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dergraf/hilbert.erl

Created July 19, 2013 12:19
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  1. dergraf created this gist Jul 19, 2013.
    37 changes: 37 additions & 0 deletions hilbert.erl
    View file
    Original file line number Diff line number Diff line change
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    -module(hilbert).
    -export([curve/1, curve/7, point_to_hilbert/3]).

    -define(HILBERTMAP, [
    {a, [{{0,0},{0,d}}, {{0,1},{1,a}}, {{1,0},{3,b}}, {{1,1},{2,a}}]},
    {b, [{{0,0},{2,b}}, {{0,1},{1,b}}, {{1,0},{3,a}}, {{1,1},{0,c}}]},
    {c, [{{0,0},{2,c}}, {{0,1},{3,d}}, {{1,0},{1,c}}, {{1,1},{0,b}}]},
    {d, [{{0,0},{0,a}}, {{0,1},{3,c}}, {{1,0},{1,d}}, {{1,1},{2,d}}]}
    ]).

    curve(N) ->
    curve(0, 0, 1, 0, 0, 1, N).

    curve(X0, Y0, Xi, Xj, Yi, Yj, 0) ->
    X = X0 + ((Xi + Yi) / 2),
    Y = Y0 + ((Xj + Yj) / 2),
    io:format("~p, ~p~n", [X, Y]);
    curve(X0, Y0, Xi, Xj, Yi, Yj, N) ->
    curve(X0, Y0, Yi/2, Yj/2, Xi/2, Xj/2, N - 1),
    curve(X0 + Xi/2, Y0 + Xj/2, Xi/2, Xj/2, Yi/2, Yj/2, N - 1),
    curve(X0 + Xi/2 + Yi/2, Y0 + Xj/2 + Yj/2, Xi/2, Xj/2, Yi/2, Yj/2, N - 1),
    curve(X0 + Xi/2 + Yi, Y0 + Xj/2 + Yj, -Yi/2,-Yj/2,-Xi/2,-Xj/2, N - 1).

    point_to_hilbert(X, Y, N) ->
    CurrentSquare = a,
    Position = 0,
    point_to_hilbert(X, Y, N - 1, CurrentSquare, Position).

    point_to_hilbert(_, _, N, _, Position) when N < 0 -> Position;
    point_to_hilbert(X, Y, N, CurrentSquare, Position) ->
    NewPos = Position bsl 2,
    QuadX = case X band (1 bsl N) of 0 -> 0; _ -> 1 end,
    QuadY = case Y band (1 bsl N) of 0 -> 0; _ -> 1 end,
    {QuadPos, NewCurrentSquare} = proplists:get_value({QuadX, QuadY}, proplists:get_value(CurrentSquare, ?HILBERTMAP)),
    point_to_hilbert(X, Y, N - 1, NewCurrentSquare, NewPos bor QuadPos).