X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FGrid.hs;h=d9fa975eedc7498989d601394b7e686c72ff0d41;hb=b2e1c440b9b1bb99ae564d6600230bbd1f7d204c;hp=1a436acdc00d9276ceb1e25b7080355577822bf3;hpb=30bc407abc86ffa9a0eb4b26bdb4890f3ea423d1;p=spline3.git diff --git a/src/Grid.hs b/src/Grid.hs index 1a436ac..d9fa975 100644 --- a/src/Grid.hs +++ b/src/Grid.hs @@ -4,11 +4,19 @@ module Grid where -import Cube (Cube(Cube)) +import Data.Array (Array, array, (!)) +import qualified Data.Array.Repa as R +import Test.QuickCheck (Arbitrary(..), Gen, Positive(..)) + +import Cube (Cube(Cube), find_containing_tetrahedron) import FunctionValues -import Misc (flatten) import Point (Point) -import ThreeDimensional (contains_point) +import ScaleFactor +import Tetrahedron (polynomial) +import Values (Values3D, dims, empty3d, zoom_shape) + + +type CubeGrid = Array (Int,Int,Int) Cube -- | Our problem is defined on a Grid. The grid size is given by the @@ -16,13 +24,20 @@ import ThreeDimensional (contains_point) -- function at the grid points, which are distance h from one -- another in each direction (x,y,z). data Grid = Grid { h :: Double, -- MUST BE GREATER THAN ZERO! - function_values :: [[[Double]]] } + function_values :: Values3D } deriving (Eq, Show) +instance Arbitrary Grid where + arbitrary = do + (Positive h') <- arbitrary :: Gen (Positive Double) + fvs <- arbitrary :: Gen Values3D + return (make_grid h' fvs) + + -- | The constructor that we want people to use. If we're passed a -- non-positive grid size, we throw an error. -make_grid :: Double -> [[[Double]]] -> Grid +make_grid :: Double -> Values3D -> Grid make_grid grid_size values | grid_size <= 0 = error "grid size must be positive" | otherwise = Grid grid_size values @@ -30,45 +45,106 @@ make_grid grid_size values -- | Creates an empty grid with grid size 1. empty_grid :: Grid -empty_grid = Grid 1 [[[]]] +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 - | fvs == [[[]]] = [[[]]] - | head fvs == [[]] = [[[]]] - | 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 - zsize = (length fvs) - 1 - ysize = length (head fvs) - 1 - xsize = length (head $ head fvs) - 1 + = array (lbounds, ubounds) + [ ((i,j,k), cube_ijk) + | i <- [0..xmax], + j <- [0..ymax], + k <- [0..zmax], + let delta = h g, + let tet_vol = (1/24)*(delta^(3::Int)), + let cube_ijk = + Cube delta i j k (make_values fvs i j k) tet_vol] + 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 + | coord < offset = 0 + | otherwise = (ceiling ( (coord + offset) / cube_width )) - 1 + where + (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 - all_cubes = flatten $ cubes g - contains_our_point = flip contains_point p + (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 -> ScaleFactor -> Values3D +zoom g scale_factor + | xsize == 0 || ysize == 0 || zsize == 0 = empty3d + | otherwise = + R.force $ R.traverse arr transExtent (zoom_lookup g scale_factor) + where + arr = function_values g + (xsize, ysize, zsize) = dims arr + transExtent = zoom_shape scale_factor