X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=cfe0e6090ed20c02f6e32acfe66fcecd797dce95;hb=58cf11569acb270995d2de924dda03ef526647e2;hp=8d978f732ffeb8fe2acd7f04b46a5912ede43168;hpb=1d2e0c4c6e5d766bd3ac6834d9dec298679f7c31;p=spline3.git diff --git a/src/Cube.hs b/src/Cube.hs index 8d978f7..cfe0e60 100644 --- a/src/Cube.hs +++ b/src/Cube.hs @@ -2,10 +2,10 @@ module Cube 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, @@ -26,12 +26,14 @@ instance Show Cube where " ymin: " ++ (show (ymin c)) ++ "\n" ++ " ymax: " ++ (show (ymax c)) ++ "\n" ++ " zmin: " ++ (show (zmin c)) ++ "\n" ++ - " zmax: " ++ (show (zmax c)) ++ "\n" + " zmax: " ++ (show (zmax c)) ++ "\n" ++ + " fv: " ++ (show (Cube.fv c)) ++ "\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 @@ -86,7 +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 @@ -97,6 +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 @@ -111,43 +115,43 @@ instance ThreeDimensional Cube where -- 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) @@ -155,28 +159,26 @@ front_face c = Face v0' v1' v2' v3' 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 @@ -185,8 +187,8 @@ tetrahedron0 c = 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 = @@ -194,8 +196,8 @@ 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 @@ -204,8 +206,8 @@ tetrahedron2 c = 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 @@ -214,8 +216,8 @@ tetrahedron3 c = 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 @@ -224,8 +226,8 @@ tetrahedron4 c = 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 @@ -234,9 +236,9 @@ tetrahedron5 c = 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 = @@ -244,9 +246,9 @@ 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 = @@ -254,9 +256,183 @@ 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 = @@ -267,24 +443,20 @@ 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]