Divide a region by a predefined raster - grid

Question

I have a big grid (indicated on the image in grey) that is divided in several blocks (each with a maximum width of 3 units). Now I would like to divide a region (indicated on the grid in red) by the corresponding blocks.
To give an example, I would like the 'block regions' (represented {X,Y,Width,Height}):
A: {2,3,2,1}
B: {4,3,3,1}
C: {7,3,1,1}
D: {2,4,2,3}
...
The only information that I have is the size of the blocks in the grid (in this case 3) and the dimensions of the region:
{2,3,6,5} (= {X,Y, width, height})
Does anybody know how to do this in an efficient way? I thought about the use of mround to calculate the first boundaries of the blocks, but that lead to a dead end. Thanks in advance!

Answer 1

Math looks a bit weird because you start from 1,1 but here is the gist of it,
Find the boundaries for X/Y-axises separately (numbers divisable by blocks size with in the grid)
All sizes will blocksize, blocksize except the left/right/top/bottom most boxes
Find the width/height for these special boxes
Places corresponding sizes to corresponding boundaries
zip two lists
-export([f/2]).
f({X,Y,Width, Height}, BlockSize) ->
% all sizes will be Blocksize, Blocksize except special cases
% left/right most will have Xfd/Xld
% top/bottom most will have Yfd/Yld
Xfd = BlockSize - ( ( X - 1) rem BlockSize) ,
Xld = (X + Width - 1) rem BlockSize,
Yfd = BlockSize - ( ( Y - 1) rem BlockSize) ,
Yld = (Y + Height - 1) rem BlockSize,
Xs = divs(X, Width, BlockSize, Xfd),
Ys = divs(Y, Height, BlockSize, Yfd),
%replace last values
{Lx, _} = lists:last(Xs),
Xss = lists:keyreplace(Lx, 1, Xs, {Lx, Xld}),
{Ly, _} = lists:last(Ys),
Yss = lists:keyreplace(Ly, 1, Ys, {Ly, Yld}),
R = merge(Xss, Yss),
io:format("~p~n", [R]).
merge(X, Y) ->
XY= lists:foldl(fun(Xx, Acc) ->
lists:foldl(fun(Yy, Acc1) ->
[{Xx, Yy} | Acc1]
end, Acc, Y)
end, [], X),
lists:map(fun({{Xx, W}, {Yy, H}}) ->
{Xx, Yy, W, H}
end , XY).
divs(X, W, BlockSize, Fd) ->
R = [{X, Fd} | [{Xs, BlockSize} || Xs<- lists:seq(X, X + W), (Xs - 1) rem BlockSize =:= 0]],
lists:sort(sets:to_list(sets:from_list(R))).
>[{7,7,1,1},
{7,4,1,3},
{7,3,1,1},
{4,7,3,1},
{4,4,3,3},
{4,3,3,1},
{2,7,2,1},
{2,4,2,3},
{2,3,2,1}]

Answer 2

For the fun I wrote this one.
-module(cluster).
-compile([export_all]).
-record(point, {x,y}).
-record(area, {x,y,w,h}).
area2points(A) ->
[#point{x=X,y=Y} ||
X <- lists:seq(A#area.x, A#area.x+ A#area.w-1),
Y <- lists:seq(A#area.y, A#area.y+ A#area.h-1)].
points2area([]) -> empty;
points2area(L) ->
lists:foldl(fun(P,Acc) -> fromcorner(P,Acc) end, area(),L).
area() -> #area{}.
area(X,Y,W,H) -> #area{x=X,y=Y,w=W,h=H}.
point() -> #point{}.
point(X,Y) -> #point{x=X,y=Y}.
fromcorner(#point{x=X,y=Y},#area{x=undefined,y=undefined}) ->
#area{x=X,y=Y,w=1,h=1};
fromcorner(#point{x=X,y=Y},#area{x=Xa,y=Ya,w=W,h=H}) ->
{Xmin,Wn} = case X < Xa of
true -> {X,Xa + W - X};
false -> {Xa,max(W, X+1-Xa)}
end,
{Ymin,Hn} = case Y < Ya of
true -> {Y,Ya + H - Y};
false -> {Ya,max(H, Y+1-Ya)}
end,
#area{x=Xmin,y=Ymin,w=Wn,h=Hn}.
split(A,L) ->
LA = area2points(A),
[points2area(lists:filter(fun(P) -> lists:member(P,LA) end ,area2points(X))) || X <- L].
test() ->
Z1 = area(1,1,3,3),
Z2 = area(4,1,3,3),
Z3 = area(7,1,3,3),
Z4 = area(1,4,3,3),
Z5 = area(4,4,3,3),
Z6 = area(7,4,3,3),
Z7 = area(1,7,3,3),
Z8 = area(4,7,3,3),
Z9 = area(7,7,3,3),
World = [Z1,Z2,Z3,Z4,Z5,Z6,Z7,Z8,Z9],
A = area(2,3,6,5),
split(A,World).
76> make:all().
Recompile: ../src/cluster
up_to_date
77> l(cluster).
{module,cluster}
78> cluster:test().
[{area,2,3,2,1},
{area,4,3,3,1},
{area,7,3,1,1},
{area,2,4,2,3},
{area,4,4,3,3},
{area,7,4,1,3},
{area,2,7,2,1},
{area,4,7,3,1},
{area,7,7,1,1}]
79>