From: Michael Orlitzky Date: Sun, 2 Oct 2011 05:55:57 +0000 (-0400) Subject: Begin fixing value_at outside of the grid. X-Git-Tag: 0.0.1~119 X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=2f1d864660ff740773ea2c36ab79a837000f6452;p=spline3.git Begin fixing value_at outside of the grid. --- diff --git a/src/FunctionValues.hs b/src/FunctionValues.hs index e9da25f..9d52323 100644 --- a/src/FunctionValues.hs +++ b/src/FunctionValues.hs @@ -177,8 +177,11 @@ eval f (Quotient x y) = (eval f x) / (eval f y) -- | Takes a three-dimensional list of 'Double' and a set of 3D -- coordinates (i,j,k), and returns the value at (i,j,k) in the --- supplied list. If there is no such value, we choose a nearby --- point and use its value. +-- supplied list. If there is no such value, we calculate one +-- according to Sorokina and Zeilfelder, remark 7.3, p. 99. +-- +-- We specifically do not consider values more than one unit away +-- from our grid. -- -- Examples: -- @@ -186,7 +189,7 @@ eval f (Quotient x y) = (eval f x) / (eval f y) -- 1.0 -- -- >>> value_at Examples.trilinear (-1) 0 0 --- 1.0 +-- 0.0 -- -- >>> value_at Examples.trilinear 0 0 4 -- 1.0 @@ -196,13 +199,55 @@ eval f (Quotient x y) = (eval f x) / (eval f y) -- value_at :: Values3D -> Int -> Int -> Int -> Double value_at v3d i j k - | i < 0 = value_at v3d 0 j k - | j < 0 = value_at v3d i 0 k - | k < 0 = value_at v3d i j 0 - | xsize <= i = value_at v3d (xsize - 1) j k - | ysize <= j = value_at v3d i (ysize - 1) k - | zsize <= k = value_at v3d i j (zsize - 1) - | otherwise = idx v3d i j k + -- Put the most common case first! + | (i >= 0) && (j >= 0) && (k >= 0) = + idx v3d i j k + + -- The next three are from the first line in (7.3). + | (i == -1) && (j >= 0) && (k >= 0) = + 2*(value_at v3d 0 j k) - (value_at v3d 1 j k) + + | (i >= 0) && (j == -1) && (k >= 0) = + 2*(value_at v3d i 0 k) - (value_at v3d i 1 k) + + | (i >= 0) && (j >= 0) && (k == -1) = + 2*(value_at v3d i j 0) - (value_at v3d i j 1) + + -- The next two are from the second line in (7.3). + | (i == -1) && (j == -1) && (k >= 0) = + 2*(value_at v3d i 0 k) - (value_at v3d i 1 k) + + | (i == -1) && (j == ysize) && (k >= 0) = + 2*(value_at v3d i (ysize - 1) k) - (value_at v3d i (ysize - 2) k) + + -- The next two are from the third line in (7.3). + | (i == -1) && (j >= 0) && (k == -1) = + 2*(value_at v3d i j 0) - (value_at v3d i j 1) + + | (i == -1) && (j >= 0) && (k == zsize) = + 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2)) + + -- Repeat the above (j and k) cases for i >= 0. + | (i >= 0) && (j == -1) && (k == -1) = + 2*(value_at v3d i j 0) - (value_at v3d i j 1) + + | (i == xsize) && (j == -1) && (k >= 0) = + 2*(value_at v3d (xsize - 1) j k) - (value_at v3d (xsize - 2) j k) + + -- These two cases I made up. + | (i == -1) && (j == -1) && (k == -1) = + 2*(value_at v3d i j 0) - (value_at v3d i j 1) + + | (i == xsize) && (j == ysize) && (k == zsize) = + 2*(value_at v3d i j (zsize - 1)) - (value_at v3d i j (zsize - 2)) + + | otherwise = + let istr = show i + jstr = show j + kstr = show k + coordstr = "(" ++ istr ++ "," ++ jstr ++ "," ++ kstr ++ ")" + in + error $ "value_at called outside of domain: " ++ coordstr where (xsize, ysize, zsize) = dims v3d