找到六角形結構的邊界

Question

我有一個代碼用於在蜂窩網絡中生成六角形結構，其輸入是需要的層數和半徑。當輸入層數爲1時，它將生成7個六角形當它是2時它會產生19個細胞。現在我只需要提取沒有任何內六邊形單元格的六角形結構的外邊界。如何只能生成六邊形網格的外邊界？

enter code here 
d = input('Enter the distance') 
radius = d/sqrt(3);% radius of each hexagon 
tier = input('Enter the tier value'); 
%num = input('enter the value 0 or 1 : n_los=1 or los=0') ; 
G = ((2*2*d)/10)+1; % value required to rearrange the matrix in 3 dim 

di = 0; 
global expected_bs; 
expected_bs = (tier)^2 + (tier+1)^2 + (tier*(tier+1)); 
display(expected_bs); 
global bs_cord; %base station co-ordinates 
%bs_cord = zeros(expected_bs, 2); 
bs_cord = [0 0]; 
t = linspace(0,2*pi,7); 

% X and Y co-ordinates of 7 vertices for plotting hexagon. : TIER 1 
x_ = [ 0 0 ((sqrt(3)/2)*d) ((sqrt(3)/2)*d) 0 -((sqrt(3)/2)*d) -((sqrt(3)/2)*d) ]; 
y_ = [ 0 d (d/2) (-d/2) -d (-d/2) (d/2) ]; 
% Hexagonal cells generation 
for u=1:tier 
    g_ = u*x_;% to get first hexagon structure : x coordinate 
    h_ = u*y_;% to get first hexagon : y coordinate 

    bs = plot_cluster(g_ , h_ , t, radius ,bs);% function defined to plot the hexagon 

    if u > 1 
     m_ = u* [ 0 ((sqrt(3)/2)*d) ((sqrt(3)/2)*d) 0 -((sqrt(3)/2)*d) -((sqrt(3)/2)*d) 0 ];% to get hexagon in inclined direction 
     n_ = u* [ d (d/2) (-d/2) -d (-d/2) (d/2) d ]; 

     for i=1:(u-1) 
      for k=1:6 
       inner_cell_x = (((i * m_(k))+ ((u-i) * m_(k+1)))/(u)); % ratio method to obtain the coordinates of hexagon       
       inner_cell_y = ((i * n_(k))+ ((u-i) * n_(k+1)))/(u); 
       bs = plot_cell(inner_cell_x , inner_cell_y , t, radius, bs); 
      end 
     end 
    end 
end 

bs_cord = unique(bs_cord,'rows'); % base station coordinates unique func is for eliminating the replicated coordinates 

有人幫

Answer 1

我花了很多時間在這方面的工作令人尷尬長量。我希望它運作良好。

祕密是你需要擺脫任何重複的六邊形，然後只計算那些只有零或一個重疊頂點。

編輯加入環中心

function [X, Y, xe, ye, X0, Y0, outerCenter] = hexagon(varargin) 
%% hexagon: A hexagon cell generating function 
% Possible inputs 
% hexagon 
%  Will assume a new figure is not wanted. Using this option will call 
%  up inputs in the command window to get information about the cells. 
% hexagon(newFigure) 
%  Where newFigure is a logical, if true the cell will be shown on a 
%  new figure. If false the cell will be shown on an old figure (if 
%  available). Using this option will call up inputs in the command 
%  window to get information about the cells. 
% hexagon(D, tiers) 
%  Where newFigure is a logical, if true the cell will be shown on a 
%  new figure. If false the cell will be shown on an old figure (if 
%  available). 
% hexagon(D, tiers, newFigure) 
%  Where newFigure is a logical, if true the cell will be shown on a 
%  new figure. If false the cell will be shown on an old figure (if 
%  available). 
% 
% Outputs 
% X - cell arrays of the x-coordinates of the hexagons 
% Y - cell arrays of the y-coordinates of the hexagons 
% xe - matrix of the x-coordinates of the verticies of the edge 
% ye - matrix of the y-coordinates of the verticies of the edge 
% X - cell arrays of the x-coordinates of the hexagons on the edge 
% Y - cell arrays of the y-coordinates of the hexagons on the edge 

%% Input parsing 
    global centers 
    %These are the centers of the hexagons, with the current tier. 
    %Having this in allows the program to check if there is already a 
    %higher tier hexagon in the same space 
    centers = [0, 0, -1]; 

    if nargin == 0 
     newFigure = 0; 
     D = input('Enter the circumscribed diameter: '); 
     tiers = input('Enter the tier value: '); 
    elseif nargin == 1 
     newFigure = varargin{1}; 
     D = input('Enter the circumscribed diameter: '); 
     tiers = input('Enter the tier value: '); 
    elseif nargin == 2 
     newFigure = 0; 
     D = varargin{1}; 
     tiers = varargin{2}; 
    elseif nargin == 3 
     D = varargin{1}; 
     tiers = varargin{2}; 
     newFigure = varargin{3}; 
    elseif nargin > 3 
     error('Too many input arguements entered!') 
    end 

    x0 = input('Enter x0: '); 
    y0 = input('Enter y0: '); 

%% Call first hexagon at origin 
    [X, Y] = makeHexagon(x0, y0, D, tiers); 


%% Find edge of cell 
    [xe, ye] = findEdge(X, Y, x0, y0); 

%% Find hexagons on edge 
    [X0, Y0] = findEdgeHexagons(X, Y, xe, ye); 

%% Outside center 
    outerCenter = centers(:, [1,2]); 
    outerCenter(centers(:, 3) == 0) = []; 

%% Output and Plot 
    disp(['A ', num2str(tiers), ' tier network of hexagons has ', num2str(numel(X)), ' elements.']) 

    if newFigure 
     fig = figure; 
    else 
     fig = gcf; 
     figure(fig.Number); 
    end 

    T = [X; Y]; %Prepare to plot the hexagons 
    plot(T{:},'LineWidth',2) 
     hold on 
      T = [X0; Y0]; %Prepare to plot the hexagons 
      plot(T{:},'k','LineWidth',4) %Plot the edge 
      plot(xe, ye,'k','LineWidth',4) %Plot the edge 
     axis equal 

end 

%% Make the hexagons 
function [X, Y] = makeHexagon(x0, y0, D, tiers) 
    global centers 

    X = {}; 
    Y = {}; 

%% Find out if the center has already been claimed by a higher tier 
    [~, ib] = ismembertol([x0, y0], centers(:, [1,2]),'ByRows',true); 

    if any(ib) && (tiers > centers(ib, 3)) 
     %If it's higher tiered than a previous hexagon, then update the list 
     centers(ib, 3) = tiers; 
    elseif any(ib) && (tiers <= centers(ib, 3)) 
     %If it's equal or lower tiered than a previous hexagon, then any space 
     %it could explore is already claimed 
     %this returns an empty cell array 
     return 
    else 
     %It's in completely new space 
     centers = [centers; x0, y0, tiers]; 
    end 

%% Make the hexagon and its children 
    %Get the verticies of the hexagon, note that there are 7 verticies to 
    %close the shape 
    [x, y] = hexCoords(x0, y0, D); 

    %if it's not at the bottom, the hexagon needs to spawn its children 
    if tiers > 0 
     %The centers will alway be at 30, 90, 150, 210, 270 and 330. 
     theta = linspace(0, 5*pi/3, 6)' - pi/6; 
     centerX = sqrt(3)*D/2*cos(theta) + x0; 
     centerY = sqrt(3)*D/2*sin(theta) + y0; 

     %Call for each child, they will be one level lower 
     [X, Y] = arrayfun(@(X, Y) makeHexagon(X, Y, D, tiers - 1), centerX, centerY, 'uni', 0); 

     %Flatten the cell arrays this combines generations 0 to tiers - 1 
     X = flatten(X); 
     Y = flatten(Y); 
    end 

    %Combine previous generations with this generation 
    X = horzcat(x, X{:}); 
    Y = horzcat(y, Y{:}); 

    %Remove any shapes that are in the same spot 
    [~, i, ~] = uniquetol([X', Y'], 'ByRows', true); 

    X = num2cell(X(:, i),1); 
    Y = num2cell(Y(:, i),1); 

end 

%% Find the edge of the cell 
function [X0, Y0] = findEdge(X, Y, x0, y0) 
    %Remove the extra vertex for the closed shape 
    XY = cellfun(@(x, y) uniquetol([x(:), y(:)], 'ByRows', true), X, Y, 'uni', 0); 

    %convert the cell array into a matrix of x and y 
    XY = vertcat(XY{:}); 

    %Find how many times each vertex is used 
    [~, uniqueVerticies, MappingIndicies] = uniquetol(XY, 'ByRows', true); 
    [n, ~, ~] = histcounts(MappingIndicies, length(uniqueVerticies)); 

    %If it is once or twice it's on an edge 
    XY = XY(uniqueVerticies(n <= 2), :); 

    %Arrange the verticies angularly 
    data = sortrows([atan2(XY(:,2) - y0, XY(:,1) - x0), XY]); 

    %Finally, seperate them and put a final curl on it 
    X0 = [data(:,2); data(1,2)]; 
    Y0 = [data(:,3); data(1,3)]; 
end 

%% Find the hexagons on the edge of the cell 
function [X0, Y0] = findEdgeHexagons(X, Y, xe, ye) 

    i = cellfun(@(x, y) any(ismembertol([xe(:), ye(:)], [x(:), y(:)],'ByRows',true)) , X, Y); 
    X0 = X(i); 
    Y0 = Y(i); 

end 

%% Map the verticies of the hexagon 
function [x, y] = hexCoords(x0, y0, D) 
    %The centers will alway be at 0, 60, 120, 180, 240, 300 and 360 
    %(to close the figure). 
    theta = linspace(0, 2*pi, 7)'; 

    %Convert from polar to Cartesian coordinates 
    x = D/2 * cos(theta) + x0; 
    y = D/2 * sin(theta) + y0; 
end 

%% Flatten the cell array and remove empty elements 
function X = flatten(X) 
    X = X(~cellfun(@isempty, X)); 
    i = cellfun(@iscell, X); 

    if any(i) 
     X = horzcat(X{~i}, flatten(horzcat(X{i}))); 
    end 
end