i have code generating hexagonal structure in cellular network, input number of tiers required , radius.. when input number of tiers 1, generate 7 hexagonal cells when 2 generate 19 cells. need extract outer boundary of hexagonal structure without inner hexagonal cells.how can generate outer boundary of hexagonal network?
enter code here d = input('enter distance') radius = d/sqrt(3);% radius of each hexagon tier = input('enter tier value'); %num = input('enter value 0 or 1 : n_los=1 or los=0') ; g = ((2*2*d)/10)+1; % value required rearrange 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 , y co-ordinates of 7 vertices 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 u=1:tier g_ = u*x_;% first hexagon structure : x coordinate h_ = u*y_;% first hexagon : y coordinate bs = plot_cluster(g_ , h_ , t, radius ,bs );% function defined plot 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 ];% hexagon in inclined direction n_ = u* [ d (d/2) (-d/2) -d (-d/2) (d/2) d ]; i=1:(u-1) k=1:6 inner_cell_x = (((i * m_(k))+ ((u-i) * m_(k+1)))/(u)); % ratio method obtain 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 eliminating replicated coordinates someone please help
i spent embarrassingly long amount of time working on this. hope works well.
the secret need rid of duplicate hexagons count have vertices 0 or 1 overlap.
edit added ring center
function [x, y, xe, ye, x0, y0, outercenter] = hexagon(varargin) %% hexagon: hexagon cell generating function % possible inputs % hexagon % assume new figure not wanted. using option call % inputs in command window information cells. % hexagon(newfigure) % newfigure logical, if true cell shown on % new figure. if false cell shown on old figure (if % available). using option call inputs in command % window information cells. % hexagon(d, tiers) % newfigure logical, if true cell shown on % new figure. if false cell shown on old figure (if % available). % hexagon(d, tiers, newfigure) % newfigure logical, if true cell shown on % new figure. if false cell shown on old figure (if % available). % % outputs % x - cell arrays of x-coordinates of hexagons % y - cell arrays of y-coordinates of hexagons % xe - matrix of x-coordinates of verticies of edge % ye - matrix of y-coordinates of verticies of edge % x - cell arrays of x-coordinates of hexagons on edge % y - cell arrays of y-coordinates of hexagons on edge %% input parsing global centers %these centers of hexagons, current tier. %having in allows program check if there %higher tier hexagon in same space centers = [0, 0, -1]; if nargin == 0 newfigure = 0; d = input('enter circumscribed diameter: '); tiers = input('enter tier value: '); elseif nargin == 1 newfigure = varargin{1}; d = input('enter circumscribed diameter: '); tiers = input('enter 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 @ 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 , 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 plot hexagons plot(t{:},'linewidth',2) hold on t = [x0; y0]; %prepare plot hexagons plot( t{:},'k','linewidth',4) %plot edge plot( xe, ye,'k','linewidth',4) %plot edge axis equal end %% make hexagons function [x, y] = makehexagon(x0, y0, d, tiers) global centers x = {}; y = {}; %% find out if center has been claimed higher tier [~, ib] = ismembertol([x0, y0], centers(:, [1,2]),'byrows',true); if any(ib) && (tiers > centers(ib, 3)) %if it's higher tiered previous hexagon, update list centers(ib, 3) = tiers; elseif any(ib) && (tiers <= centers(ib, 3)) %if it's equal or lower tiered previous hexagon, space %it explore claimed %this returns empty cell array return else %it's in new space centers = [centers; x0, y0, tiers]; end %% make hexagon , children %get verticies of hexagon, note there 7 verticies %close shape [x, y] = hexcoords(x0, y0, d); %if it's not @ bottom, hexagon needs spawn children if tiers > 0 %the centers alway @ 30, 90, 150, 210, 270 , 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 each child, 1 level lower [x, y] = arrayfun(@(x, y) makehexagon(x, y, d, tiers - 1), centerx, centery, 'uni', 0); %flatten cell arrays combines generations 0 tiers - 1 x = flatten(x); y = flatten(y); end %combine previous generations generation x = horzcat(x, x{:}); y = horzcat(y, y{:}); %remove shapes in same spot [~, i, ~] = uniquetol([x', y'], 'byrows', true); x = num2cell(x(:, i),1); y = num2cell(y(:, i),1); end %% find edge of cell function [x0, y0] = findedge(x, y, x0, y0) %remove vertex closed shape xy = cellfun(@(x, y) uniquetol([x(:), y(:)], 'byrows', true), x, y, 'uni', 0); %convert cell array matrix of x , y xy = vertcat(xy{:}); %find how many times each vertex used [~, uniqueverticies, mappingindicies] = uniquetol(xy, 'byrows', true); [n, ~, ~] = histcounts(mappingindicies, length(uniqueverticies)); %if once or twice it's on edge xy = xy(uniqueverticies(n <= 2), :); %arrange verticies angularly data = sortrows([atan2(xy(:,2) - y0, xy(:,1) - x0), xy]); %finally, seperate them , put final curl on x0 = [data(:,2); data(1,2)]; y0 = [data(:,3); data(1,3)]; end %% find hexagons on edge of cell function [x0, y0] = findedgehexagons(x, y, xe, ye) = cellfun(@(x, y) any(ismembertol([xe(:), ye(:)], [x(:), y(:)],'byrows',true)) , x, y); x0 = x(i); y0 = y(i); end %% map verticies of hexagon function [x, y] = hexcoords(x0, y0, d) %the centers alway @ 0, 60, 120, 180, 240, 300 , 360 %(to close figure). theta = linspace(0, 2*pi, 7)'; %convert polar cartesian coordinates x = d/2 * cos(theta) + x0; y = d/2 * sin(theta) + y0; end %% flatten cell array , remove empty elements function x = flatten(x) x = x(~cellfun(@isempty, x)); = cellfun(@iscell, x); if any(i) x = horzcat(x{~i}, flatten(horzcat(x{i}))); end end 
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