X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FCube.hs;h=6b2121cf117ed98e6d25b6a37f02a0a8341841ee;hb=0a1f963086ef11db21da4f9d45780e7e7ea1ed7a;hp=b44f0070f5c8be1982584897efdf605884846788;hpb=01925d099b231a128f6bd51abd61bf9ff9c424b6;p=spline3.git diff --git a/src/Cube.hs b/src/Cube.hs index b44f007..6b2121c 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 @@ -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 +299,7 @@ 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 @@ -307,7 +310,7 @@ tetrahedron12 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 + fv' = rotate (Tetrahedron.fv (tetrahedron8 c)) ccwy tetrahedron13 :: Cube -> Tetrahedron @@ -318,7 +321,7 @@ tetrahedron13 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 + fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) cwz tetrahedron14 :: Cube -> Tetrahedron @@ -329,7 +332,7 @@ tetrahedron14 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) + fv' = rotate (Tetrahedron.fv (tetrahedron13 c)) (cwz . cwz) tetrahedron15 :: Cube -> Tetrahedron @@ -340,7 +343,7 @@ tetrahedron15 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 + fv' = rotate (Tetrahedron.fv (tetrahedron12 c)) ccwz tetrahedron16 :: Cube -> Tetrahedron @@ -351,7 +354,7 @@ tetrahedron16 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 + fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) cwz tetrahedron17 :: Cube -> Tetrahedron @@ -395,7 +398,7 @@ tetrahedron20 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 + fv' = rotate (Tetrahedron.fv (tetrahedron0 c)) ccwz tetrahedron21 :: Cube -> Tetrahedron @@ -406,7 +409,7 @@ tetrahedron21 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 + fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) cwy tetrahedron22 :: Cube -> Tetrahedron @@ -417,7 +420,7 @@ tetrahedron22 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 + fv' = rotate (Tetrahedron.fv (tetrahedron20 c)) (cwy . cwy) tetrahedron23 :: Cube -> Tetrahedron @@ -457,3 +460,13 @@ tetrahedrons c = tetrahedron21 c, tetrahedron22 c, tetrahedron23 c] + + +-- | Takes a 'Cube', and returns all Tetrahedra belonging to it that +-- contain the given 'Point'. +find_containing_tetrahedra :: Cube -> Point -> [Tetrahedron] +find_containing_tetrahedra c p = + filter contains_our_point all_tetrahedra + where + contains_our_point = flip contains_point p + all_tetrahedra = tetrahedrons c