahedron cube 17)
back_right_down_tetrahedra :: Cube -> V.Vector Tetrahedron
-back_right_down_tetrahedra c =
- V.singleton (tetrahedron c 8) `V.snoc`
- (tetrahedron c 9) `V.snoc`
- (tetrahedron c 13) `V.snoc`
- (tetrahedron c 14) `V.snoc`
- (tetrahedron c 17) `V.snoc`
- (tetrahedron c 18)
+back_right_down_tetrahedra cube =
+ V.singleton (tetrahedron cube 8) `V.snoc`
+ (tetrahedron cube 9) `V.snoc`
+ (tetrahedron cube 13) `V.snoc`
+ (tetrahedron cube 14) `V.snoc`
+ (tetrahedron cube 17) `V.snoc`
+ (tetrahedron cube 18)
in_top_half :: Cube -> Point -> Bool
-in_top_half c (_,_,z) =
+in_top_half cube (_,_,z) =
distance_from_top <= distance_from_bottom
where
- distance_from_top = abs $ (zmax c) - z
- distance_from_bottom = abs $ (zmin c) - z
+ distance_from_top = abs $ (zmax cube) - z
+ distance_from_bottom = abs $ (zmin cube) - z
in_front_half :: Cube -> Point -> Bool
-in_front_half c (x,_,_) =
+in_front_half cube (x,_,_) =
distance_from_front <= distance_from_back
where
- distance_from_front = abs $ (xmin c) - x
- distance_from_back = abs $ (xmax c) - x
+ distance_from_front = abs $ (xmin cube) - x
+ distance_from_back = abs $ (xmax cube) - x
in_left_half :: Cube -> Point -> Bool
-in_left_half c (_,y,_) =
+in_left_half cube (_,y,_) =
distance_from_left <= distance_from_right
where
- distance_from_left = abs $ (ymin c) - y
- distance_from_right = abs $ (ymax c) - y
+ distance_from_left = abs $ (ymin cube) - y
+ distance_from_right = abs $ (ymax cube) - y
-- | Takes a 'Cube', and returns the Tetrahedra belonging to it that
-- save us some unnecessary computations.
--
find_containing_tetrahedron :: Cube -> Point -> Tetrahedron
-find_containing_tetrahedron c p =
+find_containing_tetrahedron cube p =
candidates `V.unsafeIndex` (fromJust lucky_idx)
where
- front_half = in_front_half c p
- top_half = in_top_half c p
- left_half = in_left_half c p
+ front_half = in_front_half cube p
+ top_half = in_top_half cube p
+ left_half = in_left_half cube p
candidates =
if front_half then
if left_half then
if top_half then
- front_left_top_tetrahedra c
+ front_left_top_tetrahedra cube
else
- front_left_down_tetrahedra c
+ front_left_down_tetrahedra cube
else
if top_half then
- front_right_top_tetrahedra c
+ front_right_top_tetrahedra cube
else
- front_right_down_tetrahedra c
+ front_right_down_tetrahedra cube
else -- bottom half
if left_half then
if top_half then
- back_left_top_tetrahedra c
+ back_left_top_tetrahedra cube
else
- back_left_down_tetrahedra c
+ back_left_down_tetrahedra cube
else
if top_half then
- back_right_top_tetrahedra c
+ back_right_top_tetrahedra cube
else
- back_right_down_tetrahedra c
+ back_right_down_tetrahedra cube
-- Use the dot product instead of 'distance' here to save a
-- sqrt(). So, "distances" below really means "distances squared."
-- Quickcheck tests.
prop_opposite_octant_tetrahedra_disjoint1 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint1 c =
- disjoint (front_left_top_tetrahedra c) (front_right_down_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint1 cube =
+ disjoint (front_left_top_tetrahedra cube) (front_right_down_tetrahedra cube)
prop_opposite_octant_tetrahedra_disjoint2 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint2 c =
- disjoint (back_left_top_tetrahedra c) (back_right_down_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint2 cube =
+ disjoint (back_left_top_tetrahedra cube) (back_right_down_tetrahedra cube)
prop_opposite_octant_tetrahedra_disjoint3 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint3 c =
- disjoint (front_left_top_tetrahedra c) (back_right_top_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint3 cube =
+ disjoint (front_left_top_tetrahedra cube) (back_right_top_tetrahedra cube)
prop_opposite_octant_tetrahedra_disjoint4 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint4 c =
- disjoint (front_left_down_tetrahedra c) (back_right_down_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint4 cube =
+ disjoint (front_left_down_tetrahedra cube) (back_right_down_tetrahedra cube)
prop_opposite_octant_tetrahedra_disjoint5 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint5 c =
- disjoint (front_left_top_tetrahedra c) (back_left_down_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint5 cube =
+ disjoint (front_left_top_tetrahedra cube) (back_left_down_tetrahedra cube)
prop_opposite_octant_tetrahedra_disjoint6 :: Cube -> Bool
-prop_opposite_octant_tetrahedra_disjoint6 c =
- disjoint (front_right_top_tetrahedra c) (back_right_down_tetrahedra c)
+prop_opposite_octant_tetrahedra_disjoint6 cube =
+ disjoint (front_right_top_tetrahedra cube) (back_right_down_tetrahedra cube)
-- | Since the grid size is necessarily positive, all tetrahedra
projects / spline3.git / commitdiff