MATLAB Answers

Friedrich
3

Batman equation in MATLAB

Asked by Friedrich
on 5 Aug 2011
Latest activity Commented on by Jonas57
on 14 Oct 2017
Hi folks,
I am looking for a smart way to implement the Batman equation in MATLAB:
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 Comment

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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3 Answers

Answer by Oleg Komarov on 5 Aug 2011
Edited by Walter Roberson
on 12 Jan 2017

% 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 Comments

Nice one :)
How did you post a picture here?
Upload it somewhere and then post the link included in <<http://...>>
There's a post on fex which is a collection of repositories.
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 by Sally Al Khamees on 21 Feb 2017

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

  1 Comment

Very Nice! :D

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