X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FTetrahedron.hs;h=a6d69a2c68af2c8051d3fab76b9bcfd4e3201bfd;hb=1bf996325008f79215a607d765adb042026f7444;hp=f1614f9004b8a984b8e29ff3095072f1c16a72a4;hpb=edd0bfa30456c0f609418e730af641835b8650aa;p=spline3.git diff --git a/src/Tetrahedron.hs b/src/Tetrahedron.hs index f1614f9..a6d69a2 100644 --- a/src/Tetrahedron.hs +++ b/src/Tetrahedron.hs @@ -96,7 +96,7 @@ instance ThreeDimensional Tetrahedron where b3_unscaled = volume inner_tetrahedron where inner_tetrahedron = t { v3 = p0 } - +{-# INLINE polynomial #-} polynomial :: Tetrahedron -> (RealFunction Point) polynomial t = V.sum $ V.singleton ((c t 0 0 0 3) `cmult` (beta t 0 0 0 3)) `V.snoc` @@ -125,10 +125,8 @@ polynomial t = -- | The Bernstein polynomial on t with indices i,j,k,l. Denoted by a -- capital 'B' in the Sorokina/Zeilfelder paper. beta :: Tetrahedron -> Int -> Int -> Int -> Int -> (RealFunction Point) -beta t i j k l - | (i + j + k + l == 3) = - coefficient `cmult` (b0_term * b1_term * b2_term * b3_term) - | otherwise = error "basis function index out of bounds" +beta t i j k l = + coefficient `cmult` (b0_term * b1_term * b2_term * b3_term) where denominator = (factorial i)*(factorial j)*(factorial k)*(factorial l) coefficient = 6 / (fromIntegral denominator) @@ -141,8 +139,8 @@ beta t i j k l -- | The coefficient function. c t i j k l returns the coefficient -- c_ijkl with respect to the tetrahedron t. The definition uses -- pattern matching to mimic the definitions given in Sorokina and --- Zeilfelder, pp. 84-86. If incorrect indices are supplied, the --- function will simply error. +-- Zeilfelder, pp. 84-86. If incorrect indices are supplied, the world +-- will end. This is for performance reasons. c :: Tetrahedron -> Int -> Int -> Int -> Int -> Double c !t !i !j !k !l = coefficient i j k l @@ -271,8 +269,6 @@ c !t !i !j !k !l = + (1/96)*(lt + fl + ft + rt + bt + fr) + (1/96)*(fd + ld + bd + br + rd + bl) - coefficient _ _ _ _ = error "coefficient index out of bounds" - -- | Compute the determinant of the 4x4 matrix, @@ -308,6 +304,7 @@ det p0 p1 p2 p3 = -- | Computed using the formula from Lai & Schumaker, Definition 15.4, -- page 436. +{-# INLINE volume #-} volume :: Tetrahedron -> Double volume t | v0' == v1' = 0 @@ -325,6 +322,7 @@ volume t -- | The barycentric coordinates of a point with respect to v0. +{-# INLINE b0 #-} b0 :: Tetrahedron -> (RealFunction Point) b0 t point = (volume inner_tetrahedron) / (precomputed_volume t) where @@ -332,6 +330,7 @@ b0 t point = (volume inner_tetrahedron) / (precomputed_volume t) -- | The barycentric coordinates of a point with respect to v1. +{-# INLINE b1 #-} b1 :: Tetrahedron -> (RealFunction Point) b1 t point = (volume inner_tetrahedron) / (precomputed_volume t) where @@ -339,6 +338,7 @@ b1 t point = (volume inner_tetrahedron) / (precomputed_volume t) -- | The barycentric coordinates of a point with respect to v2. +{-# INLINE b2 #-} b2 :: Tetrahedron -> (RealFunction Point) b2 t point = (volume inner_tetrahedron) / (precomputed_volume t) where @@ -346,6 +346,7 @@ b2 t point = (volume inner_tetrahedron) / (precomputed_volume t) -- | The barycentric coordinates of a point with respect to v3. +{-# INLINE b3 #-} b3 :: Tetrahedron -> (RealFunction Point) b3 t point = (volume inner_tetrahedron) / (precomputed_volume t) where @@ -641,9 +642,8 @@ p78_24_properties = where -- | Returns the domain point of t with indices i,j,k,l. domain_point :: Tetrahedron -> Int -> Int -> Int -> Int -> Point - domain_point t i j k l - | i + j + k + l == 3 = weighted_sum `scale` (1/3) - | otherwise = error "domain point index out of bounds" + domain_point t i j k l = + weighted_sum `scale` (1/3) where v0' = (v0 t) `scale` (fromIntegral i) v1' = (v1 t) `scale` (fromIntegral j)