X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=8bf83828e9f23a97de57360ffeded92ebb92ccd2;hb=173d34c0d529830efeab39b7cca9a03856514469;hp=3d636b53a780f465b515c6e45f8ee53b6e7f10ba;hpb=3cf6c69c9c7fed364b13fa54ee78209f7485d304;p=spline3.git diff --git a/src/Grid.hs b/src/Grid.hs index 3d636b5..8bf8382 100644 --- a/src/Grid.hs +++ b/src/Grid.hs @@ -4,17 +4,20 @@ module Grid where +import Data.Array (Array, array, (!)) +import qualified Data.Array.Repa as R import Test.QuickCheck (Arbitrary(..), Gen, Positive(..)) -import Cube (Cube(Cube), find_containing_tetrahedra) +import Cube (Cube(Cube), find_containing_tetrahedron) import FunctionValues -import Misc (flatten) import Point (Point) +import ScaleFactor import Tetrahedron (polynomial) -import ThreeDimensional (contains_point) import Values (Values3D, dims, empty3d, zoom_shape) -import qualified Data.Array.Repa as R + +type CubeGrid = Array (Int,Int,Int) Cube + -- | Our problem is defined on a Grid. The grid size is given by the -- positive number h. The function values are the values of the @@ -45,62 +48,99 @@ empty_grid :: Grid empty_grid = Grid 1 empty3d --- | Returns a three-dimensional list of cubes centered on the grid +-- | Returns a three-dimensional array of cubes centered on the grid -- points of g with the appropriate 'FunctionValues'. -cubes :: Grid -> [[[Cube]]] +cubes :: Grid -> CubeGrid cubes g - | xsize == 0 || ysize == 0 || zsize == 0 = [[[]]] - | otherwise = - [[[ Cube (h g) i j k (make_values fvs i j k) | i <- [0..xsize]] - | j <- [0..ysize]] - | k <- [0..zsize]] - where - fvs = function_values g - (xsize, ysize, zsize) = dims fvs + = array (lbounds, ubounds) + [ ((i,j,k), cube_ijk) + | i <- [0..xmax], + j <- [0..ymax], + k <- [0..zmax], + let cube_ijk = Cube (h g) i j k (make_values fvs i j k)] + where + xmax = xsize - 1 + ymax = ysize - 1 + zmax = zsize - 1 + lbounds = (0, 0, 0) + ubounds = (xmax, ymax, zmax) + fvs = function_values g + (xsize, ysize, zsize) = dims fvs -- | Takes a grid and a position as an argument and returns the cube -- centered on that position. If there is no cube there (i.e. the --- position is outside of the grid), it will return 'Nothing'. -cube_at :: Grid -> Int -> Int -> Int -> Maybe Cube +-- position is outside of the grid), it will throw an error. +cube_at :: Grid -> Int -> Int -> Int -> Cube cube_at g i j k - | i < 0 = Nothing - | j < 0 = Nothing - | k < 0 = Nothing - | i >= length (cubes g) = Nothing - | j >= length ((cubes g) !! i) = Nothing - | k >= length (((cubes g) !! i) !! j) = Nothing - | otherwise = Just $ (((cubes g) !! i) !! j) !! k - - --- | Takes a 'Grid', and returns all 'Cube's belonging to it that --- contain the given 'Point'. -find_containing_cubes :: Grid -> Point -> [Cube] -find_containing_cubes g p = - filter contains_our_point all_cubes + | i < 0 = error "i < 0 in cube_at" + | i >= xsize = error "i >= xsize in cube_at" + | j < 0 = error "j < 0 in cube_at" + | j >= ysize = error "j >= ysize in cube_at" + | k < 0 = error "k < 0 in cube_at" + | k >= zsize = error "k >= zsize in cube_at" + | otherwise = (cubes g) ! (i,j,k) + where + fvs = function_values g + (xsize, ysize, zsize) = dims fvs + +-- The first cube along any axis covers (-h/2, h/2). The second +-- covers (h/2, 3h/2). The third, (3h/2, 5h/2), and so on. +-- +-- We translate the (x,y,z) coordinates forward by 'h/2' so that the +-- first covers (0, h), the second covers (h, 2h), etc. This makes +-- it easy to figure out which cube contains the given point. +calculate_containing_cube_coordinate :: Grid -> Double -> Int +calculate_containing_cube_coordinate g coord + -- Don't use a cube on the boundary if we can help it. This + -- returns cube #1 if we would have returned cube #0 and cube #1 + -- exists. + | coord == offset && (xsize > 0 && ysize > 0 && zsize > 0) = 1 + | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1 where - all_cubes = flatten $ cubes g - contains_our_point = flip contains_point p + (xsize, ysize, zsize) = dims (function_values g) + cube_width = (h g) + offset = cube_width / 2 + + +-- | Takes a 'Grid', and returns a 'Cube' containing the given 'Point'. +-- Since our grid is rectangular, we can figure this out without having +-- to check every cube. +find_containing_cube :: Grid -> Point -> Cube +find_containing_cube g p = + cube_at g i j k + where + (x, y, z) = p + i = calculate_containing_cube_coordinate g x + j = calculate_containing_cube_coordinate g y + k = calculate_containing_cube_coordinate g z + + +{-# INLINE zoom_lookup #-} +zoom_lookup :: Grid -> ScaleFactor -> a -> (R.DIM3 -> Double) +zoom_lookup g scale_factor _ = zoom_result g scale_factor + + +{-# INLINE zoom_result #-} +zoom_result :: Grid -> ScaleFactor -> R.DIM3 -> Double +zoom_result g (sfx, sfy, sfz) (R.Z R.:. i R.:. j R.:. k) = + f p + where + i' = (fromIntegral i) / (fromIntegral sfx) + j' = (fromIntegral j) / (fromIntegral sfy) + k' = (fromIntegral k) / (fromIntegral sfz) + p = (i', j', k') :: Point + c = find_containing_cube g p + t = find_containing_tetrahedron c p + f = polynomial t -zoom :: Grid -> Int -> Values3D +zoom :: Grid -> ScaleFactor -> Values3D zoom g scale_factor | xsize == 0 || ysize == 0 || zsize == 0 = empty3d | otherwise = - R.traverse arr transExtent (\_ -> newlookup) + R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor) where - fvs = function_values g - (xsize, ysize, zsize) = dims fvs - arr = fvs + arr = function_values g + (xsize, ysize, zsize) = dims arr transExtent = zoom_shape scale_factor - newlookup :: R.DIM3 -> Double - newlookup (R.Z R.:. i R.:. j R.:. k) = - f p - where - i' = fromIntegral i - j' = fromIntegral j - k' = fromIntegral k - p = (i', j', k') :: Point - c = head (find_containing_cubes g p) - t = head (find_containing_tetrahedra c p) - f = polynomial t