Batman equation in MATLAB

Question

Friedrich 2011-8-5

3
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/13131-batman-equation-in-matlab

评论： Sama Elsayed 2019-12-13

在 MATLAB Online 中打开

Hi folks,

I am looking for a smart way to implement the Batman equation in MATLAB:

http://www.freepostia.com/fimages/405CNy9J_image.jpg

I came up with this:

syms x y
eq1 = ((x/7)^2*sqrt(abs(abs(x)-3)/(abs(x)-3))+(y/3)^2*sqrt(abs(y+3/7*sqrt(33))/(y+3/7*sqrt(33)))-1);
eq2 = (abs(x/2)-((3*sqrt(33)-7)/112)*x^2-3+sqrt(1-(abs(abs(x)-2)-1)^2)-y);
eq3 = (9*sqrt(abs((abs(x)-1)*(abs(x)-.75))/((1-abs(x))*(abs(x)-.75)))-8*abs(x)-y);
eq4 = (3*abs(x)+.75*sqrt(abs((abs(x)-.75)*(abs(x)-.5))/((.75-abs(x))*(abs(x)-.5)))-y);
eq5 = (2.25*sqrt(abs((x-.5)*(x+.5))/((.5-x)*(.5+x)))-y);
eq6 = (6*sqrt(10)/7+(1.5-.5*abs(x))*sqrt(abs(abs(x)-1)/(abs(x)-1))-(6*sqrt(10)/14)*sqrt(4-(abs(x)-1)^2)-y);
axes('Xlim', [-7.25 7.25], 'Ylim', [-5 5]);
hold on
ezplot(eq1,[-8 8 -3*sqrt(33)/7 6-4*sqrt(33)/7]);
ezplot(eq2,[-4 4]);
ezplot(eq3,[-1 -0.75 -5 5]);
ezplot(eq3,[0.75 1 -5 5]);
ezplot(eq4,[-0.75 0.75 2.25 5]);
ezplot(eq5,[-0.5 0.5 -5 5]);
ezplot(eq6,[-3 -1 -5 5]);
ezplot(eq6,[1 3 -5 5]);
colormap([0 0 1])
title('Batman');
xlabel('');
ylabel('');
hold off

Any other ideas are welcome.

1 个评论
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Oleg Komarov 2011-8-5

I've submitted just less than a week ago the BATMAN equation to Martin Sona's question but he apparently deleted it (so much of my time...but cache is good)

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Answer 1

Oleg Komarov 2011-8-5

3
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/13131-batman-equation-in-matlab#answer_17935

编辑：Walter Roberson 2017-1-12

在 MATLAB Online 中打开

The "correct" version with explanations: http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real

% Grey axes
    axes('Xlim'  ,[-7 7]    , 'Xtick' ,-7:7,...
         'Ylim'  ,[-5 5]    , 'Ytick' ,-5:5,...
         'YtickL',''        , 'XtickL',''  ,...
         'Ygrid' ,'on'      , 'Xgrid' ,'on',...
         'Xcolor',[.8 .8 .8], 'Ycolor',[.8 .8 .8]);
    hold on
% Outer wings
    f1 = '(x/7)^2 * sqrt(abs(abs(x)-3)/(abs(x)-3)) + (y/3)^2 * sqrt(abs(y + 3/7*sqrt(33))/(y + 3/7*sqrt(33))) - 1';
    ezplot(f1,[-8 8 -3*sqrt(33)/7 6-4*sqrt(33)/7]);
% Bottom
    f2 = 'abs(x/2)-(3*sqrt(33)-7) * x^2/112 - 3 + sqrt(1-(abs(abs(x)-2)-1)^2) - y';
    ezplot(f2,[-4 4]);
% Outer ears
    f3 = '9 * sqrt(abs((1-abs(x))*(abs(x)-0.75)) / ((1-abs(x))*(abs(x)-0.75))) - 8*abs(x) - y';
    ezplot(f3,[-1    -0.75 -5 5]);
    ezplot(f3,[ 0.75  1    -5 5]);
% Inner ears
    f4 = '3*abs(x) + 0.75*sqrt(abs((0.75-abs(x))*(abs(x)-.5)) / ((.75-abs(x))*(abs(x)-.5))) - y';
    ezplot(f4,[-0.75 0.75 2.25 5]);
% Connect inner ears (flat line)
    f5 = '2.25*sqrt(abs(((0.5-x)*(0.5+x))/((0.5-x)*(0.5+x)))) - y';
    ezplot(f5,[-0.5 0.5 -5 5]);
% Inner wings
    f6 = '6*sqrt(10)/7 + (1.5-0.5*abs(x)) * sqrt(abs(abs(x)-1) / (abs(x)-1)) - 6*sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) - y';
    ezplot(f6,[-3 -1 -5 5]);
  ezplot(f6,[ 1  3 -5 5]);
% Change line color and width
    set(get(gca,'children'),'Color','b','Linew',2)
% Title and labels
    title('Batman'); xlabel(''); ylabel('')
% Superimpose black axes with xy-ticklabels
    xlbl(1:15,1:2) = ' '; xlbl([1,8,15],:) = ['-7';' 0';' 7'];
    ylbl(1:11,1:2) = ' '; ylbl([1,6,11],:) = ['-5';' 0';' 5'];
    axes('Xlim'  ,[-7 7], 'Xtick' ,-7:7,...
         'Ylim'  ,[-5 5], 'Ytick' ,-5:5,...
         'YtickL',ylbl  , 'XtickL',xlbl,...
         'Box'   ,'on'  , 'Color' ,'none');
*EDIT*

The link shows that all the f# are multiplied and plotted but it doesn't work because ezplot somehow plots the real part of the imaginary numbers(?).

With the piecewise implementation only the core functions should be used (but I left the extended version so that others can copy):

    f1 = '(x/7)^2 + (y/3)^2 - 1';
    f2 = 'abs(x/2)-(3*sqrt(33)-7) * x^2/112 - 3 + sqrt(1-(abs(abs(x)-2)-1)^2) - y';
    f3 = '9  - 8*abs(x) - y';
    f4 = '3*abs(x) + 0.75 - y';
    f5 = '2.25 + 0*x - y';
    f6 = '6*sqrt(10)/7 + (1.5-0.5*abs(x)) - 6*sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) - y';

The result:

3 个评论
显示 1更早的评论隐藏 1更早的评论

Oleg Komarov 2011-8-5

Upload it somewhere and then post the link included in <<http://...>>

There's a post on fex which is a collection of repositories.

Walter Roberson 2011-8-5

The post listing a partial list of repositories is http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

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Answer 2

Sally Al Khamees 2017-2-21

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/13131-batman-equation-in-matlab#answer_255753

在 MATLAB Online 中打开

Starting MATLAB R2016b, you may use fimplicit function to plot the equations.Note that I used the Symbolic Math Toolbox to create the symbolic variables x and y.

You can read more about fimplicit here https://www.mathworks.com/help/matlab/ref/fimplicit.html

syms x y
eq1 = ((x/7)^2*sqrt(abs(abs(x)-3)/(abs(x)-3))+(y/3)^2*sqrt(abs(y+3/7*sqrt(33))/(y+3/7*sqrt(33)))-1);
eq2 = (abs(x/2)-((3*sqrt(33)-7)/112)*x^2-3+sqrt(1-(abs(abs(x)-2)-1)^2)-y);
eq3 = (9*sqrt(abs((abs(x)-1)*(abs(x)-.75))/((1-abs(x))*(abs(x)-.75)))-8*abs(x)-y);
eq4 = (3*abs(x)+.75*sqrt(abs((abs(x)-.75)*(abs(x)-.5))/((.75-abs(x))*(abs(x)-.5)))-y);
eq5 = (2.25*sqrt(abs((x-.5)*(x+.5))/((.5-x)*(.5+x)))-y);
eq6 = (6*sqrt(10)/7+(1.5-.5*abs(x))*sqrt(abs(abs(x)-1)/(abs(x)-1))-(6*sqrt(10)/14)*sqrt(4-(abs(x)-1)^2)-y);
fimplicit([eq1, eq2, eq3, eq4, eq5, eq6],'Color','black','Linew',2)
xlim( [-7.25 7.25])
ylim([-5 5])
grid