X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=5b5f2af690d3230bf06595ae133a05b313b840a3;hb=374d036a09ca086d73dabd7196d888ff76b90610;hp=8287177ed17edf6307a9517d06e11548320fa7da;hpb=51adbba172ccaa70c4832809de334674a8ba6a0f;p=spline3.git diff --git a/src/Cube.hs b/src/Cube.hs index 8287177..5b5f2af 100644 --- a/src/Cube.hs +++ b/src/Cube.hs @@ -33,6 +33,7 @@ instance Show Cube where (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 @@ -87,7 +88,7 @@ zmax c = (2*k' + 1)*delta / 2 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 @@ -98,6 +99,8 @@ instance ThreeDimensional Cube where 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 @@ -139,9 +142,9 @@ 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) @@ -161,10 +164,10 @@ 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. @@ -172,10 +175,10 @@ 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 @@ -195,7 +198,7 @@ tetrahedron1 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 = @@ -205,7 +208,7 @@ tetrahedron2 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 = @@ -215,7 +218,7 @@ tetrahedron3 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 = @@ -225,7 +228,7 @@ tetrahedron4 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 = @@ -235,7 +238,7 @@ tetrahedron5 c = v1' = center (top_face c) v2' = Face.v1 (top_face c) v3' = Face.v2 (top_face c) - fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz + fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz tetrahedron6 :: Cube -> Tetrahedron tetrahedron6 c = @@ -245,7 +248,7 @@ tetrahedron6 c = v1' = center (top_face c) v2' = Face.v2 (top_face c) v3' = Face.v3 (top_face c) - fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (ccwz . ccwz) + fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) (cwz . cwz) tetrahedron7 :: Cube -> Tetrahedron tetrahedron7 c = @@ -255,7 +258,7 @@ tetrahedron7 c = v1' = center (top_face c) v2' = Face.v3 (top_face c) v3' = Face.v0 (top_face c) - fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) cwz + fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwz tetrahedron8 :: Cube -> Tetrahedron tetrahedron8 c = @@ -265,7 +268,7 @@ tetrahedron8 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 + fv' = rotate (Tetrahedron.fv (tetrahedron4 c)) ccwy tetrahedron9 :: Cube -> Tetrahedron tetrahedron9 c = @@ -275,7 +278,7 @@ tetrahedron9 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 + fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) cwx tetrahedron10 :: Cube -> Tetrahedron tetrahedron10 c = @@ -285,7 +288,7 @@ tetrahedron10 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) + fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) (cwx . cwx) tetrahedron11 :: Cube -> Tetrahedron @@ -296,7 +299,139 @@ tetrahedron11 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 + 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] @@ -312,19 +447,16 @@ tetrahedrons 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 - ] + 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]