where
import Numeric.LinearAlgebra hiding (i, scale)
+import Prelude hiding (LT)
-import Cube (back,
- Cube(datum),
- down,
- front,
- Gridded,
- left,
- right,
- top)
+import Cardinal
+import FunctionValues
import Misc (factorial)
import Point
import RealFunction
import ThreeDimensional
-data Tetrahedron = Tetrahedron { cube :: Cube,
- v0 :: Point,
- v1 :: Point,
- v2 :: Point,
- v3 :: Point }
+data Tetrahedron = Tetrahedron { fv :: FunctionValues,
+ v0 :: Point,
+ v1 :: Point,
+ v2 :: Point,
+ v3 :: Point }
deriving (Eq)
instance Show Tetrahedron where
- show t = "Tetrahedron (Cube: " ++ (show (cube t)) ++ ") " ++
- "(v0: " ++ (show (v0 t)) ++ ") (v1: " ++ (show (v1 t)) ++
- ") (v2: " ++ (show (v2 t)) ++ ") (v3: " ++ (show (v3 t)) ++
- ")\n\n"
-
-instance Gridded Tetrahedron where
- back t = back (cube t)
- down t = down (cube t)
- front t = front (cube t)
- left t = left (cube t)
- right t = right (cube t)
- top t = top (cube t)
+ show t = "Tetrahedron:\n" ++
+ " fv: " ++ (show (fv t)) ++ "\n" ++
+ " v0: " ++ (show (v0 t)) ++ "\n" ++
+ " v1: " ++ (show (v1 t)) ++ "\n" ++
+ " v2: " ++ (show (v2 t)) ++ "\n" ++
+ " v3: " ++ (show (v3 t)) ++ "\n"
instance ThreeDimensional Tetrahedron where
c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double
-c x 0 0 3 0 = datum $ (1/8) * (i + f + l + t + lt + fl + ft + flt)
- where
- f = front x
- flt = front (left (top x))
- fl = front (left x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- t = top x
-
-
-c x 0 0 0 3 = datum $ (1/8) * (i + f + r + t + rt + fr + ft + frt)
- where
- f = front x
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 0 0 2 1 = datum $ (5/24)*(i + f + t + ft) + (1/24)*(l + fl + lt + flt)
- where
- f = front x
- flt = front (left (top x))
- fl = front (left x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- t = top x
-
-
-c x 0 0 1 2 = datum $ (5/24)*(i + f + t + ft) + (1/24)*(r + fr + rt + frt)
- where
- f = front x
- frt = front (right (top x))
- fr = front (right x)
- ft = front (top x)
- i = cube x
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 0 1 2 0 = datum $
- (5/24)*(i + f) +
- (1/8)*(l + t + fl + ft) +
- (1/24)*(lt + flt)
- where
- f = front x
- flt = front (left (top x))
- fl = front (left x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- t = top x
-
-
-c x 0 1 0 2 = datum $
- (5/24)*(i + f) +
- (1/8)*(r + t + fr + ft) +
- (1/24)*(rt + frt)
- where
- f = front x
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 0 1 1 1 = datum $
- (13/48)*(i + f) +
- (7/48)*(t + ft) +
- (1/32)*(l + r + fl + fr) +
- (1/96)*(lt + rt + flt + frt)
- where
- f = front x
- flt = front (left (top x))
- fl = front (left x)
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 0 2 1 0 = datum $
- (13/48)*(i + f) +
- (17/192)*(l + t + fl + ft) +
- (1/96)*(lt + flt) +
- (1/64)*(r + d + fr + fd) +
- (1/192)*(rt + ld + frt + fld)
- where
- d = down x
- f = front x
- fd = front (down x)
- fld = front (left (down x))
- flt = front (left (top x))
- fl = front (left x)
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 0 2 0 1 = datum $
- (13/48)*(i + f) +
- (17/192)*(r + t + fr + ft) +
- (1/96)*(rt + frt) +
- (1/64)*(l + d + fl + fd) +
- (1/192)*(rd + lt + flt + frd)
- where
- d = down x
- f = front x
- fd = front (down x)
- flt = front (left (top x))
- fl = front (left x)
- frd = front (right (down x))
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-
-c x 0 3 0 0 = datum $
- (13/48)*(i + f) +
- (5/96)*(l + r + t + d + fl + fr + ft + fd) +
- (1/192)*(rt + rd + lt + ld + frt + frd + flt + fld)
- where
- d = down x
- f = front x
- fd = front (down x)
- fld = front (left (down x))
- flt = front (left (top x))
- fl = front (left x)
- frd = front (right (down x))
- fr = front (right x)
- frt = front (right (top x))
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-c x 1 0 2 0 = datum $ (1/4)*i + (1/6)*(f + l + t) + (1/12)*(lt + fl + ft)
- where
- f = front x
- fl = front (left x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- t = top x
-
-
-c x 1 0 0 2 = datum $ (1/4)*i + (1/6)*(f + r + t) + (1/12)*(rt + fr + ft)
- where
- f = front x
- fr = front (right x)
- ft = front (top x)
- i = cube x
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 1 0 1 1 = datum $
- (1/3)*i +
- (5/24)*(f + t) +
- (1/12)*ft +
- (1/24)*(l + r) +
- (1/48)*(lt + rt + fl + fr)
- where
- f = front x
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 1 1 1 0 = datum $
- (1/3)*i +
- (5/24)*f +
- (1/8)*(l + t) +
- (5/96)*(fl + ft) +
- (1/48)*(d + r + lt) +
- (1/96)*(fd + ld + rt + fr)
- where
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 1 1 0 1 = datum $
- (1/3)*i +
- (5/24)*f +
- (1/8)*(r + t) +
- (5/96)*(fr + ft) +
- (1/48)*(d + l + rt) +
- (1/96)*(fd + lt + rd + fl)
- where
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-
-
-c x 1 2 0 0 = datum $
- (1/3)*i +
- (5/24)*f +
- (7/96)*(l + r + t + d) +
- (1/32)*(fl + fr + ft + fd) +
- (1/96)*(rt + rd + lt + ld)
- where
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-
-c x 2 0 1 0 = datum $
- (3/8)*i +
- (7/48)*(f + t + l) +
- (1/48)*(r + d + b + lt + fl + ft) +
- (1/96)*(rt + bt + fr + fd + ld + bl)
- where
- b = back x
- bl = back (left x)
- bt = back (top x)
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rt = right (top x)
- t = top x
-
-
-c x 2 0 0 1 = datum $
- (3/8)*i +
- (7/48)*(f + t + r) +
- (1/48)*(l + d + b + rt + fr + ft) +
- (1/96)*(lt + bt + fl + fd + rd + br)
- where
- b = back x
- br = back (right x)
- bt = back (top x)
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-
-
-c x 2 1 0 0 = datum $
- (3/8)*i +
- (1/12)*(t + r + l + d) +
- (1/64)*(ft + fr + fl + fd) +
- (7/48)*f +
- (1/48)*b +
- (1/96)*(rt + ld + lt + rd) +
- (1/192)*(bt + br + bl + bd)
- where
- b = back x
- bd = back (down x)
- bl = back (left x)
- br = back (right x)
- bt = back (top x)
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
-
-c x 3 0 0 0 = datum $
- (3/8)*i +
- (1/12)*(t + f + l + r + d + b) +
- (1/96)*(lt + fl + ft + rt + bt + fr) +
- (1/96)*(fd + ld + bd + br + rd + bl)
- where
- b = back x
- bd = back (down x)
- bl = back (left x)
- br = back (right x)
- bt = back (top x)
- d = down x
- f = front x
- fd = front (down x)
- fl = front (left x)
- fr = front (right x)
- ft = front (top x)
- i = cube x
- l = left x
- ld = left (down x)
- lt = left (top x)
- r = right x
- rd = right (down x)
- rt = right (top x)
- t = top x
-
+c t 0 0 3 0 = eval (fv t) $
+ (1/8) * (I + F + L + T + LT + FL + FT + FLT)
+
+c t 0 0 0 3 = eval (fv t) $
+ (1/8) * (I + F + R + T + RT + FR + FT + FRT)
+
+c t 0 0 2 1 = eval (fv t) $
+ (5/24)*(I + F + T + FT) +
+ (1/24)*(L + FL + LT + FLT)
+
+c t 0 0 1 2 = eval (fv t) $
+ (5/24)*(I + F + T + FT) +
+ (1/24)*(R + FR + RT + FRT)
+
+c t 0 1 2 0 = eval (fv t) $
+ (5/24)*(I + F) +
+ (1/8)*(L + T + FL + FT) +
+ (1/24)*(LT + FLT)
+
+c t 0 1 0 2 = eval (fv t) $
+ (5/24)*(I + F) +
+ (1/8)*(R + T + FR + FT) +
+ (1/24)*(RT + FRT)
+
+c t 0 1 1 1 = eval (fv t) $
+ (13/48)*(I + F) +
+ (7/48)*(T + FT) +
+ (1/32)*(L + R + FL + FR) +
+ (1/96)*(LT + RT + FLT + FRT)
+
+c t 0 2 1 0 = eval (fv t) $
+ (13/48)*(I + F) +
+ (17/192)*(L + T + FL + FT) +
+ (1/96)*(LT + FLT) +
+ (1/64)*(R + D + FR + FD) +
+ (1/192)*(RT + LD + FRT + FLD)
+
+c t 0 2 0 1 = eval (fv t) $
+ (13/48)*(I + F) +
+ (17/192)*(R + T + FR + FT) +
+ (1/96)*(RT + FRT) +
+ (1/64)*(L + D + FL + FD) +
+ (1/192)*(RD + LT + FLT + FRD)
+
+c t 0 3 0 0 = eval (fv t) $
+ (13/48)*(I + F) +
+ (5/96)*(L + R + T + D + FL + FR + FT + FD) +
+ (1/192)*(RT + RD + LT + LD + FRT + FRD + FLT + FLD)
+
+c t 1 0 2 0 = eval (fv t) $
+ (1/4)*I +
+ (1/6)*(F + L + T) +
+ (1/12)*(LT + FL + FT)
+
+c t 1 0 0 2 = eval (fv t) $
+ (1/4)*I +
+ (1/6)*(F + R + T) +
+ (1/12)*(RT + FR + FT)
+
+c t 1 0 1 1 = eval (fv t) $
+ (1/3)*I +
+ (5/24)*(F + T) +
+ (1/12)*FT +
+ (1/24)*(L + R) +
+ (1/48)*(LT + RT + FL + FR)
+
+c t 1 1 1 0 = eval (fv t) $
+ (1/3)*I +
+ (5/24)*F +
+ (1/8)*(L + T) +
+ (5/96)*(FL + FT) +
+ (1/48)*(D + R + LT) +
+ (1/96)*(FD + LD + RT + FR)
+
+c t 1 1 0 1 = eval (fv t) $
+ (1/3)*I +
+ (5/24)*F +
+ (1/8)*(R + T) +
+ (5/96)*(FR + FT) +
+ (1/48)*(D + L + RT) +
+ (1/96)*(FD + LT + RD + FL)
+
+c t 1 2 0 0 = eval (fv t) $
+ (1/3)*I +
+ (5/24)*F +
+ (7/96)*(L + R + T + D) +
+ (1/32)*(FL + FR + FT + FD) +
+ (1/96)*(RT + RD + LT + LD)
+
+c t 2 0 1 0 = eval (fv t) $
+ (3/8)*I +
+ (7/48)*(F + T + L) +
+ (1/48)*(R + D + B + LT + FL + FT) +
+ (1/96)*(RT + BT + FR + FD + LD + BL)
+
+c t 2 0 0 1 = eval (fv t) $
+ (3/8)*I +
+ (7/48)*(F + T + R) +
+ (1/48)*(L + D + B + RT + FR + FT) +
+ (1/96)*(LT + BT + FL + FD + RD + BR)
+
+c t 2 1 0 0 = eval (fv t) $
+ (3/8)*I +
+ (1/12)*(T + R + L + D) +
+ (1/64)*(FT + FR + FL + FD) +
+ (7/48)*F +
+ (1/48)*B +
+ (1/96)*(RT + LD + LT + RD) +
+ (1/192)*(BT + BR + BL + BD)
+
+c t 3 0 0 0 = eval (fv t) $
+ (3/8)*I +
+ (1/12)*(T + F + L + R + D + B) +
+ (1/96)*(LT + FL + FT + RT + BT + FR) +
+ (1/96)*(FD + LD + BD + BR + RD + BL)
c _ _ _ _ _ = error "coefficient index out of bounds"
projects / spline3.git / blobdiff