寻找六角形结构的边界

本文介绍了寻找六角形结构的边界的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！ 问题描述

我有一个用于在蜂窝网络中生成六边形结构的代码，它的输入是所需的层数和半径.当输入的层数为1时，它将生成7个六边形单元，当其为2时，它将生成产生19个细胞.现在我只需要提取六边形结构的外边界而没有任何内部六边形单元，如何只生成六边形网络的外边界?

I have a code for generating hexagonal structure in a cellular network, its input is number of tiers required and radius.. when the input to a number of tiers is 1, it will generate 7 hexagonal cells when it is 2 it will generate 19 cells. Now I need to extract only the outer boundary of my hexagonal structure without any inner hexagonal cells.How can I generate only the outer boundary of the hexagonal network?

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

请有人帮忙

推荐答案

我花了很长时间尴尬地解决了这个问题.我希望它能很好地工作.

I spent an embarrassingly long amount of time working on this. I hope it works well.

秘密是，您需要去除所有重复的六边形，然后仅计算那些顶点只有零个或一个重叠的六边形.

The secret is you need to get rid of any duplicate hexagons then only count those that have vertices with only zero or one overlap.

编辑添加的戒指中心

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